1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296
|
#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@UNPUBLISHED{LP98,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;
}
|