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218 lines
7.2 KiB
C
218 lines
7.2 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2013 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/*********************************************************************/
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/* */
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/* MODULE_NAME:ulog.c */
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/* */
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/* FUNCTION:ulog */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
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/* mpexp.c mplog.c mpa.c */
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/* ulog.tbl */
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/* */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include "endian.h"
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include <math_private.h>
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#ifndef SECTION
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# define SECTION
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#endif
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void __mplog(mp_no *, mp_no *, int);
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/*********************************************************************/
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double
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SECTION
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__ieee754_log(double x) {
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#define M 4
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static const int pr[M]={8,10,18,32};
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int i,j,n,ux,dx,p;
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#if 0
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int k;
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#endif
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double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
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sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
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t1,t2,t7,t8,t,ra,rb,ww,
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a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
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#ifndef DLA_FMS
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double t3,t4,t5,t6;
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#endif
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number num;
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mp_no mpx,mpy,mpy1,mpy2,mperr;
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#include "ulog.tbl"
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#include "ulog.h"
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/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
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num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
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n=0;
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if (__builtin_expect(ux < 0x00100000, 0)) {
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if (__builtin_expect(((ux & 0x7fffffff) | dx) == 0, 0))
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return MHALF/ZERO; /* return -INF */
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if (__builtin_expect(ux < 0, 0))
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return (x-x)/ZERO; /* return NaN */
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n -= 54; x *= two54.d; /* scale x */
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num.d = x;
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}
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if (__builtin_expect(ux >= 0x7ff00000, 0))
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return x+x; /* INF or NaN */
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/* Regular values of x */
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w = x-ONE;
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if (__builtin_expect(ABS(w) > U03, 1)) { goto case_03; }
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/*--- Stage I, the case abs(x-1) < 0.03 */
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t8 = MHALF*w;
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EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
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EADD(w,a,b,bb)
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/* Evaluate polynomial II */
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polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
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w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
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c = (aa+bb)+polII;
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/* End stage I, case abs(x-1) < 0.03 */
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if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y;
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/*--- Stage II, the case abs(x-1) < 0.03 */
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a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
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w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
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EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
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ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
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MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(w,ZERO, s3,ss3, b, bb,t1,t2)
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/* End stage II, case abs(x-1) < 0.03 */
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if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y;
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goto stage_n;
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/*--- Stage I, the case abs(x-1) > 0.03 */
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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n += (num.i[HIGH_HALF] >> 20) - 1023;
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num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
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if (num.d > SQRT_2) { num.d *= HALF; n++; }
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u = num.d; dbl_n = (double) n;
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/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
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num.d += h1.d;
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i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
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/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
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num.d = u*Iu[i].d + h2.d;
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j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
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/* Compute w=(u-ui*vj)/(ui*vj) */
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p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
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q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0;
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/* Evaluate polynomial I */
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polI = w+(a2.d+a3.d*w)*w*w;
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/* Add up everything */
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nln2a = dbl_n*LN2A;
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luai = Lu[i][0].d; lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d; lvbj = Lv[j][1].d;
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EADD(luai,lvaj,sij,ssij)
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EADD(nln2a,sij,A ,ttij)
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B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
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B = polI+B0;
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/* End stage I, case abs(x-1) >= 0.03 */
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if ((y=A+(B+E1)) == A+(B-E1)) return y;
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/*--- Stage II, the case abs(x-1) > 0.03 */
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/* Improve the accuracy of r0 */
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EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
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t=r0*((ONE-sa)-sb);
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EADD(r0,t,ra,rb)
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/* Compute w */
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MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)
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EADD(A,B0,a0,aa0)
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/* Evaluate polynomial III */
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s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
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EADD(c2.d,s1,s2,ss2)
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MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
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ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)
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/* End stage II, case abs(x-1) >= 0.03 */
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if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;
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/* Final stages. Use multi-precision arithmetic. */
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stage_n:
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for (i=0; i<M; i++) {
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p = pr[i];
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__dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
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__mplog(&mpx,&mpy,p);
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__dbl_mp(e[i].d,&mperr,p);
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__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
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__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
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if (y1==y2) return y1;
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}
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return y1;
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}
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#ifndef __ieee754_log
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strong_alias (__ieee754_log, __log_finite)
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#endif
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