921 lines
28 KiB
C
921 lines
28 KiB
C
/* (C) 2007-2008 Timothy B. Terriberry
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(C) 2008 Jean-Marc Valin */
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/*
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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- Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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- Neither the name of the Xiph.org Foundation nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#include "os_support.h"
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#include <stdlib.h>
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#include <string.h>
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#include "cwrs.h"
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#include "mathops.h"
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#include "arch.h"
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/*Guaranteed to return a conservatively large estimate of the binary logarithm
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with frac bits of fractional precision.
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Tested for all possible 32-bit inputs with frac=4, where the maximum
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overestimation is 0.06254243 bits.*/
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int log2_frac(ec_uint32 val, int frac)
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{
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int l;
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l=EC_ILOG(val);
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if(val&val-1){
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/*This is (val>>l-16), but guaranteed to round up, even if adding a bias
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before the shift would cause overflow (e.g., for 0xFFFFxxxx).*/
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if(l>16)val=(val>>l-16)+((val&(1<<l-16)-1)+(1<<l-16)-1>>l-16);
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else val<<=16-l;
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l=l-1<<frac;
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/*Note that we always need one iteration, since the rounding up above means
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that we might need to adjust the integer part of the logarithm.*/
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do{
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int b;
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b=(int)(val>>16);
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l+=b<<frac;
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val=val+b>>b;
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val=val*val+0x7FFF>>15;
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}
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while(frac-->0);
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/*If val is not exactly 0x8000, then we have to round up the remainder.*/
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return l+(val>0x8000);
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}
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/*Exact powers of two require no rounding.*/
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else return l-1<<frac;
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}
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#define MASK32 (0xFFFFFFFF)
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/*INV_TABLE[i] holds the multiplicative inverse of (2*i+1) mod 2**32.*/
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static const celt_uint32_t INV_TABLE[128]={
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0x00000001,0xAAAAAAAB,0xCCCCCCCD,0xB6DB6DB7,
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0x38E38E39,0xBA2E8BA3,0xC4EC4EC5,0xEEEEEEEF,
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0xF0F0F0F1,0x286BCA1B,0x3CF3CF3D,0xE9BD37A7,
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0xC28F5C29,0x684BDA13,0x4F72C235,0xBDEF7BDF,
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0x3E0F83E1,0x8AF8AF8B,0x914C1BAD,0x96F96F97,
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0xC18F9C19,0x2FA0BE83,0xA4FA4FA5,0x677D46CF,
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0x1A1F58D1,0xFAFAFAFB,0x8C13521D,0x586FB587,
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0xB823EE09,0xA08AD8F3,0xC10C9715,0xBEFBEFBF,
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0xC0FC0FC1,0x07A44C6B,0xA33F128D,0xE327A977,
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0xC7E3F1F9,0x962FC963,0x3F2B3885,0x613716AF,
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0x781948B1,0x2B2E43DB,0xFCFCFCFD,0x6FD0EB67,
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0xFA3F47E9,0xD2FD2FD3,0x3F4FD3F5,0xD4E25B9F,
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0x5F02A3A1,0xBF5A814B,0x7C32B16D,0xD3431B57,
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0xD8FD8FD9,0x8D28AC43,0xDA6C0965,0xDB195E8F,
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0x0FDBC091,0x61F2A4BB,0xDCFDCFDD,0x46FDD947,
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0x56BE69C9,0xEB2FDEB3,0x26E978D5,0xEFDFBF7F,
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0x0FE03F81,0xC9484E2B,0xE133F84D,0xE1A8C537,
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0x077975B9,0x70586723,0xCD29C245,0xFAA11E6F,
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0x0FE3C071,0x08B51D9B,0x8CE2CABD,0xBF937F27,
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0xA8FE53A9,0x592FE593,0x2C0685B5,0x2EB11B5F,
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0xFCD1E361,0x451AB30B,0x72CFE72D,0xDB35A717,
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0xFB74A399,0xE80BFA03,0x0D516325,0x1BCB564F,
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0xE02E4851,0xD962AE7B,0x10F8ED9D,0x95AEDD07,
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0xE9DC0589,0xA18A4473,0xEA53FA95,0xEE936F3F,
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0x90948F41,0xEAFEAFEB,0x3D137E0D,0xEF46C0F7,
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0x028C1979,0x791064E3,0xC04FEC05,0xE115062F,
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0x32385831,0x6E68575B,0xA10D387D,0x6FECF2E7,
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0x3FB47F69,0xED4BFB53,0x74FED775,0xDB43BB1F,
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0x87654321,0x9BA144CB,0x478BBCED,0xBFB912D7,
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0x1FDCD759,0x14B2A7C3,0xCB125CE5,0x437B2E0F,
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0x10FEF011,0xD2B3183B,0x386CAB5D,0xEF6AC0C7,
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0x0E64C149,0x9A020A33,0xE6B41C55,0xFEFEFEFF
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};
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/*Computes (_a*_b-_c)/(2*_d+1) when the quotient is known to be exact.
