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log-de2.c
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log-de2.c
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/*
*this function computes log, correctly rounded,
using experimental techniques based on double-extended arithmetic
THIS IS EXPERIMENTAL SOFTWARE
In particular it changes rounding modes all the time without warning
nor restoring.
*
* Author : Florent de Dinechin
* Florent.de.Dinechin at ens-lyon.fr
*
To have it replace the crlibm log, do:
on pentium,
gcc -DHAVE_CONFIG_H -I. -fPIC -O2 -c log-de2.c; mv log-de2.o log_fast.o; make
on itanium,
icc -I/users/fdedinex/local/IA64/include -mcpu=itanium2\
-Qoption,cpp,--extended_float_types -IPF_fp_speculationsafe -c log-de2.c;\
mv log-de2.o log_fast.o; make
*/
#include <stdio.h>
#include <stdlib.h>
#include "crlibm.h"
#include "crlibm_private.h"
#include "double-extended.h"
#include "log-de2.h"
double log_rn(double x) {
double wi;
#if defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64)
db_number y;
int E, i, index, roundtestmask;
long double r, logirh, logirl, z, z2, z4, t,evenp,oddp, th, tl, eh,el,p1,p2,p3;
#else
long int E, i;
unsigned long int index, roundtestmask;
__fpreg xe, ye, r, logirh, logirl, z, z2, z4, t,evenp,oddp, th, tl, eh,el, c1,c2,c3,c4,c5,c6,p1,p2,p3;
#endif
E=0;
#if defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64)
/* Pentium has few registers, so load coefficients directly from memory */
#define c6 c[0]
#define c5 c[1]
#define c4 c[2]
#define c3 c[3]
#define c2 c[4]
#define c1 c[5]
/* Special case hadling on a x86 */
y.d=x;
/* Filter special cases */
if (y.i[HI] < 0x00100000){ /* x < 2^(-1022) */
if (((y.i[HI] & 0x7fffffff)|y.i[LO])==0){
return -1.0/0.0;
} /* log(+/-0) = -Inf */
if (y.i[HI] < 0){
return (x-x)/0; /* log(-x) = Nan */
}
/* Subnormal number */
E = -64;
y.d *= two64; /* make x a normal number */
}
if (y.i[HI] >= 0x7ff00000){
return x+x; /* Inf or Nan */
}
DOUBLE_EXTENDED_MODE; /* This one should be overlapped with integer computation */
#define X_NEAR_1 (y.i[HI]>MINYFAST) && (y.i[HI]<MAXYFAST)
#else
/* prefetch coefficients */
c6=c[0]; c5=c[1]; c4=c[2]; c3=c[3]; c2=c[4]; c1=c[5];
/* Special case handling on the Itanium */
xe=x;
i = _Asm_getf(2/*_FR_D*/, xe);
/* Filter special cases */
//if (__builtin_expect( (i<0x0010000000000000ULL), (1+1==3))){ /* x < 2^(-1022) */
if (i<0x0010000000000000LL){ /* x < 2^(-1022) */
if ((i & 0x7fffffffffffffffULL)==0){
return -1.0/0.0;
} /* log(+/-0) = -Inf */
if (i<0){
return (x-x)/0; /* log(-x) = Nan */
}
/* Subnormal number */
xe *= two64; /* make x a normal number */
E = -64;
i = _Asm_getf(2/*_FR_D*/, xe); /* and update i */
}
//if (__builtin_expect( (i >= 0x7ff0000000000000ULL), (1+1==3) )){
if (i >= 0x7ff0000000000000ULL){
return x+x; /* Inf or Nan */
}
#define X_NEAR_1 __builtin_expect((i>(((uint64_t) MINYFAST)<<32)) && (i<(((uint64_t) MAXYFAST)<<32)), (1+1==3))
#endif
if(X_NEAR_1) {
roundtestmask=0x7fc;
z = x - 1 ; /* Sterbenz exact */
z2 = z*z;
evenp = c6; /* c6 */
oddp = c5; /* c5 */
evenp = c4 + z2 * evenp; /* c4 */
oddp = c3 + z2 * oddp; /* c3 */
evenp = c2 + z2 * evenp; /* c2 */
t = c1 + (z * evenp + z2 * oddp);
t = z*t;
//printf("z= %1.20e, t=%1.20e \n ", (double)z, (double)t);
}
else {
#if defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64)
