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297 lines
8.1 KiB
C
297 lines
8.1 KiB
C
#include "mathops.h"
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#include <limits.h>
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/*The fastest fallback strategy for platforms with fast multiplication appears
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to be based on de Bruijn sequences~\cite{LP98}.
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Tests confirmed this to be true even on an ARM11, where it is actually faster
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than using the native clz instruction.
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Define OC_ILOG_NODEBRUIJN to use a simpler fallback on platforms where
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multiplication or table lookups are too expensive.
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@UNPUBLISHED{LP98,
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author="Charles E. Leiserson and Harald Prokop",
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title="Using de {Bruijn} Sequences to Index a 1 in a Computer Word",
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month=Jun,
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year=1998,
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note="\url{http://supertech.csail.mit.edu/papers/debruijn.pdf}"
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}*/
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#if !defined(OC_ILOG_NODEBRUIJN)&& \
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!defined(OC_CLZ32)||!defined(OC_CLZ64)&&LONG_MAX<9223372036854775807LL
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static const unsigned char OC_DEBRUIJN_IDX32[32]={
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0, 1,28, 2,29,14,24, 3,30,22,20,15,25,17, 4, 8,
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31,27,13,23,21,19,16, 7,26,12,18, 6,11, 5,10, 9
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};
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#endif
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int oc_ilog32(ogg_uint32_t _v){
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#if defined(OC_CLZ32)
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return (OC_CLZ32_OFFS-OC_CLZ32(_v))&-!!_v;
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#else
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/*On a Pentium M, this branchless version tested as the fastest version without
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multiplications on 1,000,000,000 random 32-bit integers, edging out a
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similar version with branches, and a 256-entry LUT version.*/
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# if defined(OC_ILOG_NODEBRUIJN)
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int ret;
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int m;
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ret=_v>0;
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m=(_v>0xFFFFU)<<4;
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_v>>=m;
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ret|=m;
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m=(_v>0xFFU)<<3;
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_v>>=m;
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ret|=m;
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m=(_v>0xFU)<<2;
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_v>>=m;
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ret|=m;
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m=(_v>3)<<1;
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_v>>=m;
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ret|=m;
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ret+=_v>1;
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return ret;
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/*This de Bruijn sequence version is faster if you have a fast multiplier.*/
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# else
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int ret;
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ret=_v>0;
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_v|=_v>>1;
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_v|=_v>>2;
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_v|=_v>>4;
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_v|=_v>>8;
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_v|=_v>>16;
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_v=(_v>>1)+1;
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ret+=OC_DEBRUIJN_IDX32[_v*0x77CB531U>>27&0x1F];
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return ret;
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# endif
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#endif
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}
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int oc_ilog64(ogg_int64_t _v){
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#if defined(OC_CLZ64)
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return (OC_CLZ64_OFFS-OC_CLZ64(_v))&-!!_v;
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#else
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# if defined(OC_ILOG_NODEBRUIJN)
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ogg_uint32_t v;
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int ret;
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int m;
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ret=_v>0;
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m=(_v>0xFFFFFFFFU)<<5;
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v=(ogg_uint32_t)(_v>>m);
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ret|=m;
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m=(v>0xFFFFU)<<4;
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v>>=m;
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ret|=m;
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m=(v>0xFFU)<<3;
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v>>=m;
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ret|=m;
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m=(v>0xFU)<<2;
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v>>=m;
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ret|=m;
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m=(v>3)<<1;
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v>>=m;
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ret|=m;
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ret+=v>1;
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return ret;
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# else
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/*If we don't have a 64-bit word, split it into two 32-bit halves.*/
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# if LONG_MAX<9223372036854775807LL
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ogg_uint32_t v;
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int ret;
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int m;
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ret=_v>0;
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m=(_v>0xFFFFFFFFU)<<5;
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v=(ogg_uint32_t)(_v>>m);
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ret|=m;
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v|=v>>1;
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v|=v>>2;
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v|=v>>4;
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v|=v>>8;