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_a, _b, _c, and _d may be arbitrary so long as the arbitrary precision result
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fits in 32 bits, but currently the table for multiplicative inverses is only
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valid for _d<128.*/
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static inline celt_uint32_t imusdiv32odd(celt_uint32_t _a,celt_uint32_t _b,
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celt_uint32_t _c,int _d){
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return (_a*_b-_c)*INV_TABLE[_d]&MASK32;
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}
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/*Computes (_a*_b-_c)/_d when the quotient is known to be exact.
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_d does not actually have to be even, but imusdiv32odd will be faster when
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it's odd, so you should use that instead.
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_a and _d are assumed to be small (e.g., _a*_d fits in 32 bits; currently the
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table for multiplicative inverses is only valid for _d<=256).
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_b and _c may be arbitrary so long as the arbitrary precision reuslt fits in
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32 bits.*/
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static inline celt_uint32_t imusdiv32even(celt_uint32_t _a,celt_uint32_t _b,
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celt_uint32_t _c,int _d){
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celt_uint32_t inv;
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int mask;
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int shift;
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int one;
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celt_assert(_d>0);
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shift=EC_ILOG(_d^_d-1);
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celt_assert(_d<=256);
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inv=INV_TABLE[_d-1>>shift];
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shift--;
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one=1<<shift;
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mask=one-1;
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return (_a*(_b>>shift)-(_c>>shift)+
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(_a*(_b&mask)+one-(_c&mask)>>shift)-1)*inv&MASK32;
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}
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/*Compute floor(sqrt(_val)) with exact arithmetic.
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This has been tested on all possible 32-bit inputs.*/
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static unsigned isqrt32(celt_uint32_t _val){
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unsigned b;
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unsigned g;
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int bshift;
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/*Uses the second method from
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http://www.azillionmonkeys.com/qed/sqroot.html
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The main idea is to search for the largest binary digit b such that
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(g+b)*(g+b) <= _val, and add it to the solution g.*/
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g=0;
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bshift=EC_ILOG(_val)-1>>1;
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b=1U<<bshift;
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do{
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celt_uint32_t t;
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t=((celt_uint32_t)g<<1)+b<<bshift;
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if(t<=_val){
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g+=b;
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_val-=t;
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}
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b>>=1;
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bshift--;
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}
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while(bshift>=0);
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return g;
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}
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#if 0
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/*Compute floor(sqrt(_val)) with exact arithmetic.
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This has been tested on all possible 36-bit inputs.*/
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static celt_uint32_t isqrt36(celt_uint64_t _val){
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celt_uint32_t val32;
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celt_uint32_t b;
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celt_uint32_t g;
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int bshift;
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g=0;
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b=0x20000;
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for(bshift=18;bshift-->13;){
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celt_uint64_t t;
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t=((celt_uint64_t)g<<1)+b<<bshift;
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if(t<=_val){
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g+=b;
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_val-=t;
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}
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b>>=1;
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}
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val32=(celt_uint32_t)_val;
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for(;bshift>=0;bshift--){
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celt_uint32_t t;
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t=(g<<1)+b<<bshift;
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if(t<=val32){
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g+=b;
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val32-=t;
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}
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b>>=1;
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}
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return g;
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}
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#endif
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/*Although derived separately, the pulse vector coding scheme is equivalent to
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a Pyramid Vector Quantizer \cite{Fis86}.
