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ca58f1dbeb
2001-03-12 Ulrich Drepper <drepper@redhat.com> * sysdeps/ieee754/dbl-64/e_remainder.c: Fix handling of boundary conditions. * sysdeps/ieee754/dbl-64/e_pow.c: Fix handling of boundary conditions. * sysdeps/ieee754/dbl-64/s_sin.c (__sin): Handle Inf and NaN correctly. (__cos): Likewise. * sysdeps/ieee754/dbl-64/e_asin.c (__ieee754_asin): Handle NaN correctly. (__ieee754_acos): Likewise. redefinition. * sysdeps/ieee754/dbl-64/endian.h: Define also one of BIG_ENDI and LITTLE_ENDI. * sysdeps/ieee754/dbl-64/MathLib.h (Init_Lib): Use void as parameter list.
507 lines
14 KiB
C
507 lines
14 KiB
C
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/*
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* IBM Accurate Mathematical Library
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* Copyright (c) International Business Machines Corp., 2001
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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 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 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, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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*/
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/************************************************************************/
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/* MODULE_NAME: mpa.c */
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/* */
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/* FUNCTIONS: */
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/* mcr */
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/* acr */
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/* cr */
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/* cpy */
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/* cpymn */
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/* norm */
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/* denorm */
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/* mp_dbl */
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/* dbl_mp */
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/* add_magnitudes */
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/* sub_magnitudes */
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/* add */
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/* sub */
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/* mul */
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/* inv */
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/* dvd */
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/* */
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/* Arithmetic functions for multiple precision numbers. */
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/* Relative errors are bounded */
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/************************************************************************/
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#include "endian.h"
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#include "mpa.h"
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#include "mpa2.h"
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/* mcr() compares the sizes of the mantissas of two multiple precision */
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/* numbers. Mantissas are compared regardless of the signs of the */
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/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
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/* disregarded. */
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static int mcr(const mp_no *x, const mp_no *y, int p) {
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int i;
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for (i=1; i<=p; i++) {
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if (X[i] == Y[i]) continue;
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else if (X[i] > Y[i]) return 1;
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else return -1; }
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return 0;
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}
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/* acr() compares the absolute values of two multiple precision numbers */
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int __acr(const mp_no *x, const mp_no *y, int p) {
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int i;
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if (X[0] == ZERO) {
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if (Y[0] == ZERO) i= 0;
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else i=-1;
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}
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else if (Y[0] == ZERO) i= 1;
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else {
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if (EX > EY) i= 1;
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else if (EX < EY) i=-1;
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else i= mcr(x,y,p);
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}
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return i;
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}
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/* cr90 compares the values of two multiple precision numbers */
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int __cr(const mp_no *x, const mp_no *y, int p) {
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int i;
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if (X[0] > Y[0]) i= 1;
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else if (X[0] < Y[0]) i=-1;
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else if (X[0] < ZERO ) i= __acr(y,x,p);
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else i= __acr(x,y,p);
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return i;
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}
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/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
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void __cpy(const mp_no *x, mp_no *y, int p) {
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int i;
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EY = EX;
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for (i=0; i <= p; i++) Y[i] = X[i];
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return;
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}
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/* Copy a multiple precision number x of precision m into a */
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/* multiple precision number y of precision n. In case n>m, */
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/* the digits of y beyond the m'th are set to zero. In case */
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/* n<m, the digits of x beyond the n'th are ignored. */
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/* x=y is permissible. */
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void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
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int i,k;
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EY = EX; k=MIN(m,n);
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for (i=0; i <= k; i++) Y[i] = X[i];
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for ( ; i <= n; i++) Y[i] = ZERO;
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return;
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}
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, normalized case (|x| >= 2**(-1022))) */
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static void norm(const mp_no *x, double *y, int p)
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{
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#define R radixi.d
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int i;
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#if 0
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int k;
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#endif
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double a,c,u,v,z[5];
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if (p<5) {
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if (p==1) c = X[1];
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else if (p==2) c = X[1] + R* X[2];
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else if (p==3) c = X[1] + R*(X[2] + R* X[3]);
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else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]);
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}
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else {
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for (a=ONE, z[1]=X[1]; z[1] < TWO23; )
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{a *= TWO; z[1] *= TWO; }
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for (i=2; i<5; i++) {
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z[i] = X[i]*a;
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u = (z[i] + CUTTER)-CUTTER;
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if (u > z[i]) u -= RADIX;
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z[i] -= u;
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z[i-1] += u*RADIXI;
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}
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u = (z[3] + TWO71) - TWO71;
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if (u > z[3]) u -= TWO19;
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v = z[3]-u;
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if (v == TWO18) {
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if (z[4] == ZERO) {
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for (i=5; i <= p; i++) {
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if (X[i] == ZERO) continue;
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else {z[3] += ONE; break; }
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}
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}
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else z[3] += ONE;
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}
