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271 lines
9.0 KiB
C
271 lines
9.0 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) 2001-2012 Free Software Foundation
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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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/* MODULE_NAME:uexp.c */
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/* */
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/* FUNCTION:uexp */
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/* exp1 */
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/* */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
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/* mpa.c mpexp.x slowexp.c */
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/* */
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/* An ultimate exp routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of e^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 "uexp.h"
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#include "mydefs.h"
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#include "MathLib.h"
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#include "uexp.tbl"
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#include <math_private.h>
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#include <fenv.h>
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#ifndef SECTION
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# define SECTION
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#endif
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double __slowexp(double);
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/***************************************************************************/
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/* An ultimate exp routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of e^x */
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/***************************************************************************/
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double
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SECTION
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__ieee754_exp(double x) {
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double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
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mynumber junk1, junk2, binexp = {{0,0}};
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#if 0
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int4 k;
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#endif
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int4 i,j,m,n,ex;
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double retval;
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SET_RESTORE_ROUND (FE_TONEAREST);
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junk1.x = x;
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m = junk1.i[HIGH_HALF];
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n = m&hugeint;
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if (n > smallint && n < bigint) {
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y = x*log2e.x + three51.x;
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bexp = y - three51.x; /* multiply the result by 2**bexp */
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junk1.x = y;
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eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
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t = x - bexp*ln_two1.x;
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y = t + three33.x;
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base = y - three33.x; /* t rounded to a multiple of 2**-18 */
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junk2.x = y;
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del = (t - base) - eps; /* x = bexp*ln(2) + base + del */
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eps = del + del*del*(p3.x*del + p2.x);
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binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
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i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
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j = (junk2.i[LOW_HALF]&511)<<1;
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al = coar.x[i]*fine.x[j];
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bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
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rem=(bet + bet*eps)+al*eps;
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res = al + rem;
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cor = (al - res) + rem;
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if (res == (res+cor*err_0)) { retval = res*binexp.x; goto ret; }
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else { retval = __slowexp(x); goto ret; } /*if error is over bound */
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}
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if (n <= smallint) { retval = 1.0; goto ret; }
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if (n >= badint) {
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if (n > infint) { retval = x+x; goto ret; } /* x is NaN */
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if (n < infint) { retval = (x>0) ? (hhuge*hhuge) : (tiny*tiny); goto ret; }
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/* x is finite, cause either overflow or underflow */
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if (junk1.i[LOW_HALF] != 0) { retval = x+x; goto ret; } /* x is NaN */
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retval = (x>0)?inf.x:zero; /* |x| = inf; return either inf or 0 */
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goto ret;
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}
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y = x*log2e.x + three51.x;
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bexp = y - three51.x;
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junk1.x = y;
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eps = bexp*ln_two2.x;
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t = x - bexp*ln_two1.x;
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y = t + three33.x;
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base = y - three33.x;
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junk2.x = y;
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del = (t - base) - eps;
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eps = del + del*del*(p3.x*del + p2.x);
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i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
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j = (junk2.i[LOW_HALF]&511)<<1;
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al = coar.x[i]*fine.x[j];
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bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
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rem=(bet + bet*eps)+al*eps;
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res = al + rem;
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cor = (al - res) + rem;
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if (m>>31) {
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ex=junk1.i[LOW_HALF];
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if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
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if (ex >=-1022) {
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binexp.i[HIGH_HALF] = (1023+ex)<<20;
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if (res == (res+cor*err_0)) { retval = res*binexp.x; goto ret; }
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else { retval = __slowexp(x); goto ret; } /*if error is over bound */
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}
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ex = -(1022+ex);
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binexp.i[HIGH_HALF] = (1023-ex)<<20;
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res*=binexp.x;
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cor*=binexp.x;
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eps=1.0000000001+err_0*binexp.x;
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t=1.0+res;
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y = ((1.0-t)+res)+cor;
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res=t+y;
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cor = (t-res)+y;
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if (res == (res + eps*cor))
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{ binexp.i[HIGH_HALF] = 0x00100000;
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retval = (res-1.0)*binexp.x;
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goto ret;