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Some additional notes about an early version appear at
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http://people.xiph.org/~tterribe/notes/cwrs.html, but the codebook ordering
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and the definitions of some terms have evolved since that was written.
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The conversion from a pulse vector to an integer index (encoding) and back
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(decoding) is governed by two related functions, V(N,K) and U(N,K).
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V(N,K) = the number of combinations, with replacement, of N items, taken K
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at a time, when a sign bit is added to each item taken at least once (i.e.,
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the number of N-dimensional unit pulse vectors with K pulses).
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One way to compute this is via
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V(N,K) = K>0 ? sum(k=1...K,2**k*choose(N,k)*choose(K-1,k-1)) : 1,
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where choose() is the binomial function.
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A table of values for N<10 and K<10 looks like:
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V[10][10] = {
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{1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{1, 2, 2, 2, 2, 2, 2, 2, 2, 2},
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{1, 4, 8, 12, 16, 20, 24, 28, 32, 36},
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{1, 6, 18, 38, 66, 102, 146, 198, 258, 326},
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{1, 8, 32, 88, 192, 360, 608, 952, 1408, 1992},
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{1, 10, 50, 170, 450, 1002, 1970, 3530, 5890, 9290},
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{1, 12, 72, 292, 912, 2364, 5336, 10836, 20256, 35436},
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{1, 14, 98, 462, 1666, 4942, 12642, 28814, 59906, 115598},
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{1, 16, 128, 688, 2816, 9424, 27008, 68464, 157184, 332688},
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{1, 18, 162, 978, 4482, 16722, 53154, 148626, 374274, 864146}
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};
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U(N,K) = the number of such combinations wherein N-1 objects are taken at
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most K-1 at a time.
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This is given by
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U(N,K) = sum(k=0...K-1,V(N-1,k))
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= K>0 ? (V(N-1,K-1) + V(N,K-1))/2 : 0.
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The latter expression also makes clear that U(N,K) is half the number of such
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combinations wherein the first object is taken at least once.
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Although it may not be clear from either of these definitions, U(N,K) is the
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natural function to work with when enumerating the pulse vector codebooks,
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not V(N,K).
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U(N,K) is not well-defined for N=0, but with the extension
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U(0,K) = K>0 ? 0 : 1,
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the function becomes symmetric: U(N,K) = U(K,N), with a similar table:
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U[10][10] = {
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{1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 1, 1, 1, 1, 1, 1, 1, 1, 1},
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{0, 1, 3, 5, 7, 9, 11, 13, 15, 17},
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{0, 1, 5, 13, 25, 41, 61, 85, 113, 145},
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{0, 1, 7, 25, 63, 129, 231, 377, 575, 833},
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{0, 1, 9, 41, 129, 321, 681, 1289, 2241, 3649},
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{0, 1, 11, 61, 231, 681, 1683, 3653, 7183, 13073},
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{0, 1, 13, 85, 377, 1289, 3653, 8989, 19825, 40081},
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{0, 1, 15, 113, 575, 2241, 7183, 19825, 48639, 108545},
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{0, 1, 17, 145, 833, 3649, 13073, 40081, 108545, 265729}
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};
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With this extension, V(N,K) may be written in terms of U(N,K):
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V(N,K) = U(N,K) + U(N,K+1)
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for all N>=0, K>=0.
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Thus U(N,K+1) represents the number of combinations where the first element
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is positive or zero, and U(N,K) represents the number of combinations where
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it is negative.
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With a large enough table of U(N,K) values, we could write O(N) encoding
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and O(min(N*log(K),N+K)) decoding routines, but such a table would be
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prohibitively large for small embedded devices (K may be as large as 32767
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for small N, and N may be as large as 200).
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Both functions obey the same recurrence relation:
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V(N,K) = V(N-1,K) + V(N,K-1) + V(N-1,K-1),
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U(N,K) = U(N-1,K) + U(N,K-1) + U(N-1,K-1),
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for all N>0, K>0, with different initial conditions at N=0 or K=0.
