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@UNPUBLISHED{LP98,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