#include "internal.h"
#include "mathops.h"
/*The fastest fallback strategy for platforms with fast multiplication appears
to be based on de Bruijn sequences~\cite{LP98}.
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@UNPUBLISHED{LP98,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)
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;
_v|=_v>>1;
_v|=_v>>2;
_v|=_v>>4;
_v|=_v>>8;
_v|=_v>>16;
ret=_v&1;
_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 we don't have a fast 64-bit word implementation, split it into two 32-bit
halves.*/
# if defined(OC_ILOG_NODEBRUIJN)|| \
defined(OC_CLZ32)||LONG_MAX<9223372036854775807LL
ogg_uint32_t v;
int ret;
int m;
m=(_v>0xFFFFFFFFU)<<5;
v=(ogg_uint32_t)(_v>>m);
# if defined(OC_CLZ32)
ret=m+OC_CLZ32_OFFS-OC_CLZ32(v)&-!!v;
# elif defined(OC_ILOG_NODEBRUIJN)
ret=v>0|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
v|=v>>1;
v|=v>>2;
v|=v>>4;
v|=v>>8;
v|=v>>16;
ret=v&1|m;
v=(v>>1)+1;
ret+=OC_DEBRUIJN_IDX32[v*0x77CB531U>>27&0x1F];
# endif
return ret;
/*Otherwise do it in one 64-bit multiply.*/
# 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;
_v|=_v>>1;
_v|=_v>>2;
_v|=_v>>4;
_v|=_v>>8;
_v|=_v>>16;
_v|=_v>>32;
ret=(int)_v&1;
_v=(_v>>1)+1;
ret+=OC_DEBRUIJN_IDX64[_v*0x218A392CD3D5DBF>>58&0x3F];
return ret;
# 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;
}
/*Polynomial approximation of a binary exponential.
Q10 input, Q0 output.*/
ogg_uint32_t oc_bexp32_q10(int _z){
unsigned n;
int ipart;
ipart=_z>>10;
n=(_z&(1<<10)-1)<<4;
n=(n*((n*((n*((n*3548>>15)+6817)>>15)+15823)>>15)+22708)>>15)+16384;
return 14-ipart>0?n+(1<<13-ipart)>>14-ipart:n<<ipart-14;
}
/*Polynomial approximation of a binary logarithm.
Q0 input, Q10 output.*/
int oc_blog32_q10(ogg_uint32_t _w){
int n;
int ipart;
int fpart;
if(_w<=0)return -1;
ipart=OC_ILOGNZ_32(_w);
n=(ipart-16>0?_w>>ipart-16:_w<<16-ipart)-32768-16384;
fpart=(n*((n*((n*((n*-1402>>15)+2546)>>15)-5216)>>15)+15745)>>15)-6793;
return (ipart<<10)+(fpart>>4);
}
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