[Docs] [txt|pdf] [Tracker] [Email] [Diff1] [Diff2] [Nits]

Versions: 00 01 02

AVT Working Group                                             J-M. Valin
Internet-Draft                                     Octasic Semiconductor
Intended status: Standards Track                           T. Terriberry
Expires: January 9, 2011                             Xiph.Org Foundation
G. Maxwell
Juniper Networks
C. Montgomery
Xiph.Org Foundation
July 8, 2010

Constrained-Energy Lapped Transform (CELT) Codec
draft-valin-celt-codec-02

Abstract

CELT [celt-website] is an open-source voice codec suitable for use in
very low delay Voice over IP (VoIP) type applications.  This document
describes the encoding and decoding process.

Status of this Memo

This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF).  Note that other groups may also distribute
working documents as Internet-Drafts.  The list of current Internet-
Drafts is at http://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time.  It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."

This Internet-Draft will expire on January 9, 2011.

Copyright (c) 2010 IETF Trust and the persons identified as the

This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document.  Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document.  Code Components extracted from this document must

Valin, et al.            Expires January 9, 2011                [Page 1]


Internet-Draft                 CELT codec                      July 2010

include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.

1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   5
2.  Overview of the CELT Codec  . . . . . . . . . . . . . . . . .   6
2.1.  Bit-stream definition . . . . . . . . . . . . . . . . . .   6
3.  CELT Modes  . . . . . . . . . . . . . . . . . . . . . . . . .   8
4.  CELT Encoder  . . . . . . . . . . . . . . . . . . . . . . . .  11
4.1.  Range Coder . . . . . . . . . . . . . . . . . . . . . . .  12
4.1.1.  Encoding Symbols  . . . . . . . . . . . . . . . . . .  12
4.1.2.  Encoding Uniformly Distributed Integers . . . . . . .  13
4.1.3.  Finalizing the Stream . . . . . . . . . . . . . . . .  14
4.1.4.  Current Bit Usage . . . . . . . . . . . . . . . . . .  14
4.2.  Encoder Feature Selection . . . . . . . . . . . . . . . .  14
4.2.1.  Intra-frame energy (I)  . . . . . . . . . . . . . . .  15
4.2.2.  Pitch prediction (P)  . . . . . . . . . . . . . . . .  16
4.2.3.  Short blocks (S)  . . . . . . . . . . . . . . . . . .  16
4.2.4.  Spectral folding (F)  . . . . . . . . . . . . . . . .  17
4.3.  Forward MDCT  . . . . . . . . . . . . . . . . . . . . . .  17
4.4.  Bands and Normalization . . . . . . . . . . . . . . . . .  17
4.5.  Energy Envelope Quantization  . . . . . . . . . . . . . .  17
4.5.1.  Coarse energy quantization  . . . . . . . . . . . . .  17
4.5.2.  Fine energy quantization  . . . . . . . . . . . . . .  18
4.6.  Bit Allocation  . . . . . . . . . . . . . . . . . . . . .  19
4.7.  Pitch Prediction  . . . . . . . . . . . . . . . . . . . .  20
4.8.  Spherical Vector Quantization . . . . . . . . . . . . . .  20
4.8.1.  Bits to Pulses  . . . . . . . . . . . . . . . . . . .  20
4.8.2.  PVQ Search  . . . . . . . . . . . . . . . . . . . . .  21
4.8.3.  Index Encoding  . . . . . . . . . . . . . . . . . . .  21
4.9.  Stereo support  . . . . . . . . . . . . . . . . . . . . .  22
4.10. Synthesis . . . . . . . . . . . . . . . . . . . . . . . .  23
4.11. Variable Bitrate (VBR)  . . . . . . . . . . . . . . . . .  23
5.  CELT Decoder  . . . . . . . . . . . . . . . . . . . . . . . .  24
5.1.  Range Decoder . . . . . . . . . . . . . . . . . . . . . .  24
5.1.1.  Decoding Symbols  . . . . . . . . . . . . . . . . . .  25
5.1.2.  Decoding Uniformly Distributed Integers . . . . . . .  26
5.1.3.  Current Bit Usage . . . . . . . . . . . . . . . . . .  26
5.2.  Energy Envelope Decoding  . . . . . . . . . . . . . . . .  27
5.3.  Pitch prediction decoding . . . . . . . . . . . . . . . .  27
5.4.  Spherical VQ Decoder  . . . . . . . . . . . . . . . . . .  27
5.4.1.  Index Decoding  . . . . . . . . . . . . . . . . . . .  27
5.4.2.  Normalised Vector Decoding  . . . . . . . . . . . . .  27
5.5.  Denormalization . . . . . . . . . . . . . . . . . . . . .  28
5.6.  Inverse MDCT  . . . . . . . . . . . . . . . . . . . . . .  28

Valin, et al.            Expires January 9, 2011                [Page 2]


Internet-Draft                 CELT codec                      July 2010

5.7.  Packet Loss Concealment (PLC) . . . . . . . . . . . . . .  28
6.  Security Considerations . . . . . . . . . . . . . . . . . . .  29
7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  30
8.  Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  31
9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  32
9.1.  Normative References  . . . . . . . . . . . . . . . . . .  32
9.2.  Informative References  . . . . . . . . . . . . . . . . .  32
Appendix A.  Reference Implementation . . . . . . . . . . . . . .  33
A.1.  Makefile  . . . . . . . . . . . . . . . . . . . . . . . .  33
A.2.  testcelt.c  . . . . . . . . . . . . . . . . . . . . . . .  34
A.3.  celt.h  . . . . . . . . . . . . . . . . . . . . . . . . .  38
A.4.  celt.c  . . . . . . . . . . . . . . . . . . . . . . . . .  46
A.5.  modes.h . . . . . . . . . . . . . . . . . . . . . . . . .  90
A.6.  modes.c . . . . . . . . . . . . . . . . . . . . . . . . .  93
A.7.  bands.h . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.8.  bands.c . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.9.  cwrs.h  . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.10. cwrs.c  . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.11. vq.h  . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.12. vq.c  . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.13. pitch.h . . . . . . . . . . . . . . . . . . . . . . . . . 156
A.14. pitch.c . . . . . . . . . . . . . . . . . . . . . . . . . 157
A.15. rate.h  . . . . . . . . . . . . . . . . . . . . . . . . . 162
A.16. rate.c  . . . . . . . . . . . . . . . . . . . . . . . . . 166
A.17. plc.h . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A.18. plc.c . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A.19. mdct.h  . . . . . . . . . . . . . . . . . . . . . . . . . 176
A.20. mdct.c  . . . . . . . . . . . . . . . . . . . . . . . . . 178
A.21. ecintrin.h  . . . . . . . . . . . . . . . . . . . . . . . 185
A.22. entcode.h . . . . . . . . . . . . . . . . . . . . . . . . 188
A.23. entcode.c . . . . . . . . . . . . . . . . . . . . . . . . 190
A.24. entenc.h  . . . . . . . . . . . . . . . . . . . . . . . . 191
A.25. entenc.c  . . . . . . . . . . . . . . . . . . . . . . . . 194
A.26. entdec.h  . . . . . . . . . . . . . . . . . . . . . . . . 196
A.27. entdec.c  . . . . . . . . . . . . . . . . . . . . . . . . 199
A.28. mfrngcod.h  . . . . . . . . . . . . . . . . . . . . . . . 201
A.29. rangeenc.c  . . . . . . . . . . . . . . . . . . . . . . . 203
A.30. rangedec.c  . . . . . . . . . . . . . . . . . . . . . . . 208
A.31. laplace.h . . . . . . . . . . . . . . . . . . . . . . . . 213
A.32. laplace.c . . . . . . . . . . . . . . . . . . . . . . . . 215
A.33. quant_bands.h . . . . . . . . . . . . . . . . . . . . . . 218
A.34. quant_bands.c . . . . . . . . . . . . . . . . . . . . . . 220
A.35. arch.h  . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.36. mathops.h . . . . . . . . . . . . . . . . . . . . . . . . 230
A.37. os_support.h  . . . . . . . . . . . . . . . . . . . . . . 240
A.38. stack_alloc.h . . . . . . . . . . . . . . . . . . . . . . 244
A.39. celt_types.h  . . . . . . . . . . . . . . . . . . . . . . 247
A.40. _kiss_fft_guts.h  . . . . . . . . . . . . . . . . . . . . 248

Valin, et al.            Expires January 9, 2011                [Page 3]


Internet-Draft                 CELT codec                      July 2010

A.41. kiss_fft.h  . . . . . . . . . . . . . . . . . . . . . . . 253
A.42. kiss_fft.c  . . . . . . . . . . . . . . . . . . . . . . . 257
A.43. kiss_fftr.h . . . . . . . . . . . . . . . . . . . . . . . 273
A.44. kiss_fftr.c . . . . . . . . . . . . . . . . . . . . . . . 275
A.45. kfft_single.h . . . . . . . . . . . . . . . . . . . . . . 279
A.46. kfft_double.h . . . . . . . . . . . . . . . . . . . . . . 281
A.47. config.h  . . . . . . . . . . . . . . . . . . . . . . . . 283
Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . . 284

Valin, et al.            Expires January 9, 2011                [Page 4]


Internet-Draft                 CELT codec                      July 2010

1.  Introduction

This document describes the CELT codec, which is designed for
transmitting full-bandwidth audio with very low delay.  It is
suitable for encoding both speech and music at rates starting at 32
kbit/s.  It is primarily designed for transmission over the Internet
and protocols such as RTP [rfc3550], but also includes a certain
amount of robustness to bit errors, where this could be done at no
significant cost.

The novel aspect of CELT compared to most other codecs is its very
low delay, below 10 ms.  There are two main advantages to having a
very low delay audio link.  The lower delay itself is important for
some interactions, such as playing music remotely.  Another advantage
is its behavior in the presence of acoustic echo.  When the round-
trip audio delay is sufficiently low, acoustic echo is no longer
perceived as a distinct repetition, but rather as extra
reverberation.  Applications of CELT include:

o  Collaborative network music performance

o  High-quality teleconferencing

o  Wireless audio equipment

The source code for the reference implementation of the CELT codec is
provided in Appendix A.  This source code is the normative
specification of the codec.  The corresponding text description in
this document is provided for informative purposes.

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [rfc2119].

Valin, et al.            Expires January 9, 2011                [Page 5]


Internet-Draft                 CELT codec                      July 2010

2.  Overview of the CELT Codec

CELT stands for _Constrained Energy Lapped Transform_.  This is the
fundamental principle of the codec: the quantization process is
designed in such a way as to preserve the energy in a certain number
of bands.  The theoretical aspects of the codec are described in
greater detail [celt-tasl] and [celt-eusipco].  Although these papers
describe slightly older versions of the codec (version 0.3.2 and
0.5.1, respectively), the principles remain the same.

CELT is a transform codec, based on the Modified Discrete Cosine
Transform (MDCT).  The MDCT is derived from the DCT-IV by adding an
overlap with time-domain aliasing cancellation [mdct].  The main
characteristics of CELT are as follows:

o  Ultra-low algorithmic delay (scalable, typically 4 to 9 ms)

o  Sampling rates from 32 kHz to 48 kHz and above (full audio
bandwidth)

o  Applicability to both speech and music

o  Support for mono and stereo

o  Adaptive bit-rate from 32 kbit/s to 128 kbit/s per channel and
above

o  Scalable complexity

o  Robustness to packet loss (scalable trade-off between quality and
loss-robustness)

o  Open source implementation (floating-point and fixed-point)

o  No known intellectual property issues

2.1.  Bit-stream definition

This document contains a detailed description of both the encoder and
the decoder, along with a reference implementation.  In most
circumstances, and unless otherwise stated, the calculations do *not*
need to produce results that are bit-identical with the reference
implementation, so alternate algorithms can sometimes be used.
However, there are a few (clearly identified) cases, such as the bit
allocation, where bit-exactness with the reference implementation is
required.  An implementation is considered to be compatible if, for
any valid bit-stream, the decoder's output is perceptually
indistinguishable from the output produced by the reference decoder.

Valin, et al.            Expires January 9, 2011                [Page 6]


Internet-Draft                 CELT codec                      July 2010

The CELT codec does not use a standard _bit-packer_, but rather uses
a range coder to pack both integers and entropy-coded symbols.  In
mono mode, the bit-stream generated by the encoder contains the
following parameters (in order):

o  Feature flags I, P, S, F (2-4 bits)

o  if P=1

*  Pitch period

o  if S=1

*  Transient scalefactor

*  if scalefactor=(1 or 2) AND more than 2 short MDCTs

+  ID of block before transient

*  if scalefactor=3

+  Transient time

o  Coarse energy encoding (for each band)

o  Fine energy encoding (for each band)

o  For each band

*  if P=1 and band is at the beginning of a pitch band

+  Pitch gain bit

*  PVQ indices

o  More fine energy (using all remaining bits)

Note that due to the use of a range coder, all of the parameters have
to be encoded and decoded in order.

The CELT bit-stream is "octet-based" in the sense that the encoder
always produces an integer number of octets when encoding a frame.
Also, the bit-rate used by the CELT encoder can *only* be determined
by the number of octets produced.  In many cases (e.g.  UDP/RTP), the
transport layer already encodes the data length, so no extra
information is necessary to signal the bit-rate.  In cases where this
is not true, or when there are multiple compressed frames per packet,
the size of each compressed frame MUST be signalled in some way.

Valin, et al.            Expires January 9, 2011                [Page 7]


Internet-Draft                 CELT codec                      July 2010

3.  CELT Modes

The operation of both the encoder and decoder depends on the mode
data.  A mode definition can be created by celt_create_mode()
(modes.c (Appendix A.6)) based on three parameters:

o  frame size (number of samples)

o  sampling rate (samples per second)

o  number of channels (1 or 2)

The frame size can be any even number of samples from 64 to 1024,
inclusively.  The sampling rate must be between 32000 Hz and 96000
Hz.  The mode data that is created defines how the encoder and the
decoder operate.  More specifically, the following information is
contained in the mode object:

o  Frame size

o  Sampling rate

o  Windowing overlap

o  Number of channels

o  Definition of the bands

o  Definition of the _pitch bands_

o  Decay coefficients of the Laplace distributions for coarse energy

o  Bit allocation matrix

The windowing overlap is the amount of overlap between the frames.
CELT uses a low-overlap window that is typically half of the frame
size.  For a frame size of 256 samples, the overlap is 128 samples,
so the total algorithmic delay is 256+128=384.  CELT divides the
audio into frequency bands, for which the energy is preserved.  These
bands are chosen to follow the ear's critical bands, with the
exception that each band has to contain at least 3 frequency bins.

The energy bands are based on the Bark scale.  The Bark band edges
(in Hz) are defined as [0, 100, 200, 300, 400, 510, 630, 770, 920,
1080, 1270, 1480, 1720, 2000, 2320, 2700, 3150, 3700, 4400, 5300,
6400, 7700, 9500, 12000, 15500, 20000].  The actual bands used by the
codec depend on the sampling rate and the frame size being used.  The
mapping from Hz to MDCT bins is done by multiplying by sampling_rate/

Valin, et al.            Expires January 9, 2011                [Page 8]


Internet-Draft                 CELT codec                      July 2010

(2*frame_size) and rounding to the nearest value.  An exception is
made for the lower frequencies to ensure that all bands contain at
least 3 MDCT bins.  The definition of the Bark bands is computed in
compute_ebands() (modes.c (Appendix A.6)).

CELT includes a pitch predictor for which the gains are defined over
a set of _pitch bands_.  The pitch bands are defined (in Hz) as [0,
345, 689, 1034, 1378, 2067, 3273, 5340, 6374].  The Hz values are
mapped to MDCT bins in the same was as the energy bands.  The pitch
band boundaries are aligned to energy band boundaries.  The
definition of the pitch bands is computed in compute_pbands()
(modes.c (Appendix A.6)).

The mode contains a bit allocation table that is derived from a
prototype allocation table, specified in the band_allocation matrix
(modes.c (Appendix A.6)).  Each row of the table is a single
prototype allocation, in bits per Bark band, and assuming 256-sample
frames.  These rows must be projected onto the actual band layout in
use at the current frame size and sample rate, using exact integer
calculations.  The reference implementation pre-computes these
projections in compute_allocation_table() (modes.c (Appendix A.6))
and any other implementation MUST produces bit-identical allocation
results.

Every entry in the allocation table is multiplied by the current
number of channels and the current frame size.  Each prototype
allocation is projected independently using the following process:
the upper band frequencies (in Hz) from the current Bark band and
current CELT band are compared.  (When the process begins, these will
each be the first band, but will increment independently.)  If the
current Bark band's upper edge frequency is less than the current
CELT band's upper edge frequency, the entire value of the Bark band
plus any carried remainder is assigned to the current CELT band, and
the process continues with the next Bark band in sequence and zero
remainder.  If the current Bark band's upper edge frequency is equal
to or greater than that of the current CELT band, the CELT band will
receive only part of this Bark band's allocation.  This portion
allocated to the CELT band is then calculated by multiplying the Bark
band's allocation by the difference in Hz between the Bark band's
upper frequency and the current CELT band's lower frequency, adding
the width of the current Bark band divided by two, and then dividing
this total by the width of the current Bark band in Hz.  The partial
value plus any carried remainder is added to the current CELT band,
and the difference between the partial value and the Bark target is
taken as the new carried remainder.  The process begins then again
starting at the next CELT band and next Bark band.  Once all bands in
a prototype allocation have been considered, any remainder is added
to the last CELT band.  All of the resulting values are rescaled by

Valin, et al.            Expires January 9, 2011                [Page 9]


Internet-Draft                 CELT codec                      July 2010

adding 128 and dividing by 256.

Valin, et al.            Expires January 9, 2011               [Page 10]


Internet-Draft                 CELT codec                      July 2010

4.  CELT Encoder

The top-level function for encoding a CELT frame in the reference
implementation is celt_encode() (celt.c (Appendix A.4)).  The basic
block diagram of the CELT encoder is illustrated in Figure 1.  The
encoder contains most of the building blocks of the decoder and can,
with very little extra computation, compute the signal that would be
decoded by the decoder.  CELT has three main quantizers denoted Q1,
Q2 and Q3.  These apply to band energies (Section 4.5), pitch gains
(Section 4.7) and normalized MDCT bins (Section 4.8), respectively.

+-----------+        +--+
+--|  Energy   |-+----->|Q1|------+
|  |computation| |      +--+      |
|  +-----------+ |                |
|          +-----+                |
|          v                      v
+------+  +-+--+  +-+  +-+  +-+  +--+  +---+  +-+  +-----+  +-+
->|Window|->|MDCT|->|-|->|/|->|-|->|Q3|->|Mix|->|*|->|IMDCT|->|+|-+->
+---+--+  +----+  +-+  +-+  +-+  +--+  +---+  +-+  +-----+  +-+ |
|             ^                                            |
|             +--------------------------+                 |
+-+                                      |                 |
|              +----------+   +--+   +-+-+               |
+------------->|pitch gain|-->|Q2|-->| * |               |
|              +----------+   +--+   +---+               |
|                    ^                 ^                 |
|                    +-----------------+                 |
v                                      |                 |
+------------+                        +------+-----+           |
|Pitch period|                        |Delay, MDCT,|           |
|estimation  |----------------------->|  Normalize |           |
+------------+                        +------------+           |
^                                      ^                 |
+--------------------------------------+-----------------+

Block diagram of the CELT encoder

Figure 1

The input audio first goes through a pre-emphasis filter (just before
the windowing in Figure 1), which attenuates the _spectral tilt_.
The filter is has the transfer function A(z)=1-alpha_p*z^-1, with
alpha_p=0.8.  The inverse of the pre-emphasis is applied at the
decoder.

Valin, et al.            Expires January 9, 2011               [Page 11]


Internet-Draft                 CELT codec                      July 2010

4.1.  Range Coder

CELT uses an entropy coder based upon [range-coding], which is itself
a rediscovery of the FIFO arithmetic code introduced by
[coding-thesis].  It is very similar to arithmetic encoding, except
that encoding is done with digits in any base instead of with bits,
so it is faster when using larger bases (i.e.: an octet).  All of the
calculations in the range coder must use bit-exact integer
arithmetic.

The range coder also acts as the bit-packer for CELT.  It is used in
three different ways, to encode:

o  entropy-coded symbols with a fixed probability model using
ec_encode(), (rangeenc.c (Appendix A.29))

o  integers from 0 to 2^M-1 using ec_enc_uint() or ec_enc_bits(),
(entenc.c (Appendix A.25))

o  integers from 0 to N-1 (where N is not a power of two) using
ec_enc_uint(). (entenc.c (Appendix A.25))

The range encoder maintains an internal state vector composed of the
four-tuple (low,rng,rem,ext), representing the low end of the current
range, the size of the current range, a single buffered output octet,
and a count of additional carry-propagating output octets.  Both rng
and low are 32-bit unsigned integer values, rem is an octet value or
the special value -1, and ext is an integer with at least 16 bits.
This state vector is initialized at the start of each each frame to
the value (0,2^31,-1,0).

Each symbol is drawn from a finite alphabet and coded in a separate
context which describes the size of the alphabet and the relative
frequency of each symbol in that alphabet.  CELT only uses static
contexts; they are not adapted to the statistics of the data that is
coded.

4.1.1.  Encoding Symbols

The main encoding function is ec_encode() (rangeenc.c
(Appendix A.29)), which takes as an argument a three-tuple (fl,fh,ft)
describing the range of the symbol to be encoded in the current
context, with 0 <= fl < fh <= ft <= 65535.  The values of this tuple
are derived from the probability model for the symbol.  Let f(i) be
the frequency of the ith symbol in the current context.  Then the
three-tuple corresponding to the kth symbol is given by
fl=sum(f(i),i<k), fh=fl+f(i), and ft=sum(f(i)).

Valin, et al.            Expires January 9, 2011               [Page 12]


Internet-Draft                 CELT codec                      July 2010

ec_encode() updates the state of the encoder as follows.  If fl is
greater than zero, then low = low + rng - (rng/ft)*(ft-fl) and rng =
(rng/ft)*(fh-fl).  Otherwise, low is unchanged and rng = rng - (rng/
ft)*(fh-fl).  The divisions here are exact integer division.  After
this update, the range is normalized.

To normalize the range, the following process is repeated until rng >
2^23.  First, the top 9 bits of low, (low>>23), are placed into a
carry buffer.  Then, low is set to (low << 8 & 0x7FFFFFFF) and rng is
set to (rng<<8).  This process is carried out by ec_enc_normalize()
(rangeenc.c (Appendix A.29)).

The 9 bits produced in each iteration of the normalization loop
consist of 8 data bits and a carry flag.  The final value of the
output bits is not determined until carry propagation is accounted
for.  Therefore the reference implementation buffers a single (non-
propagating) output octet and keeps a count of additional propagating
(0xFF) output octets.  An implementation MAY choose to use any
mathematically equivalent scheme to perform carry propagation.

The function ec_enc_carry_out() (rangeenc.c (Appendix A.29)) performs
this buffering.  It takes a 9-bit input value, c, from the
normalization 8-bit output and a carry bit.  If c is 0xFF, then ext
is incremented and no octets are output.  Otherwise, if rem is not
the special value -1, then the octet (rem+(c>>8)) is output.  Then
ext octets are output with the value 0 if the carry bit is set, or
0xFF if it is not, and rem is set to the lower 8 bits of c.  After
this, ext is set to zero.

In the reference implementation, a special version of ec_encode()
called ec_encode_bin() (rangeenc.c (Appendix A.29)) is defined to
take a two-tuple (fl,ftb), where 0 <= fl < 2^ftb and ftb < 16.  It is
mathematically equivalent to calling ec_encode() with the three-tuple
(fl,fl+1,1<<ftb), but avoids using division.

4.1.2.  Encoding Uniformly Distributed Integers

Functions ec_enc_uint() or ec_enc_bits() are based on ec_encode() and
encode one of N equiprobable symbols, each with a frequency of 1,
where N may be as large as 2^32-1.  Because ec_encode() is limited to
a total frequency of 2^16-1, this is done by encoding a series of
symbols in smaller contexts.

ec_enc_bits() (entenc.c (Appendix A.25)) is defined, like
ec_encode_bin(), to take a two-tuple (fl,ftb), with 0 <= fl < 2^ftb
and ftb < 32.  While ftb is greater than 8, it encodes bits (ftb-8)
to (ftb-1) of fl, e.g., (fl>>ftb-8&0xFF) using ec_encode_bin() and
subtracts 8 from ftb.  Then, it encodes the remaining bits of fl,

Valin, et al.            Expires January 9, 2011               [Page 13]


Internet-Draft                 CELT codec                      July 2010

e.g., (fl&(1<<ftb)-1), again using ec_encode_bin().

ec_enc_uint() (entenc.c (Appendix A.25)) takes a two-tuple (fl,ft),
where ft is not necessarily a power of two.  Let ftb be the location
of the highest 1 bit in the two's-complement representation of
(ft-1), or -1 if no bits are set.  If ftb>8, then the top 8 bits of
fl are encoded using ec_encode() with the three-tuple (fl>>ftb-
8,(fl>>ftb-8)+1,(ft-1>>ftb-8)+1), and the remaining bits are encoded
with ec_enc_bits using the two-tuple (fl&(1<<ftb-8)-1,ftb-8).
Otherwise, fl is encoded with ec_encode() directly using the three-
tuple (fl,fl+1,ft).

4.1.3.  Finalizing the Stream

After all symbols are encoded, the stream must be finalized by
outputting a value inside the current range.  Let end be the integer
in the interval [low,low+rng) with the largest number of trailing
zero bits.  Then while end is not zero, the top 9 bits of end, e.g.,
(end>>23), are sent to the carry buffer, and end is replaced by
(end<<8&0x7FFFFFFF).  Finally, if the value in carry buffer, rem, is
neither zero nor the special value -1, or the carry count, ext, is
greater than zero, then 9 zero bits are sent to the carry buffer.
After the carry buffer is finished outputting octets, the rest of the
output buffer is padded with zero octets.  Finally, rem is set to the
special value -1.  This process is implemented by ec_enc_done()
(rangeenc.c (Appendix A.29)).

4.1.4.  Current Bit Usage

The bit allocation routines in CELT need to be able to determine a
conservative upper bound on the number of bits that have been used to
encode the current frame thus far.  This drives allocation decisions
and ensures that the range code will not overflow the output buffer.
This is computed in the reference implementation to fractional bit
precision by the function ec_enc_tell() (rangeenc.c (Appendix A.29)).
Like all operations in the range encoder, it must be implemented in a
bit-exact manner.

4.2.  Encoder Feature Selection

The CELT codec has several optional features that can be switched on
or off in each frame, some of which are mutually exclusive.  The four
main flags are intra-frame energy (I), pitch (P), short blocks (S),
and folding (F).  Those are described in more detail below.  There
are eight valid combinations of these four features, and they are
encoded into the stream first using a variable length code (Table 1).
It is left to the implementor to choose when to enable each of the
flags, with the only restriction that the combination of the four

Valin, et al.            Expires January 9, 2011               [Page 14]


Internet-Draft                 CELT codec                      July 2010

flags MUST correspond to a valid entry in Table 1.

Encoding of the feature flags

+---+---+---+---+----------+
| I | P | S | F | Encoding |
+---+---+---+---+----------+
| 0 | 0 | 0 | 1 |       00 |
|   |   |   |   |          |
| 0 | 1 | 0 | 1 |       01 |
|   |   |   |   |          |
| 1 | 0 | 0 | 1 |      110 |
|   |   |   |   |          |
| 1 | 0 | 1 | 1 |      111 |
|   |   |   |   |          |
| 0 | 0 | 0 | 0 |     1000 |
|   |   |   |   |          |
| 0 | 0 | 1 | 1 |     1001 |
|   |   |   |   |          |
| 0 | 1 | 0 | 0 |     1010 |
|   |   |   |   |          |
| 1 | 0 | 0 | 0 |     1011 |
+---+---+---+---+----------+

Table 1

4.2.1.  Intra-frame energy (I)

CELT uses prediction to encode the energy in each frequency band.  In
order to make frames independent, however, it is possible to disable
the part of the prediction that depends on previous frames.  This is
called _intra-frame energy_ and requires around 12 more bits per
frame.  It is enabled with the _I_ bit (Table.  flags-encoding
(Table 1)).  The use of intra energy is OPTIONAL and the decision
method is left to the implementor.  The reference code describes one
way of deciding which frames would benefit most from having their
energy encoded without prediction.  The intra_decision()
(quant_bands.c (Appendix A.34)) function looks for frames where the
log-spectral distance between consecutive frames is more than 9 dB.
When such a difference is found between two frames, the next frame
(not the one for which the difference is detected) is marked encoded
with intra energy.  The one-frame delay is to ensure that when a
frame containing a transient is lost, then the next frame will be
decoded without accumulating error from the lost frame.

Valin, et al.            Expires January 9, 2011               [Page 15]


Internet-Draft                 CELT codec                      July 2010

4.2.2.  Pitch prediction (P)

CELT can use a pitch predictor (also known as long-term predictor) to
improve the voice quality at lower bit-rates.  When the _P_ bit is
set, the pitch period is encoded after the flag bits.  The value
encoded is an integer in the range [0, 1024-N-overlap-1].

4.2.3.  Short blocks (S)

To improve audio quality during transients, CELT can use a _short
block_ multiple-MDCT transform.  Unlike other transform codecs, the
multiple MDCTs are jointly quantized as if the coefficients were
obtained from a single MDCT.  For that reason, it is better to
consider the short block case as using a different transform of the
same length rather than as multiple independent MDCTs.  In the
reference implementation, the decision to use short blocks is made by
transient_analysis() (celt.c (Appendix A.4)) based on the pre-
emphasized signal's peak values, but other methods can be used.  When
the _S_ bit is set, a 2-bit transient scalefactor is encoded directly
after the flag bits.  If the scalefactor is 0, then the multiple-MDCT
output is unmodified.  If the scalefactor is 1 or 2, then the output
of the MDCTs that follow the transient is scaled down by
2^scalefactor.  If the scalefactor is equal to 3, then a time-domain
pre-emphasis window is applied *before* computing the MDCTs and no
further scaling is applied to the MDCTs output.  The window value is
1 from the beginning of the frame to 16 samples before the transient
time.  It is a Hanning window from there to the transient time, and
then the value is 1/8 up to the end of the frame.  The Hanning window
part is defined as:

static const float transientWindow[16] = { 0.0085135, 0.0337639,
0.0748914, 0.1304955, 0.1986827, 0.2771308, 0.3631685, 0.4538658,
0.5461342, 0.6368315, 0.7228692, 0.8013173, 0.8695045, 0.9251086,
0.9662361, 0.9914865};

When the scalefactor is 3, the transient time is the exact time of
the transient determined by the encoder and encoded as an integer
number of samples with the range [0, N+overlap-1] directly after the
scalefactor.

In the case where the scalefactor is 1 or 2 and the mode is defined
to use more than 2 MDCTs, the last MDCT to which the scaling is *not*
applied is encoded using an integer in the range [0, B-2], where B is
the number of short MDCTs used for the mode.

Valin, et al.            Expires January 9, 2011               [Page 16]


Internet-Draft                 CELT codec                      July 2010

4.2.4.  Spectral folding (F)

The last encoding feature in CELT is spectral folding.  It is
designed to prevent _birdie_ artifacts caused by the sparse spectra
often generated by low-bitrate transform codecs.  When folding is
enabled, a copy of the low-frequency spectrum is added to the higher-
frequency bands (above ~6400 Hz).  The folding operation is described
in more detail in Section 4.8.

4.3.  Forward MDCT

The MDCT implementation has no special characteristics.  The input is
a windowed signal (after pre-emphasis) of 2*N samples and the output
is N frequency-domain samples.  A _low-overlap_ window is used to
reduce the algorithmic delay.  It is derived from a basic (full
overlap) window that is the same as the one used in the Vorbis codec:
W(n)=[sin(pi/2*sin(pi/2*(n+.5)/L))]^2.  The low-overlap window is
created by zero-padding the basic window and inserting ones in the
middle, such that the resulting window still satisfies power
complementarity.  The MDCT is computed in mdct_forward() (mdct.c
(Appendix A.20)), which includes the windowing operation and a
scaling of 2/N.

4.4.  Bands and Normalization

The MDCT output is divided into bands that are designed to match the
ear's critical bands, with the exception that each band has to be at
least 3 bins wide.  For each band, the encoder computes the energy
that will later be encoded.  Each band is then normalized by the
square root of the *non-quantized* energy, such that each band now
forms a unit vector X. The energy and the normalization are computed
by compute_band_energies() and normalise_bands() (bands.c
(Appendix A.8)), respectively.

4.5.  Energy Envelope Quantization

It is important to quantize the energy with sufficient resolution
because any energy quantization error cannot be compensated for at a
later stage.  Regardless of the resolution used for encoding the
shape of a band, it is perceptually important to preserve the energy
in each band.  CELT uses a coarse-fine strategy for encoding the
energy in the base-2 log domain, as implemented in quant_bands.c
(Appendix A.34)

4.5.1.  Coarse energy quantization

The coarse quantization of the energy uses a fixed resolution of 6 dB
and is the only place where entropy coding is used.  To minimize the

Valin, et al.            Expires January 9, 2011               [Page 17]


Internet-Draft                 CELT codec                      July 2010

bitrate, prediction is applied both in time (using the previous
frame) and in frequency (using the previous bands).  The 2-D
z-transform of the prediction filter is: A(z_l, z_b)=(1-a*z_l^-1)*(1-
z_b^-1)/(1-b*z_b^-1) where b is the band index and l is the frame
index.  The prediction coefficients are a=0.8 and b=0.7 when not
using intra energy and a=b=0 when using intra energy.  The time-
domain prediction is based on the final fine quantization of the
previous frame, while the frequency domain (within the current frame)
prediction is based on coarse quantization only (because the fine
quantization has not been computed yet).  We approximate the ideal
probability distribution of the prediction error using a Laplace
distribution.  The coarse energy quantization is performed by
quant_coarse_energy() and quant_coarse_energy() (quant_bands.c
(Appendix A.34)).

The Laplace distribution for each band is defined by a 16-bit (Q15)
decay parameter.  Thus, the value 0 has a frequency count of
p[0]=2*(16384*(16384-decay)/(16384+decay)).  The values +/- i each
have a frequency count p[i] = (p[i-1]*decay)>>14.  The value of p[i]
is always rounded down (to avoid exceeding 32768 as the sum of all
frequency counts), so it is possible for the sum to be less than
32768.  In that case additional values with a frequency count of 1
are encoded.  The signed values corresponding to symbols 0, 1, 2, 3,
4, ... are [0, +1, -1, +2, -2, ...].  The encoding of the Laplace-
distributed values is implemented in ec_laplace_encode() (laplace.c
(Appendix A.32)).

4.5.2.  Fine energy quantization

After the coarse energy quantization and encoding, the bit allocation
is computed (Section 4.6) and the number of bits to use for refining
the energy quantization is determined for each band.  Let B_i be the
number of fine energy bits for band i; the refinement is an integer f
in the range [0,2^B_i-1].  The mapping between f and the correction
applied to the coarse energy is equal to (f+1/2)/2^B_i - 1/2.  Fine
energy quantization is implemented in quant_fine_energy()
(quant_bands.c (Appendix A.34)).

If any bits are unused at the end of the encoding process, these bits
are used to increase the resolution of the fine energy encoding in
some bands.  Priority is given to the bands for which the allocation
(Section 4.6) was rounded down.  At the same level of priority, lower
bands are encoded first.  Refinement bits are added until there are
no unused bits.  This is implemented in quant_energy_finalise()
(quant_bands.c (Appendix A.34)).

Valin, et al.            Expires January 9, 2011               [Page 18]


Internet-Draft                 CELT codec                      July 2010

4.6.  Bit Allocation

Bit allocation is performed based only on information available to
both the encoder and decoder.  The same calculations are performed in
a bit-exact manner in both the encoder and decoder to ensure that the
result is always exactly the same.  Any mismatch would cause an error
in the decoded output.  The allocation is computed by
compute_allocation() (rate.c (Appendix A.16)), which is used in both
the encoder and the decoder.

For a given band, the bit allocation is nearly constant across frames
that use the same number of bits for Q1, yielding a pre-defined
signal-to-mask ratio (SMR) for each band.  Because the bands each
have a width of one Bark, this is equivalent to modeling the masking
occurring within each critical band, while ignoring inter-band
masking and tone-vs-noise characteristics.  While this is not an
optimal bit allocation, it provides good results without requiring
the transmission of any allocation information.

For every encoded or decoded frame, a target allocation must be
computed using the projected allocation.  In the reference
implementation this is performed by compute_allocation() (rate.c
(Appendix A.16)).  The target computation begins by calculating the
available space as the number of whole bits which can be fit in the
frame after Q1 is stored according to the range coder (ec_[enc/
dec]_tell()) and then multiplying by 8.  Then the two projected
prototype allocations whose sums multiplied by 8 are nearest to that
value are determined.  These two projected prototype allocations are
then interpolated by finding the highest integer interpolation
coefficient in the range 0-8 such that the sum of the higher
prototype times the coefficient, plus the sum of the lower prototype
multiplied by the difference of 16 and the coefficient, is less than
or equal to the available sixteenth-bits.  The reference
implementation performs this step using a binary search in
interp_bits2pulses() (rate.c (Appendix A.16)).  The target allocation
is the interpolation coefficient times the higher prototype, plus the
lower prototype multiplied by the difference of 16 and the
coefficient, for each of the CELT bands.

Because the computed target will sometimes be somewhat smaller than
the available space, the excess space is divided by the number of
bands, and this amount is added equally to each band.  Any remaining
space is added to the target one sixteenth-bit at a time, starting
from the first band.  The new target now matches the available space,
in sixteenth-bits, exactly.

The allocation target is separated into a portion used for fine
energy and a portion used for the Spherical Vector Quantizer (PVQ).

Valin, et al.            Expires January 9, 2011               [Page 19]


Internet-Draft                 CELT codec                      July 2010

The fine energy quantizer operates in whole-bit steps.  For each band
the number of bits per channel used for fine energy is calculated by
50 minus the log2_frac(), with 1/16 bit precision, of the number of
MDCT bins in the band.  That result is multiplied by the number of
bins in the band and again by twice the number of channels, and then
the value is set to zero if it is less than zero.  Added to that
result is 16 times the number of MDCT bins times the number of
channels, and it is finally divided by 32 times the number of MDCT
bins times the number of channels.  If the result times the number of
channels is greater than than the target divided by 16, the result is
set to the target divided by the number of channels divided by 16.
Then if the value is greater than 7 it is reset to 7 because a larger
amount of fine energy resolution was determined not to be make an
improvement in perceived quality.  The resulting number of fine
energy bits per channel is then multiplied by the number of channels
and then by 16, and subtracted from the target allocation.  This
final target allocation is what is used for the PVQ.

4.7.  Pitch Prediction

This section needs to be updated.

4.8.  Spherical Vector Quantization

CELT uses a Pyramid Vector Quantization (PVQ) [PVQ] codebook for
quantizing the details of the spectrum in each band that have not
been predicted by the pitch predictor.  The PVQ codebook consists of
all sums of K signed pulses in a vector of N samples, where two
pulses at the same position are required to have the same sign.  Thus
the codebook includes all integer codevectors y of N dimensions that
satisfy sum(abs(y(j))) = K.

In bands where neither pitch nor folding is used, the PVQ is used to
encode the unit vector that results from the normalization in
Section 4.4 directly.  Given a PVQ codevector y, the unit vector X is
obtained as X = y/||y||, where ||.|| denotes the L2 norm.

4.8.1.  Bits to Pulses

Although the allocation is performed in 1/16 bit units, the
quantization requires an integer number of pulses K. To do this, the
encoder searches for the value of K that produces the number of bits
that is the nearest to the allocated value (rounding down if exactly
half-way between two values), subject to not exceeding the total
number of bits available.  The computation is performed in 1/16 of
bits using log2_frac() and ec_enc_tell().  The number of codebooks
entries can be computed as explained in Section 4.8.3.  The
difference between the number of bits allocated and the number of

Valin, et al.            Expires January 9, 2011               [Page 20]


Internet-Draft                 CELT codec                      July 2010

bits used is accumulated to a _balance_ (initialised to zero) that
helps adjusting the allocation for the next bands.  One third of the
balance is subtracted from the bit allocation of the next band to
help achieving the target allocation.  The only exceptions are the
band before the last and the last band, for which half the balance
and the whole balance are subtracted, respectively.

4.8.2.  PVQ Search

The search for the best codevector y is performed by alg_quant()
(vq.c (Appendix A.12)).  There are several possible approaches to the
search with a tradeoff between quality and complexity.  The method
used in the reference implementation computes an initial codeword y1
by projecting the residual signal R = X - p' onto the codebook
pyramid of K-1 pulses:

y0 = round_towards_zero( (K-1) * R / sum(abs(R)))

Depending on N, K and the input data, the initial codeword y0 may
contain from 0 to K-1 non-zero values.  All the remaining pulses,
with the exception of the last one, are found iteratively with a
greedy search that minimizes the normalized correlation between y and
R:

J = -R^T*y / ||y||

The search described above is considered to be a good trade-off
between quality and computational cost.  However, there are other
possible ways to search the PVQ codebook and the implementors MAY use
any other search methods.

4.8.3.  Index Encoding

The best PVQ codeword is encoded as a uniformly-distributed integer
value by encode_pulses() (cwrs.c (Appendix A.10)).  The codeword is
converted to a unique index in the same way as specified in [PVQ].
The indexing is based on the calculation of V(N,K) (denoted N(L,K) in
[PVQ]), which is the number of possible combinations of K pulses in N
samples.  The number of combinations can be computed recursively as
V(N,K) = V(N+1,K) + V(N,K+1) + V(N+1,K+1), with V(N,0) = 1 and V(0,K)
= 0, K != 0.  There are many different ways to compute V(N,K),
including pre-computed tables and direct use of the recursive
formulation.  The reference implementation applies the recursive
formulation one line (or column) at a time to save on memory use,
along with an alternate, univariate recurrence to initialise an
arbitrary line, and direct polynomial solutions for small N. All of
these methods are equivalent, and have different trade-offs in speed,
memory usage, and code size.  Implementations MAY use any methods

Valin, et al.            Expires January 9, 2011               [Page 21]


Internet-Draft                 CELT codec                      July 2010

they like, as long as they are equivalent to the mathematical
definition.

The indexing computations are performed using 32-bit unsigned
integers.  For large codebooks, 32-bit integers are not sufficient.
slightly sub-optimal by splitting each band into two equal (or near-
equal) vectors of size (N+1)/2 and N/2, respectively.  The number of
pulses in the first half, K1, is first encoded as an integer in the
range [0,K].  Then, two codebooks are encoded with V((N+1)/2, K1) and
V(N/2, K-K1).  The split operation is performed recursively, in case
one (or both) of the split vectors still requires more than 32 bits.
For compatibility reasons, the handling of codebooks of more than 32
bits MUST be implemented with the splitting method, even if 64-bit
arithmetic is available.

4.9.  Stereo support

When encoding a stereo stream, some parameters are shared across the
left and right channels, while others are transmitted separately for
each channel, or jointly encoded.  Only one copy of the flags for the
features, transients and pitch (pitch period and gains) are
transmitted.  The coarse and fine energy parameters are transmitted
separately for each channel.  Both the coarse energy and fine energy
(including the remaining fine bits at the end of the stream) have the
left and right bands interleaved in the stream, with the left band
encoded first.

The main difference between mono and stereo coding is the PVQ coding
of the normalized vectors.  In stereo mode, a normalized mid-side
(M-S) encoding is used.  Let L and R be the normalized vector of a
certain band for the left and right channels, respectively.  The mid
and side vectors are computed as M=L+R and S=L-R and no longer have
unit norm.

From M and S, an angular parameter theta=2/pi*atan2(||S||, ||M||) is
computed.  The theta parameter is converted to a Q14 fixed-point
parameter itheta, which is quantized on a scale from 0 to 1 with an
interval of 2^-qb, where qb = (b-2*(N-1)*(40-log2_frac(N,4)))/
(32*(N-1)), b is the number of bits allocated to the band, and
log2_frac() is defined in cwrs.c (Appendix A.10).  From here on, the
value of itheta MUST be treated in a bit-exact manner since both the
encoder and decoder rely on it to infer the bit allocation.

Let m=M/||M|| and s=S/||S||; m and s are separately encoded with the
PVQ encoder described in Section 4.8.  The number of bits allocated
to m and s depends on the value of itheta.  The number of bits
allocated to coding m is obtained by:

Valin, et al.            Expires January 9, 2011               [Page 22]


Internet-Draft                 CELT codec                      July 2010

imid = bitexact_cos(itheta);

iside = bitexact_cos(16384-itheta);

delta = (N-1)*(log2_frac(iside,6)-log2_frac(imid,6))>>2;

qalloc = log2_frac((1<<qb)+1,4);

mbits = (b-qalloc/2-delta)/2;

where bitexact_cos() is a fixed-point cosine approximation that MUST
be bit-exact with the reference implementation in mathops.h
(Appendix A.36).  The spectral folding operation is performed
independently for the mid and side vectors.

4.10.  Synthesis

After all the quantization is completed, the quantized energy is used
along with the quantized normalized band data to resynthesize the
MDCT spectrum.  The inverse MDCT (Section 5.6) and the weighted
overlap-add are applied and the signal is stored in the _synthesis
buffer_ so it can be used for pitch prediction.  The encoder MAY omit
this step of the processing if it knows that it will not be using the
pitch predictor for the next few frames.  If the de-emphasis filter
(Section 5.6) is applied to this resynthesized signal, then the
output will be the same (within numerical precision) as the decoder's
output.

4.11.  Variable Bitrate (VBR)

Each CELT frame can be encoded in a different number of octets,
making it possible to vary the bitrate at will.  This property can be
used to implement source-controlled variable bitrate (VBR).  Support
for VBR is OPTIONAL for the encoder, but a decoder MUST be prepared
to decode a stream that changes its bit-rate dynamically.  The method
used to vary the bit-rate in VBR mode is left to the implementor, as
long as each frame can be decoded by the reference decoder.

Valin, et al.            Expires January 9, 2011               [Page 23]


Internet-Draft                 CELT codec                      July 2010

5.  CELT Decoder

Like most audio codecs, the CELT decoder is less complex than the
encoder, as can be observed in the decoder block diagram in Figure 2.
In fact, most of the operations performed by the decoder are also
performed by the encoder.

+--+
|Q1|-------------+
+--+             |
v
+--+  +-----+  +---+  +-----+
|Q3|->| Mix |->| * |->|IMDCT|-+-> output
+--+  +-----+  +---+  +-----+ |
^      ^                    |
+------+                    |
|                    |
+--+   +-+-+                  |
|Q2|-->| * |                  |
+--+   +---+                  |
^                    |
|                    |
+------+-----+              |
+------------+  |Delay, MDCT,|              |
|Pitch period|->|  Normalize |              |
+------------+  +------------+              |
^                    |
+--------------------+

Block diagram of the CELT decoder

Figure 2

The decoder extracts information from the range-coded bit-stream in
the same order as it was encoded by the encoder.  In some
circumstances, it is possible for a decoded value to be out of range
due to a very small amount of redundancy in the encoding of large
integers by the range coder.  In that case, the decoder should assume
there has been an error in the coding, decoding, or transmission and
SHOULD take measures to conceal the error and/or report to the
application that a problem has occurred.

5.1.  Range Decoder

The range decoder extracts the symbols and integers encoded using the
range encoder in Section 4.1.  The range decoder maintains an

Valin, et al.            Expires January 9, 2011               [Page 24]


Internet-Draft                 CELT codec                      July 2010

internal state vector composed of the two-tuple (dif,rng),
representing the difference between the high end of the current range
and the actual coded value, and the size of the current range,
respectively.  Both dif and rng are 32-bit unsigned integer values.
rng is initialized to 2^7. dif is initialized to rng minus the top 7
bits of the first input octet.  Then the range is immediately
normalized, using the procedure described in the following section.

5.1.1.  Decoding Symbols

Decoding symbols is a two-step process.  The first step determines a
value fs that lies within the range of some symbol in the current
context.  The second step updates the range decoder state with the
three-tuple (fl,fh,ft) corresponding to that symbol, as defined in
Section 4.1.1.

The first step is implemented by ec_decode() (rangedec.c
(Appendix A.30)), and computes fs = ft-min((dif-1)/(rng/ft)+1,ft),
where ft is the sum of the frequency counts in the current context,
as described in Section 4.1.1.  The divisions here are exact integer
division.

In the reference implementation, a special version of ec_decode()
called ec_decode_bin() (rangeenc.c (Appendix A.29)) is defined using
the parameter ftb instead of ft.  It is mathematically equivalent to
calling ec_decode() with ft = (1<<ftb), but avoids one of the
divisions.

