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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.
636 lines
20 KiB
C
636 lines
20 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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/* MODULE_NAME:uasncs.c */
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/* */
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/* FUNCTIONS: uasin */
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/* uacos */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
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/* doasin.c sincos32.c dosincos.c mpa.c */
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/* sincos.tbl asincos.tbl powtwo.tbl root.tbl */
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/* */
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/* Ultimate asin/acos routines. Given an IEEE double machine */
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/* number x, compute the correctly rounded value of */
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/* arcsin(x)or arccos(x) according to the function called. */
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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 "asincos.tbl"
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#include "root.tbl"
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#include "powtwo.tbl"
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#include "MathLib.h"
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#include "uasncs.h"
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void __doasin(double x, double dx, double w[]);
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void __dubsin(double x, double dx, double v[]);
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void __dubcos(double x, double dx, double v[]);
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void __docos(double x, double dx, double v[]);
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double __sin32(double x, double res, double res1);
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double __cos32(double x, double res, double res1);
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/***************************************************************************/
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/* An ultimate asin routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of arcsin(x) */
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/***************************************************************************/
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double __ieee754_asin(double x){
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double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2];
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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) return x; /* for x->0 => sin(x)=x */
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/*----------------------2^-26 <= |x| < 2^ -3 -----------------*/
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else
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if (k < 0x3fc00000) {
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x2 = x*x;
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t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
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res = x+t; /* res=arcsin(x) according to Taylor series */
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cor = (x-res)+t;
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if (res == res+1.025*cor) return res;
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else {
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x1 = x+big;
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xx = x*x;
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x1 -= big;
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x2 = x - x1;
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p = x1*x1*x1;
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s1 = a1.x*p;
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s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
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((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
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res1 = x+s1;
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s2 = ((x-res1)+s1)+s2;
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res = res1+s2;
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cor = (res1-res)+s2;
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if (res == res+1.00014*cor) return res;
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else {
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__doasin(x,0,w);
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if (w[0]==(w[0]+1.00000001*w[1])) return w[0];
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else {
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y=ABS(x);
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res=ABS(w[0]);
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res1=ABS(w[0]+1.1*w[1]);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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}
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/*---------------------0.125 <= |x| < 0.5 -----------------------------*/
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else if (k < 0x3fe00000) {
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if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15);
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else n = 11*((k&0x000fffff)>>14)+352;
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if (m>0) xx = x - asncs.x[n];
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else xx = -x - asncs.x[n];
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t = asncs.x[n+1]*xx;
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p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
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+xx*asncs.x[n+6]))))+asncs.x[n+7];
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t+=p;
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res =asncs.x[n+8] +t;
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cor = (asncs.x[n+8]-res)+t;
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if (res == res+1.05*cor) return (m>0)?res:-res;
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else {
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r=asncs.x[n+8]+xx*asncs.x[n+9];
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t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]);
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res = r+t;
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cor = (r-res)+t;
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if (res == res+1.0005*cor) return (m>0)?res:-res;
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else {
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res1=res+1.1*cor;
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z=0.5*(res1-res);
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__dubsin(res,z,w);
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z=(w[0]-ABS(x))+w[1];
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if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
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else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
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else {
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y=ABS(x);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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} /* else if (k < 0x3fe00000) */
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/*-------------------- 0.5 <= |x| < 0.75 -----------------------------*/
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else
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if (k < 0x3fe80000) {
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n = 1056+((k&0x000fe000)>>11)*3;
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if (m>0) xx = x - asncs.x[n];
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else xx = -x - asncs.x[n];
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t = asncs.x[n+1]*xx;
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p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
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+xx*(asncs.x[n+6]+xx*asncs.x[n+7])))))+asncs.x[n+8];
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t+=p;
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res =asncs.x[n+9] +t;
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cor = (asncs.x[n+9]-res)+t;
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if (res == res+1.01*cor) return (m>0)?res:-res;
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else {
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r=asncs.x[n+9]+xx*asncs.x[n+10];
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t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]);