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This allows us to construct a row of one of the tables above given the
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previous row or the next row.
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Thus we can derive O(NK) encoding and decoding routines with O(K) memory
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using only addition and subtraction.
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When encoding, we build up from the U(2,K) row and work our way forwards.
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When decoding, we need to start at the U(N,K) row and work our way backwards,
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which requires a means of computing U(N,K).
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U(N,K) may be computed from two previous values with the same N:
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U(N,K) = ((2*N-1)*U(N,K-1) - U(N,K-2))/(K-1) + U(N,K-2)
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for all N>1, and since U(N,K) is symmetric, a similar relation holds for two
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previous values with the same K:
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U(N,K>1) = ((2*K-1)*U(N-1,K) - U(N-2,K))/(N-1) + U(N-2,K)
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for all K>1.
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This allows us to construct an arbitrary row of the U(N,K) table by starting
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with the first two values, which are constants.
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This saves roughly 2/3 the work in our O(NK) decoding routine, but costs O(K)
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multiplications.
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Similar relations can be derived for V(N,K), but are not used here.
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For N>0 and K>0, U(N,K) and V(N,K) take on the form of an (N-1)-degree
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polynomial for fixed N.
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The first few are
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U(1,K) = 1,
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U(2,K) = 2*K-1,
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U(3,K) = (2*K-2)*K+1,
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U(4,K) = (((4*K-6)*K+8)*K-3)/3,
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U(5,K) = ((((2*K-4)*K+10)*K-8)*K+3)/3,
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and
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V(1,K) = 2,
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V(2,K) = 4*K,
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V(3,K) = 4*K*K+2,
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V(4,K) = 8*(K*K+2)*K/3,
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V(5,K) = ((4*K*K+20)*K*K+6)/3,
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for all K>0.
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This allows us to derive O(N) encoding and O(N*log(K)) decoding routines for
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small N (and indeed decoding is also O(N) for N<3).
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@ARTICLE{Fis86,
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author="Thomas R. Fischer",
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title="A Pyramid Vector Quantizer",
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journal="IEEE Transactions on Information Theory",
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volume="IT-32",
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number=4,
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pages="568--583",
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month=Jul,
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year=1986
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}*/
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/*Determines if V(N,K) fits in a 32-bit unsigned integer.
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N and K are themselves limited to 15 bits.*/
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int fits_in32(int _n, int _k)
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{
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static const celt_int16_t maxN[15] = {
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32767, 32767, 32767, 1476, 283, 109, 60, 40,
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29, 24, 20, 18, 16, 14, 13};
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static const celt_int16_t maxK[15] = {
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32767, 32767, 32767, 32767, 1172, 238, 95, 53,
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36, 27, 22, 18, 16, 15, 13};
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if (_n>=14)
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{
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if (_k>=14)
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return 0;
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else
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return _n <= maxN[_k];
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} else {
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return _k <= maxK[_n];
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}
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}
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/*Compute U(1,_k).*/
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static inline unsigned ucwrs1(int _k){
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return _k?1:0;
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}
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/*Compute V(1,_k).*/
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static inline unsigned ncwrs1(int _k){
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return _k?2:1;
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}
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/*Compute U(2,_k).
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Note that this may be called with _k=32768 (maxK[2]+1).*/
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static inline unsigned ucwrs2(unsigned _k){
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return _k?_k+(_k-1):0;
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}
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/*Compute V(2,_k).*/
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static inline celt_uint32_t ncwrs2(int _k){
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return _k?4*(celt_uint32_t)_k:1;
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}
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/*Compute U(3,_k).