The decoder then identifies the symbol in the current context
corresponding to fs; i.e., the one whose three-tuple (fl,fh,ft)
satisfies fl <= fs < fh.  This tuple is used to update the decoder
state according to dif = dif - (rng/ft)*(ft-fh), and if fl is greater
than zero, rng = (rng/ft)*(fh-fl), or otherwise rng = rng - (rng/
ft)*(ft-fh).  After this update, the range is normalized.

To normalize the range, the following process is repeated until rng >
2^23.  First, rng is set to (rng<8)&0xFFFFFFFF.  Then the next 8 bits
of input are read into sym, using the remaining bit from the previous
input octet as the high bit of sym, and the top 7 bits of the next
octet for the remaining bits of sym.  If no more input octets remain,
zero bits are used instead.  Then, dif is set to (dif<<8)-sym&
0xFFFFFFFF (i.e., using wrap-around if the subtraction overflows a
32-bit register).  Finally, if dif is larger than 2^31, dif is then
set to dif - 2^31.  This process is carried out by ec_dec_normalize()
(rangedec.c (Appendix A.30)).

Valin, et al.            Expires January 9, 2011               [Page 25]


Internet-Draft                 CELT codec                      July 2010

5.1.2.  Decoding Uniformly Distributed Integers

Functions ec_dec_uint() or ec_dec_bits() are based on ec_decode() and
decode one of N equiprobable symbols, each with a frequency of 1,
where N may be as large as 2^32-1.  Because ec_decode() is limited to
a total frequency of 2^16-1, this is done by decoding a series of
symbols in smaller contexts.

ec_dec_bits() (entdec.c (Appendix A.27)) is defined, like
ec_decode_bin(), to take a single parameter ftb, with ftb < 32. and
ftb < 32, and produces an ftb-bit decoded integer value, t,
initialized to zero.  While ftb is greater than 8, it decodes the
next 8 most significant bits of the integer, s = ec_decode_bin(8),
bits to the current value of t, t = t<<8 | s, and subtracts 8 from
ftb.  Then it decodes the remaining bits of the integer, s =
ec_decode_bin(ftb), updates the decoder state with the 3 tuple (s,s+
1,1<<ftb), and adds those bits to the final values of t, t = t<<ftb |
s.

ec_dec_uint() (entdec.c (Appendix A.27)) takes a single parameter,
ft, which is not necessarily a power of two, and returns an integer,
t, with a value between 0 and ft-1, inclusive, which is initialized
to zero.  Let ftb be the location of the highest 1 bit in the two's-
complement representation of (ft-1), or -1 if no bits are set.  If
ftb>8, then the top 8 bits of t are decoded using t = ec_decode((ft-
1>>ftb-8)+1), the decoder state is updated with the three-tuple (s,s+
1,(ft-1>>ftb-8)+1), and the remaining bits are decoded with t =
t<<ftb-8|ec_dec_bits(ftb-8).  If, at this point, t >= ft, then the
current frame is corrupt, and decoding should stop.  If the original
value of ftb was not greater than 8, then t is decoded with t =
ec_decode(ft), and the decoder state is updated with the three-tuple
(t,t+1,ft).

5.1.3.  Current Bit Usage

The bit allocation routines in CELT need to be able to determine a
conservative upper bound on the number of bits that have been used to
decode from the current frame thus far.  This drives allocation
decisions which must match those made in the encoder.  This is
computed in the reference implementation to fractional bit precision
by the function ec_dec_tell() (rangedec.c (Appendix A.30)).  Like all
operations in the range decoder, it must be implemented in a bit-
exact manner, and must produce exactly the same value returned by
ec_enc_tell() after encoding the same symbols.

Valin, et al.            Expires January 9, 2011               [Page 26]


Internet-Draft                 CELT codec                      July 2010

5.2.  Energy Envelope Decoding

The energy of each band is extracted from the bit-stream in two steps
according to the same coarse-fine strategy used in the encoder.
First, the coarse energy is decoded in unquant_coarse_energy()
(quant_bands.c (Appendix A.34)) based on the probability of the
Laplace model used by the encoder.

After the coarse energy is decoded, the same allocation function as
used in the encoder is called (Section 4.6).  This determines the
number of bits to decode for the fine energy quantization.  The
decoding of the fine energy bits is performed by
unquant_fine_energy() (quant_bands.c (Appendix A.34)).  Finally, like
the encoder, the remaining bits in the stream (that would otherwise
go unused) are decoded using unquant_energy_finalise() (quant_bands.c
(Appendix A.34)).

5.3.  Pitch prediction decoding

If the pitch bit is set, then the pitch period is extracted from the
bit-stream.  The pitch gain bits are extracted within the PVQ
decoding as encoded by the encoder.  When the folding bit is set, the
folding prediction is computed in exactly the same way as the
encoder, with the same gain, by the function intra_fold() (vq.c
(Appendix A.12)).

5.4.  Spherical VQ Decoder

In order to correctly decode the PVQ codewords, the decoder must
perform exactly the same bits to pulses conversion as the encoder
(see Section 4.8.1).

5.4.1.  Index Decoding

The decoding of the codeword from the index is performed as specified
in [PVQ], as implemented in function decode_pulses() (cwrs.c
(Appendix A.10)).

5.4.2.  Normalised Vector Decoding

The spherical codebook is decoded by alg_unquant() (vq.c
(Appendix A.12)).  The index of the PVQ entry is obtained from the
range coder and converted to a pulse vector by decode_pulses()
(cwrs.c (Appendix A.10)).

The decoded normalized vector for each band is equal to

X' = y/||y||,

Valin, et al.            Expires January 9, 2011               [Page 27]


Internet-Draft                 CELT codec                      July 2010

This operation is implemented in mix_pitch_and_residual() (vq.c
(Appendix A.12)), which is the same function as used in the encoder.

5.5.  Denormalization

Just like each band was normalized in the encoder, the last step of
the decoder before the inverse MDCT is to denormalize the bands.
Each decoded normalized band is multiplied by the square root of the
decoded energy.  This is done by denormalise_bands() (bands.c
(Appendix A.8)).

5.6.  Inverse MDCT

The inverse MDCT implementation has no special characteristics.  The
input is N frequency-domain samples and the output is 2*N time-domain
samples, while scaling by 1/2.  The output is windowed using the same
_low-overlap_ window as the encoder.  The IMDCT and windowing are
performed by mdct_backward (mdct.c (Appendix A.20)).  If a time-
domain pre-emphasis window was applied in the encoder, the (inverse)
time-domain de-emphasis window is applied on the IMDCT result.  After
the overlap-add process, the signal is de-emphasized using the
inverse of the pre-emphasis filter used in the encoder: 1/A(z)=1/
(1-alpha_p*z^-1).

5.7.  Packet Loss Concealment (PLC)

Packet loss concealment (PLC) is an optional decoder-side feature
which SHOULD be included when transmitting over an unreliable
channel.  Because PLC is not part of the bit-stream, there are
several possible ways to implement PLC with different complexity/
quality trade-offs.  The PLC in the reference implementation finds a
periodicity in the decoded signal and repeats the windowed waveform
using the pitch offset.  The windowed waveform is overlapped in such
a way as to preserve the time-domain aliasing cancellation with the
previous frame and the next frame.  This is implemented in
celt_decode_lost() (mdct.c (Appendix A.4)).

Valin, et al.            Expires January 9, 2011               [Page 28]


Internet-Draft                 CELT codec                      July 2010

6.  Security Considerations

A potential denial-of-service threat exists for data encodings using
compression techniques that have non-uniform receiver-end
computational load.  The attacker can inject pathological datagrams
into the stream which are complex to decode and cause the receiver to
become overloaded.  However, this encoding does not exhibit any
significant non-uniformity.

With the exception of the first four bits, the bit-stream produced by
CELT for an unknown audio stream is not easily predictable, due to
the use of entropy coding.  This should make CELT less vulnerable to
attacks based on plaintext guessing when encryption is used.  Also,
since almost all possible bit combinations can be interpreted as a
valid bit-stream, it is likely more difficult to determine from the
decrypted bit-stream whether a guessed decryption key is valid.

When operating CELT in variable-bitrate (VBR) mode, some of the
properties described above no longer hold.  More specifically, the
size of the packet leaks a very small, but non-zero, amount of
information about both the original signal and the bit-stream
plaintext.

Valin, et al.            Expires January 9, 2011               [Page 29]


Internet-Draft                 CELT codec                      July 2010

7.  IANA Considerations

This document has no actions for IANA.

Valin, et al.            Expires January 9, 2011               [Page 30]


Internet-Draft                 CELT codec                      July 2010

8.  Acknowledgments

The authors would also like to thank the CELT users who contributed
patches, bug reports, feature requests, suggestions or comments.

Valin, et al.            Expires January 9, 2011               [Page 31]


Internet-Draft                 CELT codec                      July 2010

9.  References

9.1.  Normative References

[rfc2119]  Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", RFC 2119.

[rfc3550]  Schulzrinne, H., Casner, S., Frederick, R., and V.
Jacobson, "RTP: A Transport Protocol for real-time
applications", RFC 3550.

9.2.  Informative References

[celt-tasl]
Valin, JM., Terriberry, T., Montgomery, C., and G.
Maxwell, "A High-Quality Speech and Audio Codec With Less
Than 10 ms delay", To appear in IEEE Transactions on
Audio, Speech and Language Processing 2009.

[celt-eusipco]
Valin, JM., Terriberry, T., and G. Maxwell, "A Full-
Bandwidth Audio Codec with Low Complexity and Very Low
Delay", Accepted for EUSIPCO 2009.

[celt-website]
"The CELT ultra-low delay audio codec", CELT
website http://www.celt-codec.org/.

[mdct]     "Modified Discrete Cosine Transform", MDCT http://
en.wikipedia.org/wiki/Modified_discrete_cosine_transform.

[range-coding]
Nigel, G. and N. Martin, "Range encoding: An algorithm for
removing redundancy from a digitised message", Proc.
Institution of Electronic and Radio Engineers
International Conference on Video and Data Recording ,
1979.

[coding-thesis]
Pasco, R., "Source coding algorithms for fast data
compression", Ph.D. thesis Dept. of Electrical
Engineering, Stanford University, May 1976.

[PVQ]      Fischer, T., "A Pyramid Vector Quantizer", IEEE Trans. on
Information Theory, Vol. 32 pp. 568-583, July 1986.

Valin, et al.            Expires January 9, 2011               [Page 32]


Internet-Draft                 CELT codec                      July 2010

Appendix A.  Reference Implementation

This appendix contains the complete source code for a floating-point
reference implementation of the CELT codec written in C. This
implementation is derived from version 0.8.1 of the implementation
available on the [celt-website], which can be compiled for either
floating-point or fixed-point architectures.

The implementation can be compiled with either a C89 or a C99
compiler.  It is reasonably optimized for most platforms such that
only architecture-specific optimizations are likely to be useful.
The FFT used is a slightly modified version of the KISS-FFT package,
but it is easy to substitute any other FFT library.

The testcelt executable can be used to test the encoding and decoding
process:

testcelt <rate> <channels> <frame size> <octets per packet>
[<complexity> [packet loss rate]] <input> <output>

where "rate" is the sampling rate in Hz, "channels" is the number of
channels (1 or 2), "frame size" is the number of samples in a frame
(64 to 1024) and "octets per packet" is the number of octets desired
for each compressed frame.  The input and output files are assumed to
be a 16-bit PCM file in the machine native endianness.  The optional
"complexity" argument can select the quality vs complexity tradeoff
(0-10) and the "packet loss rate" argument simulates random packet
loss (argument is in tenths or a percent).

A.1.  Makefile

CC = gcc
CFLAGS = -c -O2 -g
LIBS = -lm

OBJS = bands.o celt.o cwrs.o entcode.o entdec.o entenc.o kiss_fft.o \
kiss_fftr.o laplace.o mdct.o modes.o pitch.o \
quant_bands.o rangedec.o rangeenc.o rate.o testcelt.o vq.o plc.o

.c.o:
$(CC)$(CFLAGS) $< testcelt:$(OBJS)
$(CC) -o$@ $(OBJS)$(LIBS)

clean:
rm -f testcelt *.o

Valin, et al.            Expires January 9, 2011               [Page 33]


Internet-Draft                 CELT codec                      July 2010

A.2.  testcelt.c

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "celt.h"
#include "arch.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#define MAX_PACKET 1024

Valin, et al.            Expires January 9, 2011               [Page 34]


Internet-Draft                 CELT codec                      July 2010

int
main(int argc, char *argv[])
{
int             err;
char           *inFile,
*outFile;
FILE           *fin,
*fout;
CELTMode       *mode = NULL;
CELTEncoder    *enc;
CELTDecoder    *dec;
int             len;
celt_int32      frame_size,
channels;
int             bytes_per_packet;
unsigned char   data[MAX_PACKET];
int             rate;
int             complexity;

int             i;
double          rmsd = 0;

int             count = 0;
celt_int32      skip;
celt_int16     *in,
*out;
if (argc != 9 && argc != 8 && argc != 7)
{
fprintf(stderr, "Usage: testcelt <rate> <channels> <frame size> "
" <bytes per packet> [<complexity> [packet loss rate]] "
"<input> <output>\n");
return 1;
}

rate = atoi(argv[1]);
channels = atoi(argv[2]);
frame_size = atoi(argv[3]);
mode = celt_mode_create(rate, frame_size, NULL);

if (mode == NULL)
{
fprintf(stderr, "failed to create a mode\n");
return 1;
}

bytes_per_packet = atoi(argv[4]);
if (bytes_per_packet < 0 || bytes_per_packet > MAX_PACKET)

Valin, et al.            Expires January 9, 2011               [Page 35]


Internet-Draft                 CELT codec                      July 2010

{
fprintf(stderr, "bytes per packet must be between 0 and %d\n",
MAX_PACKET);
return 1;
}

inFile = argv[argc - 2];
fin = fopen(inFile, "rb");
if (!fin)
{
fprintf(stderr, "Could not open input file %s\n",
argv[argc - 2]);
return 1;
}
outFile = argv[argc - 1];
fout = fopen(outFile, "wb+");
if (!fout)
{
fprintf(stderr, "Could not open output file %s\n",
argv[argc - 1]);
return 1;
}

enc = celt_encoder_create(mode, channels, &err);
if (err != 0)
{
fprintf(stderr, "Failed to create the encoder: %s\n",
celt_strerror(err));
return 1;
}
dec = celt_decoder_create(mode, channels, &err);
if (err != 0)
{
fprintf(stderr, "Failed to create the decoder: %s\n",
celt_strerror(err));
return 1;
}

if (argc > 7)
{
complexity = atoi(argv[5]);
celt_encoder_ctl(enc, CELT_SET_COMPLEXITY(complexity));
}

in = (celt_int16 *) malloc(frame_size * channels *
sizeof(celt_int16));
out =
(celt_int16 *) malloc(frame_size * channels *

Valin, et al.            Expires January 9, 2011               [Page 36]


Internet-Draft                 CELT codec                      July 2010

sizeof(celt_int16));
while (!feof(fin))
{
err = fread(in, sizeof(short), frame_size * channels, fin);
if (feof(fin))
break;
len =
celt_encode_resynthesis(enc, in, in, frame_size, data,
bytes_per_packet);
if (len <= 0)
{
fprintf(stderr, "celt_encode() returned %d\n", len);
return 1;
}
/* This is for simulating bit errors */
/* This is to simulate packet loss */
if (argc == 9 && rand() % 1000 < atoi(argv[argc - 3]))
/* if (errors && (errors%2==0)) */
celt_decode(dec, NULL, len, out, frame_size);
else
celt_decode(dec, data, len, out, frame_size);

for (i = 0; i < frame_size * channels; i++)
{
rmsd += (in[i] - out[i]) * 1.0 * (in[i] - out[i]);
/* out[i] -= in[i]; */
}

count++;
fwrite(out + skip, sizeof(short), (frame_size - skip) * channels,
fout);
skip = 0;
}
;

celt_encoder_destroy(enc);
celt_decoder_destroy(dec);
fclose(fin);
fclose(fout);
celt_mode_destroy(mode);
free(in);
free(out);

if (rmsd > 0)
{
rmsd = sqrt(rmsd / (1.0 * frame_size * channels * count));
fprintf(stderr, "Error: encoder doesn't match decoder\n");
fprintf(stderr, "RMS mismatch is %f\n", rmsd);

Valin, et al.            Expires January 9, 2011               [Page 37]


Internet-Draft                 CELT codec                      July 2010

return 1;
} else
{
fprintf(stderr, "Encoder matches decoder!!\n");
}

return 0;
}

A.3.  celt.h

Foundation Copyright (c) 2008 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/**
@file celt.h
@brief Contains all the functions for encoding and decoding audio
*/

/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR

Valin, et al.            Expires January 9, 2011               [Page 38]


Internet-Draft                 CELT codec                      July 2010

TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef CELT_H
#define CELT_H

#include "celt_types.h"

#ifdef __cplusplus
extern          "C" {
#endif

#if defined(__GNUC__) && defined(CELT_BUILD)
#define EXPORT __attribute__ ((visibility ("default")))
#elif defined(WIN32)
#define EXPORT __declspec(dllexport)
#else
#define EXPORT
#endif

#define _celt_check_int(x) (((void)((x) == (celt_int32)0)), (celt_int32\
)(x))
#define _celt_check_mode_ptr_ptr(ptr) ((ptr) + ((ptr) - (CELTMode**)(pt\
r)))

/* Error codes */
/** No error */
#define CELT_OK                0
/** An (or more) invalid argument (e.g. out of range) */
/** The mode struct passed is invalid */
#define CELT_INVALID_MODE     -2
/** An internal error was detected */
#define CELT_INTERNAL_ERROR   -3
/** The data passed (e.g. compressed data to decoder) is corrupted */
#define CELT_CORRUPTED_DATA   -4
/** Invalid/unsupported request number */
#define CELT_UNIMPLEMENTED    -5
/** An encoder or decoder structure is invalid or already freed */
#define CELT_INVALID_STATE    -6
/** Memory allocation has failed */
#define CELT_ALLOC_FAIL       -7

/* Requests */
#define CELT_GET_MODE_REQUEST    1
/** Get the CELTMode used by an encoder or decoder */
#define CELT_GET_MODE(x) CELT_GET_MODE_REQUEST, _celt_check_mode_ptr_pt\

Valin, et al.            Expires January 9, 2011               [Page 39]


Internet-Draft                 CELT codec                      July 2010

r(x)
#define CELT_SET_COMPLEXITY_REQUEST    2
/** Controls the complexity from 0-10 (int) */
#define CELT_SET_COMPLEXITY(x) CELT_SET_COMPLEXITY_REQUEST, _celt_check\
_int(x)
#define CELT_SET_PREDICTION_REQUEST    4
/** Controls the use of interframe prediction.
0=Independent frames
1=Short term interframe prediction allowed
2=Long term prediction allowed
*/
#define CELT_SET_PREDICTION(x) CELT_SET_PREDICTION_REQUEST, _celt_check\
_int(x)
#define CELT_SET_VBR_RATE_REQUEST    6
/** Set the target VBR rate in bits per second(int); 0=CBR (default) */
#define CELT_SET_VBR_RATE(x) CELT_SET_VBR_RATE_REQUEST, _celt_check_int\
(x)
/** Reset the encoder/decoder memories to zero*/
#define CELT_RESET_STATE_REQUEST        8
#define CELT_RESET_STATE       CELT_RESET_STATE_REQUEST

#define CELT_SET_START_BAND_REQUEST    10000
/** Controls the complexity from 0-10 (int) */
#define CELT_SET_START_BAND(x) CELT_SET_START_BAND_REQUEST, _celt_check\
_int(x)

/** GET the lookahead used in the current mode */
/** GET the sample rate used in the current mode */
#define CELT_GET_SAMPLE_RATE  1003

/** GET the bit-stream version for compatibility check */
#define CELT_GET_BITSTREAM_VERSION 2000

/** Contains the state of an encoder. One encoder state is needed
for each stream. It is initialised once at the beginning of the
stream. Do *not* re-initialise the state for every frame.
@brief Encoder state
*/
typedef struct CELTEncoder CELTEncoder;

/** State of the decoder. One decoder state is needed for each stream.
It is initialised once at the beginning of the stream. Do *not*
re-initialise the state for every frame */
typedef struct CELTDecoder CELTDecoder;

/** The mode contains all the information necessary to create an
encoder. Both the encoder and decoder need to be initialised

Valin, et al.            Expires January 9, 2011               [Page 40]


Internet-Draft                 CELT codec                      July 2010

with exactly the same mode, otherwise the quality will be very
typedef struct CELTMode CELTMode;

/** \defgroup codec Encoding and decoding */
/* @{ */

/* Mode calls */

/** Creates a new mode struct. This will be passed to an encoder or
decoder. The mode MUST NOT BE DESTROYED until the encoders and
decoders that use it are destroyed as well.
@param Fs Sampling rate (32000 to 96000 Hz)
@param frame_size Number of samples (per channel) to encode in each
packet (even values; 64 - 512)
@param error Returned error code (if NULL, no error will be returned)
@return A newly created mode
*/
EXPORT CELTMode *celt_mode_create(celt_int32 Fs, int frame_size,
int *error);

/** Destroys a mode struct. Only call this after all encoders and
decoders using this mode are destroyed as well.
@param mode Mode to be destroyed
*/
EXPORT void     celt_mode_destroy(CELTMode * mode);

/** Query information from a mode */
EXPORT int      celt_mode_info(const CELTMode * mode, int request,
celt_int32 * value);

/* Encoder stuff */

/** Creates a new encoder state. Each stream needs its own encoder
state (can't be shared across simultaneous streams).
@param mode Contains all the information about the characteristics of
*  the stream (must be the same characteristics as used for the
*  decoder)
@param channels Number of channels
@param error Returns an error code
@return Newly created encoder state.
*/
EXPORT CELTEncoder *celt_encoder_create(const CELTMode * mode,
int channels, int *error);

/** Destroys a an encoder state.
@param st Encoder state to be destroyed
*/

Valin, et al.            Expires January 9, 2011               [Page 41]


Internet-Draft                 CELT codec                      July 2010

EXPORT void     celt_encoder_destroy(CELTEncoder * st);

/** Encodes a frame of audio.
@param st Encoder state
@param pcm PCM audio in float format, with a normal range of +/-1.0.
*          Samples with a range beyond +/-1.0 are supported but will
*          be clipped by decoders using the integer API and should
*          only be used if it is known that the far end supports
*          extended dynmaic range. There must be exactly
*          frame_size samples per channel.
@param optional_resynthesis If not NULL, the encoder copies the audio \
signal that
*          the decoder would decode. It is the same as calling the
*          decoder on the compressed data, just faster.
*          This may alias pcm.
@param compressed The compressed data is written here. This may not al\
ias pcm or
*                 optional_synthesis.
@param nbCompressedBytes Maximum number of bytes to use for compressin\
g the frame
*          (can change from one frame to another)
@return Number of bytes written to "compressed". Will be the same as
*       "nbCompressedBytes" unless the stream is VBR and will never be\
larger.
*       If negative, an error has occurred (see error codes). It is IM\
PORTANT that
*       the length returned be somehow transmitted to the decoder. Oth\
erwise, no
*       decoding is possible.
*/
EXPORT int      celt_encode_resynthesis_float(CELTEncoder * st,
const float *pcm,
float
*optional_resynthesis,
int frame_size,
unsigned char
*compressed,
int
nbCompressedBytes);

/** Encodes a frame of audio.
@param st Encoder state
@param pcm PCM audio in float format, with a normal range of +/-1.0.
*          Samples with a range beyond +/-1.0 are supported but will
*          be clipped by decoders using the integer API and should
*          only be used if it is known that the far end supports
*          extended dynmaic range. There must be exactly
*          frame_size samples per channel.

Valin, et al.            Expires January 9, 2011               [Page 42]


Internet-Draft                 CELT codec                      July 2010

@param compressed The compressed data is written here. This may not al\
ias pcm or
*                 optional_synthesis.
@param nbCompressedBytes Maximum number of bytes to use for compressin\
g the frame
*          (can change from one frame to another)
@return Number of bytes written to "compressed". Will be the same as
*       "nbCompressedBytes" unless the stream is VBR and will never be\
larger.
*       If negative, an error has occurred (see error codes). It is IM\
PORTANT that
*       the length returned be somehow transmitted to the decoder. Oth\
erwise, no
*       decoding is possible.
*/
EXPORT int      celt_encode_float(CELTEncoder * st,
const float *pcm, int frame_size,
unsigned char *compressed,
int nbCompressedBytes);

/** Encodes a frame of audio.
@param st Encoder state
@param pcm PCM audio in signed 16-bit format (native endian). There mu\
st be
*          exactly frame_size samples per channel.
@param optional_resynthesis If not NULL, the encoder copies the audio \
signal that
*                         the decoder would decode. It is the same as \
calling the
*                         decoder on the compressed data, just faster.
*                         This may alias pcm.
@param compressed The compressed data is written here. This may not al\
ias pcm or
*                         optional_synthesis.
@param nbCompressedBytes Maximum number of bytes to use for compressin\
g the frame
*                        (can change from one frame to another)
@return Number of bytes written to "compressed". Will be the same as
*       "nbCompressedBytes" unless the stream is VBR and will never be\
larger.
*       If negative, an error has occurred (see error codes). It is IM\
PORTANT that
*       the length returned be somehow transmitted to the decoder. Oth\
erwise, no
*       decoding is possible.
*/
EXPORT int      celt_encode_resynthesis(CELTEncoder * st,
const celt_int16 * pcm,

Valin, et al.            Expires January 9, 2011               [Page 43]


Internet-Draft                 CELT codec                      July 2010

celt_int16 *
optional_resynthesis,
int frame_size,
unsigned char *compressed,
int nbCompressedBytes);

/** Encodes a frame of audio.
@param st Encoder state
@param pcm PCM audio in signed 16-bit format (native endian). There mu\
st be
*          exactly frame_size samples per channel.
@param compressed The compressed data is written here. This may not al\
ias pcm or
*                         optional_synthesis.
@param nbCompressedBytes Maximum number of bytes to use for compressin\
g the frame
*                        (can change from one frame to another)
@return Number of bytes written to "compressed". Will be the same as
*       "nbCompressedBytes" unless the stream is VBR and will never be\
larger.
*       If negative, an error has occurred (see error codes). It is IM\
PORTANT that
*       the length returned be somehow transmitted to the decoder. Oth\
erwise, no
*       decoding is possible.
*/
EXPORT int      celt_encode(CELTEncoder * st,
const celt_int16 * pcm, int frame_size,
unsigned char *compressed,
int nbCompressedBytes);

/** Query and set encoder parameters
@param st Encoder state
@param request Parameter to change or query
@param value Pointer to a 32-bit int value
@return Error code
*/
EXPORT int      celt_encoder_ctl(CELTEncoder * st, int request,
...);

/* Decoder stuff */

/** Creates a new decoder state. Each stream needs its own decoder stat\
e (can't
be shared across simultaneous streams).
@param mode Contains all the information about the characteristics of \
the
stream (must be the same characteristics as used for the e\

Valin, et al.            Expires January 9, 2011               [Page 44]


Internet-Draft                 CELT codec                      July 2010

ncoder)
@param channels Number of channels
@param error Returns an error code
@return Newly created decoder state.
*/
EXPORT CELTDecoder *celt_decoder_create(const CELTMode * mode,
int channels, int *error);

/** Destroys a a decoder state.
@param st Decoder state to be destroyed
*/
EXPORT void     celt_decoder_destroy(CELTDecoder * st);

/** Decodes a frame of audio.
@param st Decoder state
@param data Compressed data produced by an encoder
@param len Number of bytes to read from "data". This MUST be exactly t\
he number
of bytes returned by the encoder. Using a larger value WILL\
NOT WORK.
@param pcm One frame (frame_size samples per channel) of decoded PCM w\
ill be
returned here in float format.
@return Error code.
*/
EXPORT int      celt_decode_float(CELTDecoder * st,
const unsigned char *data,
int len, float *pcm,
int frame_size);

/** Decodes a frame of audio.
@param st Decoder state
@param data Compressed data produced by an encoder
@param len Number of bytes to read from "data". This MUST be exactly t\
he number
of bytes returned by the encoder. Using a larger value WILL\
NOT WORK.
@param pcm One frame (frame_size samples per channel) of decoded PCM w\
ill be
returned here in 16-bit PCM format (native endian).
@return Error code.
*/
EXPORT int      celt_decode(CELTDecoder * st,
const unsigned char *data, int len,
celt_int16 * pcm, int frame_size);

/** Query and set decoder parameters
@param st Decoder state

Valin, et al.            Expires January 9, 2011               [Page 45]


Internet-Draft                 CELT codec                      July 2010

@param request Parameter to change or query
@param value Pointer to a 32-bit int value
@return Error code
*/
EXPORT int      celt_decoder_ctl(CELTDecoder * st, int request,
...);

/** Returns the English string that corresponds to an error code
* @param error Error code (negative for an error, 0 for success
* @return Constant string (must NOT be freed)
*/
EXPORT const char *celt_strerror(int error);

/* @} */

#ifdef __cplusplus
}
#endif
#endif                          /* CELT_H */

A.4.  celt.c

Foundation Copyright (c) 2008 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE

Valin, et al.            Expires January 9, 2011               [Page 46]


Internet-Draft                 CELT codec                      July 2010

DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#define CELT_C

#include "os_support.h"
#include "mdct.h"
#include <math.h>
#include "celt.h"
#include "pitch.h"
#include "bands.h"
#include "modes.h"
#include "entcode.h"
#include "quant_bands.h"
#include "rate.h"
#include "stack_alloc.h"
#include "mathops.h"
#include <stdarg.h>
#include "plc.h"

static const float preemph = (0.8f);

static const float transientWindow[16] = {
0.0085135, 0.0337639, 0.0748914, 0.1304955,
0.1986827, 0.2771308, 0.3631685, 0.4538658,
0.5461342, 0.6368315, 0.7228692, 0.8013173,
0.8695045, 0.9251086, 0.9662361, 0.9914865
};

#define ENCODERVALID   0x4c434554
#define ENCODERPARTIAL 0x5445434c
#define ENCODERFREED   0x4c004500

/** Encoder state
@brief Encoder state
*/
struct CELTEncoder {
celt_uint32     marker;
const CELTMode *mode;  /**< Mode used by the encoder */

Valin, et al.            Expires January 9, 2011               [Page 47]


Internet-Draft                 CELT codec                      July 2010

int             overlap;
int             channels;

int             pitch_enabled;        /* Complexity level is
allowed to use pitch */
int             pitch_permitted;      /* Use of the LTP is
permitted by the user */
int             pitch_available;      /* Amount of pitch buffer
available */
int             force_intra;
int             delayedIntra;
float           tonal_average;
int             fold_decision;
float           gain_prod;
float           frame_max;
int             start,
end;

/* VBR-related parameters */
celt_int32      vbr_reservoir;
celt_int32      vbr_drift;
celt_int32      vbr_offset;
celt_int32      vbr_count;

celt_int32      vbr_rate_norm;        /* Target number of 16th
bits per frame */
float          *restrict preemph_memE;
float          *restrict preemph_memD;

float          *in_mem;
float          *out_mem;
float          *pitch_buf;
float           xmem;

float          *oldBandE;
};

static int
check_encoder(const CELTEncoder * st)
{
if (st == NULL)
{
celt_warning("NULL passed as an encoder structure");
return CELT_INVALID_STATE;
}
if (st->marker == ENCODERVALID)
return CELT_OK;
if (st->marker == ENCODERFREED)

Valin, et al.            Expires January 9, 2011               [Page 48]


Internet-Draft                 CELT codec                      July 2010

celt_warning
("Referencing an encoder that has already been freed");
else
celt_warning("This is not a valid CELT encoder structure");
return CELT_INVALID_STATE;
}

CELTEncoder    *
celt_encoder_create(const CELTMode * mode, int channels, int *error)
{
int             C;
CELTEncoder    *st;

if (check_mode(mode) != CELT_OK)
{
if (error)
*error = CELT_INVALID_MODE;
return NULL;
}

if (channels < 0 || channels > 2)
{
celt_warning("Only mono and stereo supported");
if (error)
return NULL;
}

C = channels;
st = celt_alloc(sizeof(CELTEncoder));

if (st == NULL)
{
if (error)
*error = CELT_ALLOC_FAIL;
return NULL;
}
st->marker = ENCODERPARTIAL;
st->mode = mode;
st->overlap = mode->overlap;
st->channels = channels;

st->start = 0;
st->end = st->mode->nbEBands;

st->vbr_rate_norm = 0;
st->pitch_enabled = 1;
st->pitch_permitted = 1;

Valin, et al.            Expires January 9, 2011               [Page 49]


Internet-Draft                 CELT codec                      July 2010

st->pitch_available = 1;
st->force_intra = 0;
st->delayedIntra = 1;
st->tonal_average = (1.f);
st->fold_decision = 1;

st->in_mem = celt_alloc(st->overlap * C * sizeof(float));
st->out_mem =
celt_alloc((MAX_PERIOD + st->overlap) * C * sizeof(float));
st->pitch_buf =
celt_alloc(((MAX_PERIOD >> 1) + 2) * sizeof(float));

st->oldBandE =
(float *) celt_alloc(C * mode->nbEBands * sizeof(float));

st->preemph_memE = (float *) celt_alloc(C * sizeof(float));
st->preemph_memD = (float *) celt_alloc(C * sizeof(float));

if ((st->in_mem != NULL) && (st->out_mem != NULL)
&& (st->oldBandE != NULL) && (st->preemph_memE != NULL)
&& (st->preemph_memD != NULL))
{
if (error)
*error = CELT_OK;
st->marker = ENCODERVALID;
return st;
}
/* If the setup fails for some reason deallocate it. */
celt_encoder_destroy(st);
if (error)
*error = CELT_ALLOC_FAIL;
return NULL;
}

void
celt_encoder_destroy(CELTEncoder * st)
{
if (st == NULL)
{
celt_warning("NULL passed to celt_encoder_destroy");
return;
}

if (st->marker == ENCODERFREED)
{
celt_warning("Freeing an encoder which has already been freed");
return;
}

Valin, et al.            Expires January 9, 2011               [Page 50]


Internet-Draft                 CELT codec                      July 2010

if (st->marker != ENCODERVALID && st->marker != ENCODERPARTIAL)
{
celt_warning("This is not a valid CELT encoder structure");
return;
}
/* Check_mode is non-fatal here because we can still free the
encoder memory even if the mode is bad, although calling the
free functions in this order is a violation of the API. */
check_mode(st->mode);

celt_free(st->in_mem);
celt_free(st->out_mem);
celt_free(st->pitch_buf);
celt_free(st->oldBandE);

celt_free(st->preemph_memE);
celt_free(st->preemph_memD);

st->marker = ENCODERFREED;

celt_free(st);
}

static inline celt_int16
FLOAT2INT16(float x)
{
x = x * CELT_SIG_SCALE;
x = MAX32(x, -32768);
x = MIN32(x, 32767);
return (celt_int16) float2int(x);
}

static inline float
SIG2WORD16(float x)
{

return (float) x;

}

static int
transient_analysis(const float *restrict in, int len, int C,
int *transient_time, int *transient_shift,
float *frame_max, int overlap)
{
int             i,
n;
float           ratio;

Valin, et al.            Expires January 9, 2011               [Page 51]


Internet-Draft                 CELT codec                      July 2010

float           threshold;
VARDECL(float, begin);
SAVE_STACK;
ALLOC(begin, len + 1, float);
begin[0] = 0;
if (C == 1)
{
for (i = 0; i < len; i++)
begin[i + 1] = MAX32(begin[i], ABS32(in[i]));
} else
{
for (i = 0; i < len; i++)
begin[i + 1] = MAX32(begin[i], MAX32(ABS32(in[C * i]),
ABS32(in[C * i + 1])));
}
n = -1;

threshold = (((.2f)) * (begin[len]));
/* If the following condition isn't met, there's just no way we'll
have a transient */
if (*frame_max < threshold)
{
/* It's likely we have a transient, now find it */
for (i = 8; i < len - 8; i++)
{
if (begin[i + 1] < threshold)
n = i;
}
}
if (n < 32)
{
n = -1;
ratio = 0;
} else
{
ratio = ((begin[len]) / (1 + MAX32(*frame_max, begin[n - 16])));
}
if (ratio < 0)
ratio = 0;
if (ratio > 1000)
ratio = 1000;

if (ratio > 45)
*transient_shift = 3;
else
*transient_shift = 0;

*transient_time = n;

Valin, et al.            Expires January 9, 2011               [Page 52]


Internet-Draft                 CELT codec                      July 2010

*frame_max = begin[len - overlap];

RESTORE_STACK;
return ratio > 4;
}

/** Apply window and compute the MDCT for all sub-frames and
all channels in a frame */
static void
compute_mdcts(const CELTMode * mode, int shortBlocks,
float *restrict in, float *restrict out, int _C,
int LM)
{
const int       C = CHANNELS(_C);
if (C == 1 && !shortBlocks)
{
const int       overlap = OVERLAP(mode);
clt_mdct_forward(&mode->mdct, in, out, mode->window, overlap,
mode->maxLM - LM);
} else
{
const int       overlap = OVERLAP(mode);
int             N = mode->shortMdctSize << LM;
int             B = 1;
int             b,
c;
VARDECL(float, x);
VARDECL(float, tmp);
SAVE_STACK;
if (shortBlocks)
{
/* lookup = &mode->mdct[0]; */
N = mode->shortMdctSize;
B = shortBlocks;
}
ALLOC(x, N + overlap, float);
ALLOC(tmp, N, float);
for (c = 0; c < C; c++)
{
for (b = 0; b < B; b++)
{
int             j;
for (j = 0; j < N + overlap; j++)
x[j] = in[C * (b * N + j) + c];
clt_mdct_forward(&mode->mdct, x, tmp, mode->window, overlap,
shortBlocks ? mode->maxLM : mode->maxLM -
LM);
/* Interleaving the sub-frames */

Valin, et al.            Expires January 9, 2011               [Page 53]


Internet-Draft                 CELT codec                      July 2010

for (j = 0; j < N; j++)
out[(j * B + b) + c * N * B] = tmp[j];
}
}
RESTORE_STACK;
}
}

/** Compute the IMDCT and apply window for all sub-frames and
all channels in a frame */
static void
compute_inv_mdcts(const CELTMode * mode, int shortBlocks, float *X,
int transient_time, int transient_shift,
float *restrict out_mem, int _C, int LM)
{
int             c,
N4;
const int       C = CHANNELS(_C);
const int       N = mode->shortMdctSize << LM;
const int       overlap = OVERLAP(mode);
N4 = (N - overlap) >> 1;
for (c = 0; c < C; c++)
{
int             j;
if (transient_shift == 0 && C == 1 && !shortBlocks)
{
clt_mdct_backward(&mode->mdct, X,
out_mem + C * (MAX_PERIOD - N - N4),
mode->window, overlap, mode->maxLM - LM);
} else
{
VARDECL(float, x);
VARDECL(float, tmp);
int             b;
int             N2 = N;
int             B = 1;
int             n4offset = 0;
SAVE_STACK;

ALLOC(x, 2 * N, float);
ALLOC(tmp, N, float);

if (shortBlocks)
{
/* lookup = &mode->mdct[0]; */
N2 = mode->shortMdctSize;
B = shortBlocks;
n4offset = N4;

Valin, et al.            Expires January 9, 2011               [Page 54]


Internet-Draft                 CELT codec                      July 2010

}
/* Prevents problems from the imdct doing the overlap-add */
CELT_MEMSET(x + N4, 0, N2);

for (b = 0; b < B; b++)
{
/* De-interleaving the sub-frames */
for (j = 0; j < N2; j++)
tmp[j] = X[(j * B + b) + c * N2 * B];
clt_mdct_backward(&mode->mdct, tmp, x + n4offset + N2 * b,
mode->window, overlap,
shortBlocks ? mode->maxLM : mode->maxLM -
LM);
}

if (transient_shift > 0)
{

for (j = 0; j < 16; j++)
x[N4 + transient_time + j - 16] *=
1 + transientWindow[j] * ((1 << transient_shift) - 1);
for (j = transient_time; j < N + overlap; j++)
x[N4 + j] *= 1 << transient_shift;

}
/* The first and last part would need to be set to zero if we
actually wanted to use them. */
for (j = 0; j < overlap; j++)
out_mem[C * (MAX_PERIOD - N) + C * j + c] += x[j + N4];
for (j = 0; j < overlap; j++)
out_mem[C * (MAX_PERIOD) + C * (overlap - j - 1) + c] =
x[2 * N - j - N4 - 1];
for (j = 0; j < 2 * N4; j++)
out_mem[C * (MAX_PERIOD - N) + C * (j + overlap) + c] =
x[j + N4 + overlap];
RESTORE_STACK;
}
}
}

#define FLAG_NONE        0
#define FLAG_INTRA       (1U<<13)
#define FLAG_PITCH       (1U<<12)
#define FLAG_SHORT       (1U<<11)
#define FLAG_FOLD        (1U<<10)

static const int flaglist[8] = {

Valin, et al.            Expires January 9, 2011               [Page 55]


Internet-Draft                 CELT codec                      July 2010

0 /* 00 */  | FLAG_FOLD,
1 /* 01 */  | FLAG_PITCH | FLAG_FOLD,
8 /* 1000 */  | FLAG_NONE,
9 /* 1001 */  | FLAG_SHORT | FLAG_FOLD,
10 /* 1010 */  | FLAG_PITCH,
11 /* 1011 */  | FLAG_INTRA,
6 /* 110 */  | FLAG_INTRA | FLAG_FOLD,
7 /* 111 */  | FLAG_INTRA | FLAG_SHORT | FLAG_FOLD
};

static void
encode_flags(ec_enc * enc, int intra_ener, int has_pitch,
int shortBlocks, int has_fold)
{
int             i;
int             flags = FLAG_NONE;
int             flag_bits;
flags |= intra_ener ? FLAG_INTRA : 0;
flags |= has_pitch ? FLAG_PITCH : 0;
flags |= shortBlocks ? FLAG_SHORT : 0;
flags |= has_fold ? FLAG_FOLD : 0;
for (i = 0; i < 8; i++)
{
if (flags == (flaglist[i] & FLAG_MASK))
{
flag_bits = flaglist[i] & 0xf;
break;
}
}
celt_assert(i < 8);
/* printf ("enc %d: %d %d %d %d\n", flag_bits, intra_ener,
has_pitch, shortBlocks, has_fold); */
if (i < 2)
ec_enc_uint(enc, flag_bits, 4);
else if (i < 6)
{
ec_enc_uint(enc, flag_bits >> 2, 4);
ec_enc_uint(enc, flag_bits & 0x3, 4);
} else
{
ec_enc_uint(enc, flag_bits >> 1, 4);
ec_enc_uint(enc, flag_bits & 0x1, 2);
}
}

static void
decode_flags(ec_dec * dec, int *intra_ener, int *has_pitch,
int *shortBlocks, int *has_fold)

Valin, et al.            Expires January 9, 2011               [Page 56]


Internet-Draft                 CELT codec                      July 2010

{
int             i;
int             flag_bits;
flag_bits = ec_dec_uint(dec, 4);
/* printf ("(%d) ", flag_bits); */
if (flag_bits == 2)
flag_bits = (flag_bits << 2) | ec_dec_uint(dec, 4);
else if (flag_bits == 3)
flag_bits = (flag_bits << 1) | ec_dec_uint(dec, 2);
for (i = 0; i < 8; i++)
if (flag_bits == (flaglist[i] & 0xf))
break;
celt_assert(i < 8);
*intra_ener = (flaglist[i] & FLAG_INTRA) != 0;
*has_pitch = (flaglist[i] & FLAG_PITCH) != 0;
*shortBlocks = (flaglist[i] & FLAG_SHORT) != 0;
*has_fold = (flaglist[i] & FLAG_FOLD) != 0;
/* printf ("dec %d: %d %d %d %d\n", flag_bits, *intra_ener,
*has_pitch, *shortBlocks, *has_fold); */
}

void
deemphasis(float *in, float *pcm, int N, int _C, float coef,
float *mem)
{
const int       C = CHANNELS(_C);
int             c;
for (c = 0; c < C; c++)
{
int             j;
float          *restrict x;
float          *restrict y;
float           m = mem[c];
x = &in[C * (MAX_PERIOD - N) + c];
y = pcm + c;
for (j = 0; j < N; j++)
{
float           tmp = ((*x) + (coef) * (m));
m = tmp;
*y = SCALEOUT(SIG2WORD16(tmp));
x += C;
y += C;
}
mem[c] = m;
}
}

static void

Valin, et al.            Expires January 9, 2011               [Page 57]


Internet-Draft                 CELT codec                      July 2010

mdct_shape(const CELTMode * mode, float *X, int start,
int end, int N,
int mdct_weight_shift, int _C, int renorm, int M)
{
int             m,
i,
c;
const int       C = CHANNELS(_C);
for (c = 0; c < C; c++)
for (m = start; m < end; m++)
for (i = m + c * N; i < (c + 1) * N; i += M)

X[i] = (1.f / (1 << mdct_weight_shift)) * X[i];

if (renorm)
renormalise_bands(mode, X, C, M);
}

static signed char tf_select_table[4][8] = {
{0, -1, 0, -1, 0, -1, 0, -1},
{0, -1, 0, -2, 1, 0, 1 - 1},
{0, -2, 0, -3, 2, 0, 1 - 1},
{0, -2, 0, -3, 2, 0, 1 - 1},
};

static int
tf_analysis(float *bandLogE, float *oldBandE, int len, int C,
int isTransient, int *tf_res, int nbCompressedBytes)
{
int             i;
float           threshold;
VARDECL(float, metric);
float           average = 0;
float           cost0;
float           cost1;
VARDECL(int, path0);
VARDECL(int, path1);
float           lambda;
int             tf_select = 0;
SAVE_STACK;

if (nbCompressedBytes < 40)
lambda = (5.f);
else if (nbCompressedBytes < 60)
lambda = (2.f);
else if (nbCompressedBytes < 100)
lambda = (1.f);
else

Valin, et al.            Expires January 9, 2011               [Page 58]


Internet-Draft                 CELT codec                      July 2010

lambda = (.5f);

ALLOC(metric, len, float);
ALLOC(path0, len, int);
ALLOC(path1, len, int);
for (i = 0; i < len; i++)
{
metric[i] = ((bandLogE[i]) - (oldBandE[i]));
average += metric[i];
}
if (C == 2)
{
average = 0;
for (i = 0; i < len; i++)
{
metric[i] =
(.5f * (metric[i])) +
(.5f * (((bandLogE[i + len]) - (oldBandE[i + len]))));
average += metric[i];
}
}
average = ((average) / (len));
/* if (!isTransient) printf ("%f\n", average); */
if (isTransient)
{
threshold = (1.f);
tf_select = average > (3.f);
} else
{
threshold = (.5f);
tf_select = average > (1.f);
}
cost0 = 0;
cost1 = lambda;
/* Viterbi forward pass */
for (i = 1; i < len; i++)
{
float           curr0,
curr1;
float           from0,
from1;

from0 = cost0;
from1 = cost1 + lambda;
if (from0 < from1)
{
curr0 = from0;
path0[i] = 0;

Valin, et al.            Expires January 9, 2011               [Page 59]


Internet-Draft                 CELT codec                      July 2010

} else
{
curr0 = from1;
path0[i] = 1;
}

from0 = cost0 + lambda;
from1 = cost1;
if (from0 < from1)
{
curr1 = from0;
path1[i] = 0;
} else
{
curr1 = from1;
path1[i] = 1;
}
cost0 = curr0 + (metric[i] - threshold);
cost1 = curr1;
}
tf_res[len - 1] = cost0 < cost1 ? 0 : 1;
/* Viterbi backward pass to check the decisions */
for (i = len - 2; i >= 0; i--)
{
if (tf_res[i + 1] == 1)
tf_res[i] = path1[i + 1];
else
tf_res[i] = path0[i + 1];
}
RESTORE_STACK;
return tf_select;
}

static void
tf_encode(int len, int isTransient, int *tf_res,
int nbCompressedBytes, int LM, int tf_select, ec_enc * enc)
{
int             curr,
i;
if (8 * nbCompressedBytes - ec_enc_tell(enc, 0) < 100)
{
for (i = 0; i < len; i++)
tf_res[i] = isTransient;
} else
{
ec_enc_bit_prob(enc, tf_res[0], isTransient ? 16384 : 4096);
curr = tf_res[0];
for (i = 1; i < len; i++)

Valin, et al.            Expires January 9, 2011               [Page 60]