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c = (z[1] + R *(z[2] + R * z[3]))/a;
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}
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c *= X[0];
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for (i=1; i<EX; i++) c *= RADIX;
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for (i=1; i>EX; i--) c *= RADIXI;
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*y = c;
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return;
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, denormalized case (|x| < 2**(-1022))) */
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static void denorm(const mp_no *x, double *y, int p)
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{
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int i,k;
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double c,u,z[5];
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#if 0
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double a,v;
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#endif
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#define R radixi.d
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if (EX<-44 || (EX==-44 && X[1]<TWO5))
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{ *y=ZERO; return; }
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if (p==1) {
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if (EX==-42) {z[1]=X[1]+TWO10; z[2]=ZERO; z[3]=ZERO; k=3;}
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else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=ZERO; k=2;}
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else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
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}
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else if (p==2) {
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if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; z[3]=ZERO; k=3;}
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else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=X[2]; k=2;}
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else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
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}
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else {
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if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; k=3;}
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else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; k=2;}
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else {z[1]= TWO10; z[2]=ZERO; k=1;}
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z[3] = X[k];
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}
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u = (z[3] + TWO57) - TWO57;
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if (u > z[3]) u -= TWO5;
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if (u==z[3]) {
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for (i=k+1; i <= p; i++) {
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if (X[i] == ZERO) continue;
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else {z[3] += ONE; break; }
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}
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}
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c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10);
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*y = c*TWOM1032;
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return;
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision number *y. */
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/* The result is correctly rounded to the nearest/even. *x is left unchanged */
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void __mp_dbl(const mp_no *x, double *y, int p) {
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#if 0
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int i,k;
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double a,c,u,v,z[5];
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#endif
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if (X[0] == ZERO) {*y = ZERO; return; }
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if (EX> -42) norm(x,y,p);
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else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
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else denorm(x,y,p);
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}
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/* dbl_mp() converts a double precision number x into a multiple precision */
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/* number *y. If the precision p is too small the result is truncated. x is */
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/* left unchanged. */
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void __dbl_mp(double x, mp_no *y, int p) {
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int i,n;
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double u;
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/* Sign */
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if (x == ZERO) {Y[0] = ZERO; return; }
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else if (x > ZERO) Y[0] = ONE;
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else {Y[0] = MONE; x=-x; }
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/* Exponent */
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for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
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for ( ; x < ONE; EY -= ONE) x *= RADIX;
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/* Digits */
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n=MIN(p,4);
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for (i=1; i<=n; i++) {
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u = (x + TWO52) - TWO52;
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if (u>x) u -= ONE;
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Y[i] = u; x -= u; x *= RADIX; }
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for ( ; i<=p; i++) Y[i] = ZERO;
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return;
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}
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/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
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/* abs(*x) >= abs(*y) > 0. */
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/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
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/* No guard digit is used. The result equals the exact sum, truncated. */
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/* *x & *y are left unchanged. */
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static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int i,j,k;
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EZ = EX;
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i=p; j=p+ EY - EX; k=p+1;
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if (j<1)
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{__cpy(x,z,p); return; }
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else Z[k] = ZERO;
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for (; j>0; i--,j--) {
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Z[k] += X[i] + Y[j];
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if (Z[k] >= RADIX) {
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Z[k] -= RADIX;
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Z[--k] = ONE; }
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else
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Z[--k] = ZERO;
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}
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for (; i>0; i--) {
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Z[k] += X[i];
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if (Z[k] >= RADIX) {
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Z[k] -= RADIX;
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Z[--k] = ONE; }
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else
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Z[--k] = ZERO;
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}
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if (Z[1] == ZERO) {
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for (i=1; i<=p; i++) Z[i] = Z[i+1]; }
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else EZ += ONE;
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}
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/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */
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/* abs(*x) > abs(*y) > 0. */
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/* The sign of the difference *z is undefined. x&y may overlap but not x&z */
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/* or y&z. One guard digit is used. The error is less than one ulp. */
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/* *x & *y are left unchanged. */
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static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int i,j,k;
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EZ = EX;
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if (EX == EY) {
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i=j=k=p;
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Z[k] = Z[k+1] = ZERO; }
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else {
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j= EX - EY;
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if (j > p) {__cpy(x,z,p); return; }
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else {
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i=p; j=p+1-j; k=p;
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if (Y[j] > ZERO) {
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Z[k+1] = RADIX - Y[j--];
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Z[k] = MONE; }
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else {
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Z[k+1] = ZERO;
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Z[k] = ZERO; j--;}