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Note that this may be called with _k=32768 (maxK[3]+1).*/
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static inline celt_uint32_t ucwrs3(unsigned _k){
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return _k?(2*(celt_uint32_t)_k-2)*_k+1:0;
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}
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/*Compute V(3,_k).*/
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static inline celt_uint32_t ncwrs3(int _k){
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return _k?2*(2*(unsigned)_k*(celt_uint32_t)_k+1):1;
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}
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/*Compute U(4,_k).*/
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static inline celt_uint32_t ucwrs4(int _k){
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return _k?imusdiv32odd(2*_k,(2*_k-3)*(celt_uint32_t)_k+4,3,1):0;
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}
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/*Compute V(4,_k).*/
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static inline celt_uint32_t ncwrs4(int _k){
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return _k?((_k*(celt_uint32_t)_k+2)*_k)/3<<3:1;
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}
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/*Compute U(5,_k).*/
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static inline celt_uint32_t ucwrs5(int _k){
|
|
return _k?(((((_k-2)*(unsigned)_k+5)*(celt_uint32_t)_k-4)*_k)/3<<1)+1:0;
|
|
}
|
|
|
|
/*Compute V(5,_k).*/
|
|
static inline celt_uint32_t ncwrs5(int _k){
|
|
return _k?(((_k*(unsigned)_k+5)*(celt_uint32_t)_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_t *_ui,unsigned _len,celt_uint32_t _ui0){
|
|
celt_uint32_t 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=UADD32(UADD32(_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.*/
|
|
static inline void uprev(celt_uint32_t *_ui,unsigned _n,celt_uint32_t _ui0){
|
|
celt_uint32_t 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=USUB32(USUB32(_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_t ncwrs_urow(unsigned _n,unsigned _k,celt_uint32_t *_u){
|
|
celt_uint32_t 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);
|
|
}
|
|
else{
|
|
celt_uint32_t um1;
|
|
celt_uint32_t 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_t _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_t _i,int *_y){
|
|
celt_uint32_t 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);
|
|
}
|
|
|
|
/*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_t _i,int *_y){
|
|
celt_uint32_t 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_t _i,int *_y){
|
|
celt_uint32_t 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;
|
|
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_t _i,int *_y){
|
|
celt_uint32_t p;
|
|
int s;
|
|
int yj;
|
|
p=ucwrs5(_k+1);
|
|
s=-(_i>=p);
|
|
_i-=p&s;
|
|
yj=_k;
|
|
#if 0
|
|
/*Finds the maximum _k such that ucwrs5(_k)<=_i (tested for all
|
|
_i<2157192969=U(5,239)).*/
|
|
if(_i>=0x2AAAAAA9UL)_k=isqrt32(2*isqrt36(10+6*(celt_uint64_t)_i)-7)+1>>1;
|
|
else _k=_i>0?isqrt32(2*(celt_uint32_t)isqrt32(10+6*_i)-7)+1>>1:0;
|
|
p=ucwrs5(_k);
|
|
#else
|
|
/* 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;
|
|
}
|
|
}
|
|
#endif
|
|
_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_t _i,int *_y,celt_uint32_t *_u){
|
|
int j;
|
|
celt_assert(_n>0);
|
|
j=0;
|
|
do{
|
|
celt_uint32_t 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_t icwrs1(const int *_y,int *_k){
|
|
*_k=abs(_y[0]);
|
|
return _y[0]<0;
|
|
}
|
|
|
|
/*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_t icwrs2(const int *_y,int *_k){
|
|
celt_uint32_t 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_t icwrs3(const int *_y,int *_k){
|
|
celt_uint32_t 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_t icwrs4(const int *_y,int *_k){
|
|
celt_uint32_t 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;
|
|
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_t icwrs5(const int *_y,int *_k){
|
|
celt_uint32_t 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_t icwrs(int _n,int _k,celt_uint32_t *_nc,const int *_y,
|
|
celt_uint32_t *_u){
|
|
celt_uint32_t 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]);
|
|
if(_y[j]<0)i+=_u[k+1];
|
|
}
|
|
*_nc=_u[k]+_u[k+1];
|
|
return i;
|
|
}
|
|
|
|
|
|
/*Computes get_required_bits when splitting is required.