Internet-Draft                 CELT codec                      July 2010

{
ec_enc_bit_prob(enc, tf_res[i] ^ curr,
isTransient ? 4096 : 2048);
curr = tf_res[i];
}
}
ec_enc_bits(enc, tf_select, 1);
for (i = 0; i < len; i++)
tf_res[i] =
tf_select_table[LM][4 * isTransient + 2 * tf_select +
tf_res[i]];
}

static void
tf_decode(int len, int C, int isTransient, int *tf_res,
int nbCompressedBytes, int LM, ec_dec * dec)
{
int             i,
curr,
tf_select;
if (8 * nbCompressedBytes - ec_dec_tell(dec, 0) < 100)
{
for (i = 0; i < len; i++)
tf_res[i] = isTransient;
} else
{
tf_res[0] = ec_dec_bit_prob(dec, isTransient ? 16384 : 4096);
curr = tf_res[0];
for (i = 1; i < len; i++)
{
tf_res[i] =
ec_dec_bit_prob(dec, isTransient ? 4096 : 2048) ^ curr;
curr = tf_res[i];
}
}
tf_select = ec_dec_bits(dec, 1);
for (i = 0; i < len; i++)
tf_res[i] =
tf_select_table[LM][4 * isTransient + 2 * tf_select +
tf_res[i]];
}

int
celt_encode_with_ec_float(CELTEncoder * restrict st,
const float *pcm,
float *optional_resynthesis,
int frame_size, unsigned char *compressed,
int nbCompressedBytes, ec_enc * enc)

Valin, et al.            Expires January 9, 2011               [Page 61]


Internet-Draft                 CELT codec                      July 2010

{

int             i,
c,
N,
NN,
N4;
int             has_pitch;
int             pitch_index;
int             bits;
int             has_fold = 1;
int             coarse_needed;
ec_byte_buffer  buf;
ec_enc          _enc;
VARDECL(float, in);
VARDECL(float, freq);
VARDECL(float, pitch_freq);
VARDECL(float, X);
VARDECL(float, bandE);
VARDECL(float, bandLogE);
VARDECL(int, fine_quant);
VARDECL(float, error);
VARDECL(int, pulses);
VARDECL(int, offsets);
VARDECL(int, fine_priority);
VARDECL(int, tf_res);
int             intra_ener = 0;
int             shortBlocks = 0;
int             isTransient = 0;
int             transient_time;
int             transient_shift;
int             resynth;
const int       C = CHANNELS(st->channels);
int             mdct_weight_shift = 0;
int             mdct_weight_pos = 0;
int             gain_id = 0;
int             norm_rate;
int             LM,
M;
int             tf_select;
celt_int32      vbr_rate = 0;
float           max_decay;
int             nbFilledBytes,
nbAvailableBytes;
SAVE_STACK;

if (check_encoder(st) != CELT_OK)
return CELT_INVALID_STATE;

Valin, et al.            Expires January 9, 2011               [Page 62]


Internet-Draft                 CELT codec                      July 2010

if (check_mode(st->mode) != CELT_OK)
return CELT_INVALID_MODE;

if (nbCompressedBytes < 0 || pcm == NULL)

for (LM = 0; LM < 4; LM++)
if (st->mode->shortMdctSize << LM == frame_size)
break;
if (LM >= MAX_CONFIG_SIZES)
M = 1 << LM;

if (enc == NULL)
{
ec_byte_writeinit_buffer(&buf, compressed, nbCompressedBytes);
ec_enc_init(&_enc, &buf);
enc = &_enc;
nbFilledBytes = 0;
} else
{
nbFilledBytes = (ec_enc_tell(enc, 0) + 4) >> 3;
}
nbAvailableBytes = nbCompressedBytes - nbFilledBytes;

N = M * st->mode->shortMdctSize;
N4 = (N - st->overlap) >> 1;
ALLOC(in, 2 * C * N - 2 * C * N4, float);

CELT_COPY(in, st->in_mem, C * st->overlap);
for (c = 0; c < C; c++)
{
const float    *restrict pcmp = pcm + c;
float          *restrict inp = in + C * st->overlap + c;
for (i = 0; i < N; i++)
{
/* Apply pre-emphasis */
float           tmp = SCALEIN(((*pcmp)));
*inp = ((tmp) - ((((preemph) * (st->preemph_memE[c])))));
st->preemph_memE[c] = SCALEIN(*pcmp);
inp += C;
pcmp += C;
}
}
CELT_COPY(st->in_mem, in + C * (2 * N - 2 * N4 - st->overlap),
C * st->overlap);

/* Transient handling */

Valin, et al.            Expires January 9, 2011               [Page 63]


Internet-Draft                 CELT codec                      July 2010

transient_time = -1;
transient_shift = 0;
isTransient = 0;

resynth = st->pitch_available > 0 || optional_resynthesis != NULL;

if (M > 1
&& transient_analysis(in, N + st->overlap, C, &transient_time,
&transient_shift, &st->frame_max,
st->overlap))
{

float           gain_1;

/* Apply the inverse shaping window */
if (transient_shift)
{
for (c = 0; c < C; c++)
for (i = 0; i < 16; i++)
in[C * (transient_time + i - 16) + c] /= 1 +
transientWindow[i] * ((1 << transient_shift) - 1);
gain_1 = 1. / (1 << transient_shift);
for (c = 0; c < C; c++)
for (i = transient_time; i < N + st->overlap; i++)
in[C * i + c] *= gain_1;

}
isTransient = 1;
has_fold = 1;
}

if (isTransient)
shortBlocks = M;
else
shortBlocks = 0;

ALLOC(freq, C * N, float);/**< Interleaved signal MDCTs */
ALLOC(bandE, st->mode->nbEBands * C, float);
ALLOC(bandLogE, st->mode->nbEBands * C, float);
/* Compute MDCTs */
compute_mdcts(st->mode, shortBlocks, in, freq, C, LM);

norm_rate =
(nbAvailableBytes -
5) * 8 * (celt_uint32) st->mode->Fs / (C * N) >> 10;
/* Pitch analysis: we do it early to save on the peak stack space */
/* Don't use pitch if there isn't enough data available yet, or
if we're using shortBlocks */

Valin, et al.            Expires January 9, 2011               [Page 64]


Internet-Draft                 CELT codec                      July 2010

has_pitch = st->pitch_enabled && st->pitch_permitted && (N <= 512)
&& (st->pitch_available >= MAX_PERIOD) && (!shortBlocks)
&& norm_rate < 50;
if (has_pitch)
{
VARDECL(float, x_lp);
SAVE_STACK;
ALLOC(x_lp, (2 * N - 2 * N4) >> 1, float);
pitch_downsample(in, x_lp, 2 * N - 2 * N4, N, C, &st->xmem,
&st->pitch_buf[MAX_PERIOD >> 1]);
pitch_search(st->mode, x_lp, st->pitch_buf, 2 * N - 2 * N4,
MAX_PERIOD - (2 * N - 2 * N4), &pitch_index,
&st->xmem, M);
RESTORE_STACK;
}

/* Deferred allocation after find_spectral_pitch() to reduce the
peak memory usage */
ALLOC(X, C * N, float);/**< Interleaved normalised MDCTs */

ALLOC(pitch_freq, C * N, float);/**< Interleaved signal MDCTs */
if (has_pitch)
{
compute_mdcts(st->mode, 0, st->out_mem + pitch_index * C,
pitch_freq, C, LM);
has_pitch =
compute_pitch_gain(st->mode, freq, pitch_freq, norm_rate,
&gain_id, C, &st->gain_prod, M);
}

if (has_pitch)
apply_pitch(st->mode, freq, pitch_freq, gain_id, 1, C, M);

compute_band_energies(st->mode, freq, bandE, C, M);
for (i = 0; i < st->mode->nbEBands * C; i++)
bandLogE[i] = amp2Log(bandE[i]);

/* Band normalisation */
normalise_bands(st->mode, freq, X, bandE, C, M);
if (!shortBlocks
&& !folding_decision(st->mode, X, &st->tonal_average,
&st->fold_decision, C, M))
has_fold = 0;

/* Don't use intra energy when we're operating at low bit-rate */
intra_ener = st->force_intra || (!has_pitch && st->delayedIntra
&& nbAvailableBytes >
st->mode->nbEBands);

Valin, et al.            Expires January 9, 2011               [Page 65]


Internet-Draft                 CELT codec                      July 2010

if (shortBlocks
|| intra_decision(bandLogE, st->oldBandE, st->mode->nbEBands))
st->delayedIntra = 1;
else
st->delayedIntra = 0;

NN = M * st->mode->eBands[st->mode->nbEBands];
if (shortBlocks && !transient_shift)
{
float           sum[8] = { 1, 1, 1, 1, 1, 1, 1, 1 };
int             m;
for (c = 0; c < C; c++)
{
m = 0;
do
{
float           tmp = 0;
for (i = m + c * N; i < c * N + NN; i += M)
tmp += ABS32(X[i]);
sum[m++] += tmp;
}
while (m < M);
}
m = 0;
do
{
if (sum[m + 1] > 8 * sum[m])
{
mdct_weight_shift = 2;
mdct_weight_pos = m;
} else if (sum[m + 1] > 2 * sum[m] && mdct_weight_shift < 2)
{
mdct_weight_shift = 1;
mdct_weight_pos = m;
}
m++;
}
while (m < M - 1);

if (mdct_weight_shift)
mdct_shape(st->mode, X, mdct_weight_pos + 1, M, N,
mdct_weight_shift, C, 0, M);
}

encode_flags(enc, intra_ener, has_pitch, shortBlocks, has_fold);
if (has_pitch)
{
ec_enc_uint(enc, pitch_index, MAX_PERIOD - (2 * N - 2 * N4));

Valin, et al.            Expires January 9, 2011               [Page 66]


Internet-Draft                 CELT codec                      July 2010

ec_enc_uint(enc, gain_id, 16);
}
if (shortBlocks)
{
if (transient_shift)
{
ec_enc_uint(enc, transient_shift, 4);
ec_enc_uint(enc, transient_time, N + st->overlap);
} else
{
ec_enc_uint(enc, mdct_weight_shift, 4);
if (mdct_weight_shift && M != 2)
ec_enc_uint(enc, mdct_weight_pos, M - 1);
}
}

ALLOC(fine_quant, st->mode->nbEBands, int);
ALLOC(pulses, st->mode->nbEBands, int);

vbr_rate = M * st->vbr_rate_norm;
/* Computes the max bit-rate allowed in VBR more to avoid busting
the budget */
if (st->vbr_rate_norm > 0)
{
celt_int32      vbr_bound,
max_allowed;

vbr_bound = vbr_rate;
max_allowed =
(vbr_rate + vbr_bound - st->vbr_reservoir) >> (BITRES + 3);
if (max_allowed < 4)
max_allowed = 4;
if (max_allowed < nbAvailableBytes)
nbAvailableBytes = max_allowed;
}

ALLOC(tf_res, st->mode->nbEBands, int);
tf_select =
tf_analysis(bandLogE, st->oldBandE, st->mode->nbEBands, C,
isTransient, tf_res, nbAvailableBytes);

/* Bit allocation */
ALLOC(error, C * st->mode->nbEBands, float);

max_decay = .125 * nbAvailableBytes;

coarse_needed =
quant_coarse_energy(st->mode, st->start, bandLogE,

Valin, et al.            Expires January 9, 2011               [Page 67]


Internet-Draft                 CELT codec                      July 2010

st->oldBandE,
nbFilledBytes * 8 + nbAvailableBytes * 4 -
8, intra_ener, st->mode->prob, error, enc,
C, max_decay);
coarse_needed -= nbFilledBytes * 8;
coarse_needed = ((coarse_needed * 3 - 1) >> 3) + 1;
if (coarse_needed > nbAvailableBytes)
coarse_needed = nbAvailableBytes;
/* Variable bitrate */
if (vbr_rate > 0)
{
float           alpha;
celt_int32      delta;
/* The target rate in 16th bits per frame */
celt_int32      target = vbr_rate;

/* Shortblocks get a large boost in bitrate, but since they are
uncommon long blocks are not greatly effected */
if (shortBlocks)
target *= 2;
else if (M > 1)
target -= (target + 14) / 28;

/* The average energy is removed from the target and the actual
target =
target + st->vbr_offset - 588 + ec_enc_tell(enc, BITRES);

/* In VBR mode the frame size must not be reduced so much that
it would result in the coarse energy busting its budget */
target = IMAX(coarse_needed, (target + 64) / 128);
target = IMIN(nbAvailableBytes, target);
/* Make the adaptation coef (alpha) higher at the beginning */
if (st->vbr_count < 990)
{
st->vbr_count++;
alpha = celt_rcp(((st->vbr_count + 10)));
/* printf ("%d %d\n", st->vbr_count+10, alpha); */
} else
alpha = (.001f);

/* By how much did we "miss" the target on that frame */
delta = (8 << BITRES) * (celt_int32) target - vbr_rate;
/* How many bits have we used in excess of what we're allowed */
st->vbr_reservoir += delta;
/* printf ("%d\n", st->vbr_reservoir); */

/* Compute the offset we need to apply in order to reach the

Valin, et al.            Expires January 9, 2011               [Page 68]


Internet-Draft                 CELT codec                      July 2010

target */
st->vbr_drift +=
((alpha) * (delta - st->vbr_offset - st->vbr_drift));
st->vbr_offset = -st->vbr_drift;
/* printf ("%d\n", st->vbr_drift); */

/* We could use any multiple of vbr_rate as bound (depending on
the delay) */
if (st->vbr_reservoir < 0)
{
/* We're under the min value -- increase rate */
1 - (st->vbr_reservoir - 1) / (8 << BITRES);
st->vbr_reservoir += adjust * (8 << BITRES);
}
if (target < nbAvailableBytes)
nbAvailableBytes = target;
nbCompressedBytes = nbAvailableBytes + nbFilledBytes;

/* This moves the raw bits to take into account the new
compressed size */
ec_byte_shrink(&buf, nbCompressedBytes);
}

tf_encode(st->mode->nbEBands, isTransient, tf_res,
nbAvailableBytes, LM, tf_select, enc);

ALLOC(offsets, st->mode->nbEBands, int);
ALLOC(fine_priority, st->mode->nbEBands, int);

for (i = 0; i < st->mode->nbEBands; i++)
offsets[i] = 0;
bits = nbCompressedBytes * 8 - ec_enc_tell(enc, 0) - 1;
compute_allocation(st->mode, st->start, offsets, bits, pulses,
fine_quant, fine_priority, C, M);

quant_fine_energy(st->mode, st->start, bandE, st->oldBandE, error,
fine_quant, enc, C);

/* Residual quantisation */
quant_all_bands(1, st->mode, st->start, X, C == 2 ? X + N : NULL,
bandE, pulses, shortBlocks, has_fold, tf_res,
resynth, nbCompressedBytes * 8, enc, LM);

quant_energy_finalise(st->mode, st->start, bandE, st->oldBandE,
error, fine_quant, fine_priority,

Valin, et al.            Expires January 9, 2011               [Page 69]


Internet-Draft                 CELT codec                      July 2010

nbCompressedBytes * 8 - ec_enc_tell(enc, 0),
enc, C);

/* Re-synthesis of the coded audio if required */
if (resynth)
{
if (st->pitch_available > 0 && st->pitch_available < MAX_PERIOD)
st->pitch_available += N;

if (mdct_weight_shift)
{
mdct_shape(st->mode, X, 0, mdct_weight_pos + 1, N,
mdct_weight_shift, C, 1, M);
}

/* Synthesis */
denormalise_bands(st->mode, X, freq, bandE, C, M);

CELT_MOVE(st->out_mem, st->out_mem + C * N,
C * (MAX_PERIOD + st->overlap - N));

if (has_pitch)
apply_pitch(st->mode, freq, pitch_freq, gain_id, 0, C, M);

compute_inv_mdcts(st->mode, shortBlocks, freq, transient_time,
transient_shift, st->out_mem, C, LM);

/* De-emphasis and put everything back at the right place in
the synthesis history */
if (optional_resynthesis != NULL)
{
deemphasis(st->out_mem, optional_resynthesis, N, C, preemph,
st->preemph_memD);

}
}

/* If there's any room left (can only happen for very high rates),
fill it with zeros */
while (nbCompressedBytes * 8 - ec_enc_tell(enc, 0) >= 8)
ec_enc_bits(enc, 0, 8);
ec_enc_done(enc);

RESTORE_STACK;
return nbCompressedBytes;
}
int
celt_encode_with_ec(CELTEncoder * restrict st,

Valin, et al.            Expires January 9, 2011               [Page 70]


Internet-Draft                 CELT codec                      July 2010

const celt_int16 * pcm,
celt_int16 * optional_resynthesis,
int frame_size, unsigned char *compressed,
int nbCompressedBytes, ec_enc * enc)
{
int             j,
ret,
C,
N,
LM,
M;
VARDECL(float, in);
SAVE_STACK;

if (check_encoder(st) != CELT_OK)
return CELT_INVALID_STATE;

if (check_mode(st->mode) != CELT_OK)
return CELT_INVALID_MODE;

if (pcm == NULL)

for (LM = 0; LM < 4; LM++)
if (st->mode->shortMdctSize << LM == frame_size)
break;
if (LM >= MAX_CONFIG_SIZES)
M = 1 << LM;

C = CHANNELS(st->channels);
N = M * st->mode->shortMdctSize;
ALLOC(in, C * N, float);
for (j = 0; j < C * N; j++)
{
in[j] = SCALEOUT(pcm[j]);
}

if (optional_resynthesis != NULL)
{
ret =
celt_encode_with_ec_float(st, in, in, frame_size, compressed,
nbCompressedBytes, enc);
for (j = 0; j < C * N; j++)
optional_resynthesis[j] = FLOAT2INT16(in[j]);
} else
{
ret =

Valin, et al.            Expires January 9, 2011               [Page 71]


Internet-Draft                 CELT codec                      July 2010

celt_encode_with_ec_float(st, in, NULL, frame_size,
compressed, nbCompressedBytes,
enc);
}
RESTORE_STACK;
return ret;
}

int
celt_encode(CELTEncoder * restrict st, const celt_int16 * pcm,
int frame_size, unsigned char *compressed,
int nbCompressedBytes)
{
return celt_encode_with_ec(st, pcm, NULL, frame_size, compressed,
nbCompressedBytes, NULL);
}

int
celt_encode_float(CELTEncoder * restrict st, const float *pcm,
int frame_size, unsigned char *compressed,
int nbCompressedBytes)
{
return celt_encode_with_ec_float(st, pcm, NULL, frame_size,
compressed, nbCompressedBytes,
NULL);
}

int
celt_encode_resynthesis(CELTEncoder * restrict st,
const celt_int16 * pcm,
celt_int16 * optional_resynthesis,
int frame_size, unsigned char *compressed,
int nbCompressedBytes)
{
return celt_encode_with_ec(st, pcm, optional_resynthesis,
frame_size, compressed,
nbCompressedBytes, NULL);
}

int
celt_encode_resynthesis_float(CELTEncoder * restrict st,
const float *pcm,
float *optional_resynthesis,
int frame_size,
unsigned char *compressed,
int nbCompressedBytes)
{
return celt_encode_with_ec_float(st, pcm, optional_resynthesis,

Valin, et al.            Expires January 9, 2011               [Page 72]


Internet-Draft                 CELT codec                      July 2010

frame_size, compressed,
nbCompressedBytes, NULL);
}

int
celt_encoder_ctl(CELTEncoder * restrict st, int request, ...)
{
va_list         ap;

if (check_encoder(st) != CELT_OK)
return CELT_INVALID_STATE;

va_start(ap, request);
if ((request != CELT_GET_MODE_REQUEST)
&& (check_mode(st->mode) != CELT_OK))
switch (request)
{
case CELT_GET_MODE_REQUEST:
{
const CELTMode **value = va_arg(ap, const CELTMode **);
if (value == 0)
*value = st->mode;
}
break;
case CELT_SET_COMPLEXITY_REQUEST:
{
int             value = va_arg(ap, celt_int32);
if (value < 0 || value > 10)
if (value <= 2)
{
st->pitch_enabled = 0;
st->pitch_available = 0;
} else
{
st->pitch_enabled = 1;
if (st->pitch_available < 1)
st->pitch_available = 1;
}
}
break;
case CELT_SET_START_BAND_REQUEST:
{
celt_int32      value = va_arg(ap, celt_int32);
if (value < 0 || value >= st->mode->nbEBands)

Valin, et al.            Expires January 9, 2011               [Page 73]


Internet-Draft                 CELT codec                      July 2010

st->start = value;
}
break;
case CELT_SET_PREDICTION_REQUEST:
{
int             value = va_arg(ap, celt_int32);
if (value < 0 || value > 2)
if (value == 0)
{
st->force_intra = 1;
st->pitch_permitted = 0;
} else if (value == 1)
{
st->force_intra = 0;
st->pitch_permitted = 0;
} else
{
st->force_intra = 0;
st->pitch_permitted = 1;
}
}
break;
case CELT_SET_VBR_RATE_REQUEST:
{
celt_int32      value = va_arg(ap, celt_int32);
int             frame_rate;
int             N = st->mode->shortMdctSize;
if (value < 0)
if (value > 3072000)
value = 3072000;
frame_rate = ((st->mode->Fs << 3) + (N >> 1)) / N;
st->vbr_rate_norm =
((value << (BITRES + 3)) + (frame_rate >> 1)) / frame_rate;
}
break;
case CELT_RESET_STATE:
{
const CELTMode *mode = st->mode;
int             C = st->channels;

if (st->pitch_available > 0)
st->pitch_available = 1;

CELT_MEMSET(st->in_mem, 0, st->overlap * C);
CELT_MEMSET(st->out_mem, 0, (MAX_PERIOD + st->overlap) * C);

Valin, et al.            Expires January 9, 2011               [Page 74]


Internet-Draft                 CELT codec                      July 2010

CELT_MEMSET(st->oldBandE, 0, C * mode->nbEBands);

CELT_MEMSET(st->preemph_memE, 0, C);
CELT_MEMSET(st->preemph_memD, 0, C);
st->delayedIntra = 1;

st->fold_decision = 1;
st->tonal_average = (1.f);
st->gain_prod = 0;
st->vbr_reservoir = 0;
st->vbr_drift = 0;
st->vbr_offset = 0;
st->vbr_count = 0;
st->xmem = 0;
st->frame_max = 0;
CELT_MEMSET(st->pitch_buf, 0, (MAX_PERIOD >> 1) + 2);
}
break;
default:
}
va_end(ap);
return CELT_OK;
va_end(ap);
return CELT_INVALID_MODE;
va_end(ap);
va_end(ap);
return CELT_UNIMPLEMENTED;
}

/**********************************************************************/
/* */
/* DECODER */
/* */
/**********************************************************************/
#define DECODE_BUFFER_SIZE 2048

#define DECODERVALID   0x4c434454
#define DECODERPARTIAL 0x5444434c
#define DECODERFREED   0x4c004400

/** Decoder state
@brief Decoder state
*/

Valin, et al.            Expires January 9, 2011               [Page 75]


Internet-Draft                 CELT codec                      July 2010

struct CELTDecoder {
celt_uint32     marker;
const CELTMode *mode;
int             overlap;
int             channels;

int             start,
end;
ec_byte_buffer  buf;
ec_enc          enc;

float          *restrict preemph_memD;

float          *out_mem;
float          *decode_mem;

float          *oldBandE;

float          *lpc;

int             last_pitch_index;
int             loss_count;
};

int
check_decoder(const CELTDecoder * st)
{
if (st == NULL)
{
celt_warning("NULL passed a decoder structure");
return CELT_INVALID_STATE;
}
if (st->marker == DECODERVALID)
return CELT_OK;
if (st->marker == DECODERFREED)
celt_warning
("Referencing a decoder that has already been freed");
else
celt_warning("This is not a valid CELT decoder structure");
return CELT_INVALID_STATE;
}

CELTDecoder    *
celt_decoder_create(const CELTMode * mode, int channels, int *error)
{
int             C;
CELTDecoder    *st;

Valin, et al.            Expires January 9, 2011               [Page 76]


Internet-Draft                 CELT codec                      July 2010

if (check_mode(mode) != CELT_OK)
{
if (error)
*error = CELT_INVALID_MODE;
return NULL;
}

if (channels < 0 || channels > 2)
{
celt_warning("Only mono and stereo supported");
if (error)
return NULL;
}

C = CHANNELS(channels);
st = celt_alloc(sizeof(CELTDecoder));

if (st == NULL)
{
if (error)
*error = CELT_ALLOC_FAIL;
return NULL;
}

st->marker = DECODERPARTIAL;
st->mode = mode;
st->overlap = mode->overlap;
st->channels = channels;

st->start = 0;
st->end = st->mode->nbEBands;

st->decode_mem =
celt_alloc((DECODE_BUFFER_SIZE +
st->overlap) * C * sizeof(float));
st->out_mem = st->decode_mem + DECODE_BUFFER_SIZE - MAX_PERIOD;

st->oldBandE =
(float *) celt_alloc(C * mode->nbEBands * sizeof(float));

st->preemph_memD = (float *) celt_alloc(C * sizeof(float));

st->lpc = (float *) celt_alloc(C * LPC_ORDER * sizeof(float));

st->loss_count = 0;

if ((st->decode_mem != NULL) && (st->out_mem != NULL)

Valin, et al.            Expires January 9, 2011               [Page 77]


Internet-Draft                 CELT codec                      July 2010

&& (st->oldBandE != NULL) && (st->lpc != NULL)
&& (st->preemph_memD != NULL))
{
if (error)
*error = CELT_OK;
st->marker = DECODERVALID;
return st;
}
/* If the setup fails for some reason deallocate it. */
celt_decoder_destroy(st);
if (error)
*error = CELT_ALLOC_FAIL;
return NULL;
}

void
celt_decoder_destroy(CELTDecoder * st)
{
if (st == NULL)
{
celt_warning("NULL passed to celt_decoder_destroy");
return;
}

if (st->marker == DECODERFREED)
{
celt_warning("Freeing a decoder which has already been freed");
return;
}

if (st->marker != DECODERVALID && st->marker != DECODERPARTIAL)
{
celt_warning("This is not a valid CELT decoder structure");
return;
}

/* Check_mode is non-fatal here because we can still free the
encoder memory even if the mode is bad, although calling the
free functions in this order is a violation of the API. */
check_mode(st->mode);

celt_free(st->decode_mem);
celt_free(st->oldBandE);
celt_free(st->preemph_memD);
celt_free(st->lpc);

st->marker = DECODERFREED;

Valin, et al.            Expires January 9, 2011               [Page 78]


Internet-Draft                 CELT codec                      July 2010

celt_free(st);
}

static void
celt_decode_lost(CELTDecoder * restrict st, float *restrict pcm,
int N, int LM)
{
int             c;
int             pitch_index;
int             overlap = st->mode->overlap;
int             i,
len;
const int       C = CHANNELS(st->channels);
int             offset;
SAVE_STACK;

len = N + st->mode->overlap;

if (st->loss_count == 0)
{
float           pitch_buf[MAX_PERIOD >> 1];
float           tmp = 0;
float           mem0[2] = { 0, 0 };
float           mem1[2] = { 0, 0 };
int             len2 = len;
/* FIXME: This is a kludge */
if (len2 > MAX_PERIOD >> 1)
len2 = MAX_PERIOD >> 1;
pitch_downsample(st->out_mem, pitch_buf, MAX_PERIOD, MAX_PERIOD,
C, mem0, mem1);
pitch_search(st->mode, pitch_buf + ((MAX_PERIOD - len2) >> 1),
pitch_buf, len2, MAX_PERIOD - len2 - 100,
&pitch_index, &tmp, 1 << LM);
pitch_index = MAX_PERIOD - len2 - pitch_index;
st->last_pitch_index = pitch_index;
} else
{
pitch_index = st->last_pitch_index;
if (st->loss_count < 5)
else
}

for (c = 0; c < C; c++)
{
/* FIXME: This is more memory than necessary */

Valin, et al.            Expires January 9, 2011               [Page 79]


Internet-Draft                 CELT codec                      July 2010

float           e[2 * MAX_PERIOD];
float           exc[2 * MAX_PERIOD];
float           ac[LPC_ORDER + 1];
float           decay = 1;
float           S1 = 0;
float           mem[LPC_ORDER] = { 0 };

offset = MAX_PERIOD - pitch_index;
for (i = 0; i < MAX_PERIOD; i++)
exc[i] = (st->out_mem[i * C + c]);

if (st->loss_count == 0)
{
_celt_autocorr(exc, ac, st->mode->window, st->mode->overlap,
LPC_ORDER, MAX_PERIOD);

/* Noise floor -40 dB */

ac[0] *= 1.0001;

/* Lag windowing */
for (i = 1; i <= LPC_ORDER; i++)
{
/* ac[i] *= exp(-.5*(2*M_PI*.002*i)*(2*M_PI*.002*i)); */

ac[i] -= ac[i] * (.008 * i) * (.008 * i);

}

_celt_lpc(st->lpc + c * LPC_ORDER, ac, LPC_ORDER);
}
fir(exc, st->lpc + c * LPC_ORDER, exc, MAX_PERIOD, LPC_ORDER,
mem);
/* for (i=0;i<MAX_PERIOD;i++)printf("%d ", exc[i]);
printf("\n"); */
/* Check if the waveform is decaying (and if so how fast) */
{
float           E1 = 1,
E2 = 1;
int             period;
if (pitch_index <= MAX_PERIOD / 2)
period = pitch_index;
else
period = MAX_PERIOD / 2;
for (i = 0; i < period; i++)
{
E1 +=
(((exc[MAX_PERIOD - period + i]) *

Valin, et al.            Expires January 9, 2011               [Page 80]


Internet-Draft                 CELT codec                      July 2010

(exc[MAX_PERIOD - period + i])));
E2 +=
(((exc[MAX_PERIOD - 2 * period + i]) *
(exc[MAX_PERIOD - 2 * period + i])));
}
if (E1 > E2)
E1 = E2;
decay = celt_sqrt(frac_div32((E1), E2));
}

/* Copy excitation, taking decay into account */
for (i = 0; i < len + st->mode->overlap; i++)
{
if (offset + i >= MAX_PERIOD)
{
offset -= pitch_index;
decay = ((decay) * (decay));
}
e[i] = ((((decay) * (exc[offset + i]))));
S1 +=
(((st->out_mem[offset + i]) * (st->out_mem[offset + i])));
}

iir(e, st->lpc + c * LPC_ORDER, e, len + st->mode->overlap,
LPC_ORDER, mem);

{
float           S2 = 0;
for (i = 0; i < len + overlap; i++)
S2 += (((e[i]) * (e[i])));
/* This checks for an "explosion" in the synthesis */

/* Float test is written this way to catch NaNs at the same
time */
if (!(S1 > 0.2f * S2))

{
for (i = 0; i < len + overlap; i++)
e[i] = 0;
} else if (S1 < S2)
{
float           ratio =
celt_sqrt(frac_div32((S1) + 1, S2 + 1.));
for (i = 0; i < len + overlap; i++)
e[i] = ((ratio) * (e[i]));
}
}

Valin, et al.            Expires January 9, 2011               [Page 81]


Internet-Draft                 CELT codec                      July 2010

for (i = 0; i < MAX_PERIOD + st->mode->overlap - N; i++)
st->out_mem[C * i + c] = st->out_mem[C * (N + i) + c];

/* Apply TDAC to the concealed audio so that it blends with the
previous and next frames */
for (i = 0; i < overlap / 2; i++)
{
float           tmp1,
tmp2;
tmp1 = ((st->mode->window[i]) * (e[i])) -
((st->mode->window[overlap - i - 1]) *
(e[overlap - i - 1]));
tmp2 =
((st->mode->window[i]) * (e[N + overlap - 1 - i])) +
((st->mode->window[overlap - i - 1]) * (e[N + i]));
st->out_mem[C * (MAX_PERIOD + i) + c] =
((st->mode->window[overlap - i - 1]) * (tmp2));
st->out_mem[C * (MAX_PERIOD + overlap - i - 1) + c] =
((st->mode->window[i]) * (tmp2));
st->out_mem[C * (MAX_PERIOD - N + i) + c] +=
((st->mode->window[i]) * (tmp1));
st->out_mem[C * (MAX_PERIOD - N + overlap - i - 1) + c] -=
((st->mode->window[overlap - i - 1]) * (tmp1));
}
for (i = 0; i < N - overlap; i++)
st->out_mem[C * (MAX_PERIOD - N + overlap + i) + c] =
}

deemphasis(st->out_mem, pcm, N, C, preemph, st->preemph_memD);

st->loss_count++;

RESTORE_STACK;
}

int
celt_decode_with_ec_float(CELTDecoder * restrict st,
const unsigned char *data, int len,
float *restrict pcm, int frame_size,
ec_dec * dec)
{

int             c,
i,
N,

Valin, et al.            Expires January 9, 2011               [Page 82]


Internet-Draft                 CELT codec                      July 2010

N4;
int             has_pitch,
has_fold;
int             pitch_index;
int             bits;
ec_dec          _dec;
ec_byte_buffer  buf;
VARDECL(float, freq);
VARDECL(float, pitch_freq);
VARDECL(float, X);
VARDECL(float, bandE);
VARDECL(int, fine_quant);
VARDECL(int, pulses);
VARDECL(int, offsets);
VARDECL(int, fine_priority);
VARDECL(int, tf_res);

int             shortBlocks;
int             isTransient;
int             intra_ener;
int             transient_time;
int             transient_shift;
int             mdct_weight_shift = 0;
const int       C = CHANNELS(st->channels);
int             mdct_weight_pos = 0;
int             gain_id = 0;
int             LM,
M;
int             nbFilledBytes,
nbAvailableBytes;
SAVE_STACK;

if (check_decoder(st) != CELT_OK)
return CELT_INVALID_STATE;

if (check_mode(st->mode) != CELT_OK)
return CELT_INVALID_MODE;

if (pcm == NULL)

for (LM = 0; LM < 4; LM++)
if (st->mode->shortMdctSize << LM == frame_size)
break;
if (LM >= MAX_CONFIG_SIZES)
M = 1 << LM;

Valin, et al.            Expires January 9, 2011               [Page 83]


Internet-Draft                 CELT codec                      July 2010

N = M * st->mode->shortMdctSize;
N4 = (N - st->overlap) >> 1;

ALLOC(freq, C * N, float);/**< Interleaved signal MDCTs */
ALLOC(X, C * N, float);/**< Interleaved normalised MDCTs */
ALLOC(bandE, st->mode->nbEBands * C, float);
for (c = 0; c < C; c++)
for (i = 0; i < M * st->mode->eBands[st->start]; i++)
X[c * N + i] = 0;

if (data == NULL)
{
celt_decode_lost(st, pcm, N, LM);
RESTORE_STACK;
return 0;
}
if (len < 0)
{
RESTORE_STACK;
}

if (dec == NULL)
{
ec_byte_readinit(&buf, (unsigned char *) data, len);
ec_dec_init(&_dec, &buf);
dec = &_dec;
nbFilledBytes = 0;
} else
{
nbFilledBytes = (ec_dec_tell(dec, 0) + 4) >> 3;
}
nbAvailableBytes = len - nbFilledBytes;

decode_flags(dec, &intra_ener, &has_pitch, &isTransient,
&has_fold);
if (isTransient)
shortBlocks = M;
else
shortBlocks = 0;

if (isTransient)
{
transient_shift = ec_dec_uint(dec, 4);
if (transient_shift == 3)
{
transient_time = ec_dec_uint(dec, N + st->mode->overlap);
} else

Valin, et al.            Expires January 9, 2011               [Page 84]


Internet-Draft                 CELT codec                      July 2010

{
mdct_weight_shift = transient_shift;
if (mdct_weight_shift && M > 2)
mdct_weight_pos = ec_dec_uint(dec, M - 1);
transient_shift = 0;
transient_time = 0;
}
} else
{
transient_time = -1;
transient_shift = 0;
}

if (has_pitch)
{
int             maxpitch = MAX_PERIOD - (2 * N - 2 * N4);
if (maxpitch < 0)
{
celt_notify
("detected pitch when not allowed, bit corruption suspected");
pitch_index = 0;
has_pitch = 0;
} else
{
pitch_index = ec_dec_uint(dec, maxpitch);
gain_id = ec_dec_uint(dec, 16);
}
} else
{
pitch_index = 0;
}

ALLOC(fine_quant, st->mode->nbEBands, int);
/* Get band energies */
unquant_coarse_energy(st->mode, st->start, bandE, st->oldBandE,
nbFilledBytes * 8 + nbAvailableBytes * 4 - 8,
intra_ener, st->mode->prob, dec, C);

ALLOC(tf_res, st->mode->nbEBands, int);
tf_decode(st->mode->nbEBands, C, isTransient, tf_res,
nbAvailableBytes, LM, dec);

ALLOC(pulses, st->mode->nbEBands, int);
ALLOC(offsets, st->mode->nbEBands, int);
ALLOC(fine_priority, st->mode->nbEBands, int);

for (i = 0; i < st->mode->nbEBands; i++)
offsets[i] = 0;

Valin, et al.            Expires January 9, 2011               [Page 85]


Internet-Draft                 CELT codec                      July 2010

bits = len * 8 - ec_dec_tell(dec, 0) - 1;
compute_allocation(st->mode, st->start, offsets, bits, pulses,
fine_quant, fine_priority, C, M);
/* bits = ec_dec_tell(dec, 0); compute_fine_allocation(st->mode,
fine_quant, (20*C+len*8/5-(ec_dec_tell(dec, 0)-bits))/C); */

unquant_fine_energy(st->mode, st->start, bandE, st->oldBandE,
fine_quant, dec, C);

ALLOC(pitch_freq, C * N, float);/**< Interleaved signal MDCTs */
if (has_pitch)
{
/* Pitch MDCT */
compute_mdcts(st->mode, 0, st->out_mem + pitch_index * C,
pitch_freq, C, LM);
}

/* Decode fixed codebook and merge with pitch */
quant_all_bands(0, st->mode, st->start, X, C == 2 ? X + N : NULL,
NULL, pulses, shortBlocks, has_fold, tf_res, 1,
len * 8, dec, LM);

unquant_energy_finalise(st->mode, st->start, bandE, st->oldBandE,
fine_quant, fine_priority,
len * 8 - ec_dec_tell(dec, 0), dec, C);

if (mdct_weight_shift)
{
mdct_shape(st->mode, X, 0, mdct_weight_pos + 1, N,
mdct_weight_shift, C, 1, M);
}

/* Synthesis */
denormalise_bands(st->mode, X, freq, bandE, C, M);

CELT_MOVE(st->decode_mem, st->decode_mem + C * N,
C * (DECODE_BUFFER_SIZE + st->overlap - N));

if (has_pitch)
apply_pitch(st->mode, freq, pitch_freq, gain_id, 0, C, M);

for (c = 0; c < C; c++)
for (i = 0; i < M * st->mode->eBands[st->start]; i++)
freq[c * N + i] = 0;

/* Compute inverse MDCTs */
compute_inv_mdcts(st->mode, shortBlocks, freq, transient_time,
transient_shift, st->out_mem, C, LM);

Valin, et al.            Expires January 9, 2011               [Page 86]


Internet-Draft                 CELT codec                      July 2010

deemphasis(st->out_mem, pcm, N, C, preemph, st->preemph_memD);
st->loss_count = 0;
RESTORE_STACK;
return 0;
}
int
celt_decode_with_ec(CELTDecoder * restrict st,
const unsigned char *data, int len,
celt_int16 * restrict pcm, int frame_size,
ec_dec * dec)
{
int             j,
ret,
C,
N,
LM,
M;
VARDECL(float, out);
SAVE_STACK;

if (check_decoder(st) != CELT_OK)
return CELT_INVALID_STATE;

if (check_mode(st->mode) != CELT_OK)
return CELT_INVALID_MODE;

if (pcm == NULL)

for (LM = 0; LM < 4; LM++)
if (st->mode->shortMdctSize << LM == frame_size)
break;
if (LM >= MAX_CONFIG_SIZES)
M = 1 << LM;

C = CHANNELS(st->channels);
N = M * st->mode->shortMdctSize;
ALLOC(out, C * N, float);

ret =
celt_decode_with_ec_float(st, data, len, out, frame_size, dec);

for (j = 0; j < C * N; j++)
pcm[j] = FLOAT2INT16(out[j]);

RESTORE_STACK;
return ret;

Valin, et al.            Expires January 9, 2011               [Page 87]


Internet-Draft                 CELT codec                      July 2010

}

int
celt_decode(CELTDecoder * restrict st, const unsigned char *data,
int len, celt_int16 * restrict pcm, int frame_size)
{
return celt_decode_with_ec(st, data, len, pcm, frame_size, NULL);
}

int
celt_decode_float(CELTDecoder * restrict st,
const unsigned char *data, int len,
float *restrict pcm, int frame_size)
{
return celt_decode_with_ec_float(st, data, len, pcm, frame_size,
NULL);
}

int
celt_decoder_ctl(CELTDecoder * restrict st, int request, ...)
{
va_list         ap;

if (check_decoder(st) != CELT_OK)
return CELT_INVALID_STATE;

va_start(ap, request);
if ((request != CELT_GET_MODE_REQUEST)
&& (check_mode(st->mode) != CELT_OK))
switch (request)
{
case CELT_GET_MODE_REQUEST:
{
const CELTMode **value = va_arg(ap, const CELTMode **);
if (value == 0)
*value = st->mode;
}
break;
case CELT_SET_START_BAND_REQUEST:
{
celt_int32      value = va_arg(ap, celt_int32);
if (value < 0 || value >= st->mode->nbEBands)
st->start = value;
}
break;

Valin, et al.            Expires January 9, 2011               [Page 88]


Internet-Draft                 CELT codec                      July 2010

case CELT_RESET_STATE:
{
const CELTMode *mode = st->mode;
int             C = st->channels;

CELT_MEMSET(st->decode_mem, 0,
(DECODE_BUFFER_SIZE + st->overlap) * C);
CELT_MEMSET(st->oldBandE, 0, C * mode->nbEBands);

CELT_MEMSET(st->preemph_memD, 0, C);

st->loss_count = 0;

CELT_MEMSET(st->lpc, 0, C * LPC_ORDER);
}
break;
default:
}
va_end(ap);
return CELT_OK;
va_end(ap);
return CELT_INVALID_MODE;
va_end(ap);
va_end(ap);
return CELT_UNIMPLEMENTED;
}

const char     *
celt_strerror(int error)
{
static const char *error_strings[8] = {
"success",
"invalid argument",
"invalid mode",
"internal error",
"corrupted stream",
"request not implemented",
"invalid state",
"memory allocation failed"
};
if (error > 0 || error < -7)
return "unknown error";
else

Valin, et al.            Expires January 9, 2011               [Page 89]


Internet-Draft                 CELT codec                      July 2010

return error_strings[-error];
}

A.5.  modes.h

Foundation Copyright (c) 2008 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef MODES_H
#define MODES_H

#include "celt_types.h"
#include "celt.h"
#include "arch.h"
#include "mdct.h"

Valin, et al.            Expires January 9, 2011               [Page 90]


Internet-Draft                 CELT codec                      July 2010

#include "pitch.h"
#include "entenc.h"
#include "entdec.h"

#define MAX_CONFIG_SIZES 5

#define CELT_BITSTREAM_VERSION 0x8000000c

#ifdef STATIC_MODES
#include "static_modes.h"
#endif

#define MAX_PERIOD 1024

#ifndef MCHANNELS
# ifdef DISABLE_STEREO
#  define MCHANNELS(mode) (1)
# else
#  define MCHANNELS(mode) ((mode)->nbChannels)
# endif
#endif

#ifndef CHANNELS
# ifdef DISABLE_STEREO
#  define CHANNELS(_C) (1)
# else
#  define CHANNELS(_C) (_C)
# endif
#endif

#ifndef OVERLAP
#define OVERLAP(mode) ((mode)->overlap)
#endif

#ifndef FRAMESIZE
#define FRAMESIZE(mode) ((mode)->mdctSize)
#endif

/** Mode definition (opaque)
@brief Mode definition
*/
struct CELTMode {
celt_uint32     marker_start;
celt_int32      Fs;
int             overlap;

int             nbEBands;
int             pitchEnd;

Valin, et al.            Expires January 9, 2011               [Page 91]


Internet-Draft                 CELT codec                      July 2010

const celt_int16 *eBands;  /**< Definition for each "pseudo-critical \
band" */

float           ePredCoef;
/**< Prediction coefficient for the energy encoding \
*/

int             nbAllocVectors;
/**< Number of lines in the matrix below */
const unsigned char *allocVectors;  /**< Number of bits in each band \
for several rates */

const celt_int16 *const **bits;
const celt_int16 *const *(_bits[MAX_CONFIG_SIZES]);   /**< Cache for \
pulses->bits mapping in each band */

/* Stuff that could go in the {en,de}coder, but we save space this
way */
mdct_lookup     mdct;

const float    *window;

int             maxLM;
int             nbShortMdcts;
int             shortMdctSize;

int            *prob;
const celt_int16 *logN;
celt_uint32     marker_end;
};

int             check_mode(const CELTMode * mode);

/* Prototypes for _ec versions of the encoder/decoder calls (not
public) */
int             celt_encode_with_ec(CELTEncoder * restrict st,
const celt_int16 * pcm,
celt_int16 *
optional_resynthesis,
int frame_size,
unsigned char *compressed,
int nbCompressedBytes,
ec_enc * enc);
int             celt_encode_with_ec_float(CELTEncoder * restrict st,
const float *pcm,
float
*optional_resynthesis,
int frame_size,

Valin, et al.            Expires January 9, 2011               [Page 92]


Internet-Draft                 CELT codec                      July 2010

unsigned char *compressed,
int nbCompressedBytes,
ec_enc * enc);
int             celt_decode_with_ec(CELTDecoder * restrict st,
const unsigned char *data,
int len,
celt_int16 * restrict pcm,
int frame_size, ec_dec * dec);
int             celt_decode_with_ec_float(CELTDecoder * restrict st,
const unsigned char *data,
int len,
float *restrict pcm,
int frame_size,
ec_dec * dec);
#endif

A.6.  modes.c

Foundation Copyright (c) 2008 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,

Valin, et al.            Expires January 9, 2011               [Page 93]


Internet-Draft                 CELT codec                      July 2010

OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "celt.h"
#include "modes.h"
#include "rate.h"
#include "os_support.h"
#include "stack_alloc.h"
#include "quant_bands.h"

#define MODEVALID   0xa110ca7e
#define MODEPARTIAL 0x7eca10a1
#define MODEFREED   0xb10cf8ee

#define M_PI 3.141592653

int
celt_mode_info(const CELTMode * mode, int request,
celt_int32 * value)
{
if (check_mode(mode) != CELT_OK)
return CELT_INVALID_MODE;
switch (request)
{
*value = mode->overlap;
break;
case CELT_GET_BITSTREAM_VERSION:
*value = CELT_BITSTREAM_VERSION;
break;
case CELT_GET_SAMPLE_RATE:
*value = mode->Fs;
break;
default:
return CELT_UNIMPLEMENTED;
}
return CELT_OK;
}

/* Defining 25 critical bands for the full 0-20 kHz audio bandwidth
Taken from
http://ccrma.stanford.edu/~jos/bbt/Bark_Frequency_Scale.html */
#define BARK_BANDS 25

Valin, et al.            Expires January 9, 2011               [Page 94]


Internet-Draft                 CELT codec                      July 2010

static const celt_int16 bark_freq[BARK_BANDS + 1] = {
0, 100, 200, 300, 400,
510, 630, 770, 920, 1080,
1270, 1480, 1720, 2000, 2320,
2700, 3150, 3700, 4400, 5300,
6400, 7700, 9500, 12000, 15500,
20000
};

/* This allocation table is per critical band. When creating a mode,
the bits get added together into the codec bands, which are
sometimes larger than one critical band at low frequency */

#define BITALLOC_SIZE 12

static const celt_int16 eband5ms[] = {
0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 20, 24, 28, 34, 40, 48,
60, 78, 100
};

static const unsigned char band_allocation[] = {
/* 0 200 400 600 800 1k 1.2 1.4 1.6 2k 2.4 2.8 3.2 4k 4.8 5.6 6.8
8k 9.6 12k 15.6 */
10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
10, 3, 8, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
10, 6, 8, 6, 5, 4, 3, 2, 7, 10, 11, 9, 7, 3, 1, 0, 0, 0, 0, 0, 0,
10, 10, 14, 11, 10, 8, 6, 5, 10, 12, 13, 11, 8, 4, 2, 1, 0, 0, 0,
0, 0,
13, 10, 17, 16, 14, 12, 10, 8, 12, 14, 14, 12, 9, 5, 3, 2, 2, 1, 0,
0, 0,
17, 21, 23, 26, 24, 20, 17, 16, 17, 18, 16, 14, 11, 6, 3, 2, 2, 1,
1, 0, 0,
21, 21, 36, 32, 28, 24, 23, 23, 22, 18, 18, 14, 11, 7, 5, 5, 5, 3,
3, 0, 0,
31, 35, 40, 32, 30, 28, 26, 26, 25, 24, 19, 15, 15, 13, 9, 9, 8, 7,
5, 2, 0,
42, 46, 46, 37, 35, 34, 33, 32, 34, 35, 32, 31, 27, 24, 23, 23, 18,
14, 11, 7, 0,
46, 49, 46, 46, 42, 43, 44, 47, 50, 52, 51, 48, 39, 32, 27, 24, 22,
19, 17, 11, 5,
53, 53, 49, 48, 55, 66, 71, 71, 71, 65, 64, 64, 56, 47, 41, 37, 31,
24, 20, 16, 10,
60, 64, 74, 74, 87, 103, 106, 102, 101, 100, 101, 95, 80, 69, 63,
55, 47, 36, 26, 21, 15,
};

static celt_int16 *
compute_ebands(celt_int32 Fs, int frame_size, int res, int *nbEBands)