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res = r+t;
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cor = (r-res)+t;
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if (res == res+1.0005*cor) return (m>0)?res:-res;
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else {
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res1=res+1.1*cor;
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z=0.5*(res1-res);
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__dubsin(res,z,w);
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z=(w[0]-ABS(x))+w[1];
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if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
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else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
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else {
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y=ABS(x);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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} /* else if (k < 0x3fe80000) */
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/*--------------------- 0.75 <= |x|< 0.921875 ----------------------*/
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else
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if (k < 0x3fed8000) {
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n = 992+((k&0x000fe000)>>13)*13;
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if (m>0) xx = x - asncs.x[n];
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else xx = -x - asncs.x[n];
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t = asncs.x[n+1]*xx;
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p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+xx*(asncs.x[n+5]
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+xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+xx*asncs.x[n+8]))))))+asncs.x[n+9];
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t+=p;
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res =asncs.x[n+10] +t;
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cor = (asncs.x[n+10]-res)+t;
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if (res == res+1.01*cor) return (m>0)?res:-res;
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else {
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r=asncs.x[n+10]+xx*asncs.x[n+11];
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t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]);
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res = r+t;
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cor = (r-res)+t;
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if (res == res+1.0008*cor) return (m>0)?res:-res;
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else {
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res1=res+1.1*cor;
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z=0.5*(res1-res);
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y=hp0.x-res;
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z=((hp0.x-y)-res)+(hp1.x-z);
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__dubcos(y,z,w);
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z=(w[0]-ABS(x))+w[1];
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if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
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else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
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else {
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y=ABS(x);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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} /* else if (k < 0x3fed8000) */
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/*-------------------0.921875 <= |x| < 0.953125 ------------------------*/
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else
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if (k < 0x3fee8000) {
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n = 884+((k&0x000fe000)>>13)*14;
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if (m>0) xx = x - asncs.x[n];
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else xx = -x - asncs.x[n];
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t = asncs.x[n+1]*xx;
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p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
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xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
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+xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
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xx*asncs.x[n+9])))))))+asncs.x[n+10];
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t+=p;
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res =asncs.x[n+11] +t;
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cor = (asncs.x[n+11]-res)+t;
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if (res == res+1.01*cor) return (m>0)?res:-res;
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else {
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r=asncs.x[n+11]+xx*asncs.x[n+12];
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t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]);
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res = r+t;
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cor = (r-res)+t;
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if (res == res+1.0007*cor) return (m>0)?res:-res;
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else {
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res1=res+1.1*cor;
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z=0.5*(res1-res);
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y=(hp0.x-res)-z;
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z=y+hp1.x;
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y=(y-z)+hp1.x;
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__dubcos(z,y,w);
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z=(w[0]-ABS(x))+w[1];
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if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
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else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
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else {
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y=ABS(x);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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} /* else if (k < 0x3fee8000) */
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/*--------------------0.953125 <= |x| < 0.96875 ------------------------*/
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else
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if (k < 0x3fef0000) {
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n = 768+((k&0x000fe000)>>13)*15;
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if (m>0) xx = x - asncs.x[n];
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else xx = -x - asncs.x[n];
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t = asncs.x[n+1]*xx;
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p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
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xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
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+xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
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xx*(asncs.x[n+9]+xx*asncs.x[n+10]))))))))+asncs.x[n+11];
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t+=p;
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res =asncs.x[n+12] +t;
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cor = (asncs.x[n+12]-res)+t;
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if (res == res+1.01*cor) return (m>0)?res:-res;
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else {
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r=asncs.x[n+12]+xx*asncs.x[n+13];
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t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]);
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res = r+t;
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cor = (r-res)+t;
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if (res == res+1.0007*cor) return (m>0)?res:-res;
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else {
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res1=res+1.1*cor;
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z=0.5*(res1-res);
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y=(hp0.x-res)-z;
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z=y+hp1.x;
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y=(y-z)+hp1.x;
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__dubcos(z,y,w);
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z=(w[0]-ABS(x))+w[1];
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if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
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else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