|
|
_left_bits and _right_bits must contain the required bits for the left and
|
|
right sides of the split, respectively (which themselves may require
|
|
splitting).*/
|
|
static void get_required_split_bits(celt_int16_t *_bits,
|
|
const celt_int16_t *_left_bits,const celt_int16_t *_right_bits,
|
|
int _n,int _maxk,int _frac){
|
|
int k;
|
|
for(k=_maxk;k-->0;){
|
|
/*If we've reached a k where everything fits in 32 bits, evaluate the
|
|
remaining required bits directly.*/
|
|
if(fits_in32(_n,k)){
|
|
get_required_bits(_bits,_n,k+1,_frac);
|
|
break;
|
|
}
|
|
else{
|
|
int worst_bits;
|
|
int i;
|
|
/*Due to potentially recursive splitting, it's difficult to derive an
|
|
analytic expression for the location of the worst-case split index.
|
|
We simply check them all.*/
|
|
worst_bits=0;
|
|
for(i=0;i<=k;i++){
|
|
int split_bits;
|
|
split_bits=_left_bits[i]+_right_bits[k-i];
|
|
if(split_bits>worst_bits)worst_bits=split_bits;
|
|
}
|
|
_bits[k]=log2_frac(k+1,_frac)+worst_bits;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*Computes get_required_bits for a pair of N values.
|
|
_n1 and _n2 must either be equal or two consecutive integers.
|
|
Returns the buffer used to store the required bits for _n2, which is either
|
|
_bits1 if _n1==_n2 or _bits2 if _n1+1==_n2.*/
|
|
static celt_int16_t *get_required_bits_pair(celt_int16_t *_bits1,
|
|
celt_int16_t *_bits2,celt_int16_t *_tmp,int _n1,int _n2,int _maxk,int _frac){
|
|
celt_int16_t *tmp2;
|
|
/*If we only need a single set of required bits...*/
|
|
if(_n1==_n2){
|
|
/*Stop recursing if everything fits.*/
|
|
if(fits_in32(_n1,_maxk-1))get_required_bits(_bits1,_n1,_maxk,_frac);
|
|
else{
|
|
_tmp=get_required_bits_pair(_bits2,_tmp,_bits1,
|
|
_n1>>1,_n1+1>>1,_maxk,_frac);
|
|
get_required_split_bits(_bits1,_bits2,_tmp,_n1,_maxk,_frac);
|
|
}
|
|
return _bits1;
|
|
}
|
|
/*Otherwise we need two distinct sets...*/
|
|
celt_assert(_n1+1==_n2);
|
|
/*Stop recursing if everything fits.*/
|
|
if(fits_in32(_n2,_maxk-1)){
|
|
get_required_bits(_bits1,_n1,_maxk,_frac);
|
|
get_required_bits(_bits2,_n2,_maxk,_frac);
|
|
}
|
|
/*Otherwise choose an evaluation order that doesn't require extra buffers.*/
|
|
else if(_n1&1){
|
|
/*This special case isn't really needed, but can save some work.*/
|
|
if(fits_in32(_n1,_maxk-1)){
|
|
tmp2=get_required_bits_pair(_tmp,_bits1,_bits2,
|
|
_n2>>1,_n2>>1,_maxk,_frac);
|
|
get_required_split_bits(_bits2,_tmp,tmp2,_n2,_maxk,_frac);
|
|
get_required_bits(_bits1,_n1,_maxk,_frac);
|
|
}
|
|
else{
|
|
_tmp=get_required_bits_pair(_bits2,_tmp,_bits1,
|
|
_n1>>1,_n1+1>>1,_maxk,_frac);
|
|
get_required_split_bits(_bits1,_bits2,_tmp,_n1,_maxk,_frac);
|
|
get_required_split_bits(_bits2,_tmp,_tmp,_n2,_maxk,_frac);