Valin, et al.            Expires January 9, 2011               [Page 95]


Internet-Draft                 CELT codec                      July 2010

{
celt_int16     *eBands;
int             i,
lin,
low,
high,
nBark,
offset = 0;

if (Fs == 400 * (celt_int32) frame_size && Fs >= 40000)
{
*nbEBands = sizeof(eband5ms) / sizeof(eband5ms[0]) - 1;
eBands = celt_alloc(sizeof(celt_int16) * (*nbEBands + 2));
for (i = 0; i < *nbEBands + 2; i++)
eBands[i] = eband5ms[i];
eBands[*nbEBands + 1] = frame_size;
return eBands;
}
/* Find the number of critical bands supported by our sampling
rate */
for (nBark = 1; nBark < BARK_BANDS; nBark++)
if (bark_freq[nBark + 1] * 2 >= Fs)
break;

/* Find where the linear part ends (i.e. where the spacing is more
than min_width */
for (lin = 0; lin < nBark; lin++)
if (bark_freq[lin + 1] - bark_freq[lin] >= res)
break;

low = (bark_freq[lin] + res / 2) / res;
high = nBark - lin;
*nbEBands = low + high;
eBands = celt_alloc(sizeof(celt_int16) * (*nbEBands + 2));

if (eBands == NULL)
return NULL;

/* Linear spacing (min_width) */
for (i = 0; i < low; i++)
eBands[i] = i;
if (low > 0)
offset = eBands[low - 1] * res - bark_freq[lin - 1];
/* Spacing follows critical bands */
for (i = 0; i < high; i++)
{
int             target = bark_freq[lin + i];
eBands[i + low] = (target + (offset + res) / 2) / res;

Valin, et al.            Expires January 9, 2011               [Page 96]


Internet-Draft                 CELT codec                      July 2010

offset = eBands[i + low] * res - target;
}
/* Enforce the minimum spacing at the boundary */
for (i = 0; i < *nbEBands; i++)
if (eBands[i] < i)
eBands[i] = i;
eBands[*nbEBands] = (bark_freq[nBark] + res / 2) / res;
eBands[*nbEBands + 1] = frame_size;
if (eBands[*nbEBands] > eBands[*nbEBands + 1])
eBands[*nbEBands] = eBands[*nbEBands + 1];
for (i = 1; i < *nbEBands - 1; i++)
{
if (eBands[i + 1] - eBands[i] < eBands[i] - eBands[i - 1])
{
eBands[i] -=
(2 * eBands[i] - eBands[i - 1] - eBands[i + 1]) / 2;
}
}
/* for (i=0;i<= *nbEBands+1;i++) printf ("%d ", eBands[i]); printf
("\n"); exit(1); */
/* FIXME: Remove last band if too small */
return eBands;
}

static void
compute_allocation_table(CELTMode * mode, int res)
{
int             i,
j;
unsigned char  *allocVectors;
int             maxBands =
sizeof(eband5ms) / sizeof(eband5ms[0]) - 1;

mode->nbAllocVectors = BITALLOC_SIZE;
allocVectors =
celt_alloc(sizeof(unsigned char) *
(BITALLOC_SIZE * mode->nbEBands));
if (allocVectors == NULL)
return;

/* Check for standard mode */
if (mode->Fs == 400 * (celt_int32) mode->shortMdctSize
&& mode->Fs >= 40000)
{
for (i = 0; i < BITALLOC_SIZE * mode->nbEBands; i++)
allocVectors[i] = band_allocation[i];
mode->allocVectors = allocVectors;
return;

Valin, et al.            Expires January 9, 2011               [Page 97]


Internet-Draft                 CELT codec                      July 2010

}
/* If not the standard mode, interpolate */

/* Compute per-codec-band allocation from per-critical-band matrix
*/
for (i = 0; i < BITALLOC_SIZE; i++)
{
celt_int32      current = 0;
int             eband = 0;
/* We may be looping over too many bands, but eband will stop
being incremented once we reach the last band */
for (j = 0; j < maxBands; j++)
{
int             edge,
low,
high;
celt_int32      alloc;
alloc =
band_allocation[i * maxBands +
j] * (mode->eBands[eband + 1] -
mode->eBands[eband]) << 4;
low = eband5ms[j] * 200;
high = eband5ms[j + 1] * 200;
edge = mode->eBands[eband + 1] * res;
while (edge <= high && eband < mode->nbEBands)
{
celt_int32      num;
int             den,
bits;
int             N =
(mode->eBands[eband + 1] - mode->eBands[eband]);
num = alloc * (edge - low);
den = high - low;
/* Divide with rounding */
bits = (2 * num + den) / (2 * den);
allocVectors[i * mode->nbEBands + eband] =
(2 * (current + bits) + (N << 4)) / (2 * N << 4);
/* Remove the part of the band we just allocated */
low = edge;
alloc -= bits;

/* Move to next eband */
current = 0;
eband++;
edge = mode->eBands[eband + 1] * res;
}
current += alloc;
}

Valin, et al.            Expires January 9, 2011               [Page 98]


Internet-Draft                 CELT codec                      July 2010

if (eband < mode->nbEBands)
{
int             N =
(mode->eBands[eband + 1] - mode->eBands[eband]);
allocVectors[i * mode->nbEBands + eband] =
(2 * current + (N << 4)) / (2 * N << 4);
}
}
/* printf ("\n"); for (i=0;i<BITALLOC_SIZE;i++) { for
(j=0;j<mode->nbEBands;j++) printf ("%d ",
allocVectors[i*mode->nbEBands+j]); printf ("\n"); } exit(0); */

mode->allocVectors = allocVectors;
}

CELTMode       *
celt_mode_create(celt_int32 Fs, int frame_size, int *error)
{
int             i;
int             LM;
int             res;
CELTMode       *mode = NULL;
float          *window;
celt_int16     *logN;
ALLOC_STACK;

if (global_stack == NULL)
goto failure;

/* The good thing here is that permutation of the arguments will
automatically be invalid */

if (Fs < 32000 || Fs > 96000)
{
celt_warning("Sampling rate must be between 32 kHz and 96 kHz");
if (error)
return NULL;
}
if (frame_size < 64 || frame_size > 1024 || frame_size % 2 != 0)
{
celt_warning
("Only even frame sizes from 64 to 1024 are supported");
if (error)
return NULL;
}

Valin, et al.            Expires January 9, 2011               [Page 99]


Internet-Draft                 CELT codec                      July 2010

mode = celt_alloc(sizeof(CELTMode));
if (mode == NULL)
goto failure;
mode->marker_start = MODEPARTIAL;
mode->Fs = Fs;
mode->ePredCoef = (.8f);

if (frame_size >= 640 && (frame_size % 16) == 0)
{
LM = 3;
} else if (frame_size >= 320 && (frame_size % 8) == 0)
{
LM = 2;
} else if (frame_size >= 160 && (frame_size % 4) == 0)
{
LM = 1;
} else
{
LM = 0;
}

mode->maxLM = LM;
mode->nbShortMdcts = 1 << LM;
mode->shortMdctSize = frame_size / mode->nbShortMdcts;
res = (mode->Fs + mode->shortMdctSize) / (2 * mode->shortMdctSize);

mode->eBands =
compute_ebands(Fs, mode->shortMdctSize, res, &mode->nbEBands);
if (mode->eBands == NULL)
goto failure;

mode->pitchEnd = 4000 * (celt_int32) mode->shortMdctSize / Fs;

/* Overlap must be divisible by 4 */
if (mode->nbShortMdcts > 1)
mode->overlap = (mode->shortMdctSize >> 2) << 2;
else
mode->overlap = (frame_size >> 3) << 2;

compute_allocation_table(mode, res);
if (mode->allocVectors == NULL)
goto failure;

window = (float *) celt_alloc(mode->overlap * sizeof(float));
if (window == NULL)
goto failure;

for (i = 0; i < mode->overlap; i++)

Valin, et al.            Expires January 9, 2011              [Page 100]


Internet-Draft                 CELT codec                      July 2010

window[i] =
1.0f * sin(.5 * M_PI *
sin(.5 * M_PI * (i + .5) / mode->overlap) *
sin(.5 * M_PI * (i + .5) / mode->overlap));

mode->window = window;

mode->bits = mode->_bits + 1;
for (i = 0; (1 << i) <= mode->nbShortMdcts; i++)
{
mode->bits[i] =
(const celt_int16 **) compute_alloc_cache(mode, 1 << i);
if (mode->bits[i] == NULL)
goto failure;
}
mode->bits[-1] =
(const celt_int16 **) compute_alloc_cache(mode, 0);
if (mode->bits[-1] == NULL)
goto failure;

logN =
(celt_int16 *) celt_alloc(mode->nbEBands * sizeof(celt_int16));
if (logN == NULL)
goto failure;

for (i = 0; i < mode->nbEBands; i++)
logN[i] =
log2_frac(mode->eBands[i + 1] - mode->eBands[i], BITRES);
mode->logN = logN;

clt_mdct_init(&mode->mdct,
2 * mode->shortMdctSize * mode->nbShortMdcts, LM);
if ((mode->mdct.trig == NULL) || (mode->mdct.kfft == NULL))
goto failure;

mode->prob = quant_prob_alloc(mode);
if (mode->prob == NULL)
goto failure;

mode->marker_start = MODEVALID;
mode->marker_end = MODEVALID;
if (error)
*error = CELT_OK;
return mode;
failure:
if (error)
*error = CELT_INVALID_MODE;
if (mode != NULL)

Valin, et al.            Expires January 9, 2011              [Page 101]


Internet-Draft                 CELT codec                      July 2010

celt_mode_destroy(mode);
return NULL;
}

void
celt_mode_destroy(CELTMode * mode)
{
int             i,
m;
const celt_int16 *prevPtr = NULL;
if (mode == NULL)
{
celt_warning("NULL passed to celt_mode_destroy");
return;
}

if (mode->marker_start == MODEFREED
|| mode->marker_end == MODEFREED)
{
celt_warning("Freeing a mode which has already been freed");
return;
}

if (mode->marker_start != MODEVALID
&& mode->marker_start != MODEPARTIAL)
{
celt_warning("This is not a valid CELT mode structure");
return;
}
mode->marker_start = MODEFREED;

for (m = 0; (1 << m) <= mode->nbShortMdcts; m++)
{
if (mode->bits[m] != NULL)
{
for (i = 0; i < mode->nbEBands; i++)
{
if (mode->bits[m][i] != prevPtr)
{
prevPtr = mode->bits[m][i];
celt_free((int *) mode->bits[m][i]);
}
}
}
celt_free((celt_int16 **) mode->bits[m]);
}
if (mode->bits[-1] != NULL)
{

Valin, et al.            Expires January 9, 2011              [Page 102]


Internet-Draft                 CELT codec                      July 2010

for (i = 0; i < mode->nbEBands; i++)
{
if (mode->bits[-1][i] != prevPtr)
{
prevPtr = mode->bits[-1][i];
celt_free((int *) mode->bits[-1][i]);
}
}
}
celt_free((celt_int16 **) mode->bits[-1]);

celt_free((celt_int16 *) mode->eBands);
celt_free((celt_int16 *) mode->allocVectors);

celt_free((float *) mode->window);
celt_free((celt_int16 *) mode->logN);

clt_mdct_clear(&mode->mdct);

quant_prob_free(mode->prob);
mode->marker_end = MODEFREED;
celt_free((CELTMode *) mode);
}

int
check_mode(const CELTMode * mode)
{
if (mode == NULL)
return CELT_INVALID_MODE;
if (mode->marker_start == MODEVALID
&& mode->marker_end == MODEVALID)
return CELT_OK;
if (mode->marker_start == MODEFREED
|| mode->marker_end == MODEFREED)
celt_warning("Using a mode that has already been freed");
else
celt_warning("This is not a valid CELT mode");
return CELT_INVALID_MODE;
}

A.7.  bands.h

Foundation Copyright (c) 2008-2009 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/*
Redistribution and use in source and binary forms, with or

Valin, et al.            Expires January 9, 2011              [Page 103]


Internet-Draft                 CELT codec                      July 2010

without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef BANDS_H
#define BANDS_H

#include "arch.h"
#include "modes.h"
#include "entenc.h"
#include "entdec.h"
#include "rate.h"

/** Compute the amplitude (sqrt energy) in each of the bands
* @param m Mode data
* @param X Spectrum
* @param bands Square root of the energy for each band (returned)
*/
void            compute_band_energies(const CELTMode * m,
const float *X, float *bands,
int _C, int M);

Valin, et al.            Expires January 9, 2011              [Page 104]


Internet-Draft                 CELT codec                      July 2010

/* void compute_noise_energies(const CELTMode *m, const celt_sig *X,
const celt_word16 *tonality, celt_ener *bank); */

/** Normalise each band of X such that the energy in each band is
equal to 1
* @param m Mode data
* @param X Spectrum (returned normalised)
* @param bands Square root of the energy for each band
*/
void            normalise_bands(const CELTMode * m,
const float *restrict freq,
float *restrict X,
const float *bands, int _C, int M);

void            renormalise_bands(const CELTMode * m,
float *restrict X, int _C, int M);

/** Denormalise each band of X to restore full amplitude
* @param m Mode data
* @param X Spectrum (returned de-normalised)
* @param bands Square root of the energy for each band
*/
void            denormalise_bands(const CELTMode * m,
const float *restrict X,
float *restrict freq,
const float *bands, int _C, int M);

/** Compute the pitch predictor gain for each pitch band
* @param m Mode data
* @param X Spectrum to predict
* @param P Pitch vector (normalised)
* @param gains Gain computed for each pitch band (returned)
* @param bank Square root of the energy for each band
*/
int             compute_pitch_gain(const CELTMode * m,
const float *X, const float *P,
int norm_rate, int *gain_id,
int _C, float *gain_prod, int M);

void            apply_pitch(const CELTMode * m, float *X,
const float *P, int gain_id, int pred,
int _C, int M);

int             folding_decision(const CELTMode * m, float *X,
float *average, int *last_decision,
int _C, int M);

/** Quantisation/encoding of the residual spectrum

Valin, et al.            Expires January 9, 2011              [Page 105]


Internet-Draft                 CELT codec                      July 2010

* @param m Mode data
* @param X Residual (normalised)
* @param total_bits Total number of bits that can be used for the fram\
e (including the ones already spent)
* @param enc Entropy encoder
*/
void            quant_all_bands(int encode, const CELTMode * m,
int start, float *X, float *Y,
const float *bandE, int *pulses,
int time_domain, int fold,
int *tf_res, int resynth,
int total_bits, void *enc, int M);

void            stereo_decision(const CELTMode * m,
float *restrict X, int *stereo_mode,
int len, int M);

#endif                          /* BANDS_H */

A.8.  bands.c

Foundation Copyright (c) 2008-2009 Gregory Maxwell Written by
Jean-Marc Valin and Gregory Maxwell */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE

Valin, et al.            Expires January 9, 2011              [Page 106]


Internet-Draft                 CELT codec                      July 2010

LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include <math.h>
#include "bands.h"
#include "modes.h"
#include "vq.h"
#include "cwrs.h"
#include "stack_alloc.h"
#include "os_support.h"
#include "mathops.h"
#include "rate.h"
/* Compute the amplitude (sqrt energy) in each of the bands */
void
compute_band_energies(const CELTMode * m, const float *X,
float *bank, int _C, int M)
{
int             i,
c,
N;
const celt_int16 *eBands = m->eBands;
const int       C = CHANNELS(_C);
N = M * m->eBands[m->nbEBands + 1];
for (c = 0; c < C; c++)
{
for (i = 0; i < m->nbEBands; i++)
{
int             j;
float           sum = 1e-10;
for (j = M * eBands[i]; j < M * eBands[i + 1]; j++)
sum += X[j + c * N] * X[j + c * N];
bank[i + c * m->nbEBands] = sqrt(sum);
/* printf ("%f ", bank[i+c*m->nbEBands]); */
}
}
/* printf ("\n"); */
}

/* Normalise each band such that the energy is one. */
void

Valin, et al.            Expires January 9, 2011              [Page 107]


Internet-Draft                 CELT codec                      July 2010

normalise_bands(const CELTMode * m, const float *restrict freq,
float *restrict X, const float *bank, int _C, int M)
{
int             i,
c,
N;
const celt_int16 *eBands = m->eBands;
const int       C = CHANNELS(_C);
N = M * m->eBands[m->nbEBands + 1];
for (c = 0; c < C; c++)
{
for (i = 0; i < m->nbEBands; i++)
{
int             j;
float           g = 1.f / (1e-10f + bank[i + c * m->nbEBands]);
for (j = M * eBands[i]; j < M * eBands[i + 1]; j++)
X[j + c * N] = freq[j + c * N] * g;
}
}
}

void
renormalise_bands(const CELTMode * m, float *restrict X, int _C,
int M)
{
int             i,
c;
const celt_int16 *eBands = m->eBands;
const int       C = CHANNELS(_C);
for (c = 0; c < C; c++)
{
i = 0;
do
{
renormalise_vector(X + M * eBands[i] +
c * M * eBands[m->nbEBands + 1], 1.0f,
M * eBands[i + 1] - M * eBands[i], 1);
}
while (++i < m->nbEBands);
}
}

/* De-normalise the energy to produce the synthesis from the
unit-energy bands */
void
denormalise_bands(const CELTMode * m, const float *restrict X,
float *restrict freq, const float *bank, int _C,
int M)

Valin, et al.            Expires January 9, 2011              [Page 108]


Internet-Draft                 CELT codec                      July 2010

{
int             i,
c,
N;
const celt_int16 *eBands = m->eBands;
const int       C = CHANNELS(_C);
N = M * m->eBands[m->nbEBands + 1];
if (C > 2)
celt_fatal
("denormalise_bands() not implemented for >2 channels");
for (c = 0; c < C; c++)
{
float          *restrict f;
const float    *restrict x;
f = freq + c * N;
x = X + c * N;
for (i = 0; i < m->nbEBands; i++)
{
int             j,
end;
float           g = (bank[i + c * m->nbEBands]);
j = M * eBands[i];
end = M * eBands[i + 1];
do
{
*f++ = (((*x) * (g)));
x++;
}
while (++j < end);
}
for (i = M * eBands[m->nbEBands];
i < M * eBands[m->nbEBands + 1]; i++)
*f++ = 0;
}
}

int
compute_pitch_gain(const CELTMode * m, const float *X,
const float *P, int norm_rate, int *gain_id,
int _C, float *gain_prod, int M)
{
int             j,
c;
float           g;
float           delta;
const int       C = CHANNELS(_C);
float           Sxy = 0,
Sxx = 0,

Valin, et al.            Expires January 9, 2011              [Page 109]


Internet-Draft                 CELT codec                      July 2010

Syy = 0;
int             len = M * m->pitchEnd;
int             N = M * m->eBands[m->nbEBands + 1];
delta = ((1.0f) / (len));
for (c = 0; c < C; c++)
{
float           gg = 1.0f;
for (j = 0; j < len; j++)
{
float           Xj,
Pj;
Xj = ((X[j + c * N]));
Pj = ((gg) * (((P[j + c * N]))));
Sxy = ((Sxy) + (Xj) * (Pj));
Sxx = ((Sxx) + (Pj) * (Pj));
Syy = ((Syy) + (Xj) * (Xj));
gg = ((gg) - (delta));
}
}
{
float           fact = .04f * norm_rate;
if (fact < 1)
fact = 1;
g = Sxy / (.1f + Sxx + .03f * Syy);
if (Sxy < .5f * fact * celt_sqrt(1 + Sxx * Syy))
g = 0;
/* This MUST round down so that we don't over-estimate the gain */
*gain_id = floor(20 * (g - .5f));
}

/* This prevents the pitch gain from being above 1.0 for too long
by bounding the maximum error amplification factor to 2.0 */
g = (((.5f)) + ((((.05f)) * (*gain_id))));
*gain_prod = MAX16((1.f), ((*gain_prod) * (g)));
if (*gain_prod > (2.f))
{
*gain_id = 9;
*gain_prod = (2.f);
}

if (*gain_id < 0)
{
*gain_id = 0;
return 0;
} else
{
if (*gain_id > 15)
*gain_id = 15;

Valin, et al.            Expires January 9, 2011              [Page 110]


Internet-Draft                 CELT codec                      July 2010

return 1;
}
}

void
apply_pitch(const CELTMode * m, float *X, const float *P,
int gain_id, int pred, int _C, int M)
{
int             j,
c,
N;
float           gain;
float           delta;
const int       C = CHANNELS(_C);
int             len = M * m->pitchEnd;

N = M * m->eBands[m->nbEBands + 1];
gain = (((.5f)) + ((((.05f)) * (gain_id))));
delta = ((gain) / (len));
if (pred)
gain = -gain;
else
delta = -delta;
for (c = 0; c < C; c++)
{
float           gg = gain;
for (j = 0; j < len; j++)
{
X[j + c * N] += (((gg) * (P[j + c * N])));
gg = ((gg) + (delta));
}
}
}

static void
stereo_band_mix(const CELTMode * m, float *X, float *Y,
const float *bank, int stereo_mode, int bandID,
int dir, int N)
{
int             i = bandID;
int             j;
float           a1,
a2;
if (stereo_mode == 0)
{
/* Do mid-side when not doing intensity stereo */
a1 = (.70711f);
a2 = dir * (.70711f);

Valin, et al.            Expires January 9, 2011              [Page 111]


Internet-Draft                 CELT codec                      July 2010

} else
{
float           left,
right;
float           norm;

left = (bank[i]);
right = (bank[i + m->nbEBands]);
norm =
1e-15f + celt_sqrt(1e-15f + ((left) * (left)) +
((right) * (right)));
a1 = ((((left))) / (norm));
a2 = dir * ((((right))) / (norm));
}
for (j = 0; j < N; j++)
{
float           r,
l;
l = X[j];
r = Y[j];
X[j] = ((a1) * (l)) + ((a2) * (r));
Y[j] = ((a1) * (r)) - ((a2) * (l));
}
}

int
folding_decision(const CELTMode * m, float *X, float *average,
int *last_decision, int _C, int M)
{
int             i,
c,
N0;
int             NR = 0;
float           ratio = 1e-15f;
const int       C = CHANNELS(_C);
const celt_int16 *restrict eBands = m->eBands;

N0 = M * m->eBands[m->nbEBands + 1];

for (c = 0; c < C; c++)
{
for (i = 0; i < m->nbEBands; i++)
{
int             j,
N;
int             max_i = 0;
float           max_val = 1e-15f;
float           floor_ener = 1e-15f;

Valin, et al.            Expires January 9, 2011              [Page 112]


Internet-Draft                 CELT codec                      July 2010

float          *restrict x = X + M * eBands[i] + c * N0;
N = M * eBands[i + 1] - M * eBands[i];
for (j = 0; j < N; j++)
{
if (ABS16(x[j]) > max_val)
{
max_val = ABS16(x[j]);
max_i = j;
}
}

floor_ener = (1.) - ((max_val) * (max_val));
if (max_i < N - 1)
floor_ener -= ((x[(max_i + 1)]) * (x[(max_i + 1)]));
if (max_i < N - 2)
floor_ener -= ((x[(max_i + 2)]) * (x[(max_i + 2)]));
if (max_i > 0)
floor_ener -= ((x[(max_i - 1)]) * (x[(max_i - 1)]));
if (max_i > 1)
floor_ener -= ((x[(max_i - 2)]) * (x[(max_i - 2)]));
floor_ener = MAX32(floor_ener, 1e-15f);

if (N > 7)
{
float           r;
float           den = celt_sqrt(floor_ener);
den = MAX32((.02f), den);
r = ((((max_val))) / (den));
ratio = ((ratio) + ((r)));
NR++;
}
}
}
if (NR > 0)
ratio = ((ratio) / (NR));
ratio = (((.5f * (ratio))) + ((.5f * (*average))));
if (!*last_decision)
{
*last_decision = (ratio < (1.8f));
} else
{
*last_decision = (ratio < (3.f));
}
*average = (ratio);
return *last_decision;
}

static void

Valin, et al.            Expires January 9, 2011              [Page 113]


Internet-Draft                 CELT codec                      July 2010

interleave_vector(float *X, int N0, int stride)
{
int             i,
j;
VARDECL(float, tmp);
int             N;
SAVE_STACK;
N = N0 * stride;
ALLOC(tmp, N, float);
for (i = 0; i < stride; i++)
for (j = 0; j < N0; j++)
tmp[j * stride + i] = X[i * N0 + j];
for (j = 0; j < N; j++)
X[j] = tmp[j];
RESTORE_STACK;
}

static void
deinterleave_vector(float *X, int N0, int stride)
{
int             i,
j;
VARDECL(float, tmp);
int             N;
SAVE_STACK;
N = N0 * stride;
ALLOC(tmp, N, float);
for (i = 0; i < stride; i++)
for (j = 0; j < N0; j++)
tmp[i * N0 + j] = X[j * stride + i];
for (j = 0; j < N; j++)
X[j] = tmp[j];
RESTORE_STACK;
}

static void
haar1(float *X, int N0, int stride)
{
int             i,
j;
N0 >>= 1;
for (i = 0; i < stride; i++)
for (j = 0; j < N0; j++)
{
float           tmp = X[stride * 2 * j + i];
X[stride * 2 * j + i] =
(((.7070678f)) *
(X[stride * 2 * j + i] + X[stride * (2 * j + 1) + i]));

Valin, et al.            Expires January 9, 2011              [Page 114]


Internet-Draft                 CELT codec                      July 2010

X[stride * (2 * j + 1) + i] =
(((.7070678f)) * (tmp - X[stride * (2 * j + 1) + i]));
}
}

/* This function is responsible for encoding and decoding a band for
both the mono and stereo case. Even in the mono case, it can
split the band in two and transmit the energy difference with the
two half-bands. It can be called recursively so bands can end up
being split in 8 parts. */
static void
quant_band(int encode, const CELTMode * m, int i, float *X, float *Y,
int N, int b, int spread, int tf_change, float *lowband,
int resynth, void *ec, celt_int32 * remaining_bits,
int LM, float *lowband_out, const float *bandE, int level)
{
int             q;
int             curr_bits;
int             stereo,
split;
int             imid = 0,
iside = 0;
int             N0 = N;
int             N_B = N;
int             N_B0;
int             time_divide = 0;
int             recombine = 0;

N_B0 = N_B;

split = stereo = Y != NULL;

/* Special case for one sample */
if (N == 1)
{
int             c;
float          *x = X;
for (c = 0; c < 1 + stereo; c++)
{
int             sign = 0;
if (b >= 1 << BITRES && *remaining_bits >= 1 << BITRES)
{
if (encode)
{
sign = x[0] < 0;

Valin, et al.            Expires January 9, 2011              [Page 115]


Internet-Draft                 CELT codec                      July 2010

ec_enc_bits((ec_enc *) ec, sign, 1);
} else
{
sign = ec_dec_bits((ec_dec *) ec, 1);
}
*remaining_bits -= 1 << BITRES;
b -= 1 << BITRES;
}
if (resynth)
x[0] = sign ? -1.f : 1.f;
x = Y;
}
if (lowband_out)
lowband_out[0] = X[0];
return;
}

/* Band recombining to increase frequency resolution */
if (!stereo && spread > 1 && level == 0 && tf_change > 0)
{
while (spread > 1 && tf_change > 0)
{
N_B <<= 1;
if (encode)
if (lowband)
recombine++;
tf_change--;
}
N_B0 = N_B;
}

/* Increasing the time resolution */
if (!stereo && level == 0)
{
while ((N_B & 1) == 0 && tf_change < 0 && spread <= (1 << LM))
{
if (encode)
if (lowband)
N_B >>= 1;
time_divide++;
tf_change++;

Valin, et al.            Expires January 9, 2011              [Page 116]


Internet-Draft                 CELT codec                      July 2010

}
N_B0 = N_B;
}

/* Reorganize the samples in time order instead of frequency order
*/
if (!stereo && spread0 > 1 && level == 0)
{
if (encode)
if (lowband)
}

/* If we need more than 32 bits, try splitting the band in two. */
if (!stereo && LM != -1 && b > 32 << BITRES && N > 2)
{
if (LM > 0 || (N & 1) == 0)
{
N >>= 1;
Y = X + N;
split = 1;
LM -= 1;
}
}

if (split)
{
int             qb;
int             itheta = 0;
int             mbits,
sbits,
delta;
int             qalloc;
float           mid,
side;
int             offset,
N2;
offset = m->logN[i] + (LM << BITRES) - QTHETA_OFFSET;

/* Decide on the resolution to give to the split parameter theta
*/
N2 = 2 * N - 1;
if (stereo && N > 2)
N2--;
qb = (b + N2 * offset) / (N2 << BITRES);

Valin, et al.            Expires January 9, 2011              [Page 117]


Internet-Draft                 CELT codec                      July 2010

if (qb > (b >> (BITRES + 1)) - 1)
qb = (b >> (BITRES + 1)) - 1;

if (qb < 0)
qb = 0;
if (qb > 14)
qb = 14;

qalloc = 0;
if (qb != 0)
{
int             shift;
shift = 14 - qb;

if (encode)
{
if (stereo)
stereo_band_mix(m, X, Y, bandE, qb == 0, i, 1, N);

mid = renormalise_vector(X, 1.0f, N, 1);
side = renormalise_vector(Y, 1.0f, N, 1);

/* theta is the atan() of the ration between the
(normalized) side and mid. With just that parameter, we
can re-scale both mid and side because we know that 1)
they have unit norm and 2) they are orthogonal. */

itheta = floor(.5f + 16384 * 0.63662f * atan2(side, mid));

itheta = (itheta + (1 << shift >> 1)) >> shift;
}

/* Entropy coding of the angle. We use a uniform pdf for the
first stereo split but a triangular one for the rest. */
if (stereo || qb > 9 || spread > 1)
{
if (encode)
ec_enc_uint((ec_enc *) ec, itheta, (1 << qb) + 1);
else
itheta = ec_dec_uint((ec_dec *) ec, (1 << qb) + 1);
qalloc = log2_frac((1 << qb) + 1, BITRES);
} else
{
int             fs = 1,
ft;
ft = ((1 << qb >> 1) + 1) * ((1 << qb >> 1) + 1);
if (encode)
{

Valin, et al.            Expires January 9, 2011              [Page 118]


Internet-Draft                 CELT codec                      July 2010

int             j;
int             fl = 0;
j = 0;
while (1)
{
if (j == itheta)
break;
fl += fs;
if (j < (1 << qb >> 1))
fs++;
else
fs--;
j++;
}
ec_encode((ec_enc *) ec, fl, fl + fs, ft);
} else
{
int             fl = 0;
int             j,
fm;
fm = ec_decode((ec_dec *) ec, ft);
j = 0;
while (1)
{
if (fm < fl + fs)
break;
fl += fs;
if (j < (1 << qb >> 1))
fs++;
else
fs--;
j++;
}
itheta = j;
ec_dec_update((ec_dec *) ec, fl, fl + fs, ft);
}
qalloc = log2_frac(ft, BITRES) - log2_frac(fs, BITRES) + 1;
}
itheta <<= shift;
}

if (itheta == 0)
{
imid = 32767;
iside = 0;
delta = -10000;
} else if (itheta == 16384)
{

Valin, et al.            Expires January 9, 2011              [Page 119]


Internet-Draft                 CELT codec                      July 2010

imid = 0;
iside = 32767;
delta = 10000;
} else
{
imid = bitexact_cos(itheta);
iside = bitexact_cos(16384 - itheta);
/* This is the mid vs side allocation that minimizes squared
error in that band. */
delta =
(N - 1) * (log2_frac(iside, BITRES + 2) -
log2_frac(imid, BITRES + 2)) >> 2;
}

/* This is a special case for N=2 that only works for stereo and
takes advantage of the fact that mid and side are orthogonal
to encode the side with just one bit. */
if (N == 2 && stereo)
{
int             c,
c2;
int             sign = 1;
float           v[2],
w[2];
float          *x2,
*y2;
mbits = b - qalloc;
sbits = 0;
if (itheta != 0 && itheta != 16384)
sbits = 1 << BITRES;
mbits -= sbits;
c = itheta > 8192 ? 1 : 0;
*remaining_bits -= qalloc + sbits;

x2 = X;
y2 = Y;
if (encode)
{
c2 = 1 - c;

if (c == 0)
{
v[0] = x2[0];
v[1] = x2[1];
w[0] = y2[0];
w[1] = y2[1];
} else
{

Valin, et al.            Expires January 9, 2011              [Page 120]


Internet-Draft                 CELT codec                      July 2010

v[0] = y2[0];
v[1] = y2[1];
w[0] = x2[0];
w[1] = x2[1];
}
/* Here we only need to encode a sign for the side */
if (v[0] * w[1] - v[1] * w[0] > 0)
sign = 1;
else
sign = -1;
}
quant_band(encode, m, i, v, NULL, N, mbits, spread, tf_change,
lowband, resynth, ec, remaining_bits, LM,
lowband_out, NULL, level + 1);
if (sbits)
{
if (encode)
{
ec_enc_bits((ec_enc *) ec, sign == 1, 1);
} else
{
sign = 2 * ec_dec_bits((ec_dec *) ec, 1) - 1;
}
} else
{
sign = 1;
}
w[0] = -sign * v[1];
w[1] = sign * v[0];
if (c == 0)
{
x2[0] = v[0];
x2[1] = v[1];
y2[0] = w[0];
y2[1] = w[1];
} else
{
x2[0] = w[0];
x2[1] = w[1];
y2[0] = v[0];
y2[1] = v[1];
}
} else
{
/* "Normal" split code */
float          *next_lowband2 = NULL;
float          *next_lowband_out1 = NULL;
int             next_level = 0;

Valin, et al.            Expires January 9, 2011              [Page 121]


Internet-Draft                 CELT codec                      July 2010

/* Give more bits to low-energy MDCTs than they would
otherwise deserve */
if (spread > 1 && !stereo)
delta >>= 1;

mbits = (b - qalloc / 2 - delta) / 2;
if (mbits > b - qalloc)
mbits = b - qalloc;
if (mbits < 0)
mbits = 0;
sbits = b - qalloc - mbits;
*remaining_bits -= qalloc;

if (lowband && !stereo)
next_lowband2 = lowband + N;
if (stereo)
next_lowband_out1 = lowband_out;
else
next_level = level + 1;

quant_band(encode, m, i, X, NULL, N, mbits, spread, tf_change,
lowband, resynth, ec, remaining_bits, LM,
next_lowband_out1, NULL, next_level);
quant_band(encode, m, i, Y, NULL, N, sbits, spread, tf_change,
next_lowband2, resynth, ec, remaining_bits, LM,
NULL, NULL, level);
}

} else
{
/* This is the basic no-split case */
q = bits2pulses(m, m->bits[LM][i], N, b);
curr_bits = pulses2bits(m->bits[LM][i], N, q);
*remaining_bits -= curr_bits;

/* Ensures we can never bust the budget */
while (*remaining_bits < 0 && q > 0)
{
*remaining_bits += curr_bits;
q--;
curr_bits = pulses2bits(m->bits[LM][i], N, q);
*remaining_bits -= curr_bits;
}

if (encode)
alg_quant(X, N, q, spread, lowband, resynth, (ec_enc *) ec);
else
alg_unquant(X, N, q, spread, lowband, (ec_dec *) ec);

Valin, et al.            Expires January 9, 2011              [Page 122]


Internet-Draft                 CELT codec                      July 2010

}

/* This code is used by the decoder and by the resynthesis-enabled
encoder */
if (resynth)
{
int             k;

if (split)
{
int             j;
float           mid,
side;

mid = (1.f / 32768) * imid;
side = (1.f / 32768) * iside;

for (j = 0; j < N; j++)
X[j] = ((X[j]) * (mid));
for (j = 0; j < N; j++)
Y[j] = ((Y[j]) * (side));
}

if (!stereo && spread0 > 1 && level == 0)
{
if (lowband)
}

/* Undo time-freq changes that we did earlier */
N_B = N_B0;
for (k = 0; k < time_divide; k++)
{
N_B <<= 1;
if (lowband)
}

for (k = 0; k < recombine; k++)
{
if (lowband)
N_B >>= 1;

Valin, et al.            Expires January 9, 2011              [Page 123]


Internet-Draft                 CELT codec                      July 2010

}

if (lowband_out && !stereo)
{
int             j;
float           n;
n = celt_sqrt(((N0)));
for (j = 0; j < N0; j++)
lowband_out[j] = ((n) * (X[j]));
}

if (stereo)
{
stereo_band_mix(m, X, Y, bandE, 0, i, -1, N);
renormalise_vector(X, 1.0f, N, 1);
renormalise_vector(Y, 1.0f, N, 1);
}
}
}

void
quant_all_bands(int encode, const CELTMode * m, int start, float *_X,
float *_Y, const float *bandE, int *pulses,
int shortBlocks, int fold, int *tf_res, int resynth,
int total_bits, void *ec, int LM)
{
int             i,
balance;
celt_int32      remaining_bits;
const celt_int16 *restrict eBands = m->eBands;
float          *restrict norm;
VARDECL(float, _norm);
int             B;
int             M;
float          *lowband;
int             update_lowband = 1;
int             C = _Y != NULL ? 2 : 1;
SAVE_STACK;

M = 1 << LM;
B = shortBlocks ? M : 1;
spread = fold ? B : 0;
ALLOC(_norm, M * eBands[m->nbEBands + 1], float);
norm = _norm;

balance = 0;

Valin, et al.            Expires January 9, 2011              [Page 124]


Internet-Draft                 CELT codec                      July 2010

lowband = NULL;
for (i = start; i < m->nbEBands; i++)
{
int             tell;
int             b;
int             N;
int             curr_balance;
float          *restrict X,
*restrict Y;
int             tf_change = 0;

X = _X + M * eBands[i];
if (_Y != NULL)
Y = _Y + M * eBands[i];
else
Y = NULL;
N = M * eBands[i + 1] - M * eBands[i];
if (encode)
tell = ec_enc_tell((ec_enc *) ec, BITRES);
else
tell = ec_dec_tell((ec_dec *) ec, BITRES);

if (i != start)
balance -= tell;
remaining_bits = (total_bits << BITRES) - tell - 1;
curr_balance = (m->nbEBands - i);
if (curr_balance > 3)
curr_balance = 3;
curr_balance = balance / curr_balance;
b = IMIN(remaining_bits + 1, pulses[i] + curr_balance);
if (b < 0)
b = 0;
/* Prevents ridiculous bit depths */
if (b > C * 16 * N << BITRES)
b = C * 16 * N << BITRES;

if (M * eBands[i] - N >= M * eBands[start])
{
if (update_lowband)
lowband = norm + M * eBands[i] - N;
} else
lowband = NULL;

tf_change = tf_res[i];
quant_band(encode, m, i, X, Y, N, b, spread, tf_change, lowband,
resynth, ec, &remaining_bits, LM,
norm + M * eBands[i], bandE, 0);

Valin, et al.            Expires January 9, 2011              [Page 125]


Internet-Draft                 CELT codec                      July 2010

balance += pulses[i] + tell;

/* Update the folding position only as long as we have 2
bit/sample depth */
update_lowband = (b >> BITRES) > 2 * N;
}
RESTORE_STACK;
}

A.9.  cwrs.h

Foundation Copyright (c) 2007-2009 Timothy B. Terriberry Written
by Timothy B. Terriberry and Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef CWRS_H

Valin, et al.            Expires January 9, 2011              [Page 126]


Internet-Draft                 CELT codec                      July 2010

#define CWRS_H

#include "arch.h"
#include "stack_alloc.h"
#include "entenc.h"
#include "entdec.h"

int             log2_frac(ec_uint32 val, int frac);

void            get_required_bits(celt_int16 * bits, int N, int K,
int frac);

void            encode_pulses(const int *_y, int N, int K,
ec_enc * enc);

void            decode_pulses(int *_y, int N, int K, ec_dec * dec);

#endif                          /* CWRS_H */

A.10.  cwrs.c

Foundation Copyright (c) 2007-2009 Timothy B. Terriberry Written
by Timothy B. Terriberry and Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE

Valin, et al.            Expires January 9, 2011              [Page 127]


Internet-Draft                 CELT codec                      July 2010

LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "os_support.h"
#include <stdlib.h>
#include <string.h>
#include "cwrs.h"
#include "mathops.h"
#include "arch.h"

/* Guaranteed to return a conservatively large estimate of the
binary logarithm with frac bits of fractional precision. Tested
for all possible 32-bit inputs with frac=4, where the maximum
overestimation is 0.06254243 bits. */
int
log2_frac(ec_uint32 val, int frac)
{
int             l;
l = EC_ILOG(val);
if (val & val - 1)
{
/* This is (val>>l-16), but guaranteed to round up, even if
adding a bias before the shift would cause overflow (e.g.,
for 0xFFFFxxxx). */
if (l > 16)
val =
(val >> l - 16) + ((val & (1 << l - 16) - 1) +
(1 << l - 16) - 1 >> l - 16);
else
val <<= 16 - l;
l = l - 1 << frac;
/* Note that we always need one iteration, since the rounding up
above means that we might need to adjust the integer part of
the logarithm. */
do
{
int             b;
b = (int) (val >> 16);
l += b << frac;
val = val + b >> b;

Valin, et al.            Expires January 9, 2011              [Page 128]


Internet-Draft                 CELT codec                      July 2010

val = val * val + 0x7FFF >> 15;
}
while (frac-- > 0);
/* If val is not exactly 0x8000, then we have to round up the
remainder. */
return l + (val > 0x8000);
}
/* Exact powers of two require no rounding. */
else
return l - 1 << frac;
}

/* INV_TABLE[i] holds the multiplicative inverse of (2*i+1) mod
2**32. */
static const celt_uint32 INV_TABLE[64] = {
0x00000001, 0xAAAAAAAB, 0xCCCCCCCD, 0xB6DB6DB7,
0x38E38E39, 0xBA2E8BA3, 0xC4EC4EC5, 0xEEEEEEEF,
0xF0F0F0F1, 0x286BCA1B, 0x3CF3CF3D, 0xE9BD37A7,
0xC28F5C29, 0x684BDA13, 0x4F72C235, 0xBDEF7BDF,
0xC18F9C19, 0x2FA0BE83, 0xA4FA4FA5, 0x677D46CF,
0x1A1F58D1, 0xFAFAFAFB, 0x8C13521D, 0x586FB587,
0xC0FC0FC1, 0x07A44C6B, 0xA33F128D, 0xE327A977,
0xC7E3F1F9, 0x962FC963, 0x3F2B3885, 0x613716AF,
0x781948B1, 0x2B2E43DB, 0xFCFCFCFD, 0x6FD0EB67,
0xFA3F47E9, 0xD2FD2FD3, 0x3F4FD3F5, 0xD4E25B9F,
0x5F02A3A1, 0xBF5A814B, 0x7C32B16D, 0xD3431B57,
0xD8FD8FD9, 0x8D28AC43, 0xDA6C0965, 0xDB195E8F,
0x0FDBC091, 0x61F2A4BB, 0xDCFDCFDD, 0x46FDD947,
0x56BE69C9, 0xEB2FDEB3, 0x26E978D5, 0xEFDFBF7F,
/*
0x0FE03F81,0xC9484E2B,0xE133F84D,0xE1A8C537,
0x077975B9,0x70586723,0xCD29C245,0xFAA11E6F,
0x0FE3C071,0x08B51D9B,0x8CE2CABD,0xBF937F27,
0xA8FE53A9,0x592FE593,0x2C0685B5,0x2EB11B5F,
0xFCD1E361,0x451AB30B,0x72CFE72D,0xDB35A717,
0xFB74A399,0xE80BFA03,0x0D516325,0x1BCB564F,
0xE02E4851,0xD962AE7B,0x10F8ED9D,0x95AEDD07,
0xE9DC0589,0xA18A4473,0xEA53FA95,0xEE936F3F,
0x90948F41,0xEAFEAFEB,0x3D137E0D,0xEF46C0F7,
0x028C1979,0x791064E3,0xC04FEC05,0xE115062F,
0x32385831,0x6E68575B,0xA10D387D,0x6FECF2E7,
0x3FB47F69,0xED4BFB53,0x74FED775,0xDB43BB1F,
0x87654321,0x9BA144CB,0x478BBCED,0xBFB912D7,
0x1FDCD759,0x14B2A7C3,0xCB125CE5,0x437B2E0F,

Valin, et al.            Expires January 9, 2011              [Page 129]


Internet-Draft                 CELT codec                      July 2010

0x10FEF011,0xD2B3183B,0x386CAB5D,0xEF6AC0C7,
0x0E64C149,0x9A020A33,0xE6B41C55,0xFEFEFEFF */
};

/* Computes (_a*_b-_c)/(2*_d+1) when the quotient is known to be
exact. _a, _b, _c, and _d may be arbitrary so long as the
arbitrary precision result fits in 32 bits, but currently the
table for multiplicative inverses is only valid for _d<128. */
static inline celt_uint32
imusdiv32odd(celt_uint32 _a, celt_uint32 _b, celt_uint32 _c, int _d)
{
return (_a * _b - _c) * INV_TABLE[_d] & MASK32;
}

/* Computes (_a*_b-_c)/_d when the quotient is known to be exact. _d
does not actually have to be even, but imusdiv32odd will be
faster when it's odd, so you should use that instead. _a and _d
are assumed to be small (e.g., _a*_d fits in 32 bits; currently
the table for multiplicative inverses is only valid for _d<=256).
_b and _c may be arbitrary so long as the arbitrary precision
reuslt fits in 32 bits. */
static inline celt_uint32
imusdiv32even(celt_uint32 _a, celt_uint32 _b, celt_uint32 _c, int _d)
{
celt_uint32     inv;
int             shift;
int             one;
celt_assert(_d > 0);
shift = EC_ILOG(_d ^ _d - 1);
celt_assert(_d <= 256);
inv = INV_TABLE[_d - 1 >> shift];
shift--;
one = 1 << shift;
return (_a * (_b >> shift) - (_c >> shift) +
(_a * (_b & mask) + one - (_c & mask) >> shift) -
}

/* Compute floor(sqrt(_val)) with exact arithmetic. This has been
tested on all possible 32-bit inputs. */
static unsigned
isqrt32(celt_uint32 _val)
{
unsigned        b;
unsigned        g;
int             bshift;

Valin, et al.            Expires January 9, 2011              [Page 130]


Internet-Draft                 CELT codec                      July 2010

/* Uses the second method from
http://www.azillionmonkeys.com/qed/sqroot.html The main idea is
to search for the largest binary digit b such that (g+b)*(g+b)
<= _val, and add it to the solution g. */
g = 0;
bshift = EC_ILOG(_val) - 1 >> 1;
b = 1U << bshift;
do
{
celt_uint32     t;
t = ((celt_uint32) g << 1) + b << bshift;
if (t <= _val)
{
g += b;
_val -= t;
}
b >>= 1;
bshift--;
}
while (bshift >= 0);
return g;
}

/* Although derived separately, the pulse vector coding scheme is
equivalent to a Pyramid Vector Quantizer \cite{Fis86}. Some
http://people.xiph.org/~tterribe/notes/cwrs.html, but the
codebook ordering and the definitions of some terms have evolved
since that was written.

The conversion from a pulse vector to an integer index (encoding)
and back (decoding) is governed by two related functions, V(N,K)
and U(N,K).