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}
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else { retval = __slowexp(x); goto ret; } /* if error is over bound */
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}
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else {
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binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
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if (res == (res+cor*err_0)) { retval = res*binexp.x*t256.x; goto ret; }
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else { retval = __slowexp(x); goto ret; }
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}
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ret:
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return retval;
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}
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#ifndef __ieee754_exp
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strong_alias (__ieee754_exp, __exp_finite)
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#endif
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/************************************************************************/
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/* Compute e^(x+xx)(Double-Length number) .The routine also receive */
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/* bound of error of previous calculation .If after computing exp */
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/* error bigger than allows routine return non positive number */
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/*else return e^(x + xx) (always positive ) */
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/************************************************************************/
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double
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SECTION
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__exp1(double x, double xx, double error) {
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double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
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mynumber junk1, junk2, binexp = {{0,0}};
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#if 0
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int4 k;
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#endif
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int4 i,j,m,n,ex;
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junk1.x = x;
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m = junk1.i[HIGH_HALF];
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n = m&hugeint; /* no sign */
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if (n > smallint && n < bigint) {
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y = x*log2e.x + three51.x;
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bexp = y - three51.x; /* multiply the result by 2**bexp */
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junk1.x = y;
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eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
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t = x - bexp*ln_two1.x;
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y = t + three33.x;
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base = y - three33.x; /* t rounded to a multiple of 2**-18 */
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junk2.x = y;
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del = (t - base) + (xx-eps); /* x = bexp*ln(2) + base + del */
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eps = del + del*del*(p3.x*del + p2.x);
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binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
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i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
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j = (junk2.i[LOW_HALF]&511)<<1;
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al = coar.x[i]*fine.x[j];
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bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
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rem=(bet + bet*eps)+al*eps;
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res = al + rem;
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cor = (al - res) + rem;
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if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
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else return -10.0;
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}
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if (n <= smallint) return 1.0; /* if x->0 e^x=1 */
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if (n >= badint) {
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if (n > infint) return(zero/zero); /* x is NaN, return invalid */
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if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
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/* x is finite, cause either overflow or underflow */
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if (junk1.i[LOW_HALF] != 0) return (zero/zero); /* x is NaN */
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return ((x>0)?inf.x:zero ); /* |x| = inf; return either inf or 0 */
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}
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y = x*log2e.x + three51.x;
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bexp = y - three51.x;
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junk1.x = y;
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eps = bexp*ln_two2.x;
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t = x - bexp*ln_two1.x;
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y = t + three33.x;
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base = y - three33.x;
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junk2.x = y;
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del = (t - base) + (xx-eps);
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eps = del + del*del*(p3.x*del + p2.x);
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i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
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j = (junk2.i[LOW_HALF]&511)<<1;
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al = coar.x[i]*fine.x[j];
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bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
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rem=(bet + bet*eps)+al*eps;
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res = al + rem;
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cor = (al - res) + rem;
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if (m>>31) {
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ex=junk1.i[LOW_HALF];
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if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
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if (ex >=-1022) {
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binexp.i[HIGH_HALF] = (1023+ex)<<20;
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if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
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else return -10.0;
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}
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ex = -(1022+ex);
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binexp.i[HIGH_HALF] = (1023-ex)<<20;
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res*=binexp.x;
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cor*=binexp.x;
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eps=1.00000000001+(error+err_1)*binexp.x;
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t=1.0+res;
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y = ((1.0-t)+res)+cor;
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res=t+y;
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cor = (t-res)+y;
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if (res == (res + eps*cor))
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{binexp.i[HIGH_HALF] = 0x00100000; return (res-1.0)*binexp.x;}
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else return -10.0;
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}
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else {
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binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
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if (res == (res+cor*(1.0+error+err_1)))
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return res*binexp.x*t256.x;
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else return -10.0;
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}
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}
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