mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-27 21:20:18 +00:00
218 lines
7.2 KiB
C
218 lines
7.2 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001, 2011 Free Software Foundation
|
|
*
|
|
* This program is free software; you can redistribute it and/or modify
|
|
* it under the terms of the GNU Lesser General Public License as published by
|
|
* the Free Software Foundation; either version 2.1 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* This program is distributed in the hope that it will be useful,
|
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
* GNU Lesser General Public License for more details.
|
|
*
|
|
* You should have received a copy of the GNU Lesser General Public License
|
|
* along with this program; if not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
/*********************************************************************/
|
|
/* */
|
|
/* MODULE_NAME:ulog.c */
|
|
/* */
|
|
/* FUNCTION:ulog */
|
|
/* */
|
|
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
|
|
/* mpexp.c mplog.c mpa.c */
|
|
/* ulog.tbl */
|
|
/* */
|
|
/* An ultimate log routine. Given an IEEE double machine number x */
|
|
/* it computes the correctly rounded (to nearest) value of log(x). */
|
|
/* Assumption: Machine arithmetic operations are performed in */
|
|
/* round to nearest mode of IEEE 754 standard. */
|
|
/* */
|
|
/*********************************************************************/
|
|
|
|
|
|
#include "endian.h"
|
|
#include <dla.h>
|
|
#include "mpa.h"
|
|
#include "MathLib.h"
|
|
#include <math_private.h>
|
|
|
|
#ifndef SECTION
|
|
# define SECTION
|
|
#endif
|
|
|
|
void __mplog(mp_no *, mp_no *, int);
|
|
|
|
/*********************************************************************/
|
|
/* An ultimate log routine. Given an IEEE double machine number x */
|
|
/* it computes the correctly rounded (to nearest) value of log(x). */
|
|
/*********************************************************************/
|
|
double
|
|
SECTION
|
|
__ieee754_log(double x) {
|
|
#define M 4
|
|
static const int pr[M]={8,10,18,32};
|
|
int i,j,n,ux,dx,p;
|
|
#if 0
|
|
int k;
|
|
#endif
|
|
double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
|
|
sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
|
|
t1,t2,t7,t8,t,ra,rb,ww,
|
|
a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
|
|
#ifndef DLA_FMS
|
|
double t3,t4,t5,t6;
|
|
#endif
|
|
number num;
|
|
mp_no mpx,mpy,mpy1,mpy2,mperr;
|
|
|
|
#include "ulog.tbl"
|
|
#include "ulog.h"
|
|
|
|
/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
|
|
|
|
num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
|
|
n=0;
|
|
if (__builtin_expect(ux < 0x00100000, 0)) {
|
|
if (__builtin_expect(((ux & 0x7fffffff) | dx) == 0, 0))
|
|
return MHALF/ZERO; /* return -INF */
|
|
if (__builtin_expect(ux < 0, 0))
|
|
return (x-x)/ZERO; /* return NaN */
|
|
n -= 54; x *= two54.d; /* scale x */
|
|
num.d = x;
|
|
}
|
|
if (__builtin_expect(ux >= 0x7ff00000, 0))
|
|
return x+x; /* INF or NaN */
|
|
|
|
/* Regular values of x */
|
|
|
|
w = x-ONE;
|
|
if (__builtin_expect(ABS(w) > U03, 1)) { goto case_03; }
|
|
|
|
|
|
/*--- Stage I, the case abs(x-1) < 0.03 */
|
|
|
|
t8 = MHALF*w;
|
|
EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
|
|
EADD(w,a,b,bb)
|
|
|
|
/* Evaluate polynomial II */
|
|
polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
|
|
w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
|
|
c = (aa+bb)+polII;
|
|
|
|
/* End stage I, case abs(x-1) < 0.03 */
|
|
if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y;
|
|
|
|
/*--- Stage II, the case abs(x-1) < 0.03 */
|
|
|
|
a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
|
|
w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
|
|
EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
|
|
ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
|
|
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(w,ZERO, s3,ss3, b, bb,t1,t2)
|
|
|
|
/* End stage II, case abs(x-1) < 0.03 */
|
|
if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y;
|
|
goto stage_n;
|
|
|
|
/*--- Stage I, the case abs(x-1) > 0.03 */
|
|
case_03:
|
|
|
|
/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
|
|
n += (num.i[HIGH_HALF] >> 20) - 1023;
|
|
num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
|
|
if (num.d > SQRT_2) { num.d *= HALF; n++; }
|
|
u = num.d; dbl_n = (double) n;
|
|
|
|
/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
|
|
num.d += h1.d;
|
|
i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
|
|
|
|
/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
|
|
num.d = u*Iu[i].d + h2.d;
|
|
j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
|
|
|
|
/* Compute w=(u-ui*vj)/(ui*vj) */
|
|
p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
|
|
q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0;
|
|
|
|
/* Evaluate polynomial I */
|
|
polI = w+(a2.d+a3.d*w)*w*w;
|
|
|
|
/* Add up everything */
|
|
nln2a = dbl_n*LN2A;
|
|
luai = Lu[i][0].d; lubi = Lu[i][1].d;
|
|
lvaj = Lv[j][0].d; lvbj = Lv[j][1].d;
|
|
EADD(luai,lvaj,sij,ssij)
|
|
EADD(nln2a,sij,A ,ttij)
|
|
B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
|
|
B = polI+B0;
|
|
|
|
/* End stage I, case abs(x-1) >= 0.03 */
|
|
if ((y=A+(B+E1)) == A+(B-E1)) return y;
|
|
|
|
|
|
/*--- Stage II, the case abs(x-1) > 0.03 */
|
|
|
|
/* Improve the accuracy of r0 */
|
|
EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
|
|
t=r0*((ONE-sa)-sb);
|
|
EADD(r0,t,ra,rb)
|
|
|
|
/* Compute w */
|
|
MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
|
|
EADD(A,B0,a0,aa0)
|
|
|
|
/* Evaluate polynomial III */
|
|
s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
|
|
EADD(c2.d,s1,s2,ss2)
|
|
MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
|
|
ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)
|
|
|
|
/* End stage II, case abs(x-1) >= 0.03 */
|
|
if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;
|
|
|
|
|
|
/* Final stages. Use multi-precision arithmetic. */
|
|
stage_n:
|
|
|
|
for (i=0; i<M; i++) {
|
|
p = pr[i];
|
|
__dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
|
|
__mplog(&mpx,&mpy,p);
|
|
__dbl_mp(e[i].d,&mperr,p);
|
|
__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
|
|
__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
|
|
if (y1==y2) return y1;
|
|
}
|
|
return y1;
|
|
}
|
|
#ifndef __ieee754_log
|
|
strong_alias (__ieee754_log, __log_finite)
|
|
#endif
|