V(N,K) = the number of combinations, with replacement, of N
items, taken K at a time, when a sign bit is added to each item
taken at least once (i.e., the number of N-dimensional unit pulse
vectors with K pulses). One way to compute this is via V(N,K) =
K>0 ? sum(k=1...K,2**k*choose(N,k)*choose(K-1,k-1)) : 1, where
choose() is the binomial function. A table of values for N<10 and
K<10 looks like: V[10][10] = { {1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 2, 2, 2, 2, 2, 2, 2, 2, 2}, {1, 4, 8, 12, 16, 20, 24, 28, 32,
36}, {1, 6, 18, 38, 66, 102, 146, 198, 258, 326}, {1, 8, 32, 88,
192, 360, 608, 952, 1408, 1992}, {1, 10, 50, 170, 450, 1002,
1970, 3530, 5890, 9290}, {1, 12, 72, 292, 912, 2364, 5336, 10836,
20256, 35436}, {1, 14, 98, 462, 1666, 4942, 12642, 28814, 59906,
115598}, {1, 16, 128, 688, 2816, 9424, 27008, 68464, 157184,
332688}, {1, 18, 162, 978, 4482, 16722, 53154, 148626, 374274,

Valin, et al.            Expires January 9, 2011              [Page 131]


Internet-Draft                 CELT codec                      July 2010

864146} };

U(N,K) = the number of such combinations wherein N-1 objects are
taken at most K-1 at a time. This is given by U(N,K) =
sum(k=0...K-1,V(N-1,k)) = K>0 ? (V(N-1,K-1) + V(N,K-1))/2 : 0.
The latter expression also makes clear that U(N,K) is half the
number of such combinations wherein the first object is taken at
least once. Although it may not be clear from either of these
definitions, U(N,K) is the natural function to work with when
enumerating the pulse vector codebooks, not V(N,K). U(N,K) is not
well-defined for N=0, but with the extension U(0,K) = K>0 ? 0 :
1, the function becomes symmetric: U(N,K) = U(K,N), with a
similar table: U[10][10] = { {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0,
1, 1, 1, 1, 1, 1, 1, 1, 1}, {0, 1, 3, 5, 7, 9, 11, 13, 15, 17},
{0, 1, 5, 13, 25, 41, 61, 85, 113, 145}, {0, 1, 7, 25, 63, 129,
231, 377, 575, 833}, {0, 1, 9, 41, 129, 321, 681, 1289, 2241,
3649}, {0, 1, 11, 61, 231, 681, 1683, 3653, 7183, 13073}, {0, 1,
13, 85, 377, 1289, 3653, 8989, 19825, 40081}, {0, 1, 15, 113,
575, 2241, 7183, 19825, 48639, 108545}, {0, 1, 17, 145, 833,
3649, 13073, 40081, 108545, 265729} };

With this extension, V(N,K) may be written in terms of U(N,K):
V(N,K) = U(N,K) + U(N,K+1) for all N>=0, K>=0. Thus U(N,K+1)
represents the number of combinations where the first element is
positive or zero, and U(N,K) represents the number of
combinations where it is negative. With a large enough table of
U(N,K) values, we could write O(N) encoding and
O(min(N*log(K),N+K)) decoding routines, but such a table would be
prohibitively large for small embedded devices (K may be as large
as 32767 for small N, and N may be as large as 200).

Both functions obey the same recurrence relation: V(N,K) =
V(N-1,K) + V(N,K-1) + V(N-1,K-1), U(N,K) = U(N-1,K) + U(N,K-1) +
U(N-1,K-1), for all N>0, K>0, with different initial conditions at
N=0 or K=0. This allows us to construct a row of one of the tables
above given the previous row or the next row. Thus we can derive
O(NK) encoding and decoding routines with O(K) memory using only

When encoding, we build up from the U(2,K) row and work our way
forwards. When decoding, we need to start at the U(N,K) row and
work our way backwards, which requires a means of computing
U(N,K). U(N,K) may be computed from two previous values with the
same N: U(N,K) = ((2*N-1)*U(N,K-1) - U(N,K-2))/(K-1) + U(N,K-2)
for all N>1, and since U(N,K) is symmetric, a similar relation
holds for two previous values with the same K: U(N,K>1) =
((2*K-1)*U(N-1,K) - U(N-2,K))/(N-1) + U(N-2,K) for all K>1. This
allows us to construct an arbitrary row of the U(N,K) table by

Valin, et al.            Expires January 9, 2011              [Page 132]


Internet-Draft                 CELT codec                      July 2010

starting with the first two values, which are constants. This
saves roughly 2/3 the work in our O(NK) decoding routine, but
costs O(K) multiplications. Similar relations can be derived for
V(N,K), but are not used here.

For N>0 and K>0, U(N,K) and V(N,K) take on the form of an
(N-1)-degree polynomial for fixed N. The first few are U(1,K) = 1,
U(2,K) = 2*K-1, U(3,K) = (2*K-2)*K+1, U(4,K) =
(((4*K-6)*K+8)*K-3)/3, U(5,K) = ((((2*K-4)*K+10)*K-8)*K+3)/3, and
V(1,K) = 2, V(2,K) = 4*K, V(3,K) = 4*K*K+2, V(4,K) = 8*(K*K+2)*K/3,
V(5,K) = ((4*K*K+20)*K*K+6)/3, for all K>0. This allows us to derive
O(N) encoding and O(N*log(K)) decoding routines for small N (and
indeed decoding is also O(N) for N<3).

@ARTICLE{Fis86, author="Thomas R. Fischer", title="A Pyramid Vector
Quantizer", journal="IEEE Transactions on Information Theory",
volume="IT-32", number=4, pages="568--583", month=Jul, year=1986 } */

/* Determines if V(N,K) fits in a 32-bit unsigned integer. N and K
are themselves limited to 15 bits. */
static int
fits_in32(int _n, int _k)
{
static const celt_int16 maxN[15] = {
32767, 32767, 32767, 1476, 283, 109, 60, 40,
29, 24, 20, 18, 16, 14, 13
};
static const celt_int16 maxK[15] = {
32767, 32767, 32767, 32767, 1172, 238, 95, 53,
36, 27, 22, 18, 16, 15, 13
};
if (_n >= 14)
{
if (_k >= 14)
return 0;
else
return _n <= maxN[_k];
} else
{
return _k <= maxK[_n];
}
}

/* Compute U(1,_k). */
static inline unsigned
ucwrs1(int _k)
{
return _k ? 1 : 0;

Valin, et al.            Expires January 9, 2011              [Page 133]


Internet-Draft                 CELT codec                      July 2010

}

/* Compute V(1,_k). */
static inline unsigned
ncwrs1(int _k)
{
return _k ? 2 : 1;
}

/* Compute U(2,_k). Note that this may be called with _k=32768
(maxK[2]+1). */
static inline unsigned
ucwrs2(unsigned _k)
{
return _k ? _k + (_k - 1) : 0;
}

/* Compute V(2,_k). */
static inline celt_uint32
ncwrs2(int _k)
{
return _k ? 4 * (celt_uint32) _k : 1;
}

/* Compute U(3,_k). Note that this may be called with _k=32768
(maxK[3]+1). */
static inline celt_uint32
ucwrs3(unsigned _k)
{
return _k ? (2 * (celt_uint32) _k - 2) * _k + 1 : 0;
}

/* Compute V(3,_k). */
static inline celt_uint32
ncwrs3(int _k)
{
return _k ? 2 * (2 * (unsigned) _k * (celt_uint32) _k + 1) : 1;
}

/* Compute U(4,_k). */
static inline celt_uint32
ucwrs4(int _k)
{
return _k ? imusdiv32odd(2 * _k,
(2 * _k - 3) * (celt_uint32) _k + 4, 3,
1) : 0;
}

Valin, et al.            Expires January 9, 2011              [Page 134]


Internet-Draft                 CELT codec                      July 2010

/* Compute V(4,_k). */
static inline celt_uint32
ncwrs4(int _k)
{
return _k ? ((_k * (celt_uint32) _k + 2) * _k) / 3 << 3 : 1;
}

/* Compute U(5,_k). */
static inline celt_uint32
ucwrs5(int _k)
{
return _k
? (((((_k - 2) * (unsigned) _k + 5) * (celt_uint32) _k -
4) * _k) / 3 << 1) + 1 : 0;
}

/* Compute V(5,_k). */
static inline celt_uint32
ncwrs5(int _k)
{
return _k ? (((_k * (unsigned) _k + 5) * (celt_uint32) _k * _k) /
3 << 2) + 2 : 1;
}

/* Computes the next row/column of any recurrence that obeys the
relation u[i][j]=u[i-1][j]+u[i][j-1]+u[i-1][j-1]. _ui0 is the
base case for the new row/column. */
static inline void
unext(celt_uint32 * _ui, unsigned _len, celt_uint32 _ui0)
{
celt_uint32     ui1;
unsigned        j;
/* This do-while will overrun the array if we don't have storage
for at least 2 values. */
j = 1;
do
{
ui1 = ((((_ui[j]) + (_ui[j - 1]))) + (_ui0));
_ui[j - 1] = _ui0;
_ui0 = ui1;
}
while (++j < _len);
_ui[j - 1] = _ui0;
}

/* Computes the previous row/column of any recurrence that obeys the
relation u[i-1][j]=u[i][j]-u[i][j-1]-u[i-1][j-1]. _ui0 is the
base case for the new row/column. */

Valin, et al.            Expires January 9, 2011              [Page 135]


Internet-Draft                 CELT codec                      July 2010

static inline void
uprev(celt_uint32 * _ui, unsigned _n, celt_uint32 _ui0)
{
celt_uint32     ui1;
unsigned        j;
/* This do-while will overrun the array if we don't have storage
for at least 2 values. */
j = 1;
do
{
ui1 = ((((_ui[j]) - (_ui[j - 1]))) - (_ui0));
_ui[j - 1] = _ui0;
_ui0 = ui1;
}
while (++j < _n);
_ui[j - 1] = _ui0;
}

/* Compute V(_n,_k), as well as U(_n,0..._k+1). _u: On exit, _u[i]
contains U(_n,i) for i in [0..._k+1]. */
static celt_uint32
ncwrs_urow(unsigned _n, unsigned _k, celt_uint32 * _u)
{
celt_uint32     um2;
unsigned        len;
unsigned        k;
len = _k + 2;
/* We require storage at least 3 values (e.g., _k>0). */
celt_assert(len >= 3);
_u[0] = 0;
_u[1] = um2 = 1;

if (_n <= 6 || _k > 255)

{
/* If _n==0, _u[0] should be 1 and the rest should be 0. */
/* If _n==1, _u[i] should be 1 for i>1. */
celt_assert(_n >= 2);
/* If _k==0, the following do-while loop will overflow the
buffer. */
celt_assert(_k > 0);
k = 2;
do
_u[k] = (k << 1) - 1;
while (++k < len);
for (k = 2; k < _n; k++)
unext(_u + 1, _k + 1, 1);
}

Valin, et al.            Expires January 9, 2011              [Page 136]


Internet-Draft                 CELT codec                      July 2010

else
{
celt_uint32     um1;
celt_uint32     n2m1;
_u[2] = n2m1 = um1 = (_n << 1) - 1;
for (k = 3; k < len; k++)
{
/* U(N,K) = ((2*N-1)*U(N,K-1)-U(N,K-2))/(K-1) + U(N,K-2) */
_u[k] = um2 = imusdiv32even(n2m1, um1, um2, k - 1) + um2;
if (++k >= len)
break;
_u[k] = um1 = imusdiv32odd(n2m1, um2, um1, k - 1 >> 1) + um1;
}
}

return _u[_k] + _u[_k + 1];
}

/* Returns the _i'th combination of _k elements (at most 32767)
chosen from a set of size 1 with associated sign bits. _y:
Returns the vector of pulses. */
static inline void
cwrsi1(int _k, celt_uint32 _i, int *_y)
{
int             s;
s = -(int) _i;
_y[0] = _k + s ^ s;
}

/* Returns the _i'th combination of _k elements (at most 32767)
chosen from a set of size 2 with associated sign bits. _y:
Returns the vector of pulses. */
static inline void
cwrsi2(int _k, celt_uint32 _i, int *_y)
{
celt_uint32     p;
int             s;
int             yj;
p = ucwrs2(_k + 1U);
s = -(_i >= p);
_i -= p & s;
yj = _k;
_k = _i + 1 >> 1;
p = ucwrs2(_k);
_i -= p;
yj -= _k;
_y[0] = yj + s ^ s;
cwrsi1(_k, _i, _y + 1);

Valin, et al.            Expires January 9, 2011              [Page 137]


Internet-Draft                 CELT codec                      July 2010

}

/* Returns the _i'th combination of _k elements (at most 32767)
chosen from a set of size 3 with associated sign bits. _y:
Returns the vector of pulses. */
static void
cwrsi3(int _k, celt_uint32 _i, int *_y)
{
celt_uint32     p;
int             s;
int             yj;
p = ucwrs3(_k + 1U);
s = -(_i >= p);
_i -= p & s;
yj = _k;
/* Finds the maximum _k such that ucwrs3(_k)<=_i (tested for all
_i<2147418113=U(3,32768)). */
_k = _i > 0 ? isqrt32(2 * _i - 1) + 1 >> 1 : 0;
p = ucwrs3(_k);
_i -= p;
yj -= _k;
_y[0] = yj + s ^ s;
cwrsi2(_k, _i, _y + 1);
}

/* Returns the _i'th combination of _k elements (at most 1172)
chosen from a set of size 4 with associated sign bits. _y:
Returns the vector of pulses. */
static void
cwrsi4(int _k, celt_uint32 _i, int *_y)
{
celt_uint32     p;
int             s;
int             yj;
int             kl;
int             kr;
p = ucwrs4(_k + 1);
s = -(_i >= p);
_i -= p & s;
yj = _k;
/* We could solve a cubic for k here, but the form of the direct
solution does not lend itself well to exact integer arithmetic.
Instead we do a binary search on U(4,K). */
kl = 0;
kr = _k;
for (;;)
{
_k = kl + kr >> 1;

Valin, et al.            Expires January 9, 2011              [Page 138]


Internet-Draft                 CELT codec                      July 2010

p = ucwrs4(_k);
if (p < _i)
{
if (_k >= kr)
break;
kl = _k + 1;
} else if (p > _i)
kr = _k - 1;
else
break;
}
_i -= p;
yj -= _k;
_y[0] = yj + s ^ s;
cwrsi3(_k, _i, _y + 1);
}

/* Returns the _i'th combination of _k elements (at most 238) chosen
from a set of size 5 with associated sign bits. _y: Returns the
vector of pulses. */
static void
cwrsi5(int _k, celt_uint32 _i, int *_y)
{
celt_uint32     p;
int             s;
int             yj;
p = ucwrs5(_k + 1);
s = -(_i >= p);
_i -= p & s;
yj = _k;
/* A binary search on U(5,K) avoids the need for 64-bit arithmetic
*/
{
int             kl = 0;
int             kr = _k;
for (;;)
{
_k = kl + kr >> 1;
p = ucwrs5(_k);
if (p < _i)
{
if (_k >= kr)
break;
kl = _k + 1;
} else if (p > _i)
kr = _k - 1;
else
break;

Valin, et al.            Expires January 9, 2011              [Page 139]


Internet-Draft                 CELT codec                      July 2010

}
}
_i -= p;
yj -= _k;
_y[0] = yj + s ^ s;
cwrsi4(_k, _i, _y + 1);
}

/* Returns the _i'th combination of _k elements chosen from a set of
size _n with associated sign bits. _y: Returns the vector of
pulses. _u: Must contain entries [0..._k+1] of row _n of U() on
input. Its contents will be destructively modified. */
static void
cwrsi(int _n, int _k, celt_uint32 _i, int *_y, celt_uint32 * _u)
{
int             j;
celt_assert(_n > 0);
j = 0;
do
{
celt_uint32     p;
int             s;
int             yj;
p = _u[_k + 1];
s = -(_i >= p);
_i -= p & s;
yj = _k;
p = _u[_k];
while (p > _i)
p = _u[--_k];
_i -= p;
yj -= _k;
_y[j] = yj + s ^ s;
uprev(_u, _k + 2, 0);
}
while (++j < _n);
}

/* Returns the index of the given combination of K elements chosen
from a set of size 1 with associated sign bits. _y: The vector of
pulses, whose sum of absolute values is K. _k: Returns K. */
static inline celt_uint32
icwrs1(const int *_y, int *_k)
{
*_k = abs(_y[0]);
return _y[0] < 0;
}

Valin, et al.            Expires January 9, 2011              [Page 140]


Internet-Draft                 CELT codec                      July 2010

/* Returns the index of the given combination of K elements chosen
from a set of size 2 with associated sign bits. _y: The vector of
pulses, whose sum of absolute values is K. _k: Returns K. */
static inline celt_uint32
icwrs2(const int *_y, int *_k)
{
celt_uint32     i;
int             k;
i = icwrs1(_y + 1, &k);
i += ucwrs2(k);
k += abs(_y[0]);
if (_y[0] < 0)
i += ucwrs2(k + 1U);
*_k = k;
return i;
}

/* Returns the index of the given combination of K elements chosen
from a set of size 3 with associated sign bits. _y: The vector of
pulses, whose sum of absolute values is K. _k: Returns K. */
static inline celt_uint32
icwrs3(const int *_y, int *_k)
{
celt_uint32     i;
int             k;
i = icwrs2(_y + 1, &k);
i += ucwrs3(k);
k += abs(_y[0]);
if (_y[0] < 0)
i += ucwrs3(k + 1U);
*_k = k;
return i;
}

/* Returns the index of the given combination of K elements chosen
from a set of size 4 with associated sign bits. _y: The vector of
pulses, whose sum of absolute values is K. _k: Returns K. */
static inline celt_uint32
icwrs4(const int *_y, int *_k)
{
celt_uint32     i;
int             k;
i = icwrs3(_y + 1, &k);
i += ucwrs4(k);
k += abs(_y[0]);
if (_y[0] < 0)
i += ucwrs4(k + 1);
*_k = k;

Valin, et al.            Expires January 9, 2011              [Page 141]


Internet-Draft                 CELT codec                      July 2010

return i;
}

/* Returns the index of the given combination of K elements chosen
from a set of size 5 with associated sign bits. _y: The vector of
pulses, whose sum of absolute values is K. _k: Returns K. */
static inline celt_uint32
icwrs5(const int *_y, int *_k)
{
celt_uint32     i;
int             k;
i = icwrs4(_y + 1, &k);
i += ucwrs5(k);
k += abs(_y[0]);
if (_y[0] < 0)
i += ucwrs5(k + 1);
*_k = k;
return i;
}

/* Returns the index of the given combination of K elements chosen
from a set of size _n with associated sign bits. _y: The vector
of pulses, whose sum of absolute values must be _k. _nc: Returns
V(_n,_k). */
celt_uint32
icwrs(int _n, int _k, celt_uint32 * _nc, const int *_y,
celt_uint32 * _u)
{
celt_uint32     i;
int             j;
int             k;
/* We can't unroll the first two iterations of the loop unless
_n>=2. */
celt_assert(_n >= 2);
_u[0] = 0;
for (k = 1; k <= _k + 1; k++)
_u[k] = (k << 1) - 1;
i = icwrs1(_y + _n - 1, &k);
j = _n - 2;
i += _u[k];
k += abs(_y[j]);
if (_y[j] < 0)
i += _u[k + 1];
while (j-- > 0)
{
unext(_u, _k + 2, 0);
i += _u[k];
k += abs(_y[j]);

Valin, et al.            Expires January 9, 2011              [Page 142]


Internet-Draft                 CELT codec                      July 2010

if (_y[j] < 0)
i += _u[k + 1];
}
*_nc = _u[k] + _u[k + 1];
return i;
}

void
get_required_bits(celt_int16 * _bits, int _n, int _maxk, int _frac)
{
int             k;
/*_maxk==0 => there's nothing to do.*/
celt_assert(_maxk > 0);
if (_n == 1)
{
_bits[0] = 0;
for (k = 1; k < _maxk; k++)
_bits[k] = 1 << _frac;
} else
{
_bits[0] = 0;
if (_maxk > 1)
{
VARDECL(celt_uint32, u);
SAVE_STACK;
ALLOC(u, _maxk + 1U, celt_uint32);
ncwrs_urow(_n, _maxk - 1, u);
for (k = 1; k < _maxk && fits_in32(_n, k); k++)
_bits[k] = log2_frac(u[k] + u[k + 1], _frac);
for (; k < _maxk; k++)
_bits[k] = 10000;
RESTORE_STACK;
}
}
}

void
encode_pulses(const int *_y, int _n, int _k, ec_enc * _enc)
{
celt_uint32     i;
if (_k == 0)
return;
celt_assert(fits_in32(_n, _k));
switch (_n)
{
case 1:
{
i = icwrs1(_y, &_k);

Valin, et al.            Expires January 9, 2011              [Page 143]


Internet-Draft                 CELT codec                      July 2010

celt_assert(ncwrs1(_k) == 2);
ec_enc_bits(_enc, i, 1);
}
break;

case 2:
{
i = icwrs2(_y, &_k);
ec_enc_uint(_enc, i, ncwrs2(_k));
}
break;
case 3:
{
i = icwrs3(_y, &_k);
ec_enc_uint(_enc, i, ncwrs3(_k));
}
break;
case 4:
{
i = icwrs4(_y, &_k);
ec_enc_uint(_enc, i, ncwrs4(_k));
}
break;
case 5:
{
i = icwrs5(_y, &_k);
ec_enc_uint(_enc, i, ncwrs5(_k));
}
break;

default:
{
VARDECL(celt_uint32, u);
celt_uint32     nc;
SAVE_STACK;
ALLOC(u, _k + 2U, celt_uint32);
i = icwrs(_n, _k, &nc, _y, u);
ec_enc_uint(_enc, i, nc);
RESTORE_STACK;
};
}
}

void
decode_pulses(int *_y, int _n, int _k, ec_dec * _dec)
{
if (_k == 0)
{

Valin, et al.            Expires January 9, 2011              [Page 144]


Internet-Draft                 CELT codec                      July 2010

int             i;
for (i = 0; i < _n; i++)
_y[i] = 0;
return;
}
celt_assert(fits_in32(_n, _k));
switch (_n)
{
case 1:
{
celt_assert(ncwrs1(_k) == 2);
cwrsi1(_k, ec_dec_bits(_dec, 1), _y);
}
break;

case 2:
cwrsi2(_k, ec_dec_uint(_dec, ncwrs2(_k)), _y);
break;
case 3:
cwrsi3(_k, ec_dec_uint(_dec, ncwrs3(_k)), _y);
break;
case 4:
cwrsi4(_k, ec_dec_uint(_dec, ncwrs4(_k)), _y);
break;
case 5:
cwrsi5(_k, ec_dec_uint(_dec, ncwrs5(_k)), _y);
break;

default:
{
VARDECL(celt_uint32, u);
SAVE_STACK;
ALLOC(u, _k + 2U, celt_uint32);
cwrsi(_n, _k, ec_dec_uint(_dec, ncwrs_urow(_n, _k, u)), _y, u);
RESTORE_STACK;
}
}
}

A.11.  vq.h

Foundation Written by Jean-Marc Valin */
/**
@file vq.h
@brief Vector quantisation of the residual
*/

Valin, et al.            Expires January 9, 2011              [Page 145]


Internet-Draft                 CELT codec                      July 2010

/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef VQ_H
#define VQ_H

#include "entenc.h"
#include "entdec.h"
#include "modes.h"

/** Algebraic pulse-vector quantiser. The signal x is replaced by the s\
um of
* the pitch and a combination of pulses such that its norm is still e\
qual
* to 1. This is the function that will typically require the most CPU\
.
* @param x Residual signal to quantise/encode (returns quantised versi\
on)
* @param W Perceptual weight to use when optimising (currently unused)

Valin, et al.            Expires January 9, 2011              [Page 146]


Internet-Draft                 CELT codec                      July 2010

* @param N Number of samples to encode
* @param K Number of pulses to use
* @param p Pitch vector (it is assumed that p+x is a unit vector)
* @param enc Entropy encoder state
*/
void            alg_quant(float *X, int N, int K, int spread,
float *lowband, int resynth, ec_enc * enc);

/** Algebraic pulse decoder
* @param x Decoded normalised spectrum (returned)
* @param N Number of samples to decode
* @param K Number of pulses to use
* @param p Pitch vector (automatically added to x)
* @param dec Entropy decoder state
*/
void            alg_unquant(float *X, int N, int K, int spread,
float *lowband, ec_dec * dec);

float           renormalise_vector(float *X, float value, int N,
int stride);

/** Intra-frame predictor that matches a section of the current frame (\
at lower
* frequencies) to encode the current band.
* @param x Residual signal to quantise/encode (returns quantised versi\
on)
* @param W Perceptual weight
* @param N Number of samples to encode
* @param K Number of pulses to use
* @param Y Lower frequency spectrum to use, normalised to the same sta\
ndard deviation
* @param P Pitch vector (it is assumed that p+x is a unit vector)
* @param B Stride (number of channels multiplied by the number of MDCT\
s per frame)
* @param N0 Number of valid offsets
*/
void            intra_fold(const CELTMode * m, int start, int N,
const float *restrict Y,
float *restrict P, int N0, int B, int M);

#endif                          /* VQ_H */

A.12.  vq.c

Foundation Written by Jean-Marc Valin */
/*

Valin, et al.            Expires January 9, 2011              [Page 147]


Internet-Draft                 CELT codec                      July 2010

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "mathops.h"
#include "cwrs.h"
#include "vq.h"
#include "arch.h"
#include "os_support.h"
#include "rate.h"

#define M_PI 3.141592653

static void
exp_rotation1(float *X, int len, int dir, int stride, float c,
float s)
{
int             i;
float          *Xptr;

Valin, et al.            Expires January 9, 2011              [Page 148]


Internet-Draft                 CELT codec                      July 2010

if (dir > 0)
s = -s;
Xptr = X;
for (i = 0; i < len - stride; i++)
{
float           x1,
x2;
x1 = Xptr[0];
x2 = Xptr[stride];
Xptr[stride] = ((((c) * (x2)) + ((s) * (x1))));
*Xptr++ = ((((c) * (x1)) - ((s) * (x2))));
}
Xptr = &X[len - 2 * stride - 1];
for (i = len - 2 * stride - 1; i >= 0; i--)
{
float           x1,
x2;
x1 = Xptr[0];
x2 = Xptr[stride];
Xptr[stride] = ((((c) * (x2)) + ((s) * (x1))));
*Xptr-- = ((((c) * (x1)) - ((s) * (x2))));
}
}

static void
exp_rotation(float *X, int len, int dir, int stride, int K)
{
int             i;
float           c,
s;
float           gain,
theta;
int             stride2 = 0;
/* int i; if (len>=30) { for (i=0;i<len;i++) X[i] = 0; X[14] = 1;
K=5; } */
if (2 * K >= len)
return;
gain = celt_div((float) ((1.f) * (len)), (float) (len + 10 * K));
/* FIXME: Make that HALF16 instead of HALF32 */
theta = (.5f * (((gain) * (gain))));

c = celt_cos_norm((theta));
s = celt_cos_norm((((1.0f) - (theta))));      /* sin(theta) */

if (len >= 8 * stride)
{
stride2 = 1;
/* This is just a simple way of computing sqrt(len/stride) with

Valin, et al.            Expires January 9, 2011              [Page 149]


Internet-Draft                 CELT codec                      July 2010

rounding. It's basically incrementing long as (stride2+0.5)^2
< len/stride. I _think_ it is bit-exact */
while ((stride2 * stride2 + stride2) * stride + (stride >> 2) <
len)
stride2++;
}
len /= stride;
for (i = 0; i < stride; i++)
{
if (dir < 0)
{
if (stride2)
exp_rotation1(X + i * len, len, dir, stride2, s, c);
exp_rotation1(X + i * len, len, dir, 1, c, s);
} else
{
exp_rotation1(X + i * len, len, dir, 1, c, s);
if (stride2)
exp_rotation1(X + i * len, len, dir, stride2, s, c);
}
}
/* if (len>=30) { for (i=0;i<len;i++) printf ("%f ", X[i]); printf
("\n"); exit(0); } */
}

/** Takes the pitch vector and the decoded residual vector, computes th\
e gain
that will give ||p+g*y||=1 and mixes the residual with the pitch. */
static void
normalise_residual(int *restrict iy, float *restrict X, int N, int K,
float Ryy)
{
int             i;

float           t;
float           g;

t = (Ryy);
g = celt_rsqrt_norm(t);

i = 0;
do
X[i] = ((((g) * (iy[i]))));
while (++i < N);
}

void
alg_quant(float *X, int N, int K, int spread, float *lowband,

Valin, et al.            Expires January 9, 2011              [Page 150]


Internet-Draft                 CELT codec                      July 2010

int resynth, ec_enc * enc)
{
VARDECL(float, y);
VARDECL(int, iy);
VARDECL(float, signx);
int             j,
is;
float           s;
int             pulsesLeft;
float           sum;
float           xy,
yy;
int             N_1;          /* Inverse of N, in Q14 format (even
for float) */

SAVE_STACK;

if (K == 0)
{
if (lowband != NULL && resynth)
{
for (j = 0; j < N; j++)
X[j] = lowband[j];
renormalise_vector(X, 1.0f, N, 1);
} else
{
/* This is important for encoding the side in stereo mode */
for (j = 0; j < N; j++)
X[j] = 0;
}
return;
}
K = get_pulses(K);

ALLOC(y, N, float);
ALLOC(iy, N, int);
ALLOC(signx, N, float);
N_1 = 512 / N;

sum = 0;
j = 0;
do
{
if (X[j] > 0)
signx[j] = 1;

Valin, et al.            Expires January 9, 2011              [Page 151]


Internet-Draft                 CELT codec                      July 2010

else
{
signx[j] = -1;
X[j] = -X[j];
}
iy[j] = 0;
y[j] = 0;
}
while (++j < N);

xy = yy = 0;

pulsesLeft = K;

/* Do a pre-search by projecting on the pyramid */
if (K > (N >> 1))
{
float           rcp;
j = 0;
do
{
sum += X[j];
}
while (++j < N);

if (sum <= 1e-15f)

{
X[0] = (1.f);
j = 1;
do
X[j] = 0;
while (++j < N);
sum = (1.f);
}
/* Do we have sufficient accuracy here? */
rcp = (((K - 1) * (celt_rcp(sum))));
j = 0;
do
{

iy[j] = floor(rcp * X[j]);

y[j] = (iy[j]);
yy = ((yy) + (y[j]) * (y[j]));
xy = ((xy) + (X[j]) * (y[j]));
y[j] *= 2;
pulsesLeft -= iy[j];

Valin, et al.            Expires January 9, 2011              [Page 152]


Internet-Draft                 CELT codec                      July 2010

}
while (++j < N);
}
celt_assert2(pulsesLeft >= 1,
"Allocated too many pulses in the quick pass");

while (pulsesLeft > 0)
{
int             pulsesAtOnce = 1;
int             best_id;
float           magnitude;
float           best_num = -1e15f;
float           best_den = 0;

/* Decide on how many pulses to find at once */
pulsesAtOnce = (pulsesLeft * N_1) >> 9;     /* pulsesLeft/N */
if (pulsesAtOnce < 1)
pulsesAtOnce = 1;

magnitude = (pulsesAtOnce);

best_id = 0;
/* The squared magnitude term gets added anyway, so we might as
well add it outside the loop */
yy = ((yy) + (magnitude) * (magnitude));
/* Choose between fast and accurate strategy depending on where
we are in the search */
/* This should ensure that anything we can process will have a
better score */
j = 0;
do
{
float           Rxy,
Ryy;
/* Select sign based on X[j] alone */
s = magnitude;
/* Temporary sums of the new pulse(s) */
Rxy = ((((xy) + (s) * (X[j]))));
/* We're multiplying y[j] by two so we don't have to do it
here */
Ryy = ((((yy) + (s) * (y[j]))));

/* Approximate score: we maximise Rxy/sqrt(Ryy) (we're
guaranteed that Rxy is positive because the sign is
pre-computed) */
Rxy = ((Rxy) * (Rxy));
/* The idea is to check for num/den >= best_num/best_den, but
that way we can do it without any division */

Valin, et al.            Expires January 9, 2011              [Page 153]


Internet-Draft                 CELT codec                      July 2010

/* OPT: Make sure to use conditional moves here */
if (((best_den) * (Rxy)) > ((Ryy) * (best_num)))
{
best_den = Ryy;
best_num = Rxy;
best_id = j;
}
}
while (++j < N);

j = best_id;
is = pulsesAtOnce;
s = (is);

/* Updating the sums of the new pulse(s) */
xy = xy + ((s) * (X[j]));
/* We're multiplying y[j] by two so we don't have to do it here */
yy = yy + ((s) * (y[j]));

/* Only now that we've made the final choice, update y/iy */
/* Multiplying y[j] by 2 so we don't have to do it everywhere
else */
y[j] += 2 * s;
iy[j] += is;
pulsesLeft -= pulsesAtOnce;
}
j = 0;
do
{
X[j] = ((signx[j]) * (X[j]));
if (signx[j] < 0)
iy[j] = -iy[j];
}
while (++j < N);
encode_pulses(iy, N, K, enc);

/* Recompute the gain in one pass to reduce the encoder-decoder
mismatch due to the recursive computation used in quantisation.
*/
if (resynth)
{
normalise_residual(iy, X, N, K, ((yy)));
}
RESTORE_STACK;
}

Valin, et al.            Expires January 9, 2011              [Page 154]


Internet-Draft                 CELT codec                      July 2010

/** Decode pulse vector and combine the result with the pitch vector to\
produce
the final normalised signal in the current band. */
void
alg_unquant(float *X, int N, int K, int spread, float *lowband,
ec_dec * dec)
{
int             i;
float           Ryy;
VARDECL(int, iy);
SAVE_STACK;
if (K == 0)
{
if (lowband != NULL)
{
for (i = 0; i < N; i++)
X[i] = lowband[i];
renormalise_vector(X, 1.0f, N, 1);
} else
{
/* This is important for encoding the side in stereo mode */
for (i = 0; i < N; i++)
X[i] = 0;
}
return;
}
K = get_pulses(K);
ALLOC(iy, N, int);
decode_pulses(iy, N, K, dec);
Ryy = 0;
i = 0;
do
{
Ryy = ((Ryy) + (iy[i]) * (iy[i]));
}
while (++i < N);
normalise_residual(iy, X, N, K, Ryy);
RESTORE_STACK;
}

float
renormalise_vector(float *X, float value, int N, int stride)
{
int             i;

float           E = 1e-15f;

Valin, et al.            Expires January 9, 2011              [Page 155]


Internet-Draft                 CELT codec                      July 2010

float           g;
float           t;
float          *xptr = X;
for (i = 0; i < N; i++)
{
E = ((E) + (*xptr) * (*xptr));
xptr += stride;
}

t = (E);
g = ((value) * (celt_rsqrt_norm(t)));

xptr = X;
for (i = 0; i < N; i++)
{
*xptr = ((((g) * (*xptr))));
xptr += stride;
}
return celt_sqrt(E);
}

A.13.  pitch.h

Foundation Written by Jean-Marc Valin */
/**
@file pitch.h
@brief Pitch analysis
*/

/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

Valin, et al.            Expires January 9, 2011              [Page 156]


Internet-Draft                 CELT codec                      July 2010

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef _PITCH_H
#define _PITCH_H

#include "modes.h"

void            pitch_downsample(const float *restrict x,
float *restrict x_lp, int len,
int end, int _C,
float *restrict xmem,
float *restrict filt_mem);

void            pitch_search(const CELTMode * m,
const float *restrict x_lp,
float *restrict y, int len,
int max_pitch, int *pitch, float *xmem,
int M);

#endif

A.14.  pitch.c

Foundation Written by Jean-Marc Valin */
/**
@file pitch.c
@brief Pitch analysis
*/

/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

Valin, et al.            Expires January 9, 2011              [Page 157]


Internet-Draft                 CELT codec                      July 2010

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "pitch.h"
#include "os_support.h"
#include "modes.h"
#include "stack_alloc.h"
#include "mathops.h"

void
find_best_pitch(float *xcorr, float maxcorr, float *y, int yshift,
int len, int max_pitch, int best_pitch[2])
{
int             i,
j;
float           Syy = 1;
float           best_num[2];
float           best_den[2];

best_num[0] = -1;
best_num[1] = -1;
best_den[0] = 0;

Valin, et al.            Expires January 9, 2011              [Page 158]


Internet-Draft                 CELT codec                      July 2010

best_den[1] = 0;
best_pitch[0] = 0;
best_pitch[1] = 1;
for (j = 0; j < len; j++)
Syy = ((Syy) + (y[j]) * (y[j]));
for (i = 0; i < max_pitch; i++)
{
float           score;
if (xcorr[i] > 0)
{
float           num;
float           xcorr16;
xcorr16 = ((xcorr[i]));
num = ((xcorr16) * (xcorr16));
score = num * 1. / Syy;
if (((num) * (best_den[1])) > ((best_num[1]) * (Syy)))
{
if (((num) * (best_den[0])) > ((best_num[0]) * (Syy)))
{
best_num[1] = best_num[0];
best_den[1] = best_den[0];
best_pitch[1] = best_pitch[0];
best_num[0] = num;
best_den[0] = Syy;
best_pitch[0] = i;
} else
{
best_num[1] = num;
best_den[1] = Syy;
best_pitch[1] = i;
}
}
}
Syy += (((y[i + len]) * (y[i + len]))) - (((y[i]) * (y[i])));
Syy = MAX32(1, Syy);
}
}

void
pitch_downsample(const float *restrict x, float *restrict x_lp,
int len, int end, int _C, float *restrict xmem,
float *restrict filt_mem)
{
int             i;
const int       C = CHANNELS(_C);
for (i = 1; i < len >> 1; i++)
x_lp[i] =
((.5f *

Valin, et al.            Expires January 9, 2011              [Page 159]


Internet-Draft                 CELT codec                      July 2010

((.5f * (x[(2 * i - 1) * C] + x[(2 * i + 1) * C])) +
x[2 * i * C])));
x_lp[0] = ((.5f * ((.5f * (*xmem + x[C])) + x[0])));
*xmem = x[end - C];
if (C == 2)
{
for (i = 1; i < len >> 1; i++)
x_lp[i] =
((.5f *
((.5f *
(x[(2 * i - 1) * C + 1] + x[(2 * i + 1) * C + 1])) +
x[2 * i * C + 1])));
x_lp[0] += ((.5f * ((.5f * (x[C + 1])) + x[1])));
*xmem += x[end - C + 1];
}
}

void
pitch_search(const CELTMode * m, const float *restrict x_lp,
float *restrict y, int len, int max_pitch, int *pitch,
float *xmem, int M)
{
int             i,
j;
const int       lag = MAX_PERIOD;
const int       N = M * m->eBands[m->nbEBands + 1];
int             best_pitch[2] = { 0 };
VARDECL(float, x_lp4);
VARDECL(float, y_lp4);
VARDECL(float, xcorr);
float           maxcorr = 1;
int             offset;
int             shift = 0;

SAVE_STACK;

ALLOC(x_lp4, len >> 2, float);
ALLOC(y_lp4, lag >> 2, float);
ALLOC(xcorr, max_pitch >> 1, float);

/* Downsample by 2 again */
for (j = 0; j < len >> 2; j++)
x_lp4[j] = x_lp[2 * j];
for (j = 0; j < lag >> 2; j++)
y_lp4[j] = y[2 * j];
/* Coarse search with 4x decimation */

for (i = 0; i < max_pitch >> 2; i++)

Valin, et al.            Expires January 9, 2011              [Page 160]


Internet-Draft                 CELT codec                      July 2010

{
float           sum = 0;
for (j = 0; j < len >> 2; j++)
sum = ((sum) + (x_lp4[j]) * (y_lp4[i + j]));
xcorr[i] = MAX32(-1, sum);
maxcorr = MAX32(maxcorr, sum);
}
find_best_pitch(xcorr, maxcorr, y_lp4, 0, len >> 2, max_pitch >> 2,
best_pitch);

/* Finer search with 2x decimation */
maxcorr = 1;
for (i = 0; i < max_pitch >> 1; i++)
{
float           sum = 0;
xcorr[i] = 0;
if (abs(i - 2 * best_pitch[0]) > 2
&& abs(i - 2 * best_pitch[1]) > 2)
continue;
for (j = 0; j < len >> 1; j++)
sum += (((x_lp[j]) * (y[i + j])));
xcorr[i] = MAX32(-1, sum);
maxcorr = MAX32(maxcorr, sum);
}
find_best_pitch(xcorr, maxcorr, y, shift, len >> 1, max_pitch >> 1,
best_pitch);

/* Refine by pseudo-interpolation */
if (best_pitch[0] > 0 && best_pitch[0] < (max_pitch >> 1) - 1)
{
float           a,
b,
c;
a = xcorr[best_pitch[0] - 1];
b = xcorr[best_pitch[0]];
c = xcorr[best_pitch[0] + 1];
if ((c - a) > (((.7f)) * (b - a)))
offset = 1;
else if ((a - c) > (((.7f)) * (b - c)))
offset = -1;
else
offset = 0;
} else
{
offset = 0;
}
*pitch = 2 * best_pitch[0] - offset;

Valin, et al.            Expires January 9, 2011              [Page 161]


Internet-Draft                 CELT codec                      July 2010

CELT_MOVE(y, y + (N >> 1), (lag - N) >> 1);
CELT_MOVE(y + ((lag - N) >> 1), x_lp, N >> 1);

RESTORE_STACK;

/* printf ("%d\n", *pitch); */
}

A.15.  rate.h

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef RATE_H
#define RATE_H

Valin, et al.            Expires January 9, 2011              [Page 162]


Internet-Draft                 CELT codec                      July 2010

#define MAX_PSEUDO 40
#define LOG_MAX_PSEUDO 6

#define MAX_PULSES 128
#define LOG_MAX_PULSES 7

#define BITRES 3
#define FINE_OFFSET 25
#define QTHETA_OFFSET 18

#define BITOVERFLOW 30000

#include "cwrs.h"

static inline int
get_pulses(int i)
{
return i < 8 ? i : (8 + (i & 7)) << ((i >> 3) - 1);
}

static inline int
bits2pulses(const CELTMode * m, const celt_int16 * cache, int N,
int bits)
{
int             i;
int             lo,
hi;

lo = 0;
hi = MAX_PSEUDO - 1;
for (i = 0; i < LOG_MAX_PSEUDO; i++)
{
int             mid = (lo + hi) >> 1;
/* OPT: Make sure this is implemented with a conditional move */
if (cache[mid] >= bits)
hi = mid;
else
lo = mid;
}
if (bits - cache[lo] <= cache[hi] - bits)
return lo;
else
return hi;

lo = 0;
hi = MAX_PULSES - 1;

#if 0                           /* Disabled until we can make that

Valin, et al.            Expires January 9, 2011              [Page 163]


Internet-Draft                 CELT codec                      July 2010

useful */
/* Use of more than MAX_PULSES is disabled until we are able to
cwrs that decently */
if (bits > cache[MAX_PULSES - 1] && N <= 4)
{
/* int pulses; pulses = 127; while (16 +
log2_frac(2*(pulses+1)*(pulses+1) + 1, BITRES) <= bits &&
pulses < 32767) pulses++; */
lo = 127;
switch (N)
{
case 3:
hi = 1024;
for (i = 0; i < 10; i++)
{
int             pulses = (lo + hi) >> 1;
if (log2_frac
(((((pulses) * (pulses)) >> 1) + 1) >> 1, BITRES) > bits)
hi = pulses;
else
lo = pulses;
}
break;
case 4:
hi = 1024;
for (i = 0; i < 10; i++)
{
int             pulses = (lo + hi) >> 1;
if (log2_frac
((((((pulses) * (pulses)) + 2) * (pulses))) / 3 << 3,
BITRES) > bits)
hi = pulses;
else
lo = pulses;
}
break;
}
return lo;
}
#endif
/* Instead of using the "bisection condition" we use a fixed
number of iterations because it should be faster */
/* while (hi-lo != 1) */
for (i = 0; i < LOG_MAX_PULSES; i++)
{
int             mid = (lo + hi) >> 1;
/* OPT: Make sure this is implemented with a conditional move */
if (cache[mid] >= bits)

Valin, et al.            Expires January 9, 2011              [Page 164]


Internet-Draft                 CELT codec                      July 2010

hi = mid;
else
lo = mid;
}
if (bits - cache[lo] <= cache[hi] - bits)
return lo;
else
return hi;
}

static inline int
pulses2bits(const celt_int16 * cache, int N, int pulses)
{
#if 0                           /* Use of more than MAX_PULSES is
disabled until we are able to
cwrs that decently */
if (pulses > 127)
{
int             bits;
switch (N)
{
case 3:
bits =
log2_frac(((((pulses) * (pulses)) >> 1) + 1) >> 1, BITRES);
break;
case 4:
bits =
log2_frac((((((pulses) * (pulses)) +
2) * (pulses))) / 3 << 3, BITRES);
break;
}
/* printf ("%d <- %d\n", bits, pulses); */
return bits;
}
#endif
return cache[pulses];
}

/** Computes a cache of the pulses->bits mapping in each band */
celt_int16    **compute_alloc_cache(CELTMode * m, int M);

/** Compute the pulse allocation, i.e. how many pulses will go in each
* band.
@param m mode
@param offsets Requested increase or decrease in the number of bits for
each band
@param total Number of bands
@param pulses Number of pulses per band (returned)

Valin, et al.            Expires January 9, 2011              [Page 165]


Internet-Draft                 CELT codec                      July 2010

*/
void            compute_allocation(const CELTMode * m, int start,
int *offsets, int total,
int *pulses, int *ebits,
int *fine_priority, int _C,
int M);

#endif

A.16.  rate.c

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

Valin, et al.            Expires January 9, 2011              [Page 166]


Internet-Draft                 CELT codec                      July 2010

#include <math.h>
#include "modes.h"
#include "cwrs.h"
#include "arch.h"
#include "os_support.h"

#include "entcode.h"
#include "rate.h"

celt_int16    **
compute_alloc_cache(CELTMode * m, int M)
{
int             i,
prevN;
int             error = 0;
celt_int16    **bits;
const celt_int16 *eBands = m->eBands;

bits = celt_alloc(m->nbEBands * sizeof(celt_int16 *));
if (bits == NULL)
return NULL;

prevN = -1;
for (i = 0; i < m->nbEBands; i++)
{
int             N;
if (M > 0)
N = M * (eBands[i + 1] - eBands[i]);
else
N = (eBands[i + 1] - eBands[i]) >> 1;
if (N == 0)
{
bits[i] = NULL;
continue;
}
if (N == prevN)
{
bits[i] = bits[i - 1];
} else
{
bits[i] = celt_alloc(MAX_PSEUDO * sizeof(celt_int16));
if (bits[i] != NULL)
{
int             j;
celt_int16      tmp[MAX_PULSES];
get_required_bits(tmp, N, MAX_PULSES, BITRES);
for (j = 0; j < MAX_PSEUDO; j++)
bits[i][j] = tmp[get_pulses(j)];

Valin, et al.            Expires January 9, 2011              [Page 167]


Internet-Draft                 CELT codec                      July 2010

} else
{
error = 1;
}
prevN = N;
}
}
if (error)
{
const celt_int16 *prevPtr = NULL;
if (bits != NULL)
{
for (i = 0; i < m->nbEBands; i++)
{
if (bits[i] != prevPtr && bits[i] != NULL)
{
prevPtr = bits[i];
celt_free((int *) bits[i]);
}
}
free(bits);
bits = NULL;
}
}
return bits;
}

static inline void
interp_bits2pulses(const CELTMode * m, int start, int *bits1,
int *bits2, int total, int *bits, int *ebits,
int *fine_priority, int len, int _C, int M)
{
int             psum;
int             lo,
hi;
int             j;
int             logM;
const int       C = CHANNELS(_C);
SAVE_STACK;

logM = log2_frac(M, BITRES);
lo = 0;
hi = 1 << BITRES;
while (hi - lo != 1)
{
int             mid = (lo + hi) >> 1;
psum = 0;
for (j = start; j < len; j++)

Valin, et al.            Expires January 9, 2011              [Page 168]


Internet-Draft                 CELT codec                      July 2010

psum +=
(((1 << BITRES) - mid) * bits1[j] +
mid * bits2[j]) >> BITRES;
if (psum > (total << BITRES))
hi = mid;
else
lo = mid;
}
psum = 0;
/* printf ("interp bisection gave %d\n", lo); */
for (j = start; j < len; j++)
{
bits[j] =
(((1 << BITRES) - lo) * bits1[j] + lo * bits2[j]) >> BITRES;
psum += bits[j];
}
/* Allocate the remaining bits */
{
int             left,
perband;
left = (total << BITRES) - psum;
perband = left / (len - start);
for (j = start; j < len; j++)
bits[j] += perband;
left = left - len * perband;
for (j = start; j < start + left; j++)
bits[j]++;
}
for (j = start; j < len; j++)
{
int             N,
d;
int             offset;

N = M * (m->eBands[j + 1] - m->eBands[j]);
/* Compensate for the extra DoF in stereo */
d = (C * N + ((C == 2 && N > 2) ? 1 : 0)) << BITRES;
offset = FINE_OFFSET - m->logN[j] - logM;
/* Offset for the number of fine bits compared to their "fair
share" of total/N */
offset = bits[j] - offset * N * C;
/* Compensate for the prediction gain in stereo */
if (C == 2)
offset -= 1 << BITRES;
if (offset < 0)
offset = 0;
ebits[j] = (2 * offset + d) / (2 * d);
fine_priority[j] = ebits[j] * d >= offset;

Valin, et al.            Expires January 9, 2011              [Page 169]


Internet-Draft                 CELT codec                      July 2010

if (N == 1)
ebits[j] = (bits[j] / C >> BITRES) - 1;
/* Make sure not to bust */
if (C * ebits[j] > (bits[j] >> BITRES))
ebits[j] = bits[j] / C >> BITRES;

if (ebits[j] > 7)
ebits[j] = 7;
/* The bits used for fine allocation can't be used for pulses */
bits[j] -= C * ebits[j] << BITRES;
if (bits[j] < 0)
bits[j] = 0;
}
RESTORE_STACK;
}

void
compute_allocation(const CELTMode * m, int start, int *offsets,
int total, int *pulses, int *ebits,
int *fine_priority, int _C, int M)
{
int             lo,
hi,
len,
j;
const int       C = CHANNELS(_C);
VARDECL(int, bits1);
VARDECL(int, bits2);
SAVE_STACK;

len = m->nbEBands;
ALLOC(bits1, len, int);
ALLOC(bits2, len, int);

lo = 0;
hi = m->nbAllocVectors - 1;
while (hi - lo != 1)
{
int             psum = 0;
int             mid = (lo + hi) >> 1;
for (j = start; j < len; j++)
{
int             N = m->eBands[j + 1] - m->eBands[j];
bits1[j] =
(C * M * N * m->allocVectors[mid * len + j] + offsets[j]);
if (bits1[j] < 0)
bits1[j] = 0;
psum += bits1[j];

Valin, et al.            Expires January 9, 2011              [Page 170]


Internet-Draft                 CELT codec                      July 2010

/* printf ("%d ", bits[j]); */
}
/* printf ("\n"); */
if (psum > (total << BITRES))
hi = mid;
else
lo = mid;
/* printf ("lo = %d, hi = %d\n", lo, hi); */
}
/* printf ("interp between %d and %d\n", lo, hi); */
for (j = start; j < len; j++)
{
int             N = m->eBands[j + 1] - m->eBands[j];
bits1[j] =
C * M * N * m->allocVectors[lo * len + j] + offsets[j];
bits2[j] =
C * M * N * m->allocVectors[hi * len + j] + offsets[j];
if (bits1[j] < 0)
bits1[j] = 0;
if (bits2[j] < 0)
bits2[j] = 0;
}
interp_bits2pulses(m, start, bits1, bits2, total, pulses, ebits,
fine_priority, len, C, M);
RESTORE_STACK;
}

A.17.  plc.h

/* Copyright (c) 2009-2010 Xiph.Org Foundation Written by Jean-Marc
Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written

Valin, et al.            Expires January 9, 2011              [Page 171]


Internet-Draft                 CELT codec                      July 2010

permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef PLC_H
#define PLC_H

#include "arch.h"

#define LPC_ORDER 24

void            _celt_lpc(float *_lpc, const float *ac, int p);

void            fir(const float *x,
const float *num,
float *y, int N, int ord, float *mem);

void            iir(const float *x,
const float *den,
float *y, int N, int ord, float *mem);

void            _celt_autocorr(const float *x, float *ac,
const float *window, int overlap,
int lag, int n);

#endif                          /* PLC_H */

A.18.  plc.c

/* Copyright (c) 2009-2010 Xiph.Org Foundation Written by Jean-Marc
Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

Valin, et al.            Expires January 9, 2011              [Page 172]


Internet-Draft                 CELT codec                      July 2010

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "plc.h"
#include "stack_alloc.h"
#include "mathops.h"

void
_celt_lpc(float *_lpc,          /* out: [0...p-1] LPC coefficients */
const float *ac,      /* in: [0...p] autocorrelation
values */
int p)
{
int             i,
j;
float           r;
float           error = ac[0];

float          *lpc = _lpc;

for (i = 0; i < p; i++)
lpc[i] = 0;

Valin, et al.            Expires January 9, 2011              [Page 173]


Internet-Draft                 CELT codec                      July 2010

if (ac[0] != 0)
{
for (i = 0; i < p; i++)
{
/* Sum up this iteration's reflection coefficient */
float           rr = 0;
for (j = 0; j < i; j++)
rr += ((lpc[j]) * (ac[i - j]));
rr += (ac[i + 1]);
r = -frac_div32((rr), error);
/* Update LPC coefficients and total error */
lpc[i] = (r);
for (j = 0; j < (i + 1) >> 1; j++)
{
float           tmp1,
tmp2;
tmp1 = lpc[j];
tmp2 = lpc[i - 1 - j];
lpc[j] = tmp1 + ((r) * (tmp2));
lpc[i - 1 - j] = tmp2 + ((r) * (tmp1));
}

error = error - ((((r) * (r))) * (error));
/* Bail out once we get 30 dB gain */

if (error < .001 * ac[0])
break;

}
}

}

void
fir(const float *x,
const float *num, float *y, int N, int ord, float *mem)
{
int             i,
j;

for (i = 0; i < N; i++)
{
float           sum = ((x[i]));
for (j = 0; j < ord; j++)
{
sum += ((num[j]) * (mem[j]));
}
for (j = ord - 1; j >= 1; j--)

Valin, et al.            Expires January 9, 2011              [Page 174]


Internet-Draft                 CELT codec                      July 2010

{
mem[j] = mem[j - 1];
}
mem[0] = x[i];
y[i] = (sum);
}
}

void
iir(const float *x,
const float *den, float *y, int N, int ord, float *mem)
{
int             i,
j;
for (i = 0; i < N; i++)
{
float           sum = x[i];
for (j = 0; j < ord; j++)
{
sum -= ((den[j]) * (mem[j]));
}
for (j = ord - 1; j >= 1; j--)
{
mem[j] = mem[j - 1];
}
mem[0] = (sum);
y[i] = sum;
}
}

void
_celt_autocorr(const float *x,  /* in: [0...n-1] samples x */
float *ac,       /* out: [0...lag-1] ac values */
const float *window, int overlap, int lag, int n)
{
float           d;
int             i;
VARDECL(float, xx);
SAVE_STACK;
ALLOC(xx, n, float);
for (i = 0; i < n; i++)
xx[i] = x[i];
for (i = 0; i < overlap; i++)
{
xx[i] = ((x[i]) * (window[i]));
xx[n - i - 1] = ((x[n - i - 1]) * (window[i]));
}
while (lag >= 0)

Valin, et al.            Expires January 9, 2011              [Page 175]


Internet-Draft                 CELT codec                      July 2010

{
for (i = lag, d = 0; i < n; i++)
d += xx[i] * xx[i - lag];
ac[lag] = d;
/* printf ("%f ", ac[lag]); */
lag--;
}
/* printf ("\n"); */
ac[0] += 10;

RESTORE_STACK;
}

A.19.  mdct.h

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY

Valin, et al.            Expires January 9, 2011              [Page 176]


Internet-Draft                 CELT codec                      July 2010

OF SUCH DAMAGE. */

/* This is a simple MDCT implementation that uses a N/4 complex FFT
to do most of the work. It should be relatively straightforward
to plug in pretty much and FFT here.

