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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.
1128 lines
34 KiB
C
1128 lines
34 KiB
C
/*
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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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/* */
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/* MODULE_NAME:usncs.c */
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/* */
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/* FUNCTIONS: usin */
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/* ucos */
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/* slow */
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/* slow1 */
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/* slow2 */
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/* sloww */
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/* sloww1 */
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/* sloww2 */
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/* bsloww */
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/* bsloww1 */
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/* bsloww2 */
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/* cslow2 */
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/* csloww */
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/* csloww1 */
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/* csloww2 */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
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/* branred.c sincos32.c dosincos.c mpa.c */
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/* sincos.tbl */
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/* */
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/* An ultimate sin and routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of sin(x) or cos(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 "mydefs.h"
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#include "usncs.h"
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#include "MathLib.h"
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#include "sincos.tbl"
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static const double
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sn3 = -1.66666666666664880952546298448555E-01,
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sn5 = 8.33333214285722277379541354343671E-03,
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cs2 = 4.99999999999999999999950396842453E-01,
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cs4 = -4.16666666666664434524222570944589E-02,
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cs6 = 1.38888874007937613028114285595617E-03;
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void __dubsin(double x, double dx, double w[]);
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void __docos(double x, double dx, double w[]);
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double __mpsin(double x, double dx);
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double __mpcos(double x, double dx);
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double __mpsin1(double x);
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double __mpcos1(double x);
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static double slow(double x);
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static double slow1(double x);
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static double slow2(double x);
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static double sloww(double x, double dx, double orig);
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static double sloww1(double x, double dx, double orig);
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static double sloww2(double x, double dx, double orig, int n);
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static double bsloww(double x, double dx, double orig, int n);
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static double bsloww1(double x, double dx, double orig, int n);
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static double bsloww2(double x, double dx, double orig, int n);
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int __branred(double x, double *a, double *aa);
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static double cslow2(double x);
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static double csloww(double x, double dx, double orig);
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static double csloww1(double x, double dx, double orig);
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static double csloww2(double x, double dx, double orig, int n);
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/*******************************************************************/
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/* An ultimate sin routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of sin(x) */
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/*******************************************************************/
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double __sin(double x){
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double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
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#if 0
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double w[2];
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#endif
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mynumber u,v;
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int4 k,m,n;
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#if 0
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int4 nn;
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#endif
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u.x = x;
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m = u.i[HIGH_HALF];
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k = 0x7fffffff&m; /* no sign */
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if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
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return x;
