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-rw-r--r--drivers/theora/mathops.c296
1 files changed, 296 insertions, 0 deletions
diff --git a/drivers/theora/mathops.c b/drivers/theora/mathops.c
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+++ b/drivers/theora/mathops.c
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+#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+ @UNPUBLISHED{LP98,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;
+}
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