|
|
}
|
|
}
|
|
else{
|
|
/*There's no need to special case _n1 fitting by itself, since _n2 requires
|
|
us to recurse for both values anyway.*/
|
|
tmp2=get_required_bits_pair(_tmp,_bits1,_bits2,
|
|
_n2>>1,_n2+1>>1,_maxk,_frac);
|
|
get_required_split_bits(_bits2,_tmp,tmp2,_n2,_maxk,_frac);
|
|
get_required_split_bits(_bits1,_tmp,_tmp,_n1,_maxk,_frac);
|
|
}
|
|
return _bits2;
|
|
}
|
|
|
|
void get_required_bits(celt_int16_t *_bits,int _n,int _maxk,int _frac){
|
|
int k;
|
|
/*_maxk==0 => there's nothing to do.*/
|
|
celt_assert(_maxk>0);
|
|
if(fits_in32(_n,_maxk-1)){
|
|
_bits[0]=0;
|
|
if(_maxk>1){
|
|
VARDECL(celt_uint32_t,u);
|
|
SAVE_STACK;
|
|
ALLOC(u,_maxk+1U,celt_uint32_t);
|
|
ncwrs_urow(_n,_maxk-1,u);
|
|
for(k=1;k<_maxk;k++)_bits[k]=log2_frac(u[k]+u[k+1],_frac);
|
|
RESTORE_STACK;
|
|
}
|
|
}
|
|
else{
|
|
VARDECL(celt_int16_t,n1bits);
|
|
VARDECL(celt_int16_t,n2bits_buf);
|
|
celt_int16_t *n2bits;
|
|
SAVE_STACK;
|
|
ALLOC(n1bits,_maxk,celt_int16_t);
|
|
ALLOC(n2bits_buf,_maxk,celt_int16_t);
|
|
n2bits=get_required_bits_pair(n1bits,n2bits_buf,_bits,
|
|
_n>>1,_n+1>>1,_maxk,_frac);
|
|
get_required_split_bits(_bits,n1bits,n2bits,_n,_maxk,_frac);
|
|
RESTORE_STACK;
|
|
}
|
|
}
|
|
|
|
|
|
static inline void encode_pulses32(int _n,int _k,const int *_y,ec_enc *_enc){
|
|
celt_uint32_t i;
|
|
switch(_n){
|
|
case 1:{
|
|
i=icwrs1(_y,&_k);
|
|
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_t,u);
|
|
celt_uint32_t nc;
|
|
SAVE_STACK;
|
|
ALLOC(u,_k+2U,celt_uint32_t);
|
|
i=icwrs(_n,_k,&nc,_y,u);
|
|
ec_enc_uint(_enc,i,nc);
|
|
RESTORE_STACK;
|
|
}break;
|
|
}
|
|
}
|
|
|
|
void encode_pulses(int *_y, int N, int K, ec_enc *enc)
|
|
{
|
|
if (K==0) {
|
|
} else if(fits_in32(N,K))
|
|
{
|
|
encode_pulses32(N, K, _y, enc);
|
|
} else {
|
|
int i;
|
|
int count=0;
|
|
int split;
|
|
split = (N+1)/2;
|
|
for (i=0;i<split;i++)
|
|
count += abs(_y[i]);
|
|
ec_enc_uint(enc,count,K+1);
|
|
encode_pulses(_y, split, count, enc);
|
|
encode_pulses(_y+split, N-split, K-count, enc);
|
|
}
|
|
}
|
|
|
|
static inline void decode_pulses32(int _n,int _k,int *_y,ec_dec *_dec){
|
|
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_t,u);
|
|
SAVE_STACK;
|
|
ALLOC(u,_k+2U,celt_uint32_t);
|
|
cwrsi(_n,_k,ec_dec_uint(_dec,ncwrs_urow(_n,_k,u)),_y,u);
|
|
RESTORE_STACK;
|
|
}
|
|
}
|
|
}
|
|
|
|
void decode_pulses(int *_y, int N, int K, ec_dec *dec)
|
|
{
|
|
if (K==0) {
|
|
int i;
|
|
for (i=0;i<N;i++)
|
|
_y[i] = 0;
|
|
} else if(fits_in32(N,K))
|
|
{
|
|
decode_pulses32(N, K, _y, dec);
|
|
} else {
|
|
int split;
|
|
int count = ec_dec_uint(dec,K+1);
|
|
split = (N+1)/2;
|
|
decode_pulses(_y, split, count, dec);
|
|
decode_pulses(_y+split, N-split, K-count, dec);
|
|
}
|
|
}
|