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/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
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else if (k < 0x3fd00000){
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xx = x*x;
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/*Taylor series */
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t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x);
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res = x+t;
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cor = (x-res)+t;
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return (res == res + 1.07*cor)? res : slow(x);
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} /* else if (k < 0x3fd00000) */
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/*---------------------------- 0.25<|x|< 0.855469---------------------- */
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else if (k < 0x3feb6000) {
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u.x=(m>0)?big.x+x:big.x-x;
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y=(m>0)?x-(u.x-big.x):x+(u.x-big.x);
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xx=y*y;
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s = y + y*xx*(sn3 +xx*sn5);
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c = xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=(m>0)?sincos.x[k]:-sincos.x[k];
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ssn=(m>0)?sincos.x[k+1]:-sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ssn+s*ccs-sn*c)+cs*s;
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res=sn+cor;
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cor=(sn-res)+cor;
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return (res==res+1.025*cor)? res : slow1(x);
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} /* else if (k < 0x3feb6000) */
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/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
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else if (k < 0x400368fd ) {
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y = (m>0)? hp0.x-x:hp0.x+x;
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if (y>=0) {
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u.x = big.x+y;
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y = (y-(u.x-big.x))+hp1.x;
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}
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else {
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u.x = big.x-y;
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y = (-hp1.x) - (y+(u.x-big.x));
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}
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xx=y*y;
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s = y + y*xx*(sn3 +xx*sn5);
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c = xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ccs-s*ssn-cs*c)-sn*s;
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res=cs+cor;
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cor=(cs-res)+cor;
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return (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x);
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} /* else if (k < 0x400368fd) */
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/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
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else if (k < 0x419921FB ) {
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t = (x*hpinv.x + toint.x);
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xn = t - toint.x;
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v.x = t;
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y = (x - xn*mp1.x) - xn*mp2.x;
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n =v.i[LOW_HALF]&3;
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da = xn*mp3.x;
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a=y-da;
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da = (y-a)-da;
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eps = ABS(x)*1.2e-30;
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switch (n) { /* quarter of unit circle */
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case 0:
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case 2:
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xx = a*a;
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if (n) {a=-a;da=-da;}
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if (xx < 0.01588) {
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/*Taylor series */
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t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
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res = a+t;
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cor = (a-res)+t;
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cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
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return (res == res + cor)? res : sloww(a,da,x);
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}
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else {
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if (a>0)
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{m=1;t=a;db=da;}
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else
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{m=0;t=-a;db=-da;}
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u.x=big.x+t;
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y=t-(u.x-big.x);
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xx=y*y;
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s = y + (db+y*xx*(sn3 +xx*sn5));
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c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ssn+s*ccs-sn*c)+cs*s;
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res=sn+cor;
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cor=(sn-res)+cor;
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cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