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v|=v>>16;
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v=(v>>1)+1;
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ret+=OC_DEBRUIJN_IDX32[v*0x77CB531U>>27&0x1F];
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return ret;
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/*Otherwise do it in one 64-bit operation.*/
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# else
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static const unsigned char OC_DEBRUIJN_IDX64[64]={
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0, 1, 2, 7, 3,13, 8,19, 4,25,14,28, 9,34,20,40,
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5,17,26,38,15,46,29,48,10,31,35,54,21,50,41,57,
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63, 6,12,18,24,27,33,39,16,37,45,47,30,53,49,56,
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62,11,23,32,36,44,52,55,61,22,43,51,60,42,59,58
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};
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int ret;
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ret=_v>0;
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_v|=_v>>1;
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_v|=_v>>2;
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_v|=_v>>4;
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_v|=_v>>8;
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_v|=_v>>16;
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_v|=_v>>32;
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_v=(_v>>1)+1;
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ret+=OC_DEBRUIJN_IDX64[_v*0x218A392CD3D5DBF>>58&0x3F];
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return ret;
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# endif
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# endif
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#endif
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}
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/*round(2**(62+i)*atanh(2**(-(i+1)))/log(2))*/
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static const ogg_int64_t OC_ATANH_LOG2[32]={
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0x32B803473F7AD0F4LL,0x2F2A71BD4E25E916LL,0x2E68B244BB93BA06LL,
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0x2E39FB9198CE62E4LL,0x2E2E683F68565C8FLL,0x2E2B850BE2077FC1LL,
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0x2E2ACC58FE7B78DBLL,0x2E2A9E2DE52FD5F2LL,0x2E2A92A338D53EECLL,
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0x2E2A8FC08F5E19B6LL,0x2E2A8F07E51A485ELL,0x2E2A8ED9BA8AF388LL,
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0x2E2A8ECE2FE7384ALL,0x2E2A8ECB4D3E4B1ALL,0x2E2A8ECA94940FE8LL,
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0x2E2A8ECA6669811DLL,0x2E2A8ECA5ADEDD6ALL,0x2E2A8ECA57FC347ELL,
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0x2E2A8ECA57438A43LL,0x2E2A8ECA57155FB4LL,0x2E2A8ECA5709D510LL,
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0x2E2A8ECA5706F267LL,0x2E2A8ECA570639BDLL,0x2E2A8ECA57060B92LL,
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0x2E2A8ECA57060008LL,0x2E2A8ECA5705FD25LL,0x2E2A8ECA5705FC6CLL,
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0x2E2A8ECA5705FC3ELL,0x2E2A8ECA5705FC33LL,0x2E2A8ECA5705FC30LL,
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0x2E2A8ECA5705FC2FLL,0x2E2A8ECA5705FC2FLL
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};
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/*Computes the binary exponential of _z, a log base 2 in Q57 format.*/
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ogg_int64_t oc_bexp64(ogg_int64_t _z){
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ogg_int64_t w;
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ogg_int64_t z;
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int ipart;
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ipart=(int)(_z>>57);
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if(ipart<0)return 0;
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if(ipart>=63)return 0x7FFFFFFFFFFFFFFFLL;
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z=_z-OC_Q57(ipart);
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if(z){
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ogg_int64_t mask;
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long wlo;
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int i;
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/*C doesn't give us 64x64->128 muls, so we use CORDIC.
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This is not particularly fast, but it's not being used in time-critical
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code; it is very accurate.*/
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/*z is the fractional part of the log in Q62 format.
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We need 1 bit of headroom since the magnitude can get larger than 1
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during the iteration, and a sign bit.*/
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z<<=5;
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/*w is the exponential in Q61 format (since it also needs headroom and can
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get as large as 2.0); we could get another bit if we dropped the sign,
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but we'll recover that bit later anyway.
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Ideally this should start out as
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\lim_{n->\infty} 2^{61}/\product_{i=1}^n \sqrt{1-2^{-2i}}
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but in order to guarantee convergence we have to repeat iterations 4,
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13 (=3*4+1), and 40 (=3*13+1, etc.), so it winds up somewhat larger.*/
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w=0x26A3D0E401DD846DLL;
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for(i=0;;i++){
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mask=-(z<0);
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w+=(w>>i+1)+mask^mask;
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z-=OC_ATANH_LOG2[i]+mask^mask;
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/*Repeat iteration 4.*/
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if(i>=3)break;
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z<<=1;
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}
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for(;;i++){
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mask=-(z<0);
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w+=(w>>i+1)+mask^mask;
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z-=OC_ATANH_LOG2[i]+mask^mask;
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/*Repeat iteration 13.*/
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if(i>=12)break;
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z<<=1;
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}
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for(;i<32;i++){
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mask=-(z<0);
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w+=(w>>i+1)+mask^mask;
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z=z-(OC_ATANH_LOG2[i]+mask^mask)<<1;
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}
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wlo=0;
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/*Skip the remaining iterations unless we really require that much
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precision.