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}
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}
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for (; j>0; i--,j--) {
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Z[k] += (X[i] - Y[j]);
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if (Z[k] < ZERO) {
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Z[k] += RADIX;
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Z[--k] = MONE; }
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else
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Z[--k] = ZERO;
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}
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for (; i>0; i--) {
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Z[k] += X[i];
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if (Z[k] < ZERO) {
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Z[k] += RADIX;
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Z[--k] = MONE; }
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else
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Z[--k] = ZERO;
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}
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for (i=1; Z[i] == ZERO; i++) ;
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EZ = EZ - i + 1;
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for (k=1; i <= p+1; )
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Z[k++] = Z[i++];
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for (; k <= p; )
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Z[k++] = ZERO;
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return;
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}
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/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */
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/* but not x&z or y&z. One guard digit is used. The error is less than */
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/* one ulp. *x & *y are left unchanged. */
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void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int n;
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if (X[0] == ZERO) {__cpy(y,z,p); return; }
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else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
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if (X[0] == Y[0]) {
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if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
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else {add_magnitudes(y,x,z,p); Z[0] = Y[0]; }
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}
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else {
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if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
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else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = Y[0]; }
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else Z[0] = ZERO;
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}
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return;
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}
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/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
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/* overlap but not x&z or y&z. One guard digit is used. The error is */
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/* less than one ulp. *x & *y are left unchanged. */
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void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int n;
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if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; }
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else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
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if (X[0] != Y[0]) {
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if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
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else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
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}
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else {
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if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
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else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
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else Z[0] = ZERO;
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}
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return;
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}
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/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */
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/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */
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/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */
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/* *x & *y are left unchanged. */
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void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int i, i1, i2, j, k, k2;
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double u;
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/* Is z=0? */
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if (X[0]*Y[0]==ZERO)
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{ Z[0]=ZERO; return; }
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/* Multiply, add and carry */
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k2 = (p<3) ? p+p : p+3;
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Z[k2]=ZERO;
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for (k=k2; k>1; ) {
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if (k > p) {i1=k-p; i2=p+1; }
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else {i1=1; i2=k; }
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for (i=i1,j=i2-1; i<i2; i++,j--) Z[k] += X[i]*Y[j];
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u = (Z[k] + CUTTER)-CUTTER;
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if (u > Z[k]) u -= RADIX;
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Z[k] -= u;
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Z[--k] = u*RADIXI;
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}
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/* Is there a carry beyond the most significant digit? */
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if (Z[1] == ZERO) {
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for (i=1; i<=p; i++) Z[i]=Z[i+1];
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EZ = EX + EY - 1; }
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else
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EZ = EX + EY;
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Z[0] = X[0] * Y[0];
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return;
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}
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/* Invert a multiple precision number. Set *y = 1 / *x. */
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/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */
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/* 2.001*r**(1-p) for p>3. */
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/* *x=0 is not permissible. *x is left unchanged. */
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void __inv(const mp_no *x, mp_no *y, int p) {
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int i;
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#if 0
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int l;
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#endif
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double t;
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mp_no z,w;
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static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
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4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
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const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
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0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
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0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
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0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
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__cpy(x,&z,p); z.e=0; __mp_dbl(&z,&t,p);
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t=ONE/t; __dbl_mp(t,y,p); EY -= EX;
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for (i=0; i<np1[p]; i++) {
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__cpy(y,&w,p);
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__mul(x,&w,y,p);
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__sub(&mptwo,y,&z,p);
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__mul(&w,&z,y,p);
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}
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return;
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}
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/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
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/* are left unchanged. x&y may overlap but not x&z or y&z. */
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/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */
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/* and 3.001*r**(1-p) for p>3. *y=0 is not permissible. */
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void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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mp_no w;
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if (X[0] == ZERO) Z[0] = ZERO;
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else {__inv(y,&w,p); __mul(x,&w,z,p);}
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return;
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}
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