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return (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x);
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}
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break;
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case 1:
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case 3:
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if (a<0)
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{a=-a;da=-da;}
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u.x=big.x+a;
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y=a-(u.x-big.x)+da;
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xx=y*y;
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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s = y + y*xx*(sn3 +xx*sn5);
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c = xx*(cs2 +xx*(cs4 + xx*cs6));
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cor=(ccs-s*ssn-cs*c)-sn*s;
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res=cs+cor;
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cor=(cs-res)+cor;
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cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
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return (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n);
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break;
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}
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} /* else if (k < 0x419921FB ) */
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/*---------------------105414350 <|x|< 281474976710656 --------------------*/
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else if (k < 0x42F00000 ) {
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t = (x*hpinv.x + toint.x);
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xn = t - toint.x;
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v.x = t;
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xn1 = (xn+8.0e22)-8.0e22;
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xn2 = xn - xn1;
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y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
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n =v.i[LOW_HALF]&3;
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da = xn1*pp3.x;
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t=y-da;
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da = (y-t)-da;
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da = (da - xn2*pp3.x) -xn*pp4.x;
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a = t+da;
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da = (t-a)+da;
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eps = 1.0e-24;
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switch (n) {
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case 0:
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case 2:
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xx = a*a;
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if (n) {a=-a;da=-da;}
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if (xx < 0.01588) {
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/* Taylor series */
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t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
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res = a+t;
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cor = (a-res)+t;
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cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
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return (res == res + cor)? res : bsloww(a,da,x,n);
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}
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else {
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if (a>0) {m=1;t=a;db=da;}
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else {m=0;t=-a;db=-da;}
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u.x=big.x+t;
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y=t-(u.x-big.x);
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xx=y*y;
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s = y + (db+y*xx*(sn3 +xx*sn5));
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c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ssn+s*ccs-sn*c)+cs*s;
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res=sn+cor;
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cor=(sn-res)+cor;
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cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
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return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
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}
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break;
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case 1:
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case 3:
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if (a<0)
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{a=-a;da=-da;}
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u.x=big.x+a;
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y=a-(u.x-big.x)+da;
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xx=y*y;
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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s = y + y*xx*(sn3 +xx*sn5);
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c = xx*(cs2 +xx*(cs4 + xx*cs6));
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cor=(ccs-s*ssn-cs*c)-sn*s;
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res=cs+cor;
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cor=(cs-res)+cor;
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cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
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return (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n);
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break;
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}
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} /* else if (k < 0x42F00000 ) */