This replaces the Vorbis FFT (and uses the exact same API), which
was a bit too messy and that was ending up duplicating code
(might as well use the same FFT everywhere).

The algorithm is similar to (and inspired from) Fabrice Bellard's
MDCT implementation in FFMPEG, but has differences in signs,
ordering and scaling in many places. */

#ifndef MDCT_H
#define MDCT_H

#include "kiss_fft.h"
#include "arch.h"

typedef struct {
int             n;
int             maxshift;
kiss_fft_cfg   *kfft;
kiss_twiddle_scalar *restrict trig;
} mdct_lookup;

void            clt_mdct_init(mdct_lookup * l, int N, int maxshift);
void            clt_mdct_clear(mdct_lookup * l);

/** Compute a forward MDCT and scale by 4/N */
void            clt_mdct_forward(const mdct_lookup * l,
kiss_fft_scalar * in,
kiss_fft_scalar * out,
const float *window, int overlap,
int shift);

/** Compute a backward MDCT (no scaling) and performs weighted overlap-\
(scales implicitly by 1/2) */
void            clt_mdct_backward(const mdct_lookup * l,
kiss_fft_scalar * in,
kiss_fft_scalar * out,
const float *restrict window,
int overlap, int shift);

#endif

Valin, et al.            Expires January 9, 2011              [Page 177]


Internet-Draft                 CELT codec                      July 2010

A.20.  mdct.c

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

/* This is a simple MDCT implementation that uses a N/4 complex FFT
to do most of the work. It should be relatively straightforward
to plug in pretty much and FFT here.

This replaces the Vorbis FFT (and uses the exact same API), which
was a bit too messy and that was ending up duplicating code
(might as well use the same FFT everywhere).

The algorithm is similar to (and inspired from) Fabrice Bellard's
MDCT implementation in FFMPEG, but has differences in signs,
ordering and scaling in many places. */

Valin, et al.            Expires January 9, 2011              [Page 178]


Internet-Draft                 CELT codec                      July 2010

#include "config.h"

#include "mdct.h"
#include "kfft_double.h"
#include <math.h>
#include "os_support.h"
#include "mathops.h"
#include "stack_alloc.h"

#define M_PI 3.141592653

void
clt_mdct_init(mdct_lookup * l, int N, int maxshift)
{
int             i;
int             N2,
N4;
l->n = N;
N2 = N >> 1;
N4 = N >> 2;
l->kfft = celt_alloc(sizeof(kiss_fft_cfg) * (maxshift + 1));
l->maxshift = maxshift;
for (i = 0; i <= maxshift; i++)
{
l->kfft[i] = cpx32_fft_alloc(N >> 2 >> i);

if (l->kfft[i] == NULL)
return;

}
l->trig =
(kiss_twiddle_scalar *) celt_alloc((N4 + 1) *
sizeof
(kiss_twiddle_scalar));
if (l->trig == NULL)
return;
/* We have enough points that sine isn't necessary */
for (i = 0; i <= N4; i++)
l->trig[i] = cos(2 * M_PI * i / N);

}

void
clt_mdct_clear(mdct_lookup * l)
{
int             i;
for (i = 0; i <= l->maxshift; i++)
cpx32_fft_free(l->kfft[i]);

Valin, et al.            Expires January 9, 2011              [Page 179]


Internet-Draft                 CELT codec                      July 2010

celt_free(l->kfft);
celt_free(l->trig);
}

void
clt_mdct_forward(const mdct_lookup * l, kiss_fft_scalar * in,
kiss_fft_scalar * restrict out, const float *window,
int overlap, int shift)
{
int             i;
int             N,
N2,
N4;
kiss_twiddle_scalar sine;
VARDECL(kiss_fft_scalar, f);
SAVE_STACK;
N = l->n;
N >>= shift;
N2 = N >> 1;
N4 = N >> 2;
ALLOC(f, N2, kiss_fft_scalar);
/* sin(x) ~= x here */

sine = 2 * M_PI * (.125f) / N;

/* Consider the input to be composed of four blocks: [a, b, c, d] */
/* Window, shuffle, fold */
{
/* Temp pointers to make it really clear to the compiler what
we're doing */
const kiss_fft_scalar *restrict xp1 = in + (overlap >> 1);
const kiss_fft_scalar *restrict xp2 =
in + N2 - 1 + (overlap >> 1);
kiss_fft_scalar *restrict yp = out;
const float    *restrict wp1 = window + (overlap >> 1);
const float    *restrict wp2 = window + (overlap >> 1) - 1;
for (i = 0; i < (overlap >> 2); i++)
{
/* Real part arranged as -d-cR, Imag part arranged as -b+aR */
*yp++ = ((*wp2) * (xp1[N2])) + ((*wp1) * (*xp2));
*yp++ = ((*wp1) * (*xp1)) - ((*wp2) * (xp2[-N2]));
xp1 += 2;
xp2 -= 2;
wp1 += 2;
wp2 -= 2;
}
wp1 = window;
wp2 = window + overlap - 1;

Valin, et al.            Expires January 9, 2011              [Page 180]


Internet-Draft                 CELT codec                      July 2010

for (; i < N4 - (overlap >> 2); i++)
{
/* Real part arranged as a-bR, Imag part arranged as -c-dR */
*yp++ = *xp2;
*yp++ = *xp1;
xp1 += 2;
xp2 -= 2;
}
for (; i < N4; i++)
{
/* Real part arranged as a-bR, Imag part arranged as -c-dR */
*yp++ = -((*wp1) * (xp1[-N2])) + ((*wp2) * (*xp2));
*yp++ = ((*wp2) * (*xp1)) + ((*wp1) * (xp2[N2]));
xp1 += 2;
xp2 -= 2;
wp1 += 2;
wp2 -= 2;
}
}
/* Pre-rotation */
{
kiss_fft_scalar *restrict yp = out;
kiss_fft_scalar *t = &l->trig[0];
for (i = 0; i < N4; i++)
{
kiss_fft_scalar re,
im,
yr,
yi;
re = yp[0];
im = yp[1];
yr = -S_MUL(re, t[i << shift]) - S_MUL(im,
t[(N4 - i) << shift]);
yi = -S_MUL(im, t[i << shift]) + S_MUL(re,
t[(N4 - i) << shift]);
/* works because the cos is nearly one */
*yp++ = yr + S_MUL(yi, sine);
*yp++ = yi - S_MUL(yr, sine);
}
}

/* N/4 complex FFT, down-scales by 4/N */
cpx32_fft(l->kfft[shift], out, f, N4);

/* Post-rotate */
{
/* Temp pointers to make it really clear to the compiler what
we're doing */

Valin, et al.            Expires January 9, 2011              [Page 181]


Internet-Draft                 CELT codec                      July 2010

const kiss_fft_scalar *restrict fp = f;
kiss_fft_scalar *restrict yp1 = out;
kiss_fft_scalar *restrict yp2 = out + N2 - 1;
kiss_fft_scalar *t = &l->trig[0];
/* Temp pointers to make it really clear to the compiler what
we're doing */
for (i = 0; i < N4; i++)
{
kiss_fft_scalar yr,
yi;
yr = S_MUL(fp[1], t[(N4 - i) << shift]) + S_MUL(fp[0],
t[i << shift]);
yi = S_MUL(fp[0], t[(N4 - i) << shift]) - S_MUL(fp[1],
t[i << shift]);
/* works because the cos is nearly one */
*yp1 = yr - S_MUL(yi, sine);
*yp2 = yi + S_MUL(yr, sine);;
fp += 2;
yp1 += 2;
yp2 -= 2;
}
}
RESTORE_STACK;
}

void
clt_mdct_backward(const mdct_lookup * l, kiss_fft_scalar * in,
kiss_fft_scalar * restrict out,
const float *restrict window, int overlap,
int shift)
{
int             i;
int             N,
N2,
N4;
kiss_twiddle_scalar sine;
VARDECL(kiss_fft_scalar, f);
VARDECL(kiss_fft_scalar, f2);
SAVE_STACK;
N = l->n;
N >>= shift;
N2 = N >> 1;
N4 = N >> 2;
ALLOC(f, N2, kiss_fft_scalar);
ALLOC(f2, N2, kiss_fft_scalar);
/* sin(x) ~= x here */

sine = 2 * M_PI * (.125f) / N;

Valin, et al.            Expires January 9, 2011              [Page 182]


Internet-Draft                 CELT codec                      July 2010

/* Pre-rotate */
{
/* Temp pointers to make it really clear to the compiler what
we're doing */
const kiss_fft_scalar *restrict xp1 = in;
const kiss_fft_scalar *restrict xp2 = in + N2 - 1;
kiss_fft_scalar *restrict yp = f2;
kiss_fft_scalar *t = &l->trig[0];
for (i = 0; i < N4; i++)
{
kiss_fft_scalar yr,
yi;
yr = -S_MUL(*xp2, t[i << shift]) + S_MUL(*xp1,
t[(N4 - i) << shift]);
yi = -S_MUL(*xp2, t[(N4 - i) << shift]) - S_MUL(*xp1,
t[i << shift]);
/* works because the cos is nearly one */
*yp++ = yr - S_MUL(yi, sine);
*yp++ = yi + S_MUL(yr, sine);
xp1 += 2;
xp2 -= 2;
}
}

/* Inverse N/4 complex FFT. This one should *not* downscale even
in fixed-point */
cpx32_ifft(l->kfft[shift], f2, f, N4);

/* Post-rotate */
{
kiss_fft_scalar *restrict fp = f;
kiss_fft_scalar *t = &l->trig[0];

for (i = 0; i < N4; i++)
{
kiss_fft_scalar re,
im,
yr,
yi;
re = fp[0];
im = fp[1];
/* We'd scale up by 2 here, but instead it's done when mixing
the windows */
yr = S_MUL(re, t[i << shift]) - S_MUL(im,
t[(N4 - i) << shift]);
yi = S_MUL(im, t[i << shift]) + S_MUL(re,
t[(N4 - i) << shift]);
/* works because the cos is nearly one */

Valin, et al.            Expires January 9, 2011              [Page 183]


Internet-Draft                 CELT codec                      July 2010

*fp++ = yr - S_MUL(yi, sine);
*fp++ = yi + S_MUL(yr, sine);
}
}
/* De-shuffle the components for the middle of the window only */
{
const kiss_fft_scalar *restrict fp1 = f;
const kiss_fft_scalar *restrict fp2 = f + N2 - 1;
kiss_fft_scalar *restrict yp = f2;
for (i = 0; i < N4; i++)
{
*yp++ = -*fp1;
*yp++ = *fp2;
fp1 += 2;
fp2 -= 2;
}
}

/* Mirror on both sides for TDAC */
{
kiss_fft_scalar *restrict fp1 = f2 + N4 - 1;
kiss_fft_scalar *restrict xp1 = out + N2 - 1;
kiss_fft_scalar *restrict yp1 = out + N4 - overlap / 2;
const float    *restrict wp1 = window;
const float    *restrict wp2 = window + overlap - 1;
for (i = 0; i < N4 - overlap / 2; i++)
{
*xp1 = *fp1;
xp1--;
fp1--;
}
for (; i < N4; i++)
{
kiss_fft_scalar x1;
x1 = *fp1--;
*yp1++ += -((*wp1) * (x1));
*xp1-- += ((*wp2) * (x1));
wp1++;
wp2--;
}
}
{
kiss_fft_scalar *restrict fp2 = f2 + N4;
kiss_fft_scalar *restrict xp2 = out + N2;
kiss_fft_scalar *restrict yp2 = out + N - 1 - (N4 - overlap / 2);
const float    *restrict wp1 = window;
const float    *restrict wp2 = window + overlap - 1;
for (i = 0; i < N4 - overlap / 2; i++)

Valin, et al.            Expires January 9, 2011              [Page 184]


Internet-Draft                 CELT codec                      July 2010

{
*xp2 = *fp2;
xp2++;
fp2++;
}
for (; i < N4; i++)
{
kiss_fft_scalar x2;
x2 = *fp2++;
*yp2-- = ((*wp1) * (x2));
*xp2++ = ((*wp2) * (x2));
wp1++;
wp2--;
}
}
RESTORE_STACK;
}

A.21.  ecintrin.h

Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,

Valin, et al.            Expires January 9, 2011              [Page 185]


Internet-Draft                 CELT codec                      July 2010

PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

/* Some common macros for potential platform-specific optimization. */
#include <math.h>
#include <limits.h>
#if !defined(_ecintrin_H)
# define _ecintrin_H (1)

/* Some specific platforms may have optimized intrinsic or inline
assembly versions of these functions which can substantially
improve performance. We define macros for them to allow easy
incorporation of these non-ANSI features. */

/* Note that we do not provide a macro for abs(), because it is
provided as a library function, which we assume is translated
into an intrinsic to avoid the function call overhead and then
implemented in the smartest way for the target platform. With
modern gcc (4.x), this is true: it uses cmov instructions if the
architecture supports it and branchless bit-twiddling if it does
not (the speed difference between the two approaches is not
measurable). Interestingly, the bit-twiddling method was patented
in 2000 (US 6,073,150) by Sun Microsystems, despite prior art
dating back to at least 1996:
http://web.archive.org/web/19961201174141/www.x86.org/ftp/articles/p\
entopt/PENTOPT.TXT
On gcc 3.x, however, our assumption is not true, as abs() is transla\
ted to a
conditional jump, which is horrible on deeply piplined architectures\
(e.g., all
consumer architectures for the past decade or more) when the sign ca\
nnot be reliably
predicted. */

/* Modern gcc (4.x) can compile the naive versions of min and max
with cmov if given an appropriate architecture, but the
branchless bit-twiddling versions are just as fast, and do not
require any special target architecture. Earlier gcc versions
(3.x) compiled both code to the same assembly instructions,
because of the way they represented ((_b)>(_a)) internally. */
#define EC_MAXI(_a,_b)      ((_a)-((_a)-(_b)&-((_b)>(_a))))
#define EC_MINI(_a,_b)      ((_a)+((_b)-(_a)&-((_b)<(_a))))
/* This has a chance of compiling branchless, and is just as fast as
the bit-twiddling method, which is slightly less portable, since

Valin, et al.            Expires January 9, 2011              [Page 186]


Internet-Draft                 CELT codec                      July 2010

it relies on a sign-extended rightshift, which is not guaranteed
by ANSI (but present on every relevant platform). */
#define EC_SIGNI(_a)        (((_a)>0)-((_a)<0))
/* Slightly more portable than relying on a sign-extended
right-shift (which is not guaranteed by ANSI), and just as fast,
since gcc (3.x and 4.x both) compile it into the right-shift
anyway. */
/* Clamps an integer into the given range. If _a>_c, then the lower
bound _a is respected over the upper bound _c (this behavior is
required to meet our documented API behavior). _a: The lower
bound. _b: The value to clamp. _c: The upper boud. */
#define EC_CLAMPI(_a,_b,_c) (EC_MAXI(_a,EC_MINI(_b,_c)))

/* Count leading zeros. This macro should only be used for
implementing ec_ilog(), if it is defined. All other code should
#ifdef __GNUC_PREREQ
#if __GNUC_PREREQ(3,4)
# if INT_MAX>=2147483647
#  define EC_CLZ0 sizeof(unsigned)*CHAR_BIT
#  define EC_CLZ(_x) (__builtin_clz(_x))
# elif LONG_MAX>=2147483647L
#  define EC_CLZ0 sizeof(unsigned long)*CHAR_BIT
#  define EC_CLZ(_x) (__builtin_clzl(_x))
# endif
#endif
#endif

#if defined(EC_CLZ)
/* Note that __builtin_clz is not defined when _x==0, according to
the gcc documentation (and that of the BSR instruction that
implements it on x86). The majority of the time we can never pass
it zero. When we need to, it can be special cased. */
# define EC_ILOG(_x) (EC_CLZ0-EC_CLZ(_x))
#elif defined(ENABLE_TI_DSPLIB)
#include "dsplib.h"
#define EC_ILOG(x) (31 - _lnorm(x))
#else
# define EC_ILOG(_x) (ec_ilog(_x))
#endif

#endif

Valin, et al.            Expires January 9, 2011              [Page 187]


Internet-Draft                 CELT codec                      July 2010

A.22.  entcode.h

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "celt_types.h"

#if !defined(_entcode_H)
# define _entcode_H (1)
# include <limits.h>
# include "ecintrin.h"

typedef celt_int32 ec_int32;
typedef celt_uint32 ec_uint32;
typedef struct ec_byte_buffer ec_byte_buffer;

Valin, et al.            Expires January 9, 2011              [Page 188]


Internet-Draft                 CELT codec                      July 2010

/* The number of bits to code at a time when coding bits directly. */
# define EC_UNIT_BITS  (8)
/* The mask for the given bits. */

/* Simple libogg1-style buffer. */
struct ec_byte_buffer {
unsigned char  *buf;
unsigned char  *ptr;
unsigned char  *end_ptr;
long            storage;
};

/* Encoding functions. */
void            ec_byte_writeinit_buffer(ec_byte_buffer * _b,
unsigned char *_buf,
long _size);
void            ec_byte_shrink(ec_byte_buffer * _b, long _size);
void            ec_byte_writeinit(ec_byte_buffer * _b);
void            ec_byte_writetrunc(ec_byte_buffer * _b, long _bytes);
void            ec_byte_write1(ec_byte_buffer * _b, unsigned _value);
void            ec_byte_write_at_end(ec_byte_buffer * _b,
unsigned _value);
void            ec_byte_write4(ec_byte_buffer * _b,
ec_uint32 _value);
void            ec_byte_writecopy(ec_byte_buffer * _b, void *_source,
long _bytes);
void            ec_byte_writeclear(ec_byte_buffer * _b);
/* Decoding functions. */
unsigned char *_buf, long _bytes);
int             ec_byte_look1(ec_byte_buffer * _b);
unsigned char   ec_byte_look_at_end(ec_byte_buffer * _b);
int             ec_byte_look4(ec_byte_buffer * _b, ec_uint32 * _val);
int             ec_byte_read4(ec_byte_buffer * _b, ec_uint32 * _val);
/* Shared functions. */
static inline void
ec_byte_reset(ec_byte_buffer * _b)
{
_b->ptr = _b->buf;
}

static inline long
ec_byte_bytes(ec_byte_buffer * _b)
{

Valin, et al.            Expires January 9, 2011              [Page 189]


Internet-Draft                 CELT codec                      July 2010

return _b->ptr - _b->buf;
}

static inline unsigned char *
ec_byte_get_buffer(ec_byte_buffer * _b)
{
return _b->buf;
}

int             ec_ilog(ec_uint32 _v);

#endif

A.23.  entcode.c

/* Copyright (c) 2001-2008 Timothy B. Terriberry */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

Valin, et al.            Expires January 9, 2011              [Page 190]


Internet-Draft                 CELT codec                      July 2010

#include "config.h"

#include "entcode.h"

int
ec_ilog(ec_uint32 _v)
{

/* On a Pentium M, this branchless version tested as the fastest
on 1,000,000,000 random 32-bit integers, edging out a similar
version with branches, and a 256-entry LUT version. */
int             ret;
int             m;
ret = !!_v;
m = !!(_v & 0xFFFF0000) << 4;
_v >>= m;
ret |= m;
m = !!(_v & 0xFF00) << 3;
_v >>= m;
ret |= m;
m = !!(_v & 0xF0) << 2;
_v >>= m;
ret |= m;
m = !!(_v & 0xC) << 1;
_v >>= m;
ret |= m;
ret += !!(_v & 0x2);
return ret;

}

A.24.  entenc.h

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

Valin, et al.            Expires January 9, 2011              [Page 191]


Internet-Draft                 CELT codec                      July 2010

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#if !defined(_entenc_H)
# define _entenc_H (1)
# include <stddef.h>
# include "entcode.h"

typedef struct ec_enc ec_enc;

/* The entropy encoder. */
struct ec_enc {
/* Buffered output. */
ec_byte_buffer *buf;
/* A buffered output symbol, awaiting carry propagation. */
int             rem;
/* Number of extra carry propagating symbols. */
size_t          ext;
/* The number of values in the current range. */
ec_uint32       rng;
/* The low end of the current range (inclusive). */
ec_uint32       low;
/* Byte that will be written at the end */
unsigned char   end_byte;
/* Number of valid bits in end_byte */
int             end_bits_left;
int             nb_end_bits;
};

/* Initializes the encoder. _buf: The buffer to store output bytes
in. This must have already been initialized for writing and
reset. */

Valin, et al.            Expires January 9, 2011              [Page 192]


Internet-Draft                 CELT codec                      July 2010

void            ec_enc_init(ec_enc * _this, ec_byte_buffer * _buf);
/* Encodes a symbol given its frequency information. The frequency
information must be discernable by the decoder, assuming it has
read only the previous symbols from the stream. It is allowable
to change the frequency information, or even the entire source
alphabet, so long as the decoder can tell from the context of the
previously encoded information that it is supposed to do so as
well. _fl: The cumulative frequency of all symbols that come
before the one to be encoded. _fh: The cumulative frequency of all
symbols up to and including the one to be encoded. Together with
_fl, this defines the range [_fl,_fh) in which the decoded value
will fall. _ft: The sum of the frequencies of all the symbols */
void            ec_encode(ec_enc * _this, unsigned _fl, unsigned _fh,
unsigned _ft);
void            ec_encode_bin(ec_enc * _this, unsigned _fl,
unsigned _fh, unsigned _bits);
void            ec_encode_raw(ec_enc * _this, unsigned _fl,
unsigned _fh, unsigned bits);
/* Encodes a sequence of raw bits in the stream. _fl: The bits to
encode. _ftb: The number of bits to encode. This must be at least
one, and no more than 32. */
void            ec_enc_bits(ec_enc * _this, ec_uint32 _fl, int _ftb);
/* Encodes a raw unsigned integer in the stream. _fl: The integer to
encode. _ft: The number of integers that can be encoded (one more
than the max). This must be at least one, and no more than
2**32-1. */
void            ec_enc_uint(ec_enc * _this, ec_uint32 _fl,
ec_uint32 _ft);

/* Encode a bit that has a _prob/65536 probability of being a one */
void            ec_enc_bit_prob(ec_enc * _this, int val,
unsigned _prob);

/* Returns the number of bits "used" by the encoded symbols so far.
This same number can be computed by the decoder, and is suitable
for making coding decisions. _b: The number of extra bits of
precision to include. At most 16 will be accurate. Return: The
number of bits scaled by 2**_b. This will always be slightly
larger than the exact value (e.g., all rounding error is in the
positive direction). */
long            ec_enc_tell(ec_enc * _this, int _b);

/* Indicates that there are no more symbols to encode. All reamining
output bytes are flushed to the output buffer. ec_enc_init() must
be called before the encoder can be used again. */
void            ec_enc_done(ec_enc * _this);

#endif

Valin, et al.            Expires January 9, 2011              [Page 193]


Internet-Draft                 CELT codec                      July 2010

A.25.  entenc.c

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "os_support.h"
#include "entenc.h"
#include "arch.h"

void
ec_byte_writeinit_buffer(ec_byte_buffer * _b, unsigned char *_buf,
long _size)
{
_b->ptr = _b->buf = _buf;

Valin, et al.            Expires January 9, 2011              [Page 194]


Internet-Draft                 CELT codec                      July 2010

_b->end_ptr = _b->buf + _size - 1;
_b->storage = _size;
}

void
ec_byte_shrink(ec_byte_buffer * _b, long _size)
{
_b->end_ptr = _b->buf + _size - 1;
_b->storage = _size;
}

void
ec_byte_write1(ec_byte_buffer * _b, unsigned _value)
{
ptrdiff_t       endbyte;
endbyte = _b->ptr - _b->buf;
if (endbyte >= _b->storage)
{
celt_fatal("range encoder overflow\n");
}
*(_b->ptr++) = (unsigned char) _value;
}

void
ec_byte_write_at_end(ec_byte_buffer * _b, unsigned _value)
{
if (_b->end_ptr < _b->ptr)
{
celt_fatal("byte buffer collision");
}
*(_b->end_ptr--) = (unsigned char) _value;
}

void
ec_enc_bits(ec_enc * _this, ec_uint32 _fl, int _ftb)
{
unsigned        fl;
unsigned        ft;
while (_ftb > EC_UNIT_BITS)
{
_ftb -= EC_UNIT_BITS;
fl = (unsigned) (_fl >> _ftb) & EC_UNIT_MASK;
ec_encode_raw(_this, fl, fl + 1, EC_UNIT_BITS);
}
ft = 1 << _ftb;
fl = (unsigned) _fl & ft - 1;
ec_encode_raw(_this, fl, fl + 1, _ftb);
}

Valin, et al.            Expires January 9, 2011              [Page 195]


Internet-Draft                 CELT codec                      July 2010

void
ec_enc_uint(ec_enc * _this, ec_uint32 _fl, ec_uint32 _ft)
{
unsigned        ft;
unsigned        fl;
int             ftb;
/* In order to optimize EC_ILOG(), it is undefined for the value
0. */
celt_assert(_ft > 1);
_ft--;
ftb = EC_ILOG(_ft);
if (ftb > EC_UNIT_BITS)
{
ftb -= EC_UNIT_BITS;
ft = (_ft >> ftb) + 1;
fl = (unsigned) (_fl >> ftb);
ec_encode(_this, fl, fl + 1, ft);
ec_enc_bits(_this, _fl, ftb);
} else
{
ec_encode(_this, _fl, _fl + 1, _ft + 1);
}
}

A.26.  entdec.h

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND

Valin, et al.            Expires January 9, 2011              [Page 196]


Internet-Draft                 CELT codec                      July 2010

CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#if !defined(_entdec_H)
# define _entdec_H (1)
# include "entcode.h"

typedef struct ec_dec ec_dec;

/* The entropy decoder. */
struct ec_dec {
/* The buffer to decode. */
ec_byte_buffer *buf;
/* The remainder of a buffered input symbol. */
int             rem;
/* The number of values in the current range. */
ec_uint32       rng;
/* The difference between the top of the current range and the
input value. */
ec_uint32       dif;
/* Normalization factor. */
ec_uint32       nrm;
/* Byte that will be written at the end */
unsigned char   end_byte;
/* Number of valid bits in end_byte */
int             end_bits_left;
int             nb_end_bits;
};

/* Initializes the decoder. _buf: The input buffer to use. Return: 0
on success, or a negative value on error. */
void            ec_dec_init(ec_dec * _this, ec_byte_buffer * _buf);
/* Calculates the cumulative frequency for the next symbol. This can
then be fed into the probability model to determine what that
symbol is, and the additional frequency information required to
advance to the next symbol. This function cannot be called more
than once without a corresponding call to ec_dec_update(), or
decoding will not proceed correctly. _ft: The total frequency of

Valin, et al.            Expires January 9, 2011              [Page 197]


Internet-Draft                 CELT codec                      July 2010

the symbols in the alphabet the next symbol was encoded with.
Return: A cumulative frequency representing the encoded symbol.
If the cumulative frequency of all the symbols before the one
that was encoded was fl, and the cumulative frequency of all the
symbols up to and including the one encoded is fh, then the
returned value will fall in the range [fl,fh). */
unsigned        ec_decode(ec_dec * _this, unsigned _ft);
unsigned        ec_decode_bin(ec_dec * _this, unsigned _bits);
unsigned        ec_decode_raw(ec_dec * _this, unsigned bits);

/* Advance the decoder past the next symbol using the frequency
information the symbol was encoded with. Exactly one call to
ec_decode() must have been made so that all necessary
intermediate calculations are performed. _fl: The cumulative
frequency of all symbols that come before the symbol decoded.
_fh: The cumulative frequency of all symbols up to and including
the symbol decoded. Together with _fl, this defines the range
[_fl,_fh) in which the value returned above must fall. _ft: The
total frequency of the symbols in the alphabet the symbol decoded
was encoded in. This must be the same as passed to the preceding
call to ec_decode(). */
void            ec_dec_update(ec_dec * _this, unsigned _fl,
unsigned _fh, unsigned _ft);
/* Extracts a sequence of raw bits from the stream. The bits must
have been encoded with ec_enc_bits(). No call to ec_dec_update()
is necessary after this call. _ftb: The number of bits to
extract. This must be at least one, and no more than 32. Return:
The decoded bits. */
ec_uint32       ec_dec_bits(ec_dec * _this, int _ftb);
/* Extracts a raw unsigned integer with a non-power-of-2 range from
the stream. The bits must have been encoded with ec_enc_uint().
No call to ec_dec_update() is necessary after this call. _ft: The
number of integers that can be decoded (one more than the max).
This must be at least one, and no more than 2**32-1. Return: The
decoded bits. */
ec_uint32       ec_dec_uint(ec_dec * _this, ec_uint32 _ft);

/* Decode a bit that has a _prob/65536 probability of being a one */
int             ec_dec_bit_prob(ec_dec * _this, unsigned _prob);

/* Returns the number of bits "used" by the encoded symbols so far.
This same number can be computed by the encoder, and is suitable
for making coding decisions. _b: The number of extra bits of
precision to include. At most 16 will be accurate. Return: The
number of bits scaled by 2**_b. This will always be slightly
larger than the exact value (e.g., all rounding error is in the
positive direction). */
long            ec_dec_tell(ec_dec * _this, int _b);

Valin, et al.            Expires January 9, 2011              [Page 198]


Internet-Draft                 CELT codec                      July 2010

#endif

A.27.  entdec.c

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include <stddef.h>
#include "entdec.h"
#include "os_support.h"
#include "arch.h"

void
ec_byte_readinit(ec_byte_buffer * _b, unsigned char *_buf,

Valin, et al.            Expires January 9, 2011              [Page 199]


Internet-Draft                 CELT codec                      July 2010

long _bytes)
{
_b->buf = _b->ptr = _buf;
_b->storage = _bytes;
_b->end_ptr = _b->buf + _bytes - 1;
}

unsigned char
ec_byte_look_at_end(ec_byte_buffer * _b)
{
if (_b->end_ptr < _b->buf)
{
celt_fatal
("Trying to read raw bits before the beginning of the stream");
}
return *(_b->end_ptr--);
}

void
{
_b->ptr++;
}

int
{
ptrdiff_t       endbyte;
endbyte = _b->ptr - _b->buf;
if (endbyte >= _b->storage)
return -1;
else
return *(_b->ptr++);
}

ec_uint32
ec_dec_bits(ec_dec * _this, int _ftb)
{
ec_uint32       t;
unsigned        s;
t = 0;
while (_ftb > EC_UNIT_BITS)
{
s = ec_decode_raw(_this, EC_UNIT_BITS);
t = t << EC_UNIT_BITS | s;
_ftb -= EC_UNIT_BITS;
}

Valin, et al.            Expires January 9, 2011              [Page 200]


Internet-Draft                 CELT codec                      July 2010

s = ec_decode_raw(_this, _ftb);
/* ec_dec_update(_this,s,s+1,ft); */
t = t << _ftb | s;
return t;
}

ec_uint32
ec_dec_uint(ec_dec * _this, ec_uint32 _ft)
{
ec_uint32       t;
unsigned        ft;
unsigned        s;
int             ftb;
t = 0;
/* In order to optimize EC_ILOG(), it is undefined for the value
0. */
celt_assert(_ft > 1);
_ft--;
ftb = EC_ILOG(_ft);
if (ftb > EC_UNIT_BITS)
{
ftb -= EC_UNIT_BITS;
ft = (unsigned) (_ft >> ftb) + 1;
s = ec_decode(_this, ft);
ec_dec_update(_this, s, s + 1, ft);
t = t << EC_UNIT_BITS | s;
t = t << ftb | ec_dec_bits(_this, ftb);
if (t > _ft)
{
celt_notify("uint decode error");
t = _ft;
}
return t;
} else
{
_ft++;
s = ec_decode(_this, (unsigned) _ft);
ec_dec_update(_this, s, s + 1, (unsigned) _ft);
t = t << ftb | s;
return t;
}
}

A.28.  mfrngcod.h

2008-2009 Xiph.Org Foundation */

Valin, et al.            Expires January 9, 2011              [Page 201]


Internet-Draft                 CELT codec                      July 2010

/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#if !defined(_mfrngcode_H)
# define _mfrngcode_H (1)
# include "entcode.h"

/* Constants used by the entropy encoder/decoder. */

/* The number of bits to output at a time. */
# define EC_SYM_BITS   (8)
/* The total number of bits in each of the state registers. */
# define EC_CODE_BITS  (32)
/* The maximum symbol value. */
# define EC_SYM_MAX    ((1U<<EC_SYM_BITS)-1)
/* Bits to shift by to move a symbol into the high-order position. */
# define EC_CODE_SHIFT (EC_CODE_BITS-EC_SYM_BITS-1)
/* Carry bit of the high-order range symbol. */
# define EC_CODE_TOP   (((ec_uint32)1U)<<EC_CODE_BITS-1)

Valin, et al.            Expires January 9, 2011              [Page 202]


Internet-Draft                 CELT codec                      July 2010

/* Low-order bit of the high-order range symbol. */
# define EC_CODE_BOT   (EC_CODE_TOP>>EC_SYM_BITS)
/* Code for which propagating carries are possible. */
# define EC_CODE_CARRY (((ec_uint32)EC_SYM_MAX)<<EC_CODE_SHIFT)
/* The number of bits available for the last, partial symbol in the
code field. */
# define EC_CODE_EXTRA ((EC_CODE_BITS-2)%EC_SYM_BITS+1)
/* A mask for the bits available in the coding buffer. This allows
different platforms to use a variable with more bits, if it is
convenient. We will only use EC_CODE_BITS of it. */

#endif

A.29.  rangeenc.c

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT

Valin, et al.            Expires January 9, 2011              [Page 203]


Internet-Draft                 CELT codec                      July 2010

OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "arch.h"
#include "entenc.h"
#include "mfrngcod.h"

/* A range encoder. See rangedec.c and the references for
implementation details \cite{Mar79,MNW98}.

@INPROCEEDINGS{Mar79, author="Martin, G.N.N.", title="Range
encoding: an algorithm for removing redundancy from a digitised
message", booktitle="Video \& Data Recording Conference",
author="Alistair Moffat and Radford Neal and Ian H. Witten",
title="Arithmetic Coding Revisited", journal="{ACM} Transactions
on Information Systems", year=1998, volume=16, number=3,
pages="256--294", month=Jul,
URL="http://www.stanford.edu/class/ee398/handouts/papers/Moffat98Ari\
thmCoding.pdf"
} */

/* Outputs a symbol, with a carry bit. If there is a potential to
propagate a carry over several symbols, they are buffered until
it can be determined whether or not an actual carry will occur.
If the counter for the buffered symbols overflows, then the
stream becomes undecodable. This gives a theoretical limit of a
few billion symbols in a single packet on 32-bit systems. The
alternative is to truncate the range in order to force a carry,
but requires similar carry tracking in the decoder, needlessly
slowing it down. */
static void
ec_enc_carry_out(ec_enc * _this, int _c)
{
if (_c != EC_SYM_MAX)
{
/* No further carry propagation possible, flush buffer. */
int             carry;
carry = _c >> EC_SYM_BITS;
/* Don't output a byte on the first write. This compare should
be taken care of by branch-prediction thereafter. */
if (_this->rem >= 0)
ec_byte_write1(_this->buf, _this->rem + carry);
if (_this->ext > 0)
{
unsigned        sym;

Valin, et al.            Expires January 9, 2011              [Page 204]


Internet-Draft                 CELT codec                      July 2010

sym = EC_SYM_MAX + carry & EC_SYM_MAX;
do
ec_byte_write1(_this->buf, sym);
while (--(_this->ext) > 0);
}
_this->rem = _c & EC_SYM_MAX;
} else
_this->ext++;
}

static inline void
ec_enc_normalize(ec_enc * _this)
{
/* If the range is too small, output some bits and rescale it. */
while (_this->rng <= EC_CODE_BOT)
{
ec_enc_carry_out(_this, (int) (_this->low >> EC_CODE_SHIFT));
/* Move the next-to-high-order symbol into the high-order
position. */
_this->low = _this->low << EC_SYM_BITS & EC_CODE_TOP - 1;
_this->rng <<= EC_SYM_BITS;
}
}

void
ec_enc_init(ec_enc * _this, ec_byte_buffer * _buf)
{
_this->buf = _buf;
_this->rem = -1;
_this->ext = 0;
_this->low = 0;
_this->rng = EC_CODE_TOP;
_this->end_byte = 0;
_this->end_bits_left = 8;
_this->nb_end_bits = 0;
}

void
ec_encode(ec_enc * _this, unsigned _fl, unsigned _fh, unsigned _ft)
{
ec_uint32       r;
r = _this->rng / _ft;
if (_fl > 0)
{
_this->low += _this->rng - ((r) * ((_ft - _fl)));
_this->rng = ((r) * ((_fh - _fl)));
} else
_this->rng -= ((r) * ((_ft - _fh)));

Valin, et al.            Expires January 9, 2011              [Page 205]


Internet-Draft                 CELT codec                      July 2010

ec_enc_normalize(_this);
}

void
ec_encode_bin(ec_enc * _this, unsigned _fl, unsigned _fh,
unsigned _bits)
{
ec_uint32       r;
r = _this->rng >> _bits;
if (_fl > 0)
{
_this->low += _this->rng - ((r) * (((1 << _bits) - _fl)));
_this->rng = ((r) * ((_fh - _fl)));
} else
_this->rng -= ((r) * (((1 << _bits) - _fh)));
ec_enc_normalize(_this);
}

/* The probability of having a "one" is given in 1/65536. */
void
ec_enc_bit_prob(ec_enc * _this, int _val, unsigned _prob)
{
ec_uint32       r;
ec_uint32       s;
ec_uint32       l;
r = _this->rng;
l = _this->low;
s = (r >> 16) * _prob;
r -= s;
if (_val)
_this->low = l + r;
_this->rng = _val ? s : r;
ec_enc_normalize(_this);
}

void
ec_encode_raw(ec_enc * _this, unsigned _fl, unsigned _fh,
unsigned bits)
{
_this->nb_end_bits += bits;
while (bits >= _this->end_bits_left)
{
_this->end_byte |= (_fl << (8 - _this->end_bits_left)) & 0xff;
_fl >>= _this->end_bits_left;
ec_byte_write_at_end(_this->buf, _this->end_byte);
_this->end_byte = 0;
bits -= _this->end_bits_left;
_this->end_bits_left = 8;

Valin, et al.            Expires January 9, 2011              [Page 206]


Internet-Draft                 CELT codec                      July 2010

}
_this->end_byte |= (_fl << (8 - _this->end_bits_left)) & 0xff;
_this->end_bits_left -= bits;
}

long
ec_enc_tell(ec_enc * _this, int _b)
{
ec_uint32       r;
int             l;
long            nbits;
nbits =
(ec_byte_bytes(_this->buf) + (_this->rem >= 0) +
_this->ext) * EC_SYM_BITS;
/* To handle the non-integral number of bits still left in the
encoder state, we compute the number of bits of low that must
be encoded to ensure that the value is inside the range for any
possible subsequent bits. */
nbits += EC_CODE_BITS + 1 + _this->nb_end_bits;
nbits <<= _b;
l = EC_ILOG(_this->rng);
r = _this->rng >> l - 16;
while (_b-- > 0)
{
int             b;
r = r * r >> 15;
b = (int) (r >> 16);
l = l << 1 | b;
r >>= b;
}
return nbits - l;
}

void
ec_enc_done(ec_enc * _this)
{
ec_uint32       msk;
ec_uint32       end;
int             l;
/* We output the minimum number of bits that ensures that the
symbols encoded thus far will be decoded correctly regardless
of the bits that follow. */
l = EC_CODE_BITS - EC_ILOG(_this->rng);
msk = EC_CODE_TOP - 1 >> l;
end = _this->low + msk & ~msk;
if ((end | msk) >= _this->low + _this->rng)
{
l++;

Valin, et al.            Expires January 9, 2011              [Page 207]


Internet-Draft                 CELT codec                      July 2010

msk >>= 1;
end = _this->low + msk & ~msk;
}
while (l > 0)
{
ec_enc_carry_out(_this, (int) (end >> EC_CODE_SHIFT));
end = end << EC_SYM_BITS & EC_CODE_TOP - 1;
l -= EC_SYM_BITS;
}
/* If we have a buffered byte flush it into the output buffer. */
if (_this->rem >= 0 || _this->ext > 0)
{
ec_enc_carry_out(_this, 0);
_this->rem = -1;
}
{
unsigned char  *ptr = _this->buf->ptr;
while (ptr <= _this->buf->end_ptr)
*ptr++ = 0;
if (_this->end_bits_left != 8)
*_this->buf->end_ptr |= _this->end_byte;
}
}

A.30.  rangedec.c

2008-2009 Xiph.Org Foundation */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND

Valin, et al.            Expires January 9, 2011              [Page 208]


Internet-Draft                 CELT codec                      July 2010

CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "arch.h"
#include "entdec.h"
#include "mfrngcod.h"

/* A range decoder. This is an entropy decoder based upon
\cite{Mar79}, which is itself a rediscovery of the FIFO
arithmetic code introduced by \cite{Pas76}. It is very similar to
arithmetic encoding, except that encoding is done with digits in
any base, instead of with bits, and so it is faster when using
larger bases (i.e.: a byte). The author claims an average waste
of $\frac{1}{2}\log_b(2b)$ bits, where $b$ is the base, longer
than the theoretical optimum, but to my knowledge there is no
published justification for this claim. This only seems true when
using near-infinite precision arithmetic so that the process is
carried out with no rounding errors.

IBM (the author's employer) never sought to patent the idea, and
to my knowledge the algorithm is unencumbered by any patents,
though its performance is very competitive with proprietary
arithmetic coding. The two are based on very similar ideas,
however. An excellent description of implementation details is
available at http://www.arturocampos.com/ac_range.html A recent
work \cite{MNW98} which proposes several changes to arithmetic
encoding for efficiency actually re-discovers many of the
principles behind range encoding, and presents a good theoretical
analysis of them.