/* Extract exponent and mantissa */
E += (y.i[HI]>>20)-1023; /* extract the exponent */
index = (y.i[HI] & 0x000fffff);
y.i[HI] = index | 0x3ff00000; /* do exponent = 0 */
index = index >> (20-L);
/* now y.d holds 1+f, and E is the exponent */
logirh = argredtable[index].h;
r = (long double) (argredtable[index].r); /* approx to 1/y.d */
z = r*(long double)y.d - 1. ; /* even without an FMA, all exact */
if(E>12 || E<-12) { /* faster and less accurate polynomial evaluation */
roundtestmask=0x7fe;
p1 = logirh + z*c1; p2 = c2 + z*c3; p3 = c4 + z*c5; z2 = z*z;
p1 = p1 + z2*p2; p3 = p3 + z2*c6; z4=z2*z2;
t = p1 + z4*p3;
t = t + E*ln2h;
}
else {
roundtestmask=0x7f0;
p1 = c5 + z*c6; z2 = z*z;
p2 = c3 + z*c4; p3 = c1+z*c2;
t = p2 + z2*p1;
t = p3 + z2*t;
t = logirh + z*t;
t = t + E*ln2h;
}
#if 0
if(E>12 || E<-12)
roundtestmask=0x7fe;
else
roundtestmask=0x7f0;
p1 = c5 + z*c6; z2 = z*z;
p2 = c3 + z*c4; p3 = c1+z*c2;
t = p2 + z2*p1;
t = p3 + z2*t;
t = logirh + z*t;
#endif
#else /* Itanium here*/
/* Extract exponent and mantissa */
E += (i>>52)-1023;
//printf("\nE = %llx\n", E);
i = i & 0x000fffffffffffffULL; /* keep only mantissa */
ye = _Asm_setf(2/*_FR_D*/, i | 0x3ff0000000000000ULL ); /* exponent = 0*/
index = i >> (52-L);
//printf("\nindex= %lld\n", index);
//printf("\n ye = %1.20Le\n",(long double)ye);
/* now ye holds 1+f, and E is the exponent */
logirh = argredtable[index].h;
_Asm_frcpa(&r, 1.0L, ye, 1/*_SF1*/);
z = r*ye - 1. ; /* even without an FMA, all exact */
if(E>12 || E<-12) { /* faster and less accurate polynomial evaluation */
roundtestmask=0x7fe;
p1 = logirh + z*c1; p2 = c2 + z*c3; p3 = c4 + z*c5; z2 = z*z;
p1 = p1 + z2*p2; p3 = p3 + z2*c6; z4=z2*z2;
t = p1 + z4*p3;
t = t + E*ln2h;
}
else {
roundtestmask=0x7f0;
p1 = c5 + z*c6; z2 = z*z;
p2 = c3 + z*c4; p3 = c1+z*c2;
t = p2 + z2*p1;
t = p3 + z2*t;
t = logirh + z*t;
t = t + E*ln2h;
}
#endif
//printf(" x=%1.20Le\n r=%1.20Le\n z=%1.20Le\n logirh=%1.20Le\n ",(long double)xe, (long double)r,(long double)z, (long double)logirh);
/* Polynomial evaluation, unrolled to go through Gappa */
//printf("t=%1.20e \n ", (double)t);
}
#if 0 /* to time the first step only */
BACK_TO_DOUBLE_MODE; return (double)t;
#endif
/* To test the second step only, comment out the following line */
DE_TEST_AND_RETURN_RN(t, roundtestmask);
/* Accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
t = c13h;
t = c12h + z*t;
t = c11h + z*t;
t = c10h + z*t;
t = c9h + z*t;
t = c8h + z*t;
//printf("\n t = %1.20Le\n", (long double)t);
Mul12_ext(&th, &tl, z, t);
Add22_ext(&th, &tl, c7h,c7l, th,tl);
FMA22_ext(&th, &tl, z,0, th,tl, c6h,c6l);
FMA22_ext(&th, &tl, z,0, th,tl, c5h,c5l);
FMA22_ext(&th, &tl, z,0, th,tl, c4h,c4l);
FMA22_ext(&th, &tl, z,0, th,tl, c3h,c3l);
FMA22_ext(&th, &tl, z,0, th,tl, c2h,c2l);
FMA22_ext(&th, &tl, z,0, th,tl, c1h,c1l);
if((X_NEAR_1)) {
Mul22_ext(&th, &tl, z,0, th,tl);
}
else{
FMA22_ext(&th, &tl, z,0, th,tl, logirh, argredtable[index].l);
/* the following is not a FMA22 (Eln2 > th+tl) */
Mul22_ext(&eh, &el, ln2h,ln2l, E, 0);
Add22_ext(&th, &tl, eh,el, th,tl);
}
BACK_TO_DOUBLE_MODE;
return (double) (th+tl); /* The exact sum of these double-extended is rounded to the nearest */
}
double log_ru(double x) { return x;};
double log_rd(double x) { return x;};
double log_rz(double x) { return x;};