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/* -----------------281474976710656 <|x| <2^1024----------------------------*/
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else if (k < 0x7ff00000) {
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n = __branred(x,&a,&da);
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switch (n) {
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case 0:
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if (a*a < 0.01588) return bsloww(a,da,x,n);
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else return bsloww1(a,da,x,n);
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break;
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case 2:
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if (a*a < 0.01588) return bsloww(-a,-da,x,n);
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else return bsloww1(-a,-da,x,n);
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break;
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case 1:
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case 3:
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return bsloww2(a,da,x,n);
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break;
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}
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} /* else if (k < 0x7ff00000 ) */
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/*--------------------- |x| > 2^1024 ----------------------------------*/
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else return x / x;
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return 0; /* unreachable */
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}
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/*******************************************************************/
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/* An ultimate cos routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of cos(x) */
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/*******************************************************************/
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double __cos(double x)
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{
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double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
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mynumber u,v;
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int4 k,m,n;
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u.x = x;
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m = u.i[HIGH_HALF];
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k = 0x7fffffff&m;
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if (k < 0x3e400000 ) return 1.0; /* |x|<2^-27 => cos(x)=1 */
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else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */
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y=ABS(x);
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u.x = big.x+y;
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y = y-(u.x-big.x);
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xx=y*y;
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s = y + y*xx*(sn3 +xx*sn5);
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c = xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ccs-s*ssn-cs*c)-sn*s;
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res=cs+cor;
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cor=(cs-res)+cor;
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return (res==res+1.020*cor)? res : cslow2(x);
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} /* else if (k < 0x3feb6000) */
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else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */;
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y=hp0.x-ABS(x);
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a=y+hp1.x;
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da=(y-a)+hp1.x;
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xx=a*a;
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if (xx < 0.01588) {
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t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
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res = a+t;
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cor = (a-res)+t;
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cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31;
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return (res == res + cor)? res : csloww(a,da,x);
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}
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else {
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if (a>0) {m=1;t=a;db=da;}
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else {m=0;t=-a;db=-da;}
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u.x=big.x+t;
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y=t-(u.x-big.x);
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xx=y*y;
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s = y + (db+y*xx*(sn3 +xx*sn5));
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c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
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k=u.i[LOW_HALF]<<2;
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sn=sincos.x[k];
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ssn=sincos.x[k+1];
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cs=sincos.x[k+2];
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ccs=sincos.x[k+3];
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cor=(ssn+s*ccs-sn*c)+cs*s;
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res=sn+cor;
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cor=(sn-res)+cor;
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cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31;
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return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
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}
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} /* else if (k < 0x400368fd) */
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|