End of stream is handled by writing out the smallest number of
bits that ensures that the stream will be correctly decoded
regardless of the value of any subsequent bits. ec_dec_tell() can
be used to determine how many bits were needed to decode all the
symbols thus far; other data can be packed in the remaining bits
of the input buffer. @PHDTHESIS{Pas76, author="Richard Clark

Valin, et al.            Expires January 9, 2011              [Page 209]


Internet-Draft                 CELT codec                      July 2010

Pasco", title="Source coding algorithms for fast data
compression", school="Dept. of Electrical Engineering, Stanford
University", address="Stanford, CA", month=May, year=1976 }
@INPROCEEDINGS{Mar79, author="Martin, G.N.N.", title="Range
encoding: an algorithm for removing redundancy from a digitised
message", booktitle="Video & Data Recording Conference",
author="Alistair Moffat and Radford Neal and Ian H. Witten",
title="Arithmetic Coding Revisited", journal="{ACM} Transactions
on Information Systems", year=1998, volume=16, number=3,
pages="256--294", month=Jul,
URL="http://www.stanford.edu/class/ee398/handouts/papers/Moffat98Ari\
thmCoding.pdf"
} */

/* Gets the next byte of input. After all the bytes in the current
packet have been consumed, and the extra end code returned if
needed, this function will continue to return zero each time it
is called. Return: The next byte of input. */
static int
ec_dec_in(ec_dec * _this)
{
int             ret;
if (ret < 0)
{
ret = 0;
/* Needed to keep oc_dec_tell() operating correctly. */
}
return ret;
}

/* Normalizes the contents of dif and rng so that rng lies entirely
in the high-order symbol. */
static inline void
ec_dec_normalize(ec_dec * _this)
{
/* If the range is too small, rescale it and input some bits. */
while (_this->rng <= EC_CODE_BOT)
{
int             sym;
_this->rng <<= EC_SYM_BITS;
/* Use up the remaining bits from our last symbol. */
sym = _this->rem << EC_CODE_EXTRA & EC_SYM_MAX;
/* Read the next value from the input. */
_this->rem = ec_dec_in(_this);
/* Take the rest of the bits we need from this new symbol. */

Valin, et al.            Expires January 9, 2011              [Page 210]


Internet-Draft                 CELT codec                      July 2010

sym |= _this->rem >> EC_SYM_BITS - EC_CODE_EXTRA;
_this->dif = (_this->dif << EC_SYM_BITS) - sym & EC_CODE_MASK;
/* dif can never be larger than EC_CODE_TOP. This is equivalent
if(_this->dif>EC_CODE_TOP)_this->dif-=EC_CODE_TOP; */
_this->dif ^= _this->dif & _this->dif - 1 & EC_CODE_TOP;
}
}

void
ec_dec_init(ec_dec * _this, ec_byte_buffer * _buf)
{
_this->buf = _buf;
_this->rem = ec_dec_in(_this);
_this->rng = 1U << EC_CODE_EXTRA;
_this->dif =
_this->rng - (_this->rem >> EC_SYM_BITS - EC_CODE_EXTRA);
/* Normalize the interval. */
ec_dec_normalize(_this);
/*_this->end_byte=ec_byte_look_at_end(_this->buf);*/
_this->end_bits_left = 0;
_this->nb_end_bits = 0;
}

unsigned
ec_decode(ec_dec * _this, unsigned _ft)
{
unsigned        s;
_this->nrm = _this->rng / _ft;
s = (unsigned) ((_this->dif - 1) / _this->nrm);
return _ft - EC_MINI(s + 1, _ft);
}

unsigned
ec_decode_bin(ec_dec * _this, unsigned _bits)
{
unsigned        s;
_this->nrm = _this->rng >> _bits;
s = (unsigned) ((_this->dif - 1) / _this->nrm);
return (1 << _bits) - EC_MINI(s + 1, 1 << _bits);
}

unsigned
ec_decode_raw(ec_dec * _this, unsigned bits)
{
unsigned        value = 0;
int             count = 0;
_this->nb_end_bits += bits;

Valin, et al.            Expires January 9, 2011              [Page 211]


Internet-Draft                 CELT codec                      July 2010

while (bits >= _this->end_bits_left)
{
value |= _this->end_byte >> (8 - _this->end_bits_left) << count;
count += _this->end_bits_left;
bits -= _this->end_bits_left;
_this->end_byte = ec_byte_look_at_end(_this->buf);
_this->end_bits_left = 8;
}
value |=
((_this->
end_byte >> (8 - _this->end_bits_left)) & ((1 << bits) -
1)) << count;
_this->end_bits_left -= bits;
return value;
}

void
ec_dec_update(ec_dec * _this, unsigned _fl, unsigned _fh,
unsigned _ft)
{
ec_uint32       s;
s = ((_this->nrm) * ((_ft - _fh)));
_this->dif -= s;
_this->rng =
_fl > 0 ? ((_this->nrm) * ((_fh - _fl))) : _this->rng - s;
ec_dec_normalize(_this);
}

/* The probability of having a "one" is given in 1/65536. */
int
ec_dec_bit_prob(ec_dec * _this, unsigned _prob)
{
ec_uint32       r;
ec_uint32       s;
ec_uint32       d;
int             val;
r = _this->rng;
d = _this->dif;
s = (r >> 16) * _prob;
val = d <= s;
if (!val)
_this->dif = d - s;
_this->rng = val ? s : r - s;
ec_dec_normalize(_this);
return val;
}

long

Valin, et al.            Expires January 9, 2011              [Page 212]


Internet-Draft                 CELT codec                      July 2010

ec_dec_tell(ec_dec * _this, int _b)
{
ec_uint32       r;
int             l;
long            nbits;
nbits =
(ec_byte_bytes(_this->buf) -
(EC_CODE_BITS + EC_SYM_BITS - 1) / EC_SYM_BITS) * EC_SYM_BITS;
/* To handle the non-integral number of bits still left in the
decoder state, we compute the number of bits of low that must
be encoded to ensure that the value is inside the range for any
possible subsequent bits. */
nbits += EC_CODE_BITS + 1 + _this->nb_end_bits;
nbits <<= _b;
l = EC_ILOG(_this->rng);
r = _this->rng >> l - 16;
while (_b-- > 0)
{
int             b;
r = r * r >> 15;
b = (int) (r >> 16);
l = l << 1 | b;
r >>= b;
}
return nbits - l;
}

A.31.  laplace.h

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written

Valin, et al.            Expires January 9, 2011              [Page 213]


Internet-Draft                 CELT codec                      July 2010

permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "entenc.h"
#include "entdec.h"

int             ec_laplace_get_start_freq(int decay);

/** Encode a value that is assumed to be the realisation of a
Laplace-distributed random process
@param enc Entropy encoder state
@param value Value to encode
@param decay Probability of the value +/- 1, multiplied by 16384
*/
void            ec_laplace_encode(ec_enc * enc, int *value,
int decay);

void            ec_laplace_encode_start(ec_enc * enc, int *value,
int decay, int fs);

/** Decode a value that is assumed to be the realisation of a
Laplace-distributed random process
@param dec Entropy decoder state
@param decay Probability of the value +/- 1, multiplied by 16384
@return Value decoded
*/
int             ec_laplace_decode(ec_dec * dec, int decay);

int             ec_laplace_decode_start(ec_dec * dec, int decay,
int fs);

Valin, et al.            Expires January 9, 2011              [Page 214]


Internet-Draft                 CELT codec                      July 2010

A.32.  laplace.c

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "laplace.h"

int
ec_laplace_get_start_freq(int decay)
{
int             fs =
(((ec_uint32) 32768) * (16384 - decay)) / (16384 + decay);
/* Making fs even so we're sure that all the range is used for +/-
values */

Valin, et al.            Expires January 9, 2011              [Page 215]


Internet-Draft                 CELT codec                      July 2010

fs -= (fs & 1);
return fs;
}

void
ec_laplace_encode_start(ec_enc * enc, int *value, int decay, int fs)
{
int             i;
int             fl;
unsigned int    ft;
int             s = 0;
int             val = *value;
if (val < 0)
{
s = 1;
val = -val;
}
ft = 32768;
fl = -fs;
for (i = 0; i < val; i++)
{
int             tmp_l,
tmp_s;
tmp_l = fl;
tmp_s = fs;
fl += fs * 2;
fs = (fs * (ec_int32) decay) >> 14;
if (fs == 0)
{
if (fl + 2 <= ft)
{
fs = 1;
} else
{
fs = tmp_s;
fl = tmp_l;
if (s)
*value = -i;
else
*value = i;
break;
}
}
}
if (fl < 0)
fl = 0;
if (s)
fl += fs;

Valin, et al.            Expires January 9, 2011              [Page 216]


Internet-Draft                 CELT codec                      July 2010

ec_encode_bin(enc, fl, fl + fs, 15);
}

void
ec_laplace_encode(ec_enc * enc, int *value, int decay)
{
int             fs = ec_laplace_get_start_freq(decay);
ec_laplace_encode_start(enc, value, decay, fs);
}

int
ec_laplace_decode_start(ec_dec * dec, int decay, int fs)
{
int             val = 0;
int             fl,
fh,
fm;
unsigned int    ft;
fl = 0;
ft = 32768;
fh = fs;
fm = ec_decode_bin(dec, 15);
while (fm >= fh && fs != 0)
{
fl = fh;
fs = (fs * (ec_int32) decay) >> 14;
if (fs == 0 && fh + 2 <= ft)
{
fs = 1;
}
fh += fs * 2;
val++;
}
if (fl > 0)
{
if (fm >= fl + fs)
{
val = -val;
fl += fs;
} else
{
fh -= fs;
}
}
/* Preventing an infinite loop in case something screws up in the
decoding */
if (fl == fh)
fl--;

Valin, et al.            Expires January 9, 2011              [Page 217]


Internet-Draft                 CELT codec                      July 2010

ec_dec_update(dec, fl, fh, ft);
return val;
}

int
ec_laplace_decode(ec_dec * dec, int decay)
{
int             fs = ec_laplace_get_start_freq(decay);
return ec_laplace_decode_start(dec, decay, fs);
}

A.33.  quant_bands.h

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

Valin, et al.            Expires January 9, 2011              [Page 218]


Internet-Draft                 CELT codec                      July 2010

#ifndef QUANT_BANDS
#define QUANT_BANDS

#include "arch.h"
#include "modes.h"
#include "entenc.h"
#include "entdec.h"
#include "mathops.h"

static inline float
amp2Log(float amp)
{
return celt_log2(MAX32((.001f), (amp)));
}

static inline float
log2Amp(float lg)
{
return (celt_exp2((lg)));
}

int            *quant_prob_alloc(const CELTMode * m);
void            quant_prob_free(int *freq);

void            compute_fine_allocation(const CELTMode * m,
int *bits, int budget);

int             intra_decision(float *eBands, float *oldEBands,
int len);

unsigned        quant_coarse_energy(const CELTMode * m, int start,
const float *eBands,
float *oldEBands, int budget,
int intra, int *prob,
float *error, ec_enc * enc,
int _C, float max_decay);

void            quant_fine_energy(const CELTMode * m, int start,
float *eBands, float *oldEBands,
float *error, int *fine_quant,
ec_enc * enc, int _C);

void            quant_energy_finalise(const CELTMode * m, int start,
float *eBands,
float *oldEBands, float *error,
int *fine_quant,
int *fine_priority,
int bits_left, ec_enc * enc,

Valin, et al.            Expires January 9, 2011              [Page 219]


Internet-Draft                 CELT codec                      July 2010

int _C);

void            unquant_coarse_energy(const CELTMode * m, int start,
float *eBands,
float *oldEBands, int budget,
int intra, int *prob,
ec_dec * dec, int _C);

void            unquant_fine_energy(const CELTMode * m, int start,
float *eBands, float *oldEBands,
int *fine_quant, ec_dec * dec,
int _C);

void            unquant_energy_finalise(const CELTMode * m,
int start, float *eBands,
float *oldEBands,
int *fine_quant,
int *fine_priority,
int bits_left, ec_dec * dec,
int _C);

#endif                          /* QUANT_BANDS */

A.34.  quant_bands.c

Foundation Written by Jean-Marc Valin */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,

Valin, et al.            Expires January 9, 2011              [Page 220]


Internet-Draft                 CELT codec                      July 2010

INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#include "config.h"

#include "quant_bands.h"
#include "laplace.h"
#include <math.h>
#include "os_support.h"
#include "arch.h"
#include "mathops.h"
#include "stack_alloc.h"

#define E_MEANS_SIZE (5)

const float     eMeans[E_MEANS_SIZE] =
{ (7.5f), -(1.33f), -(2.f), -(0.42f), (0.17f) };

/* FIXME: Implement for stereo */
int
intra_decision(float *eBands, float *oldEBands, int len)
{
int             i;
float           dist = 0;
for (i = 0; i < len; i++)
{
float           d = ((eBands[i]) - (oldEBands[i]));
dist = ((dist) + (d) * (d));
}
return (dist) > 2 * len;
}

int            *
quant_prob_alloc(const CELTMode * m)
{
int             i;
int            *prob;
prob = celt_alloc(4 * m->nbEBands * sizeof(int));
if (prob == NULL)

Valin, et al.            Expires January 9, 2011              [Page 221]


Internet-Draft                 CELT codec                      July 2010

return NULL;
for (i = 0; i < m->nbEBands; i++)
{
prob[2 * i] = 6000 - i * 200;
prob[2 * i + 1] = ec_laplace_get_start_freq(prob[2 * i]);
}
for (i = 0; i < m->nbEBands; i++)
{
prob[2 * m->nbEBands + 2 * i] = 9000 - i * 240;
prob[2 * m->nbEBands + 2 * i + 1] =
ec_laplace_get_start_freq(prob[2 * m->nbEBands + 2 * i]);
}
return prob;
}

void
quant_prob_free(int *freq)
{
celt_free(freq);
}

unsigned
quant_coarse_energy(const CELTMode * m, int start,
const float *eBands, float *oldEBands,
int budget, int intra, int *prob, float *error,
ec_enc * enc, int _C, float max_decay)
{
int             i,
c;
unsigned        bits_used = 0;
float           prev[2] = { 0, 0 };
float           coef = m->ePredCoef;
float           beta;
const int       C = CHANNELS(_C);

if (intra)
{
coef = 0;
prob += 2 * m->nbEBands;
}
/* The .8 is a heuristic */
beta = (((.8f)) * (coef));

/* Encode at a fixed coarse resolution */
for (i = start; i < m->nbEBands; i++)
{
c = 0;
do

Valin, et al.            Expires January 9, 2011              [Page 222]


Internet-Draft                 CELT codec                      July 2010

{
int             qi;
float           q;
float           x;
float           f;
float           mean =
(i - start <
E_MEANS_SIZE) ? ((((eMeans[i - start]))) -
(((coef) * (eMeans[i - start])))) : 0;
x = eBands[i + c * m->nbEBands];

f = x - mean - coef * oldEBands[i + c * m->nbEBands] - prev[c];
/* Rounding to nearest integer here is really important! */
qi = (int) floor(.5f + f);

if (qi < 0 && x < oldEBands[i + c * m->nbEBands] - max_decay)
{
qi += (oldEBands[i + c * m->nbEBands] - max_decay - x);
if (qi > 0)
qi = 0;
}
/* If we don't have enough bits to encode all the energy, just
assume something safe. We allow slightly busting the budget
here */
bits_used = ec_enc_tell(enc, 0);
if (bits_used > budget)
{
qi = -1;
error[i + c * m->nbEBands] = (.5f);
} else
{
ec_laplace_encode_start(enc, &qi, prob[2 * i],
prob[2 * i + 1]);
error[i + c * m->nbEBands] = (f) - (qi);
}
q = (qi);

oldEBands[i + c * m->nbEBands] =
(((coef) * (oldEBands[i + c * m->nbEBands])) + mean +
prev[c] + ((q)));
prev[c] = mean + prev[c] + ((q)) - ((beta) * (q));
}
while (++c < C);
}
return bits_used;
}

void

Valin, et al.            Expires January 9, 2011              [Page 223]


Internet-Draft                 CELT codec                      July 2010

quant_fine_energy(const CELTMode * m, int start, float *eBands,
float *oldEBands, float *error, int *fine_quant,
ec_enc * enc, int _C)
{
int             i,
c;
const int       C = CHANNELS(_C);

/* Encode finer resolution */
for (i = start; i < m->nbEBands; i++)
{
celt_int16      frac = 1 << fine_quant[i];
if (fine_quant[i] <= 0)
continue;
c = 0;
do
{
int             q2;
float           offset;

q2 = (int) floor((error[i + c * m->nbEBands] + .5f) * frac);

if (q2 > frac - 1)
q2 = frac - 1;
if (q2 < 0)
q2 = 0;
ec_enc_bits(enc, q2, fine_quant[i]);

offset =
(q2 + .5f) * (1 << (14 - fine_quant[i])) * (1.f / 16384) -
.5f;

oldEBands[i + c * m->nbEBands] += offset;
error[i + c * m->nbEBands] -= offset;
/* printf ("%f ", error[i] - offset); */
}
while (++c < C);
}
}

void
quant_energy_finalise(const CELTMode * m, int start, float *eBands,
float *oldEBands, float *error,
int *fine_quant, int *fine_priority,
int bits_left, ec_enc * enc, int _C)
{
int             i,
prio,

Valin, et al.            Expires January 9, 2011              [Page 224]


Internet-Draft                 CELT codec                      July 2010

c;
const int       C = CHANNELS(_C);

/* Use up the remaining bits */
for (prio = 0; prio < 2; prio++)
{
for (i = start; i < m->nbEBands && bits_left >= C; i++)
{
if (fine_quant[i] >= 7 || fine_priority[i] != prio)
continue;
c = 0;
do
{
int             q2;
float           offset;
q2 = error[i + c * m->nbEBands] < 0 ? 0 : 1;
ec_enc_bits(enc, q2, 1);

offset =
(q2 -
.5f) * (1 << (14 - fine_quant[i] - 1)) * (1.f / 16384);

oldEBands[i + c * m->nbEBands] += offset;
bits_left--;
}
while (++c < C);
}
}
c = 0;
do
{
for (i = start; i < m->nbEBands; i++)
{
eBands[i + c * m->nbEBands] =
log2Amp(oldEBands[i + c * m->nbEBands]);
if (oldEBands[i + c * m->nbEBands] < -(7.f))
oldEBands[i + c * m->nbEBands] = -(7.f);
}
}
while (++c < C);
}

void
unquant_coarse_energy(const CELTMode * m, int start, float *eBands,
float *oldEBands, int budget, int intra,
int *prob, ec_dec * dec, int _C)
{
int             i,

Valin, et al.            Expires January 9, 2011              [Page 225]


Internet-Draft                 CELT codec                      July 2010

c;
float           prev[2] = { 0, 0 };
float           coef = m->ePredCoef;
float           beta;
const int       C = CHANNELS(_C);

if (intra)
{
coef = 0;
prob += 2 * m->nbEBands;
}
/* The .8 is a heuristic */
beta = (((.8f)) * (coef));

/* Decode at a fixed coarse resolution */
for (i = start; i < m->nbEBands; i++)
{
c = 0;
do
{
int             qi;
float           q;
float           mean =
(i - start <
E_MEANS_SIZE) ? ((((eMeans[i - start]))) -
(((coef) * (eMeans[i - start])))) : 0;
/* If we didn't have enough bits to encode all the energy,
just assume something safe. We allow slightly busting the
budget here */
if (ec_dec_tell(dec, 0) > budget)
qi = -1;
else
qi = ec_laplace_decode_start(dec, prob[2 * i],
prob[2 * i + 1]);
q = (qi);

oldEBands[i + c * m->nbEBands] =
(((coef) * (oldEBands[i + c * m->nbEBands])) + mean +
prev[c] + ((q)));
prev[c] = mean + prev[c] + ((q)) - ((beta) * (q));
}
while (++c < C);
}
}

void
unquant_fine_energy(const CELTMode * m, int start, float *eBands,
float *oldEBands, int *fine_quant, ec_dec * dec,

Valin, et al.            Expires January 9, 2011              [Page 226]


Internet-Draft                 CELT codec                      July 2010

int _C)
{
int             i,
c;
const int       C = CHANNELS(_C);
/* Decode finer resolution */
for (i = start; i < m->nbEBands; i++)
{
if (fine_quant[i] <= 0)
continue;
c = 0;
do
{
int             q2;
float           offset;
q2 = ec_dec_bits(dec, fine_quant[i]);

offset =
(q2 + .5f) * (1 << (14 - fine_quant[i])) * (1.f / 16384) -
.5f;

oldEBands[i + c * m->nbEBands] += offset;
}
while (++c < C);
}
}

void
unquant_energy_finalise(const CELTMode * m, int start, float *eBands,
float *oldEBands, int *fine_quant,
int *fine_priority, int bits_left,
ec_dec * dec, int _C)
{
int             i,
prio,
c;
const int       C = CHANNELS(_C);

/* Use up the remaining bits */
for (prio = 0; prio < 2; prio++)
{
for (i = start; i < m->nbEBands && bits_left >= C; i++)
{
if (fine_quant[i] >= 7 || fine_priority[i] != prio)
continue;
c = 0;
do
{

Valin, et al.            Expires January 9, 2011              [Page 227]


Internet-Draft                 CELT codec                      July 2010

int             q2;
float           offset;
q2 = ec_dec_bits(dec, 1);

offset =
(q2 -
.5f) * (1 << (14 - fine_quant[i] - 1)) * (1.f / 16384);

oldEBands[i + c * m->nbEBands] += offset;
bits_left--;
}
while (++c < C);
}
}
c = 0;
do
{
for (i = start; i < m->nbEBands; i++)
{
eBands[i + c * m->nbEBands] =
log2Amp(oldEBands[i + c * m->nbEBands]);
if (oldEBands[i + c * m->nbEBands] < -(7.f))
oldEBands[i + c * m->nbEBands] = -(7.f);
}
}
while (++c < C);
}

A.35.  arch.h

/* Copyright (C) 2003-2008 Jean-Marc Valin */
/**
@file arch.h
@brief Various architecture definitions for CELT
*/
/*
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.

Valin, et al.            Expires January 9, 2011              [Page 228]


Internet-Draft                 CELT codec                      July 2010

- Neither the name of the Xiph.org Foundation nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#ifndef ARCH_H
#define ARCH_H

#include "celt_types.h"

#define CELT_SIG_SCALE 32768.

#define celt_fatal(str) _celt_fatal(str, __FILE__, __LINE__);
#ifdef ENABLE_ASSERTIONS
#define celt_assert(cond) {if (!(cond)) \
{celt_fatal("assertion failed: " #cond);}}
#define celt_assert2(cond, message) {if (!(cond)) \
{celt_fatal("assertion failed: " #cond "\n" message);}}
#else
#define celt_assert(cond)
#define celt_assert2(cond, message)
#endif

#define ABS(x) ((x) < 0 ? (-(x)) : (x))
#define ABS16(x) ((x) < 0 ? (-(x)) : (x))
#define MIN16(a,b) ((a) < (b) ? (a) : (b))
#define MAX16(a,b) ((a) > (b) ? (a) : (b))
#define ABS32(x) ((x) < 0 ? (-(x)) : (x))
#define MIN32(a,b) ((a) < (b) ? (a) : (b))
#define MAX32(a,b) ((a) > (b) ? (a) : (b))
#define IMIN(a,b) ((a) < (b) ? (a) : (b))
#define IMAX(a,b) ((a) > (b) ? (a) : (b))

#define float2int(flt) ((int)(floor(.5+flt)))

Valin, et al.            Expires January 9, 2011              [Page 229]


Internet-Draft                 CELT codec                      July 2010

#define SCALEIN(a)      ((a)*CELT_SIG_SCALE)
#define SCALEOUT(a)     ((a)*(1/CELT_SIG_SCALE))

#ifndef GLOBAL_STACK_SIZE
#ifdef FIXED_POINT
#define GLOBAL_STACK_SIZE 25000
#else
#define GLOBAL_STACK_SIZE 40000
#endif
#endif

#endif /* ARCH_H */

A.36.  mathops.h

CSIRO Copyright (c) 2007-2009 Xiph.Org Foundation Written by
Jean-Marc Valin */
/**
@file mathops.h
@brief Various math functions
*/
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,

Valin, et al.            Expires January 9, 2011              [Page 230]


Internet-Draft                 CELT codec                      July 2010

PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef MATHOPS_H
#define MATHOPS_H

#include "arch.h"
#include "entcode.h"
#include "os_support.h"

#ifndef OVERRIDE_FIND_MAX16
static inline int
find_max16(float *x, int len)
{
float           max_corr = -1e15f;
int             i,
id = 0;
for (i = 0; i < len; i++)
{
if (x[i] > max_corr)
{
id = i;
max_corr = x[i];
}
}
return id;
}
#endif

#ifndef OVERRIDE_FIND_MAX32
static inline int
find_max32(float *x, int len)
{
float           max_corr = -1e15f;
int             i,
id = 0;
for (i = 0; i < len; i++)
{
if (x[i] > max_corr)
{
id = i;
max_corr = x[i];
}
}

Valin, et al.            Expires January 9, 2011              [Page 231]


Internet-Draft                 CELT codec                      July 2010

return id;
}
#endif

/* Multiplies two 16-bit fractional values. Bit-exactness of this
macro is important */
#define FRAC_MUL16(a,b) ((16384+((celt_int32)(celt_int16)(a)*(celt_int1\
6)(b)))>>15)

/* This is a cos() approximation designed to be bit-exact on any
platform. Bit exactness with this approximation is important
because it has an impact on the bit allocation */
static inline celt_int16
bitexact_cos(celt_int16 x)
{
celt_int32      tmp;
celt_int16      x2;
tmp = (4096 + ((celt_int32) (x) * (x))) >> 13;
if (tmp > 32767)
tmp = 32767;
x2 = tmp;
x2 = (32767 - x2) + FRAC_MUL16(x2,
(-7651 +
FRAC_MUL16(x2,
(8277 +
FRAC_MUL16(-626,
x2)))));
if (x2 > 32766)
x2 = 32766;
return 1 + x2;
}

#ifndef FIXED_POINT

#define celt_sqrt(x) ((float)sqrt(x))
#define celt_psqrt(x) ((float)sqrt(x))
#define celt_rsqrt(x) (1.f/celt_sqrt(x))
#define celt_rsqrt_norm(x) (celt_rsqrt(x))
#define celt_acos acos
#define celt_exp exp
#define celt_cos_norm(x) (cos((.5f*M_PI)*(x)))
#define celt_atan atan
#define celt_rcp(x) (1.f/(x))
#define celt_div(a,b) ((a)/(b))
#define frac_div32(a,b) ((float)(a)/(b))

#ifdef FLOAT_APPROX

Valin, et al.            Expires January 9, 2011              [Page 232]


Internet-Draft                 CELT codec                      July 2010

/* Note: This assumes radix-2 floating point with the exponent at
bits 23..30 and an offset of 127 denorm, +/- inf and NaN are
*not* handled */

/** Base-2 log approximation (log2(x)). */
static inline float
celt_log2(float x)
{
int             integer;
float           frac;
union {
float           f;
celt_uint32     i;
} in;
in.f = x;
integer = (in.i >> 23) - 127;
in.i -= integer << 23;
frac = in.f - 1.5f;
frac = -0.41445418f + frac * (0.95909232f
+ frac * (-0.33951290f +
frac * 0.16541097f));
return 1 + integer + frac;
}

/** Base-2 exponential approximation (2^x). */
static inline float
celt_exp2(float x)
{
int             integer;
float           frac;
union {
float           f;
celt_uint32     i;
} res;
integer = floor(x);
if (integer < -50)
return 0;
frac = x - integer;
/* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
res.f = 0.99992522f + frac * (0.69583354f
+ frac * (0.22606716f +
0.078024523f * frac));
res.i = (res.i + (integer << 23)) & 0x7fffffff;
return res.f;
}

#else
#define celt_log2(x) (1.442695040888963387*log(x))

Valin, et al.            Expires January 9, 2011              [Page 233]


Internet-Draft                 CELT codec                      July 2010

#define celt_exp2(x) (exp(0.6931471805599453094*(x)))
#endif

#endif

#ifdef FIXED_POINT

#include "os_support.h"

#ifndef OVERRIDE_CELT_ILOG2
/** Integer log in base2. Undefined for zero and negative numbers */
static inline celt_int16
celt_ilog2(celt_int32 x)
{
celt_assert2(x > 0,
"celt_ilog2() only defined for strictly positive numbers\
");
return EC_ILOG(x) - 1;
}
#endif

#ifndef OVERRIDE_CELT_MAXABS16
static inline float
celt_maxabs16(float *x, int len)
{
int             i;
float           maxval = 0;
for (i = 0; i < len; i++)
maxval = MAX16(maxval, ABS16(x[i]));
return maxval;
}
#endif

/** Integer log in base2. Defined for zero, but not for negative number\
s */
static inline celt_int16
celt_zlog2(float x)
{
return x <= 0 ? 0 : celt_ilog2(x);
}

/** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 ou\
t) */
static inline float
celt_rsqrt_norm(float x)
{
float           n;
float           r;

Valin, et al.            Expires January 9, 2011              [Page 234]


Internet-Draft                 CELT codec                      July 2010

float           r2;
float           y;
/* Range of n is [-16384,32767] ([-0.5,1) in Q15). */
n = x - 32768;
/* Get a rough initial guess for the root. The optimal minimax
quadratic approximation (using relative error) is r =
1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485).
Coefficients here, and the final result r, are Q14. */
r = ((23557) + (((n) * (((-13490) + (((n) * (6713))))))));
/* We want y = x*r*r-1 in Q15, but x is 32-bit Q16 and r is Q14.
We can compute the result from n and r using Q15 multiplies
with some adjustment, carefully done to avoid overflow. Range
of y is [-1564,1594]. */
r2 = ((r) * (r));
y = (((((((r2) * (n))) + (r2))) - (16384)));
/* Apply a 2nd-order Householder iteration: r +=
r*y*(y*0.375-0.5). This yields the Q14 reciprocal square root
of the Q16 x, with a maximum relative error of 1.04956E-4, a
(relative) RMSE of 2.80979E-5, and a peak absolute error of
2.26591/16384. */
return ((r) + (((r) * (((y) * (((((y) * (12288))) - (16384))))))));

}

/** Reciprocal sqrt approximation (Q30 input, Q0 output or equivalent) \
*/
static inline float
celt_rsqrt(float x)
{
int             k;
k = celt_ilog2(x) >> 1;
x = (x);
return (celt_rsqrt_norm(x));
}

/** Sqrt approximation (QX input, QX/2 output) */
static inline float
celt_sqrt(float x)
{
int             k;
float           n;
float           rt;
static const float C[5] = { 23175, 11561, -3011, 1699, -664 };
if (x == 0)
return 0;
k = (celt_ilog2(x) >> 1) - 7;
x = (x);
n = x - 32768;

Valin, et al.            Expires January 9, 2011              [Page 235]


Internet-Draft                 CELT codec                      July 2010

rt = ((C[0]) +
(((n) *
(((C[1]) +
(((n) *
(((C[2]) +
(((n) * (((C[3]) + (((n) * ((C[4])))))))))))))))));

rt = (rt);
return rt;
}

/** Sqrt approximation (QX input, QX/2 output) that assumes that the in\
put is
strictly positive */
static inline float
celt_psqrt(float x)
{
int             k;
float           n;
float           rt;
static const float C[5] = { 23175, 11561, -3011, 1699, -664 };
k = (celt_ilog2(x) >> 1) - 7;
x = (x);
n = x - 32768;
rt = ((C[0]) +
(((n) *
(((C[1]) +
(((n) *
(((C[2]) +
(((n) * (((C[3]) + (((n) * ((C[4])))))))))))))))));

rt = (rt);
return rt;
}

#define L1 32767
#define L2 -7651
#define L3 8277
#define L4 -626

static inline float
_celt_cos_pi_2(float x)
{
float           x2;

x2 = ((x) * (x));
return ((1) +
(MIN16

Valin, et al.            Expires January 9, 2011              [Page 236]


Internet-Draft                 CELT codec                      July 2010

(32766,
((((L1) - (x2))) +
(((x2) *
(((L2) +
(((x2) * (((L3) + (((L4) * (x2)))))))))))))));

}

#undef L1
#undef L2
#undef L3
#undef L4

static inline float
celt_cos_norm(float x)
{
x = x & 0x0001ffff;
if (x > ((1)))
x = ((((1))) - (x));
if (x & 0x00007fff)
{
if (x < ((1)))
{
return _celt_cos_pi_2((x));
} else
{
return (-(_celt_cos_pi_2((65536 - x))));
}
} else
{
if (x & 0x0000ffff)
return 0;
else if (x & 0x0001ffff)
return -32767;
else
return 32767;
}
}

static inline float
celt_log2(float x)
{
int             i;
float           n,
frac;
/* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
0.15530808010959576, -0.08556153059057618 */
static const float C[5] =

Valin, et al.            Expires January 9, 2011              [Page 237]


Internet-Draft                 CELT codec                      July 2010

{ -6801 + (1 << 13 - DB_SHIFT), 15746, -5217, 2545, -1401 };
if (x == 0)
return -32767;
i = celt_ilog2(x);
n = (x) - 32768 - 16384;
frac =
((C[0]) +
(((n) *
(((C[1]) +
(((n) *
(((C[2]) +
(((n) * (((C[3]) + (((n) * (C[4]))))))))))))))));
return (i - 13) + (frac);
}

/*
K0 = 1 K1 = log(2) K2 = 3-4*log(2) K3 = 3*log(2) - 2 */
#define D0 16383
#define D1 22804
#define D2 14819
#define D3 10204
/** Base-2 exponential approximation (2^x). (Q11 input, Q16 output) */
static inline float
celt_exp2(float x)
{
int             integer;
float           frac;
integer = (x);
if (integer > 14)
return 0x7f000000;
else if (integer < -15)
return 0;
frac = (x - (integer));
frac =
((D0) +
(((frac) *
(((D1) + (((frac) * (((D2) + (((D3) * (frac))))))))))));
return ((frac));
}

/** Reciprocal approximation (Q15 input, Q16 output) */
static inline float
celt_rcp(float x)
{
int             i;
float           n;
float           r;
celt_assert2(x > 0, "celt_rcp() only defined for positive values");

Valin, et al.            Expires January 9, 2011              [Page 238]


Internet-Draft                 CELT codec                      July 2010

i = celt_ilog2(x);
/* n is Q15 with range [0,1). */
n = (x) - 32768;
1.8823529411764706-0.9411764705882353*n. The coefficients and
the result are Q14 in the range [15420,30840]. */
r = ((30840) + (((-15420) * (n))));
/* Perform two Newton iterations: r -= r*((r*n)-1.Q15) =
r*((r*n)+(r-1.Q15)). */
r = ((r) - (((r) * (((((r) * (n))) + (((r) + (-32768))))))));

/* We subtract an extra 1 in the second iteration to avoid
overflow; it also neatly compensates for truncation error in
the rest of the process. */
r = ((r) -
(((1) + (((r) * (((((r) * (n))) + (((r) + (-32768))))))))));

/* r is now the Q15 solution to 2/(n+1), with a maximum relative
error of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a
peak absolute error of 1.24665/32768. */
return ((r));
}

#define celt_div(a,b) MULT32_32_Q31((celt_word32)(a),celt_rcp(b))

static inline float
frac_div32(float a, float b)
{
float           rcp;
float           result,
rem;
int             shift = 30 - celt_ilog2(b);
a = (a);
b = (b);

/* 16-bit reciprocal */
rcp = (celt_rcp((b)));
result = (((rcp) * (a)));
rem = a - ((result) * (b));
result += (((rcp) * (rem)));
return result;
}

#define M1 32767
#define M2 -21
#define M3 -11943
#define M4 4936

Valin, et al.            Expires January 9, 2011              [Page 239]


Internet-Draft                 CELT codec                      July 2010

/* Atan approximation using a 4th order polynomial. Input is in Q15
format and normalized by pi/4. Output is in Q15 format */
static inline float
celt_atan01(float x)
{
return ((x) *
(((M1) +
(((x) *
(((M2) + (((x) * (((M3) + (((M4) * (x))))))))))))));
}

#undef M1
#undef M2
#undef M3
#undef M4

/* atan2() approximation valid for positive input values */
static inline float
celt_atan2p(float y, float x)
{
if (y < x)
{
float           arg;
arg = celt_div(((y)), x);
if (arg >= 32767)
arg = 32767;
return (celt_atan01((arg)));
} else
{
float           arg;
arg = celt_div(((x)), y);
if (arg >= 32767)
arg = 32767;
return 25736 - (celt_atan01((arg)));
}
}

#endif                          /* FIXED_POINT */

#endif                          /* MATHOPS_H */

A.37.  os_support.h

/* Copyright (C) 2007 Jean-Marc Valin

File: os_support.h This is the (tiny) OS abstraction layer. Aside
from math.h, this is the only place where system headers are

Valin, et al.            Expires January 9, 2011              [Page 240]


Internet-Draft                 CELT codec                      July 2010

allowed.

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

3. The name of the author may not be used to endorse or promote
products derived from this software without specific prior
written permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR AS IS'' AND ANY EXPRESS
OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT
OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE. */

#ifndef OS_SUPPORT_H
#define OS_SUPPORT_H

#ifdef CUSTOM_SUPPORT
#  include "custom_support.h"
#endif

#include <string.h>
#include <stdio.h>
#include <stdlib.h>

/** CELT wrapper for calloc(). To do your own dynamic allocation, all y\
ou need to do is replace this function, celt_realloc and celt_free
NOTE: celt_alloc needs to CLEAR THE MEMORY */
#ifndef OVERRIDE_CELT_ALLOC
static inline void *
celt_alloc(int size)

Valin, et al.            Expires January 9, 2011              [Page 241]


Internet-Draft                 CELT codec                      July 2010

{
/* WARNING: this is not equivalent to malloc(). If you want to use
malloc() or your own allocator, YOU NEED TO CLEAR THE MEMORY
ALLOCATED. Otherwise you will experience strange bugs */
return calloc(size, 1);
}
#endif

/** Same as celt_alloc(), except that the area is only needed inside a \
CELT call (might cause problem with wideband though) */
#ifndef OVERRIDE_CELT_ALLOC_SCRATCH
static inline void *
celt_alloc_scratch(int size)
{
/* Scratch space doesn't need to be cleared */
return calloc(size, 1);
}
#endif

/** CELT wrapper for realloc(). To do your own dynamic allocation, all \
you need to do is replace this function, celt_alloc and celt_free */
#ifndef OVERRIDE_CELT_REALLOC
static inline void *
celt_realloc(void *ptr, int size)
{
return realloc(ptr, size);
}
#endif

need to do is replace this function, celt_realloc and celt_alloc */
#ifndef OVERRIDE_CELT_FREE
static inline void
celt_free(void *ptr)
{
free(ptr);
}
#endif

/** Same as celt_free(), except that the area is only needed inside a C\
ELT call (might cause problem with wideband though) */
#ifndef OVERRIDE_CELT_FREE_SCRATCH
static inline void
celt_free_scratch(void *ptr)
{
free(ptr);
}
#endif

Valin, et al.            Expires January 9, 2011              [Page 242]


Internet-Draft                 CELT codec                      July 2010

/** Copy n bytes of memory from src to dst. The 0* term provides compil\
e-time type checking  */
#ifndef OVERRIDE_CELT_COPY
#define CELT_COPY(dst, src, n) (memcpy((dst), (src), (n)*sizeof(*(dst))\
+ 0*((dst)-(src)) ))
#endif

/** Copy n bytes of memory from src to dst, allowing overlapping region\
s. The 0* term
provides compile-time type checking */
#ifndef OVERRIDE_CELT_MOVE
#define CELT_MOVE(dst, src, n) (memmove((dst), (src), (n)*sizeof(*(dst)\
) + 0*((dst)-(src)) ))
#endif

/** Set n bytes of memory to value of c, starting at address s */
#ifndef OVERRIDE_CELT_MEMSET
#define CELT_MEMSET(dst, c, n) (memset((dst), (c), (n)*sizeof(*(dst))))
#endif

#ifndef OVERRIDE_CELT_FATAL
static inline void
_celt_fatal(const char *str, const char *file, int line)
{
fprintf(stderr, "Fatal (internal) error in %s, line %d: %s\n",
file, line, str);
abort();
}
#endif

#ifndef OVERRIDE_CELT_WARNING
static inline void
celt_warning(const char *str)
{
#ifndef DISABLE_WARNINGS
fprintf(stderr, "warning: %s\n", str);
#endif
}
#endif

#ifndef OVERRIDE_CELT_WARNING_INT
static inline void
celt_warning_int(const char *str, int val)
{
#ifndef DISABLE_WARNINGS
fprintf(stderr, "warning: %s %d\n", str, val);
#endif
}

Valin, et al.            Expires January 9, 2011              [Page 243]


Internet-Draft                 CELT codec                      July 2010

#endif

#ifndef OVERRIDE_CELT_NOTIFY
static inline void
celt_notify(const char *str)
{
#endif
}
#endif

/* #ifdef __GNUC__ #pragma GCC poison printf sprintf #pragma GCC
poison malloc free realloc calloc #endif */

#endif                          /* OS_SUPPORT_H */

A.38.  stack_alloc.h

Xiph.Org Foundation */
/**
@file stack_alloc.h
@brief Temporary memory allocation on stack
*/
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE

Valin, et al.            Expires January 9, 2011              [Page 244]


Internet-Draft                 CELT codec                      July 2010

DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef STACK_ALLOC_H
#define STACK_ALLOC_H

#ifdef USE_ALLOCA
# ifdef WIN32
#  include <malloc.h>
# else
#  ifdef HAVE_ALLOCA_H
#   include <alloca.h>
#  else
#   include <stdlib.h>
#  endif
# endif
#endif

/**
* @def ALIGN(stack, size)
*
* Aligns the stack to a 'size' boundary
*
* @param stack Stack
* @param size  New size boundary
*/

/**
* @def PUSH(stack, size, type)
*
* Allocates 'size' elements of type 'type' on the stack
*
* @param stack Stack
* @param size  Number of elements
* @param type  Type of element
*/

/**
* @def VARDECL(var)
*
* Declare variable on stack

Valin, et al.            Expires January 9, 2011              [Page 245]


Internet-Draft                 CELT codec                      July 2010

*
* @param var Variable to declare
*/

/**
* @def ALLOC(var, size, type)
*
* Allocate 'size' elements of 'type' on stack
*
* @param var  Name of variable to allocate
* @param size Number of elements
* @param type Type of element
*/

#if defined(VAR_ARRAYS)

#define VARDECL(type, var)
#define ALLOC(var, size, type) type var[size]
#define SAVE_STACK
#define RESTORE_STACK
#define ALLOC_STACK

#elif defined(USE_ALLOCA)

#define VARDECL(type, var) type *var
#define ALLOC(var, size, type) var = ((type*)alloca(sizeof(type)*(size)\
))
#define SAVE_STACK
#define RESTORE_STACK
#define ALLOC_STACK

#else

#ifdef CELT_C
char           *global_stack = 0;
#else
extern char    *global_stack;
#endif                          /* CELT_C */

#ifdef ENABLE_VALGRIND

#include <valgrind/memcheck.h>

#ifdef CELT_C
char           *global_stack_top = 0;
#else
extern char    *global_stack_top;
#endif                          /* CELT_C */

Valin, et al.            Expires January 9, 2011              [Page 246]


Internet-Draft                 CELT codec                      July 2010

#define ALIGN(stack, size) ((stack) += ((size) - (long)(stack)) & ((siz\
e) - 1))
#define PUSH(stack, size, type) (VALGRIND_MAKE_MEM_NOACCESS(stack, glob\
al_stack_top-stack),ALIGN((stack),sizeof(type)/sizeof(char)),VALGRIND_M\
AKE_MEM_UNDEFINED(stack, ((size)*sizeof(type)/sizeof(char))),(stack)+=(\
2*(size)*sizeof(type)/sizeof(char)),(type*)((stack)-(2*(size)*sizeof(ty\
pe)/sizeof(char))))
#define RESTORE_STACK ((global_stack = _saved_stack),VALGRIND_MAKE_MEM_\
NOACCESS(global_stack, global_stack_top-global_stack))
#define ALLOC_STACK ((global_stack = (global_stack==0) ? ((global_stack\
_top=celt_alloc_scratch(GLOBAL_STACK_SIZE*2)+(GLOBAL_STACK_SIZE*2))-(GL\
OBAL_STACK_SIZE*2)) : global_stack),VALGRIND_MAKE_MEM_NOACCESS(global_s\
tack, global_stack_top-global_stack))

#else

#define ALIGN(stack, size) ((stack) += ((size) - (long)(stack)) & ((siz\
e) - 1))
#define PUSH(stack, size, type) (ALIGN((stack),sizeof(type)/sizeof(char\
)),(stack)+=(size)*(sizeof(type)/sizeof(char)),(type*)((stack)-(size)*(\
sizeof(type)/sizeof(char))))
#define RESTORE_STACK (global_stack = _saved_stack)
#define ALLOC_STACK (global_stack = (global_stack==0) ? celt_alloc_scra\
tch(GLOBAL_STACK_SIZE) : global_stack)

#endif                          /* ENABLE_VALGRIND */

#include "os_support.h"
#define VARDECL(type, var) type *var
#define ALLOC(var, size, type) var = PUSH(global_stack, size, type)
#define SAVE_STACK char *_saved_stack = global_stack;

#endif                          /* VAR_ARRAYS */

#endif                          /* STACK_ALLOC_H */

A.39.  celt_types.h

Valin, et al.            Expires January 9, 2011              [Page 247]


Internet-Draft                 CELT codec                      July 2010

#ifndef _CELT_TYPES_H
#define _CELT_TYPES_H

typedef short celt_int16;
typedef unsigned short celt_uint16;
typedef int celt_int32;
typedef unsigned int celt_uint32;
typedef long long celt_int64;
typedef unsigned long long celt_uint64;

#endif /* _CELT_TYPES_H */

A.40.  _kiss_fft_guts.h

/*

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer. *
Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution. * Neither the author nor the names of any
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. */

#ifndef KISS_FFT_GUTS_H

Valin, et al.            Expires January 9, 2011              [Page 248]


Internet-Draft                 CELT codec                      July 2010

#define KISS_FFT_GUTS_H

#define MIN(a,b) ((a)<(b) ? (a):(b))
#define MAX(a,b) ((a)>(b) ? (a):(b))

/* kiss_fft.h defines kiss_fft_scalar as either short or a float
type and defines typedef struct { kiss_fft_scalar r;
kiss_fft_scalar i; }kiss_fft_cpx; */
#include "kiss_fft.h"

#define MAXFACTORS 32
/* e.g. an fft of length 128 has 4 factors as far as kissfft is
concerned 4*4*4*2 */

struct kiss_fft_state {
int             nfft;
#ifndef FIXED_POINT
kiss_fft_scalar scale;
#endif
int             factors[2 * MAXFACTORS];
int            *bitrev;
kiss_twiddle_cpx twiddles[1];
};

/*
Explanation of macros dealing with complex math:

C_MUL(m,a,b) : m = a*b C_FIXDIV( c , div ) : if a fixed point
impl., c /= div. noop otherwise C_SUB( res, a,b) : res = a - b
C_SUBFROM( res , a) : res -= a C_ADDTO( res , a) : res += a */
#ifdef FIXED_POINT
#include "arch.h"

#ifdef DOUBLE_PRECISION

# define FRACBITS 31
# define SAMPPROD long long
#define SAMP_MAX 2147483647
#ifdef MIXED_PRECISION
#define TWID_MAX 32767
#define TRIG_UPSCALE 1
#else
#define TRIG_UPSCALE 65536
#define TWID_MAX 2147483647
#endif
#define EXT32(a) (a)

#else                           /* DOUBLE_PRECISION */

Valin, et al.            Expires January 9, 2011              [Page 249]


Internet-Draft                 CELT codec                      July 2010

# define FRACBITS 15
# define SAMPPROD celt_int32
#define SAMP_MAX 32767
#define TRIG_UPSCALE 1
#define EXT32(a) EXTEND32(a)

#endif                          /* !DOUBLE_PRECISION */

#define SAMP_MIN -SAMP_MAX

#if defined(CHECK_OVERFLOW)
#  define CHECK_OVERFLOW_OP(a,op,b)      if ( (SAMPPROD)(a) op (SAMPPRO\
D)(b) > SAMP_MAX || (SAMPPROD)(a) op (SAMPPROD)(b) < SAMP_MIN ) {      \
fprintf(stderr,"WARNING:overflow @ " __FILE__ "(%d): (%d " #op" %d) \
= %ld\n",__LINE__,(a),(b),(SAMPPROD)(a) op (SAMPPROD)(b) );  }