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We could have bailed out earlier for smaller iparts, but that would
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require initializing w from a table, as the limit doesn't converge to
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61-bit precision until n=30.*/
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if(ipart>30){
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/*For these iterations, we just update the low bits, as the high bits
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can't possibly be affected.
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OC_ATANH_LOG2 has also converged (it actually did so one iteration
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earlier, but that's no reason for an extra special case).*/
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for(;;i++){
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mask=-(z<0);
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wlo+=(w>>i)+mask^mask;
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z-=OC_ATANH_LOG2[31]+mask^mask;
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/*Repeat iteration 40.*/
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if(i>=39)break;
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z<<=1;
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}
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for(;i<61;i++){
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mask=-(z<0);
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wlo+=(w>>i)+mask^mask;
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z=z-(OC_ATANH_LOG2[31]+mask^mask)<<1;
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}
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}
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w=(w<<1)+wlo;
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}
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else w=(ogg_int64_t)1<<62;
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if(ipart<62)w=(w>>61-ipart)+1>>1;
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return w;
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}
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/*Computes the binary logarithm of _w, returned in Q57 format.*/
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ogg_int64_t oc_blog64(ogg_int64_t _w){
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ogg_int64_t z;
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int ipart;
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if(_w<=0)return -1;
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ipart=OC_ILOGNZ_64(_w)-1;
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if(ipart>61)_w>>=ipart-61;
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else _w<<=61-ipart;
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z=0;
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if(_w&_w-1){
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ogg_int64_t x;
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ogg_int64_t y;
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ogg_int64_t u;
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ogg_int64_t mask;
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int i;
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/*C doesn't give us 64x64->128 muls, so we use CORDIC.
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This is not particularly fast, but it's not being used in time-critical
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code; it is very accurate.*/
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/*z is the fractional part of the log in Q61 format.*/
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/*x and y are the cosh() and sinh(), respectively, in Q61 format.
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We are computing z=2*atanh(y/x)=2*atanh((_w-1)/(_w+1)).*/
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x=_w+((ogg_int64_t)1<<61);
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y=_w-((ogg_int64_t)1<<61);
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for(i=0;i<4;i++){
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mask=-(y<0);
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z+=(OC_ATANH_LOG2[i]>>i)+mask^mask;
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u=x>>i+1;
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x-=(y>>i+1)+mask^mask;
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y-=u+mask^mask;
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}
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/*Repeat iteration 4.*/
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for(i--;i<13;i++){
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mask=-(y<0);
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z+=(OC_ATANH_LOG2[i]>>i)+mask^mask;
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u=x>>i+1;
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x-=(y>>i+1)+mask^mask;
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y-=u+mask^mask;
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}
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/*Repeat iteration 13.*/
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for(i--;i<32;i++){
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mask=-(y<0);
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z+=(OC_ATANH_LOG2[i]>>i)+mask^mask;
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u=x>>i+1;
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x-=(y>>i+1)+mask^mask;
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y-=u+mask^mask;
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}
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/*OC_ATANH_LOG2 has converged.*/
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for(;i<40;i++){
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mask=-(y<0);
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z+=(OC_ATANH_LOG2[31]>>i)+mask^mask;
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u=x>>i+1;
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x-=(y>>i+1)+mask^mask;
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y-=u+mask^mask;
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}
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/*Repeat iteration 40.*/
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for(i--;i<62;i++){
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mask=-(y<0);
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z+=(OC_ATANH_LOG2[31]>>i)+mask^mask;
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u=x>>i+1;
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x-=(y>>i+1)+mask^mask;
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y-=u+mask^mask;
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}
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z=z+8>>4;
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}
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return OC_Q57(ipart)+z;
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}
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