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else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */
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t = (x*hpinv.x + toint.x);
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xn = t - toint.x;
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v.x = t;
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y = (x - xn*mp1.x) - xn*mp2.x;
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n =v.i[LOW_HALF]&3;
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da = xn*mp3.x;
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a=y-da;
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da = (y-a)-da;
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eps = ABS(x)*1.2e-30;
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switch (n) {
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case 1:
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case 3:
|
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xx = a*a;
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if (n == 1) {a=-a;da=-da;}
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if (xx < 0.01588) {
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
|
|
res = a+t;
|
|
cor = (a-res)+t;
|
|
cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
|
|
return (res == res + cor)? res : csloww(a,da,x);
|
|
}
|
|
else {
|
|
if (a>0) {m=1;t=a;db=da;}
|
|
else {m=0;t=-a;db=-da;}
|
|
u.x=big.x+t;
|
|
y=t-(u.x-big.x);
|
|
xx=y*y;
|
|
s = y + (db+y*xx*(sn3 +xx*sn5));
|
|
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
cor=(ssn+s*ccs-sn*c)+cs*s;
|
|
res=sn+cor;
|
|
cor=(sn-res)+cor;
|
|
cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
|
|
return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
|
|
}
|
|
break;
|
|
|
|
case 0:
|
|
case 2:
|
|
if (a<0) {a=-a;da=-da;}
|
|
u.x=big.x+a;
|
|
y=a-(u.x-big.x)+da;
|
|
xx=y*y;
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
s = y + y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
cor=(ccs-s*ssn-cs*c)-sn*s;
|
|
res=cs+cor;
|
|
cor=(cs-res)+cor;
|
|
cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
|
|
return (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n);
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
} /* else if (k < 0x419921FB ) */
|
|
|
|
|
|
else if (k < 0x42F00000 ) {
|
|
t = (x*hpinv.x + toint.x);
|
|
xn = t - toint.x;
|
|
v.x = t;
|
|
xn1 = (xn+8.0e22)-8.0e22;
|
|
xn2 = xn - xn1;
|
|
y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
|
|
n =v.i[LOW_HALF]&3;
|
|
da = xn1*pp3.x;
|
|
t=y-da;
|
|
da = (y-t)-da;
|
|
da = (da - xn2*pp3.x) -xn*pp4.x;
|
|
a = t+da;
|
|
da = (t-a)+da;
|
|
eps = 1.0e-24;
|
|
|
|
switch (n) {
|
|
case 1:
|
|
case 3:
|
|
xx = a*a;
|
|
if (n==1) {a=-a;da=-da;}
|
|
if (xx < 0.01588) {
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
|
|
res = a+t;
|
|
cor = (a-res)+t;
|
|
cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
|
|
return (res == res + cor)? res : bsloww(a,da,x,n);
|
|
}
|
|
else {
|
|
if (a>0) {m=1;t=a;db=da;}
|
|
else {m=0;t=-a;db=-da;}
|
|
u.x=big.x+t;
|
|
y=t-(u.x-big.x);
|
|
xx=y*y;
|
|
s = y + (db+y*xx*(sn3 +xx*sn5));
|
|
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
cor=(ssn+s*ccs-sn*c)+cs*s;
|
|
res=sn+cor;
|
|
cor=(sn-res)+cor;
|
|
cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
|
|
return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
|
|
}
|
|
break;
|
|
|
|
case 0:
|
|
case 2:
|
|
if (a<0) {a=-a;da=-da;}
|
|
u.x=big.x+a;
|
|
y=a-(u.x-big.x)+da;
|
|
xx=y*y;
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
s = y + y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
cor=(ccs-s*ssn-cs*c)-sn*s;
|
|
res=cs+cor;
|
|
cor=(cs-res)+cor;
|
|
cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
|
|
return (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n);
|
|
break;
|
|
|
|
}
|
|
|
|
} /* else if (k < 0x42F00000 ) */
|
|
|
|
else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */
|
|
|
|
n = __branred(x,&a,&da);
|
|
switch (n) {
|
|
case 1:
|
|
if (a*a < 0.01588) return bsloww(-a,-da,x,n);
|
|
else return bsloww1(-a,-da,x,n);
|
|
break;
|
|
case 3:
|
|
if (a*a < 0.01588) return bsloww(a,da,x,n);
|
|
else return bsloww1(a,da,x,n);
|
|
break;
|
|
|
|
case 0:
|
|
case 2:
|
|
return bsloww2(a,da,x,n);
|
|
break;
|
|
}
|
|
|
|
} /* else if (k < 0x7ff00000 ) */
|
|
|
|
|
|
|
|
|
|
else return x / x; /* |x| > 2^1024 */
|
|
return 0;
|
|
|
|
}
|
|
|
|
/************************************************************************/
|
|
/* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */
|
|
/* precision and if still doesn't accurate enough by mpsin or dubsin */
|
|
/************************************************************************/
|
|
|
|
static double slow(double x) {
|
|
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
|
|
double y,x1,x2,xx,r,t,res,cor,w[2];
|
|
x1=(x+th2_36)-th2_36;
|
|
y = aa.x*x1*x1*x1;
|
|
r=x+y;
|
|
x2=x-x1;
|
|
xx=x*x;
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2;
|
|
t=((x-r)+y)+t;
|
|
res=r+t;
|
|
cor = (r-res)+t;
|
|
if (res == res + 1.0007*cor) return res;
|
|
else {
|
|
__dubsin(ABS(x),0,w);
|
|
if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0];
|
|
else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
|
|
}
|
|
}
|
|
/*******************************************************************************/
|
|
/* Routine compute sin(x) for 0.25<|x|< 0.855469 by sincos.tbl and Taylor */
|
|
/* and if result still doesn't accurate enough by mpsin or dubsin */
|
|
/*******************************************************************************/
|
|
|
|
static double slow1(double x) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k]; /* Data */
|
|
ssn=sincos.x[k+1]; /* from */
|
|
cs=sincos.x[k+2]; /* tables */
|
|
ccs=sincos.x[k+3]; /* sincos.tbl */
|
|
y1 = (y+t22)-t22;
|
|
y2 = y - y1;
|
|
c1 = (cs+t22)-t22;
|
|
c2=(cs-c1)+ccs;
|
|
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c;
|
|
y=sn+c1*y1;
|
|
cor = cor+((sn-y)+c1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
if (res == res+1.0005*cor) return (x>0)?res:-res;
|
|
else {
|
|
__dubsin(ABS(x),0,w);
|
|