#endif

#   define smul(a,b) ( (SAMPPROD)(a)*(b) )
#   define sround( x )  (kiss_fft_scalar)( ( (x) + ((SAMPPROD)1<<(FRACB\
ITS-1)) ) >> FRACBITS )

#ifdef MIXED_PRECISION

#   define S_MUL(a,b) MULT16_32_Q15(b, a)

#   define C_MUL(m,a,b)       do{ (m).r = SUB32(S_MUL((a).r,(b).r) , S_\
MUL((a).i,(b).i));           (m).i = ADD32(S_MUL((a).r,(b).i) , S_MUL((\
a).i,(b).r)); }while(0)

#   define C_MULC(m,a,b)       do{ (m).r = ADD32(S_MUL((a).r,(b).r) , S\
_MUL((a).i,(b).i));           (m).i = SUB32(S_MUL((a).i,(b).r) , S_MUL(\
(a).r,(b).i)); }while(0)

#   define C_MUL4(m,a,b)       do{ (m).r = SHR(SUB32(S_MUL((a).r,(b).r)\
i) , S_MUL((a).i,(b).r)),2); }while(0)

#   define C_MULBYSCALAR( c, s )       do{ (c).r =  S_MUL( (c).r , s ) \
;          (c).i =  S_MUL( (c).i , s ) ; }while(0)

#   define DIVSCALAR(x,k)         (x) = S_MUL(  x, (TWID_MAX-((k)>>1))/\
(k)+1 )

#   define C_FIXDIV(c,div)         do {    DIVSCALAR( (c).r , div);    \
DIVSCALAR( (c).i  , div); }while (0)

Valin, et al.            Expires January 9, 2011              [Page 250]


Internet-Draft                 CELT codec                      July 2010

DD32((a).i,(b).i);     }while(0)

#define  C_SUB( res, a,b)    do {(res).r=SUB32((a).r,(b).r);  (res).i=S\
UB32((a).i,(b).i);     }while(0)

#define C_SUBFROM( res , a)    do {(res).r = ADD32((res).r,(a).r);  (re\
s).i = SUB32((res).i,(a).i);     }while(0)

#else                           /* MIXED_PRECISION */
#   define sround4( x )  (kiss_fft_scalar)( ( (x) + ((SAMPPROD)1<<(FRAC\
BITS-1)) ) >> (FRACBITS+2) )

#   define S_MUL(a,b) sround( smul(a,b) )

#   define C_MUL(m,a,b)       do{ (m).r = sround( smul((a).r,(b).r) - s\
mul((a).i,(b).i) );           (m).i = sround( smul((a).r,(b).i) + smul(\
(a).i,(b).r) ); }while(0)

#   define C_MULC(m,a,b)       do{ (m).r = sround( smul((a).r,(b).r) + \
smul((a).i,(b).i) );           (m).i = sround( smul((a).i,(b).r) - smul\
((a).r,(b).i) ); }while(0)

#   define C_MUL4(m,a,b)                do{ (m).r = sround4( smul((a).r\
,(b).r) - smul((a).i,(b).i) );                (m).i = sround4( smul((a)\
.r,(b).i) + smul((a).i,(b).r) ); }while(0)

#   define C_MULBYSCALAR( c, s )                do{ (c).r =  sround( sm\
ul( (c).r , s ) ) ;               (c).i =  sround( smul( (c).i , s ) ) \
; }while(0)

#   define DIVSCALAR(x,k)     (x) = sround( smul(  x, SAMP_MAX/k ) )

#   define C_FIXDIV(c,div)     do {    DIVSCALAR( (c).r , div);        \
DIVSCALAR( (c).i  , div); }while (0)

#endif                          /* !MIXED_PRECISION */

#else                           /* not FIXED_POINT */

#define EXT32(a) (a)

#   define S_MUL(a,b) ( (a)*(b) )
#define C_MUL(m,a,b)     do{ (m).r = (a).r*(b).r - (a).i*(b).i;        \
(m).i = (a).r*(b).i + (a).i*(b).r; }while(0)

Valin, et al.            Expires January 9, 2011              [Page 251]


Internet-Draft                 CELT codec                      July 2010

#define C_MULC(m,a,b)     do{ (m).r = (a).r*(b).r + (a).i*(b).i;       \
(m).i = (a).i*(b).r - (a).r*(b).i; }while(0)

#define C_MUL4(m,a,b) C_MUL(m,a,b)

#   define C_FIXDIV(c,div)      /* NOOP */
#   define C_MULBYSCALAR( c, s )     do{ (c).r *= (s);        (c).i *= \
(s); }while(0)

#endif

#ifndef CHECK_OVERFLOW_OP
#  define CHECK_OVERFLOW_OP(a,op,b)     /* noop */
#endif

#define  C_ADD( res, a,b)    do {         CHECK_OVERFLOW_OP((a).r,+,(b)\
.r)        CHECK_OVERFLOW_OP((a).i,+,(b).i)        (res).r=(a).r+(b).r;\
(res).i=(a).i+(b).i;     }while(0)

#define  C_SUB( res, a,b)    do {         CHECK_OVERFLOW_OP((a).r,-,(b)\
.r)        CHECK_OVERFLOW_OP((a).i,-,(b).i)        (res).r=(a).r-(b).r;\
(res).i=(a).i-(b).i;     }while(0)

#define C_ADDTO( res , a)    do {         CHECK_OVERFLOW_OP((res).r,+,(\
a).r)        CHECK_OVERFLOW_OP((res).i,+,(a).i)        (res).r += (a).r\
;  (res).i += (a).i;    }while(0)

#define C_SUBFROM( res , a)    do {        CHECK_OVERFLOW_OP((res).r,-,\
(a).r)        CHECK_OVERFLOW_OP((res).i,-,(a).i)        (res).r -= (a).\
r;  (res).i -= (a).i;     }while(0)

#ifdef FIXED_POINT
/* # define KISS_FFT_COS(phase)
TRIG_UPSCALE*floor(MIN(32767,MAX(-32767,.5+32768 * cos (phase))))
# define KISS_FFT_SIN(phase)
TRIG_UPSCALE*floor(MIN(32767,MAX(-32767,.5+32768 * sin (phase)))) */
#  define KISS_FFT_COS(phase)  floor(.5+TWID_MAX*cos (phase))
#  define KISS_FFT_SIN(phase)  floor(.5+TWID_MAX*sin (phase))
#  define HALF_OF(x) ((x)>>1)
#elif defined(USE_SIMD)
#  define KISS_FFT_COS(phase) _mm_set1_ps( cos(phase) )
#  define KISS_FFT_SIN(phase) _mm_set1_ps( sin(phase) )
#  define HALF_OF(x) ((x)*_mm_set1_ps(.5f))
#else
#  define KISS_FFT_COS(phase) (kiss_fft_scalar) cos(phase)

Valin, et al.            Expires January 9, 2011              [Page 252]


Internet-Draft                 CELT codec                      July 2010

#  define KISS_FFT_SIN(phase) (kiss_fft_scalar) sin(phase)
#  define HALF_OF(x) ((x)*.5f)
#endif

#define  kf_cexp(x,phase)     do{         (x)->r = KISS_FFT_COS(phase);\
(x)->i = KISS_FFT_SIN(phase);    }while(0)

#define  kf_cexp2(x,phase)    do{       (x)->r = TRIG_UPSCALE*celt_cos_\
norm((phase));      (x)->i = TRIG_UPSCALE*celt_cos_norm((phase)-32768);\
}while(0)

#endif                          /* KISS_FFT_GUTS_H */

A.41.  kiss_fft.h

/*
Copyright (c) 2003-2004, Mark Borgerding Lots of modifications by
Jean-Marc Valin Copyright (c) 2005-2007, Xiph.Org Foundation
Copyright (c) 2008, Xiph.Org Foundation, CSIRO

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer. *
Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution. * Neither the author nor the names of any
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE

Valin, et al.            Expires January 9, 2011              [Page 253]


Internet-Draft                 CELT codec                      July 2010

POSSIBILITY OF SUCH DAMAGE. */

#ifndef KISS_FFT_H
#define KISS_FFT_H

#include <stdlib.h>
#include <math.h>
#include "arch.h"

#ifdef __cplusplus
extern          "C" {
#endif

/*
ATTENTION! If you would like a : -- a utility that will handle
the caching of fft objects -- real-only (no imaginary time
component ) FFT -- a multi-dimensional FFT -- a command-line
utility to perform ffts -- a command-line utility to perform
fast-convolution filtering

Then see kfc.h kiss_fftr.h kiss_fftnd.h fftutil.c
kiss_fastfir.c in the tools/ directory. */

#ifdef USE_SIMD
# include <xmmintrin.h>
# define kiss_fft_scalar __m128
#define KISS_FFT_MALLOC(nbytes) memalign(16,nbytes)
#else
#define KISS_FFT_MALLOC celt_alloc
#endif

#ifdef FIXED_POINT
#include "arch.h"
#ifdef DOUBLE_PRECISION
#  define kiss_fft_scalar celt_int32
#  define kiss_twiddle_scalar celt_int32
#  define KF_SUFFIX _celt_double
#else
#  define kiss_fft_scalar celt_int16
#  define kiss_twiddle_scalar celt_int16
#  define KF_SUFFIX _celt_single
#endif
#else
# ifndef kiss_fft_scalar
/* default is float */
#   define kiss_fft_scalar float
#   define kiss_twiddle_scalar float
#   define KF_SUFFIX _celt_single

Valin, et al.            Expires January 9, 2011              [Page 254]


Internet-Draft                 CELT codec                      July 2010

# endif
#endif

/* This adds a suffix to all the kiss_fft functions so we can
easily link with more than one copy of the fft */
#define CAT_SUFFIX(a,b) a ## b
#define SUF(a,b) CAT_SUFFIX(a, b)

#define kiss_fft_alloc SUF(kiss_fft_alloc,KF_SUFFIX)
#define kf_work SUF(kf_work,KF_SUFFIX)
#define ki_work SUF(ki_work,KF_SUFFIX)
#define kiss_fft SUF(kiss_fft,KF_SUFFIX)
#define kiss_ifft SUF(kiss_ifft,KF_SUFFIX)
#define kiss_fft_stride SUF(kiss_fft_stride,KF_SUFFIX)
#define kiss_ifft_stride SUF(kiss_ifft_stride,KF_SUFFIX)

typedef struct {
kiss_fft_scalar r;
kiss_fft_scalar i;
} kiss_fft_cpx;

typedef struct {
kiss_twiddle_scalar r;
kiss_twiddle_scalar i;
} kiss_twiddle_cpx;

typedef struct kiss_fft_state *kiss_fft_cfg;

/**
*  kiss_fft_alloc
*
*  Initialize a FFT (or IFFT) algorithm's cfg/state buffer.
*
*  typical usage:      kiss_fft_cfg mycfg=kiss_fft_alloc(1024,0,NULL,N\
ULL);
*
*  The return value from fft_alloc is a cfg buffer used internally
*  by the fft routine or NULL.
*
*  If lenmem is NULL, then kiss_fft_alloc will allocate a cfg buffer u\
sing malloc.
*  The returned value should be free()d when done to avoid memory leak\
s.
*
*  The state can be placed in a user supplied buffer 'mem':
*  If lenmem is not NULL and mem is not NULL and *lenmem is large enou\
gh,
*      then the function places the cfg in mem and the size used in *l\

Valin, et al.            Expires January 9, 2011              [Page 255]


Internet-Draft                 CELT codec                      July 2010

enmem
*      and returns mem.
*
*  If lenmem is not NULL and ( mem is NULL or *lenmem is not large eno\
ugh),
*      then the function returns NULL and places the minimum cfg
*      buffer size in *lenmem.
* */

kiss_fft_cfg    kiss_fft_alloc(int nfft, void *mem,
size_t * lenmem);

void            kf_work(kiss_fft_cpx * Fout,
const kiss_fft_cpx * f,
const size_t fstride, int in_stride,
int *factors, const kiss_fft_cfg st, int N,
int s2, int m2);

/** Internal function. Can be useful when you want to do the bit-revers\
ing yourself */
void            ki_work(kiss_fft_cpx * Fout,
const kiss_fft_cpx * f,
const size_t fstride, int in_stride,
int *factors, const kiss_fft_cfg st, int N,
int s2, int m2);

/**
* kiss_fft(cfg,in_out_buf)
*
* Perform an FFT on a complex input buffer.
* for a forward FFT,
* fin should be  f[0] , f[1] , ... ,f[nfft-1]
* fout will be   F[0] , F[1] , ... ,F[nfft-1]
* Note that each element is complex and can be accessed like
f[k].r and f[k].i
* */
void            kiss_fft(kiss_fft_cfg cfg,
const kiss_fft_cpx * fin,
kiss_fft_cpx * fout);
void            kiss_ifft(kiss_fft_cfg cfg,
const kiss_fft_cpx * fin,
kiss_fft_cpx * fout);

/**
A more generic version of the above function. It reads its input from \
every Nth sample.
* */
void            kiss_fft_stride(kiss_fft_cfg cfg,

Valin, et al.            Expires January 9, 2011              [Page 256]


Internet-Draft                 CELT codec                      July 2010

const kiss_fft_cpx * fin,
kiss_fft_cpx * fout,
int fin_stride);
void            kiss_ifft_stride(kiss_fft_cfg cfg,
const kiss_fft_cpx * fin,
kiss_fft_cpx * fout,
int fin_stride);

/** If kiss_fft_alloc allocated a buffer, it is one contiguous
buffer and can be simply free()d when no longer needed*/
#define kiss_fft_free celt_free

#ifdef __cplusplus
}
#endif
#endif

A.42.  kiss_fft.c

/*
Copyright (c) 2003-2004, Mark Borgerding Lots of modifications by
Jean-Marc Valin Copyright (c) 2005-2007, Xiph.Org Foundation
Copyright (c) 2008, Xiph.Org Foundation, CSIRO

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer. *
Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution. * Neither the author nor the names of any
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,

Valin, et al.            Expires January 9, 2011              [Page 257]


Internet-Draft                 CELT codec                      July 2010

DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. */

/* config.h.  Generated from config.h.in by configure.  */
/* config.h.in.  Generated from configure.ac by autoheader.  */

/* This is a build of CELT */

/* Version extra */

/* Version major */

/* Version micro */

/* Version minor */

/* Complete version string */

#include "_kiss_fft_guts.h"
#include "arch.h"
#include "os_support.h"
#include "mathops.h"
#include "stack_alloc.h"

macros that are defined for complex numbers.  It also delares the
kf_ internal functions. */

static void
kf_bfly2(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{
kiss_fft_cpx   *Fout2;
kiss_twiddle_cpx *tw1;
int             i,
j;
kiss_fft_cpx   *Fout_beg = Fout;
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
Fout2 = Fout + m;
tw1 = st->twiddles;
for (j = 0; j < m; j++)
{

Valin, et al.            Expires January 9, 2011              [Page 258]


Internet-Draft                 CELT codec                      July 2010

kiss_fft_cpx    t;
Fout->r = (Fout->r);
Fout->i = (Fout->i);
Fout2->r = (Fout2->r);
Fout2->i = (Fout2->i);
C_MUL(t, *Fout2, *tw1);
tw1 += fstride;
C_SUB(*Fout2, *Fout, t);
++Fout2;
++Fout;
}
}
}

static void
ki_bfly2(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{
kiss_fft_cpx   *Fout2;
kiss_twiddle_cpx *tw1;
kiss_fft_cpx    t;
int             i,
j;
kiss_fft_cpx   *Fout_beg = Fout;
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
Fout2 = Fout + m;
tw1 = st->twiddles;
for (j = 0; j < m; j++)
{
C_MULC(t, *Fout2, *tw1);
tw1 += fstride;
C_SUB(*Fout2, *Fout, t);
++Fout2;
++Fout;
}
}
}

static void
kf_bfly4(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{

Valin, et al.            Expires January 9, 2011              [Page 259]


Internet-Draft                 CELT codec                      July 2010

kiss_twiddle_cpx *tw1,
*tw2,
*tw3;
kiss_fft_cpx    scratch[6];
const size_t    m2 = 2 * m;
const size_t    m3 = 3 * m;
int             i,
j;

kiss_fft_cpx   *Fout_beg = Fout;
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
tw3 = tw2 = tw1 = st->twiddles;
for (j = 0; j < m; j++)
{
C_MUL4(scratch[0], Fout[m], *tw1);
C_MUL4(scratch[1], Fout[m2], *tw2);
C_MUL4(scratch[2], Fout[m3], *tw3);

Fout->r = (Fout->r);
Fout->i = (Fout->i);
C_SUB(scratch[5], *Fout, scratch[1]);
C_SUB(scratch[4], scratch[0], scratch[2]);
Fout[m2].r = (Fout[m2].r);
Fout[m2].i = (Fout[m2].i);
C_SUB(Fout[m2], *Fout, scratch[3]);
tw1 += fstride;
tw2 += fstride * 2;
tw3 += fstride * 3;

Fout[m].r = scratch[5].r + scratch[4].i;
Fout[m].i = scratch[5].i - scratch[4].r;
Fout[m3].r = scratch[5].r - scratch[4].i;
Fout[m3].i = scratch[5].i + scratch[4].r;
++Fout;
}
}
}

static void
ki_bfly4(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{

Valin, et al.            Expires January 9, 2011              [Page 260]


Internet-Draft                 CELT codec                      July 2010

kiss_twiddle_cpx *tw1,
*tw2,
*tw3;
kiss_fft_cpx    scratch[6];
const size_t    m2 = 2 * m;
const size_t    m3 = 3 * m;
int             i,
j;

kiss_fft_cpx   *Fout_beg = Fout;
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
tw3 = tw2 = tw1 = st->twiddles;
for (j = 0; j < m; j++)
{
C_MULC(scratch[0], Fout[m], *tw1);
C_MULC(scratch[1], Fout[m2], *tw2);
C_MULC(scratch[2], Fout[m3], *tw3);

C_SUB(scratch[5], *Fout, scratch[1]);
C_SUB(scratch[4], scratch[0], scratch[2]);
C_SUB(Fout[m2], *Fout, scratch[3]);
tw1 += fstride;
tw2 += fstride * 2;
tw3 += fstride * 3;

Fout[m].r = scratch[5].r - scratch[4].i;
Fout[m].i = scratch[5].i + scratch[4].r;
Fout[m3].r = scratch[5].r + scratch[4].i;
Fout[m3].i = scratch[5].i - scratch[4].r;
++Fout;
}
}
}

static void
kf_bfly3(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{
int             i;
size_t          k;
const size_t    m2 = 2 * m;
kiss_twiddle_cpx *tw1,

Valin, et al.            Expires January 9, 2011              [Page 261]


Internet-Draft                 CELT codec                      July 2010

*tw2;
kiss_fft_cpx    scratch[5];
kiss_twiddle_cpx epi3;

kiss_fft_cpx   *Fout_beg = Fout;
epi3 = st->twiddles[fstride * m];
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
tw1 = tw2 = st->twiddles;
k = m;
do
{
C_FIXDIV(*Fout, 3);
C_FIXDIV(Fout[m], 3);
C_FIXDIV(Fout[m2], 3);

C_MUL(scratch[1], Fout[m], *tw1);
C_MUL(scratch[2], Fout[m2], *tw2);

C_SUB(scratch[0], scratch[1], scratch[2]);
tw1 += fstride;
tw2 += fstride * 2;

Fout[m].r = Fout->r - HALF_OF(scratch[3].r);
Fout[m].i = Fout->i - HALF_OF(scratch[3].i);

C_MULBYSCALAR(scratch[0], epi3.i);

Fout[m2].r = Fout[m].r + scratch[0].i;
Fout[m2].i = Fout[m].i - scratch[0].r;

Fout[m].r -= scratch[0].i;
Fout[m].i += scratch[0].r;

++Fout;
}
while (--k);
}
}

static void
ki_bfly3(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, size_t m, int N, int mm)

Valin, et al.            Expires January 9, 2011              [Page 262]


Internet-Draft                 CELT codec                      July 2010

{
size_t          i,
k;
const size_t    m2 = 2 * m;
kiss_twiddle_cpx *tw1,
*tw2;
kiss_fft_cpx    scratch[5];
kiss_twiddle_cpx epi3;

kiss_fft_cpx   *Fout_beg = Fout;
epi3 = st->twiddles[fstride * m];
for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
tw1 = tw2 = st->twiddles;
k = m;
do
{

C_MULC(scratch[1], Fout[m], *tw1);
C_MULC(scratch[2], Fout[m2], *tw2);

C_SUB(scratch[0], scratch[1], scratch[2]);
tw1 += fstride;
tw2 += fstride * 2;

Fout[m].r = Fout->r - HALF_OF(scratch[3].r);
Fout[m].i = Fout->i - HALF_OF(scratch[3].i);

C_MULBYSCALAR(scratch[0], -epi3.i);

Fout[m2].r = Fout[m].r + scratch[0].i;
Fout[m2].i = Fout[m].i - scratch[0].r;

Fout[m].r -= scratch[0].i;
Fout[m].i += scratch[0].r;

++Fout;
}
while (--k);
}
}

static void
kf_bfly5(kiss_fft_cpx * Fout,

Valin, et al.            Expires January 9, 2011              [Page 263]


Internet-Draft                 CELT codec                      July 2010

const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{
kiss_fft_cpx   *Fout0,
*Fout1,
*Fout2,
*Fout3,
*Fout4;
int             i,
u;
kiss_fft_cpx    scratch[13];
kiss_twiddle_cpx *twiddles = st->twiddles;
kiss_twiddle_cpx *tw;
kiss_twiddle_cpx ya,
yb;
kiss_fft_cpx   *Fout_beg = Fout;

ya = twiddles[fstride * m];
yb = twiddles[fstride * 2 * m];
tw = st->twiddles;

for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
Fout0 = Fout;
Fout1 = Fout0 + m;
Fout2 = Fout0 + 2 * m;
Fout3 = Fout0 + 3 * m;
Fout4 = Fout0 + 4 * m;

for (u = 0; u < m; ++u)
{
C_FIXDIV(*Fout0, 5);
C_FIXDIV(*Fout1, 5);
C_FIXDIV(*Fout2, 5);
C_FIXDIV(*Fout3, 5);
C_FIXDIV(*Fout4, 5);
scratch[0] = *Fout0;

C_MUL(scratch[1], *Fout1, tw[u * fstride]);
C_MUL(scratch[2], *Fout2, tw[2 * u * fstride]);
C_MUL(scratch[3], *Fout3, tw[3 * u * fstride]);
C_MUL(scratch[4], *Fout4, tw[4 * u * fstride]);

C_SUB(scratch[10], scratch[1], scratch[4]);
C_SUB(scratch[9], scratch[2], scratch[3]);

Valin, et al.            Expires January 9, 2011              [Page 264]


Internet-Draft                 CELT codec                      July 2010

Fout0->r += scratch[7].r + scratch[8].r;
Fout0->i += scratch[7].i + scratch[8].i;

scratch[5].r =
scratch[0].r + S_MUL(scratch[7].r,
ya.r) + S_MUL(scratch[8].r, yb.r);
scratch[5].i =
scratch[0].i + S_MUL(scratch[7].i,
ya.r) + S_MUL(scratch[8].i, yb.r);

scratch[6].r =
S_MUL(scratch[10].i, ya.i) + S_MUL(scratch[9].i, yb.i);
scratch[6].i =
-S_MUL(scratch[10].r, ya.i) - S_MUL(scratch[9].r, yb.i);

C_SUB(*Fout1, scratch[5], scratch[6]);

scratch[11].r =
scratch[0].r + S_MUL(scratch[7].r,
yb.r) + S_MUL(scratch[8].r, ya.r);
scratch[11].i =
scratch[0].i + S_MUL(scratch[7].i,
yb.r) + S_MUL(scratch[8].i, ya.r);
scratch[12].r =
-S_MUL(scratch[10].i, yb.i) + S_MUL(scratch[9].i, ya.i);
scratch[12].i =
S_MUL(scratch[10].r, yb.i) - S_MUL(scratch[9].r, ya.i);

C_SUB(*Fout3, scratch[11], scratch[12]);

++Fout0;
++Fout1;
++Fout2;
++Fout3;
++Fout4;
}
}
}

static void
ki_bfly5(kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st, int m, int N, int mm)
{
kiss_fft_cpx   *Fout0,
*Fout1,

Valin, et al.            Expires January 9, 2011              [Page 265]


Internet-Draft                 CELT codec                      July 2010

*Fout2,
*Fout3,
*Fout4;
int             i,
u;
kiss_fft_cpx    scratch[13];
kiss_twiddle_cpx *twiddles = st->twiddles;
kiss_twiddle_cpx *tw;
kiss_twiddle_cpx ya,
yb;
kiss_fft_cpx   *Fout_beg = Fout;

ya = twiddles[fstride * m];
yb = twiddles[fstride * 2 * m];
tw = st->twiddles;

for (i = 0; i < N; i++)
{
Fout = Fout_beg + i * mm;
Fout0 = Fout;
Fout1 = Fout0 + m;
Fout2 = Fout0 + 2 * m;
Fout3 = Fout0 + 3 * m;
Fout4 = Fout0 + 4 * m;

for (u = 0; u < m; ++u)
{
scratch[0] = *Fout0;

C_MULC(scratch[1], *Fout1, tw[u * fstride]);
C_MULC(scratch[2], *Fout2, tw[2 * u * fstride]);
C_MULC(scratch[3], *Fout3, tw[3 * u * fstride]);
C_MULC(scratch[4], *Fout4, tw[4 * u * fstride]);

C_SUB(scratch[10], scratch[1], scratch[4]);
C_SUB(scratch[9], scratch[2], scratch[3]);

Fout0->r += scratch[7].r + scratch[8].r;
Fout0->i += scratch[7].i + scratch[8].i;

scratch[5].r =
scratch[0].r + S_MUL(scratch[7].r,
ya.r) + S_MUL(scratch[8].r, yb.r);
scratch[5].i =
scratch[0].i + S_MUL(scratch[7].i,
ya.r) + S_MUL(scratch[8].i, yb.r);

Valin, et al.            Expires January 9, 2011              [Page 266]


Internet-Draft                 CELT codec                      July 2010

scratch[6].r =
-S_MUL(scratch[10].i, ya.i) - S_MUL(scratch[9].i, yb.i);
scratch[6].i =
S_MUL(scratch[10].r, ya.i) + S_MUL(scratch[9].r, yb.i);

C_SUB(*Fout1, scratch[5], scratch[6]);

scratch[11].r =
scratch[0].r + S_MUL(scratch[7].r,
yb.r) + S_MUL(scratch[8].r, ya.r);
scratch[11].i =
scratch[0].i + S_MUL(scratch[7].i,
yb.r) + S_MUL(scratch[8].i, ya.r);
scratch[12].r =
S_MUL(scratch[10].i, yb.i) - S_MUL(scratch[9].i, ya.i);
scratch[12].i =
-S_MUL(scratch[10].r, yb.i) + S_MUL(scratch[9].r, ya.i);

C_SUB(*Fout3, scratch[11], scratch[12]);

++Fout0;
++Fout1;
++Fout2;
++Fout3;
++Fout4;
}
}
}

static
void
compute_bitrev_table(int Fout,
int *f,
const size_t fstride,
int in_stride,
int *factors, const kiss_fft_cfg st)
{
const int       p = *factors++;       /* the radix */
const int       m = *factors++;       /* stage's fft length/p */

/* printf ("fft %d %d %d %d %d %d\n", p*m, m, p, s2,
fstride*in_stride, N); */
if (m == 1)
{
int             j;
for (j = 0; j < p; j++)

Valin, et al.            Expires January 9, 2011              [Page 267]


Internet-Draft                 CELT codec                      July 2010

{
*f = Fout + j;
f += fstride * in_stride;
}
} else
{
int             j;
for (j = 0; j < p; j++)
{
compute_bitrev_table(Fout, f, fstride * p, in_stride, factors,
st);
f += fstride * in_stride;
Fout += m;
}
}
}

void
kf_work(kiss_fft_cpx * Fout,
const kiss_fft_cpx * f,
const size_t fstride,
int in_stride,
int *factors, const kiss_fft_cfg st, int N, int s2, int m2)
{
const int       p = *factors++;       /* the radix */
const int       m = *factors++;       /* stage's fft length/p */
/* printf ("fft %d %d %d %d %d %d %d\n", p*m, m, p, s2,
fstride*in_stride, N, m2); */
if (m != 1)
kf_work(Fout, f, fstride * p, in_stride, factors, st, N * p,
fstride * in_stride, m);

switch (p)
{
case 2:
kf_bfly2(Fout, fstride, st, m, N, m2);
break;
case 4:
kf_bfly4(Fout, fstride, st, m, N, m2);
break;

case 3:
kf_bfly3(Fout, fstride, st, m, N, m2);
break;
case 5:
kf_bfly5(Fout, fstride, st, m, N, m2);
break;

Valin, et al.            Expires January 9, 2011              [Page 268]


Internet-Draft                 CELT codec                      July 2010

}
}

void
ki_work(kiss_fft_cpx * Fout,
const kiss_fft_cpx * f,
const size_t fstride,
int in_stride,
int *factors, const kiss_fft_cfg st, int N, int s2, int m2)
{
const int       p = *factors++;       /* the radix */
const int       m = *factors++;       /* stage's fft length/p */
/* printf ("fft %d %d %d %d %d %d %d\n", p*m, m, p, s2,
fstride*in_stride, N, m2); */
if (m != 1)
ki_work(Fout, f, fstride * p, in_stride, factors, st, N * p,
fstride * in_stride, m);

switch (p)
{
case 2:
ki_bfly2(Fout, fstride, st, m, N, m2);
break;
case 4:
ki_bfly4(Fout, fstride, st, m, N, m2);
break;

case 3:
ki_bfly3(Fout, fstride, st, m, N, m2);
break;
case 5:
ki_bfly5(Fout, fstride, st, m, N, m2);
break;

}
}

/* facbuf is populated by p1,m1,p2,m2, ... where p[i] * m[i] =
m[i-1] m0 = n */
static
int
kf_factor(int n, int *facbuf)
{
int             p = 4;

/* factor out powers of 4, powers of 2, then any remaining primes */
do
{

Valin, et al.            Expires January 9, 2011              [Page 269]


Internet-Draft                 CELT codec                      July 2010

while (n % p)
{
switch (p)
{
case 4:
p = 2;
break;
case 2:
p = 3;
break;
default:
p += 2;
break;
}
if (p > 32000 || (celt_int32) p * (celt_int32) p > n)
}
n /= p;
if (p > 5)
{
celt_warning("Only powers of 2, 3 and 5 are supported");
return 0;
}
*facbuf++ = p;
*facbuf++ = n;
}
while (n > 1);
return 1;
}
/*
*
* User-callable function to allocate all necessary storage space for t\
he fft.
*
* The return value is a contiguous block of memory, allocated with mal\
loc.  As such,
* It can be freed with free(), rather than a kiss_fft-specific functio\
n.
* */
kiss_fft_cfg
kiss_fft_alloc(int nfft, void *mem, size_t * lenmem)
{
kiss_fft_cfg    st = NULL;
size_t          memneeded = sizeof(struct kiss_fft_state) + sizeof(ki\
ss_twiddle_cpx) * (nfft - 1) + sizeof(int) * nfft;       /* twiddle
\
factors */

Valin, et al.            Expires January 9, 2011              [Page 270]


Internet-Draft                 CELT codec                      July 2010

if (lenmem == NULL)
{
st = (kiss_fft_cfg) KISS_FFT_MALLOC(memneeded);
} else
{
if (mem != NULL && *lenmem >= memneeded)
st = (kiss_fft_cfg) mem;
*lenmem = memneeded;
}
if (st)
{
int             i;
st->nfft = nfft;

st->scale = 1. / nfft;

for (i = 0; i < nfft; ++i)
{
const double    pi = 3.14159265358979323846264338327;
double          phase = (-2 * pi / nfft) * i;
kf_cexp(st->twiddles + i, phase);
}

if (!kf_factor(nfft, st->factors))
{
kiss_fft_free(st);
return NULL;
}

/* bitrev */
st->bitrev =
(int *) ((char *) st + memneeded - sizeof(int) * nfft);
compute_bitrev_table(0, st->bitrev, 1, 1, st->factors, st);
}
return st;
}

void
kiss_fft_stride(kiss_fft_cfg st, const kiss_fft_cpx * fin,
kiss_fft_cpx * fout, int in_stride)
{
if (fin == fout)
{
celt_fatal("In-place FFT not supported");
} else
{
/* Bit-reverse the input */
int             i;

Valin, et al.            Expires January 9, 2011              [Page 271]


Internet-Draft                 CELT codec                      July 2010

for (i = 0; i < st->nfft; i++)
{
fout[st->bitrev[i]] = fin[i];

fout[st->bitrev[i]].r *= st->scale;
fout[st->bitrev[i]].i *= st->scale;

}
kf_work(fout, fin, 1, in_stride, st->factors, st, 1, in_stride,
1);
}
}

void
kiss_fft(kiss_fft_cfg cfg, const kiss_fft_cpx * fin,
kiss_fft_cpx * fout)
{
kiss_fft_stride(cfg, fin, fout, 1);
}

void
kiss_ifft_stride(kiss_fft_cfg st, const kiss_fft_cpx * fin,
kiss_fft_cpx * fout, int in_stride)
{
if (fin == fout)
{
celt_fatal("In-place FFT not supported");
} else
{
/* Bit-reverse the input */
int             i;
for (i = 0; i < st->nfft; i++)
fout[st->bitrev[i]] = fin[i];
ki_work(fout, fin, 1, in_stride, st->factors, st, 1, in_stride,
1);
}
}

void
kiss_ifft(kiss_fft_cfg cfg, const kiss_fft_cpx * fin,
kiss_fft_cpx * fout)
{
kiss_ifft_stride(cfg, fin, fout, 1);
}

Valin, et al.            Expires January 9, 2011              [Page 272]


Internet-Draft                 CELT codec                      July 2010

A.43.  kiss_fftr.h

/*
Original version: Copyright (c) 2003-2004, Mark Borgerding
Followed by heavy modifications: Copyright (c) 2007-2008,
Jean-Marc Valin

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer. *
Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution. * Neither the author nor the names of any
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. */

#ifndef KISS_FTR_H
#define KISS_FTR_H

#include "kiss_fft.h"
#ifdef __cplusplus
extern          "C" {
#endif

#define kiss_fftr_alloc SUF(kiss_fftr_alloc,KF_SUFFIX)
#define kiss_fftr_inplace SUF(kiss_fftr_inplace,KF_SUFFIX)
#define kiss_fftr_alloc SUF(kiss_fftr_alloc,KF_SUFFIX)

Valin, et al.            Expires January 9, 2011              [Page 273]


Internet-Draft                 CELT codec                      July 2010

#define kiss_fftr_twiddles SUF(kiss_fftr_twiddles,KF_SUFFIX)
#define kiss_fftr SUF(kiss_fftr,KF_SUFFIX)
#define kiss_fftri SUF(kiss_fftri,KF_SUFFIX)

/*

Real optimized version can save about 45% cpu time vs. complex
fft of a real seq.

*/

struct kiss_fftr_state {
kiss_fft_cfg    substate;
kiss_twiddle_cpx *super_twiddles;
#ifdef USE_SIMD
#endif
};

typedef struct kiss_fftr_state *kiss_fftr_cfg;

kiss_fftr_cfg   kiss_fftr_alloc(int nfft, void *mem,
size_t * lenmem);
/*
nfft must be even

If you don't care to allocate space, use mem = lenmem = NULL */

/*
input timedata has nfft scalar points output freqdata has
nfft/2+1 complex points, packed into nfft scalar points */
void            kiss_fftr_twiddles(kiss_fftr_cfg st,
kiss_fft_scalar * freqdata);

void            kiss_fftr(kiss_fftr_cfg st,
const kiss_fft_scalar * timedata,
kiss_fft_scalar * freqdata);
void            kiss_fftr_inplace(kiss_fftr_cfg st,
kiss_fft_scalar * X);

void            kiss_fftri(kiss_fftr_cfg st,
const kiss_fft_scalar * freqdata,
kiss_fft_scalar * timedata);

/*
input freqdata has nfft/2+1 complex points, packed into nfft
scalar points output timedata has nfft scalar points */

Valin, et al.            Expires January 9, 2011              [Page 274]


Internet-Draft                 CELT codec                      July 2010

#define kiss_fftr_free speex_free

#ifdef __cplusplus
}
#endif
#endif

A.44.  kiss_fftr.c

/*
Original version: Copyright (c) 2003-2004, Mark Borgerding
Followed by heavy modifications: Copyright (c) 2007-2008,
Jean-Marc Valin

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer. *
Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution. * Neither the author nor the names of any
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. */

/* config.h.  Generated from config.h.in by configure.  */
/* config.h.in.  Generated from configure.ac by autoheader.  */

/* This is a build of CELT */

Valin, et al.            Expires January 9, 2011              [Page 275]


Internet-Draft                 CELT codec                      July 2010

/* Version extra */

/* Version major */

/* Version micro */

/* Version minor */

/* Complete version string */

#include "os_support.h"
#include "mathops.h"
#include "kiss_fftr.h"
#include "_kiss_fft_guts.h"

kiss_fftr_cfg
kiss_fftr_alloc(int nfft, void *mem, size_t * lenmem)
{
int             i;
int             twiddle_size;
kiss_fftr_cfg   st = NULL;
size_t          subsize,
memneeded;

if (nfft & 1)
{
celt_warning("Real FFT optimization must be even.\n");
return NULL;
}
nfft >>= 1;
twiddle_size = nfft / 2 + 1;
kiss_fft_alloc(nfft, NULL, &subsize);
memneeded =
sizeof(struct kiss_fftr_state) + subsize +
sizeof(kiss_twiddle_cpx) * twiddle_size;

if (lenmem == NULL)
{
st = (kiss_fftr_cfg) KISS_FFT_MALLOC(memneeded);
} else
{
if (*lenmem >= memneeded)
st = (kiss_fftr_cfg) mem;
*lenmem = memneeded;
}
if (!st)
return NULL;

Valin, et al.            Expires January 9, 2011              [Page 276]


Internet-Draft                 CELT codec                      July 2010

st->substate = (kiss_fft_cfg) (st + 1);       /* just beyond
kiss_fftr_state
struct */
st->super_twiddles =
(kiss_twiddle_cpx *) (((char *) st->substate) + subsize);
kiss_fft_alloc(nfft, st->substate, &subsize);

st->substate->scale *= .5;
for (i = 0; i < twiddle_size; ++i)
{
const double    pi = 3.14159265358979323846264338327;
double          phase = pi * (((double) i) / nfft + .5);
kf_cexp(st->super_twiddles + i, phase);
}

return st;
}

void
kiss_fftr_twiddles(kiss_fftr_cfg st, kiss_fft_scalar * freqdata)
{
/* input buffer timedata is stored row-wise */
int             k,
ncfft;
kiss_fft_cpx    f2k,
f1k,
tdc,
tw;

ncfft = st->substate->nfft;

/* The real part of the DC element of the frequency spectrum in
st->tmpbuf * contains the sum of the even-numbered elements of
the input time sequence * The imag part is the sum of the
odd-numbered elements * * The sum of tdc.r and tdc.i is the sum
of the input time sequence. * yielding DC of input time
sequence * The difference of tdc.r - tdc.i is the sum of the
input (dot product) [1,-1,1,-1... * yielding Nyquist bin of
input time sequence */

tdc.r = freqdata[0];
tdc.i = freqdata[1];
C_FIXDIV(tdc, 2);
CHECK_OVERFLOW_OP(tdc.r, +, tdc.i);
CHECK_OVERFLOW_OP(tdc.r, -, tdc.i);
freqdata[0] = tdc.r + tdc.i;
freqdata[1] = tdc.r - tdc.i;

Valin, et al.            Expires January 9, 2011              [Page 277]


Internet-Draft                 CELT codec                      July 2010

for (k = 1; k <= ncfft / 2; ++k)
{
f2k.r =
(((EXT32(freqdata[2 * k])) -
(EXT32(freqdata[2 * (ncfft - k)]))));
f2k.i =
(((EXT32(freqdata[2 * k + 1])) +
(EXT32(freqdata[2 * (ncfft - k) + 1]))));

f1k.r =
(((EXT32(freqdata[2 * k])) +
(EXT32(freqdata[2 * (ncfft - k)]))));
f1k.i =
(((EXT32(freqdata[2 * k + 1])) -
(EXT32(freqdata[2 * (ncfft - k) + 1]))));

C_MULC(tw, f2k, st->super_twiddles[k]);

freqdata[2 * k] = HALF_OF(f1k.r + tw.r);
freqdata[2 * k + 1] = HALF_OF(f1k.i + tw.i);
freqdata[2 * (ncfft - k)] = HALF_OF(f1k.r - tw.r);
freqdata[2 * (ncfft - k) + 1] = HALF_OF(tw.i - f1k.i);

}
}

void
kiss_fftr(kiss_fftr_cfg st, const kiss_fft_scalar * timedata,
kiss_fft_scalar * freqdata)
{
/* perform the parallel fft of two real signals packed in
real,imag */
kiss_fft(st->substate, (const kiss_fft_cpx *) timedata,
(kiss_fft_cpx *) freqdata);

kiss_fftr_twiddles(st, freqdata);
}

void
kiss_fftr_inplace(kiss_fftr_cfg st, kiss_fft_scalar * X)
{
kf_work((kiss_fft_cpx *) X, NULL, 1, 1, st->substate->factors,
st->substate, 1, 1, 1);
kiss_fftr_twiddles(st, X);
}

void
kiss_fftri(kiss_fftr_cfg st, const kiss_fft_scalar * freqdata,

Valin, et al.            Expires January 9, 2011              [Page 278]


Internet-Draft                 CELT codec                      July 2010

kiss_fft_scalar * timedata)
{
/* input buffer timedata is stored row-wise */
int             k,
ncfft;

ncfft = st->substate->nfft;

timedata[2 * st->substate->bitrev[0]] = freqdata[0] + freqdata[1];
timedata[2 * st->substate->bitrev[0] + 1] =
freqdata[0] - freqdata[1];
for (k = 1; k <= ncfft / 2; ++k)
{
kiss_fft_cpx    fk,
fnkc,
fek,
fok,
tmp;
int             k1,
k2;
k1 = st->substate->bitrev[k];
k2 = st->substate->bitrev[ncfft - k];
fk.r = freqdata[2 * k];
fk.i = freqdata[2 * k + 1];
fnkc.r = freqdata[2 * (ncfft - k)];
fnkc.i = -freqdata[2 * (ncfft - k) + 1];

C_SUB(tmp, fk, fnkc);
C_MUL(fok, tmp, st->super_twiddles[k]);
timedata[2 * k1] = fek.r + fok.r;
timedata[2 * k1 + 1] = fek.i + fok.i;
timedata[2 * k2] = fek.r - fok.r;
timedata[2 * k2 + 1] = fok.i - fek.i;
}
ki_work((kiss_fft_cpx *) timedata, NULL, 1, 1,
st->substate->factors, st->substate, 1, 1, 1);
}

A.45.  kfft_single.h

/* Copyright (c) 2008 Xiph.Org Foundation, CSIRO */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

Valin, et al.            Expires January 9, 2011              [Page 279]


Internet-Draft                 CELT codec                      July 2010

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef KFFT_SINGLE_H
#define KFFT_SINGLE_H

#ifdef ENABLE_TI_DSPLIB55

#include "dsplib.h"

#define real16_fft_alloc(length) NULL
#define real16_fft_free(state)
#define BITREV(state, i) (i)

#define real16_fft_inplace(state, X, nx)    (      cfft_SCALE(X,nx/2), \
cbrev(X,X,nx/2),      unpack(X,nx)    )

#define real16_ifft(state, X, Y, nx)     (      unpacki(X, nx),      ci\
fft_NOSCALE(X,nx/2),      cbrev(X,Y,nx/2)    )

#else                           /* ENABLE_TI_DSPLIB */

#ifdef FIXED_POINT

Valin, et al.            Expires January 9, 2011              [Page 280]


Internet-Draft                 CELT codec                      July 2010

#ifdef DOUBLE_PRECISION
#undef DOUBLE_PRECISION
#endif

#ifdef MIXED_PRECISION
#undef MIXED_PRECISION
#endif

#endif                          /* FIXED_POINT */

#include "kiss_fft.h"
#include "kiss_fftr.h"
#include "_kiss_fft_guts.h"

#define real16_fft_alloc(length) kiss_fftr_alloc_celt_single(length, 0,\
0);
#define real16_fft_free(state) kiss_fft_free(state)
#define real16_fft_inplace(state, X, nx) kiss_fftr_inplace(state,X)
#define BITREV(state, i) ((state)->substate->bitrev[i])
#define real16_ifft(state, X, Y, nx) kiss_fftri(state,X, Y)

#endif                          /* !ENABLE_TI_DSPLIB */

#endif                          /* KFFT_SINGLE_H */

A.46.  kfft_double.h

/* Copyright (c) 2008 Xiph.Org Foundation, CSIRO */
/*
Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided
with the distribution.

- Neither the name of the Xiph.org Foundation nor the names of
its contributors may be used to endorse or promote products
derived from this software without specific prior written
permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND

Valin, et al.            Expires January 9, 2011              [Page 281]


Internet-Draft                 CELT codec                      July 2010

CONTRIBUTORS AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE. */

#ifndef KFFT_DOUBLE_H
#define KFFT_DOUBLE_H

#ifdef ENABLE_TI_DSPLIB55

#include "dsplib.h"
#include "_kiss_fft_guts.h"

#define cpx32_fft_alloc(length) NULL
#define cpx32_fft_free(state)

#define cpx32_fft(state, X, Y, nx)    (      cfft32_SCALE(X,nx),      c\
brev32(X,Y,nx)    )

#define cpx32_ifft(state, X, Y, nx)     (      cifft32_NOSCALE(X,nx),  \
cbrev32(X,Y,nx)    )

#elif defined(ENABLE_TI_DSPLIB64)

#include "kiss_fft.h"
#include "_kiss_fft_guts.h"
#include "c64_fft.h"

#define cpx32_fft_alloc(length)     (kiss_fft_cfg)(c64_fft32_alloc(leng\
th, 0, 0))
#define cpx32_fft_free(state)         c64_fft32_free((c64_fft_t *)state)
#define cpx32_fft(state, X, Y, nx)     c64_fft32 ((c64_fft_t *)state, (\
const celt_int32 *)(X), (celt_int32 *)(Y))
#define cpx32_ifft(state, X, Y, nx)     c64_ifft32((c64_fft_t *)state, \
(const celt_int32 *)(X), (celt_int32 *)(Y))

#else                           /* ENABLE_TI_DSPLIB55/64 */

#include "kiss_fft.h"
#include "_kiss_fft_guts.h"

Valin, et al.            Expires January 9, 2011              [Page 282]


Internet-Draft                 CELT codec                      July 2010

#define cpx32_fft_alloc(length) kiss_fft_alloc(length, 0, 0);
#define cpx32_fft_free(state) kiss_fft_free(state)
#define cpx32_fft(state, X, Y, nx) kiss_fft(state,(const kiss_fft_cpx *\
)(X), (kiss_fft_cpx *)(Y))
#define cpx32_ifft(state, X, Y, nx) kiss_ifft(state,(const kiss_fft_cpx\
*)(X), (kiss_fft_cpx *)(Y))

#endif                          /* !ENABLE_TI_DSPLIB */

#endif                          /* KFFT_DOUBLE_H */

A.47.  config.h

/* config.h.  Generated from config.h.in by configure.  */
/* config.h.in.  Generated from configure.ac by autoheader.  */

/* This is a build of CELT */
#define CELT_BUILD /**/

/* Version extra */
#define CELT_EXTRA_VERSION ""

/* Version major */
#define CELT_MAJOR_VERSION 0

/* Version micro */
#define CELT_MICRO_VERSION 2

/* Version minor */
#define CELT_MINOR_VERSION 5

/* Complete version string */
#define CELT_VERSION "0.6.0"

#define restrict

Valin, et al.            Expires January 9, 2011              [Page 283]


Internet-Draft                 CELT codec                      July 2010

Jean-Marc Valin
Octasic Semiconductor
4101, Molson Street, suite 300
Montreal, Quebec  H1Y 3L1

Email: jean-marc.valin@octasic.com

Timothy B. Terriberry
Xiph.Org Foundation

Email: tterribe@xiph.org

Gregory Maxwell
Juniper Networks
2251 Corporate Park Drive, Suite 100
Herndon, VA  20171-1817
USA

Email: gmaxwell@juniper.net

Christopher Montgomery
Xiph.Org Foundation

Email: xiphmont@xiph.org

Valin, et al.            Expires January 9, 2011              [Page 284]



Html markup produced by rfcmarkup 1.126, available from https://tools.ietf.org/tools/rfcmarkup/