if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
|
|
else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
|
|
}
|
|
}
|
|
/**************************************************************************/
|
|
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by sincos.tbl */
|
|
/* and if result still doesn't accurate enough by mpsin or dubsin */
|
|
/**************************************************************************/
|
|
static double slow2(double x) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
y = hp0.x-y;
|
|
if (y>=0) {
|
|
u.x = big.x+y;
|
|
y = y-(u.x-big.x);
|
|
del = hp1.x;
|
|
}
|
|
else {
|
|
u.x = big.x-y;
|
|
y = -(y+(u.x-big.x));
|
|
del = -hp1.x;
|
|
}
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+del;
|
|
e1 = (sn+t22)-t22;
|
|
e2=(sn-e1)+ssn;
|
|
cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
|
|
y=cs-e1*y1;
|
|
cor = cor+((cs-y)-e1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
if (res == res+1.0005*cor) return (x>0)?res:-res;
|
|
else {
|
|
y=ABS(x)-hp0.x;
|
|
y1=y-hp1.x;
|
|
y2=(y-y1)-hp1.x;
|
|
__docos(y1,y2,w);
|
|
if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
|
|
else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
|
|
}
|
|
}
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
|
|
/* to use Taylor series around zero and (x+dx) */
|
|
/* in first or third quarter of unit circle.Routine receive also */
|
|
/* (right argument) the original value of x for computing error of */
|
|
/* result.And if result not accurate enough routine calls mpsin1 or dubsin */
|
|
/***************************************************************************/
|
|
|
|
static double sloww(double x,double dx, double orig) {
|
|
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
|
|
double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
|
|
union {int4 i[2]; double x;} v;
|
|
int4 n;
|
|
x1=(x+th2_36)-th2_36;
|
|
y = aa.x*x1*x1*x1;
|
|
r=x+y;
|
|
x2=(x-x1)+dx;
|
|
xx=x*x;
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
|
|
t=((x-r)+y)+t;
|
|
res=r+t;
|
|
cor = (r-res)+t;
|
|
cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
|
|
if (res == res + cor) return res;
|
|
else {
|
|
(x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
|
|
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else {
|
|
t = (orig*hpinv.x + toint.x);
|
|
xn = t - toint.x;
|
|
v.x = t;
|
|
y = (orig - xn*mp1.x) - xn*mp2.x;
|
|
n =v.i[LOW_HALF]&3;
|
|
da = xn*pp3.x;
|
|
t=y-da;
|
|
da = (y-t)-da;
|
|
y = xn*pp4.x;
|
|
a = t - y;
|
|
da = ((t-a)-y)+da;
|
|
if (n&2) {a=-a; da=-da;}
|
|
(a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
|
|
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
|
|
if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
|
|
else return __mpsin1(orig);
|
|
}
|
|
}
|
|
}
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) (Double-Length number) where x in first or */
|
|
/* third quarter of unit circle.Routine receive also (right argument) the */
|
|
/* original value of x for computing error of result.And if result not */
|
|
/* accurate enough routine calls mpsin1 or dubsin */
|
|
/***************************************************************************/
|
|
|
|
static double sloww1(double x, double dx, double orig) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
c1 = (cs+t22)-t22;
|
|
c2=(cs-c1)+ccs;
|
|
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
|
|
y=sn+c1*y1;
|
|
cor = cor+((sn-y)+c1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
|
|
if (res == res + cor) return (x>0)?res:-res;
|
|
else {
|
|
__dubsin(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else return __mpsin1(orig);
|
|
}
|
|
}
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
|
|
/* fourth quarter of unit circle.Routine receive also the original value */
|
|
/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/
|
|
/* accurate enough routine calls mpsin1 or dubsin */
|
|
/***************************************************************************/
|
|
|
|
static double sloww2(double x, double dx, double orig, int n) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
e1 = (sn+t22)-t22;
|
|
e2=(sn-e1)+ssn;
|
|
cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
|
|
y=cs-e1*y1;
|
|
cor = cor+((cs-y)-e1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
|
|
if (res == res + cor) return (n&2)?-res:res;
|
|
else {
|
|
__docos(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
|
|
if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
|
|
else return __mpsin1(orig);
|
|
}
|
|
}
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
|
|
/* is small enough to use Taylor series around zero and (x+dx) */
|
|
/* in first or third quarter of unit circle.Routine receive also */
|
|
/* (right argument) the original value of x for computing error of */
|
|
/* result.And if result not accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
static double bsloww(double x,double dx, double orig,int n) {
|
|
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
|
|
double y,x1,x2,xx,r,t,res,cor,w[2];
|
|
#if 0
|
|
double a,da,xn;
|
|
union {int4 i[2]; double x;} v;
|
|
#endif
|
|
x1=(x+th2_36)-th2_36;
|
|
y = aa.x*x1*x1*x1;
|
|
r=x+y;
|
|
x2=(x-x1)+dx;
|
|
xx=x*x;
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
|
|
t=((x-r)+y)+t;
|
|
res=r+t;
|
|
cor = (r-res)+t;
|
|
cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
|
|
if (res == res + cor) return res;
|
|
else {
|
|
(x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
|
|
cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24;
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else return (n&1)?__mpcos1(orig):__mpsin1(orig);
|
|
}
|
|
}
|
|
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
|
|
/* in first or third quarter of unit circle.Routine receive also */
|
|
/* (right argument) the original value of x for computing error of result.*/
|
|
/* And if result not accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
static double bsloww1(double x, double dx, double orig,int n) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
c1 = (cs+t22)-t22;
|
|
c2=(cs-c1)+ccs;
|
|
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
|
|
y=sn+c1*y1;
|
|
cor = cor+((sn-y)+c1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
|
|
if (res == res + cor) return (x>0)?res:-res;
|
|
else {
|
|
__dubsin(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24;
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else return (n&1)?__mpcos1(orig):__mpsin1(orig);
|
|
}
|
|
}
|
|
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
|
|
/* in second or fourth quarter of unit circle.Routine receive also the */
|
|
/* original value and quarter(n= 1or 3)of x for computing error of result. */
|
|
/* And if result not accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
static double bsloww2(double x, double dx, double orig, int n) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
e1 = (sn+t22)-t22;
|
|
e2=(sn-e1)+ssn;
|
|
cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
|
|
y=cs-e1*y1;
|
|
cor = cor+((cs-y)-e1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
|
|
if (res == res + cor) return (n&2)?-res:res;
|
|
else {
|
|
__docos(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24;
|
|
if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
|
|
else return (n&1)?__mpsin1(orig):__mpcos1(orig);
|
|
}
|
|
}
|
|
|
|
/************************************************************************/
|
|
/* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */
|
|
/* precision and if still doesn't accurate enough by mpcos or docos */
|
|
/************************************************************************/
|
|
|
|
static double cslow2(double x) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x = big.x+y;
|
|
y = y-(u.x-big.x);
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
y1 = (y+t22)-t22;
|
|
y2 = y - y1;
|
|
e1 = (sn+t22)-t22;
|
|
e2=(sn-e1)+ssn;
|
|
cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
|
|
y=cs-e1*y1;
|
|
cor = cor+((cs-y)-e1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
if (res == res+1.0005*cor)
|
|
return res;
|
|
else {
|
|
y=ABS(x);
|
|
__docos(y,0,w);
|
|
if (w[0] == w[0]+1.000000005*w[1]) return w[0];
|
|
else return __mpcos(x,0);
|
|
}
|
|
}
|
|
|
|
/***************************************************************************/
|
|
/* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/
|
|
/* to use Taylor series around zero and (x+dx) .Routine receive also */
|
|
/* (right argument) the original value of x for computing error of */
|
|
/* result.And if result not accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
|
|
static double csloww(double x,double dx, double orig) {
|
|
static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
|
|
double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
|
|
union {int4 i[2]; double x;} v;
|
|
int4 n;
|
|
x1=(x+th2_36)-th2_36;
|
|
y = aa.x*x1*x1*x1;
|
|
r=x+y;
|
|
x2=(x-x1)+dx;
|
|
xx=x*x;
|
|
/* Taylor series */
|
|
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
|
|
t=((x-r)+y)+t;
|
|
res=r+t;
|
|
cor = (r-res)+t;
|
|
cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
|
|
if (res == res + cor) return res;
|
|
else {
|
|
(x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
|
|
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else {
|
|
t = (orig*hpinv.x + toint.x);
|
|
xn = t - toint.x;
|
|
v.x = t;
|
|
y = (orig - xn*mp1.x) - xn*mp2.x;
|
|
n =v.i[LOW_HALF]&3;
|
|
da = xn*pp3.x;
|
|
t=y-da;
|
|
da = (y-t)-da;
|
|
y = xn*pp4.x;
|
|
a = t - y;
|
|
da = ((t-a)-y)+da;
|
|
if (n==1) {a=-a; da=-da;}
|
|
(a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
|
|
cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
|
|
if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
|
|
else return __mpcos1(orig);
|
|
}
|
|
}
|
|
}
|
|
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) (Double-Length number) where x in first or */
|
|
/* third quarter of unit circle.Routine receive also (right argument) the */
|
|
/* original value of x for computing error of result.And if result not */
|
|
/* accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
static double csloww1(double x, double dx, double orig) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
c1 = (cs+t22)-t22;
|
|
c2=(cs-c1)+ccs;
|
|
cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
|
|
y=sn+c1*y1;
|
|
cor = cor+((sn-y)+c1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
|
|
if (res == res + cor) return (x>0)?res:-res;
|
|
else {
|
|
__dubsin(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
|
|
if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
|
|
else return __mpcos1(orig);
|
|
}
|
|
}
|
|
|
|
|
|
/***************************************************************************/
|
|
/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
|
|
/* fourth quarter of unit circle.Routine receive also the original value */
|
|
/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/
|
|
/* accurate enough routine calls other routines */
|
|
/***************************************************************************/
|
|
|
|
static double csloww2(double x, double dx, double orig, int n) {
|
|
mynumber u;
|
|
double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
|
|
static const double t22 = 6291456.0;
|
|
int4 k;
|
|
y=ABS(x);
|
|
u.x=big.x+y;
|
|
y=y-(u.x-big.x);
|
|
dx=(x>0)?dx:-dx;
|
|
xx=y*y;
|
|
s = y*xx*(sn3 +xx*sn5);
|
|
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
|
k=u.i[LOW_HALF]<<2;
|
|
sn=sincos.x[k];
|
|
ssn=sincos.x[k+1];
|
|
cs=sincos.x[k+2];
|
|
ccs=sincos.x[k+3];
|
|
|
|
y1 = (y+t22)-t22;
|
|
y2 = (y - y1)+dx;
|
|
e1 = (sn+t22)-t22;
|
|
e2=(sn-e1)+ssn;
|
|
cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
|
|
y=cs-e1*y1;
|
|
cor = cor+((cs-y)-e1*y1);
|
|
res=y+cor;
|
|
cor=(y-res)+cor;
|
|
cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
|
|
if (res == res + cor) return (n)?-res:res;
|
|
else {
|
|
__docos(ABS(x),dx,w);
|
|
cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
|
|
if (w[0] == w[0]+cor) return (n)?-w[0]:w[0];
|
|
else return __mpcos1(orig);
|
|
}
|
|
}
|
|
|
|
weak_alias (__cos, cos)
|
|
weak_alias (__sin, sin)
|
|
|
|
#ifdef NO_LONG_DOUBLE
|
|
strong_alias (__sin, __sinl)
|
|
weak_alias (__sin, sinl)
|
|
strong_alias (__cos, __cosl)
|
|
weak_alias (__cos, cosl)
|
|
#endif
|