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else {
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y=ABS(x);
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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}
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} /* else if (k < 0x3fef0000) */
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/*--------------------0.96875 <= |x| < 1 --------------------------------*/
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else
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if (k<0x3ff00000) {
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z = 0.5*((m>0)?(1.0-x):(1.0+x));
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v.x=z;
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k=v.i[HIGH_HALF];
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t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)];
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r=1.0-t*t*z;
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t = t*(rt0+r*(rt1+r*(rt2+r*rt3)));
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c=t*z;
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t=c*(1.5-0.5*t*c);
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y=(c+t24)-t24;
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cc = (z-y*y)/(t+y);
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p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z;
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cor = (hp1.x - 2.0*cc)-2.0*(y+cc)*p;
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res1 = hp0.x - 2.0*y;
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res =res1 + cor;
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if (res == res+1.003*((res1-res)+cor)) return (m>0)?res:-res;
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else {
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c=y+cc;
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cc=(y-c)+cc;
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__doasin(c,cc,w);
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res1=hp0.x-2.0*w[0];
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cor=((hp0.x-res1)-2.0*w[0])+(hp1.x-2.0*w[1]);
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res = res1+cor;
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cor = (res1-res)+cor;
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if (res==(res+1.0000001*cor)) return (m>0)?res:-res;
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else {
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y=ABS(x);
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res1=res+1.1*cor;
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return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
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}
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}
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} /* else if (k < 0x3ff00000) */
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/*---------------------------- |x|>=1 -------------------------------*/
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else if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?hp0.x:-hp0.x;
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else
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if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x;
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else {
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u.i[HIGH_HALF]=0x7ff00000;
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v.i[HIGH_HALF]=0x7ff00000;
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u.i[LOW_HALF]=0;
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v.i[LOW_HALF]=0;
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return u.x/v.x; /* NaN */
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}
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}
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/*******************************************************************/
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/* */
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/* End of arcsine, below is arccosine */
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/* */
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/*******************************************************************/
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double __ieee754_acos(double x)
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{
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double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps;
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#if 0
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double fc;
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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;
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/*------------------- |x|<2.77556*10^-17 ----------------------*/
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if (k < 0x3c880000) return hp0.x;
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/*----------------- 2.77556*10^-17 <= |x| < 2^-3 --------------*/
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else
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if (k < 0x3fc00000) {
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x2 = x*x;
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t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
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r=hp0.x-x;
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cor=(((hp0.x-r)-x)+hp1.x)-t;
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res = r+cor;
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cor = (r-res)+cor;
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if (res == res+1.004*cor) return res;
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else {
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x1 = x+big;
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xx = x*x;
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x1 -= big;
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x2 = x - x1;
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p = x1*x1*x1;
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s1 = a1.x*p;
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s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
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((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
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res1 = x+s1;
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s2 = ((x-res1)+s1)+s2;
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r=hp0.x-res1;
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cor=(((hp0.x-r)-res1)+hp1.x)-s2;
|
|
res = r+cor;
|
|
cor = (r-res)+cor;
|
|
if (res == res+1.00004*cor) return res;
|
|
else {
|
|
__doasin(x,0,w);
|
|
r=hp0.x-w[0];
|
|
cor=((hp0.x-r)-w[0])+(hp1.x-w[1]);
|
|
res=r+cor;
|
|
cor=(r-res)+cor;
|
|
if (res ==(res +1.00000001*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fc00000) */
|
|
/*---------------------- 0.125 <= |x| < 0.5 --------------------*/
|
|
else
|
|
if (k < 0x3fe00000) {
|
|
if (k<0x3fd00000) n = 11*((k&0x000fffff)>>15);
|
|
else n = 11*((k&0x000fffff)>>14)+352;
|
|
if (m>0) xx = x - asncs.x[n];
|
|
else xx = -x - asncs.x[n];
|
|
t = asncs.x[n+1]*xx;
|
|
p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
|
|
xx*(asncs.x[n+5]+xx*asncs.x[n+6]))))+asncs.x[n+7];
|
|
t+=p;
|
|
y = (m>0)?(hp0.x-asncs.x[n+8]):(hp0.x+asncs.x[n+8]);
|
|
t = (m>0)?(hp1.x-t):(hp1.x+t);
|
|
res = y+t;
|
|
if (res == res+1.02*((y-res)+t)) return res;
|
|
else {
|
|
r=asncs.x[n+8]+xx*asncs.x[n+9];
|
|
t=((asncs.x[n+8]-r)+xx*asncs.x[n+9])+(p+xx*asncs.x[n+10]);
|
|
if (m>0)
|
|
{p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; }
|
|
else
|
|
{p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); }
|
|
res = p+t;
|
|
cor = (p-res)+t;
|
|
if (res == (res+1.0002*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
z=0.5*(res1-res);
|
|
__docos(res,z,w);
|
|
z=(w[0]-x)+w[1];
|
|
if (z>1.0e-27) return max(res,res1);
|
|
else if (z<-1.0e-27) return min(res,res1);
|
|
else return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fe00000) */
|
|
|
|
/*--------------------------- 0.5 <= |x| < 0.75 ---------------------*/
|
|
else
|
|
if (k < 0x3fe80000) {
|
|
n = 1056+((k&0x000fe000)>>11)*3;
|
|
if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
|
|
else {xx = -x - asncs.x[n]; eps=1.02; }
|
|
t = asncs.x[n+1]*xx;
|
|
p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
|
|
xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+
|
|
xx*asncs.x[n+7])))))+asncs.x[n+8];
|
|
t+=p;
|
|
y = (m>0)?(hp0.x-asncs.x[n+9]):(hp0.x+asncs.x[n+9]);
|
|
t = (m>0)?(hp1.x-t):(hp1.x+t);
|
|
res = y+t;
|
|
if (res == res+eps*((y-res)+t)) return res;
|
|
else {
|
|
r=asncs.x[n+9]+xx*asncs.x[n+10];
|
|
t=((asncs.x[n+9]-r)+xx*asncs.x[n+10])+(p+xx*asncs.x[n+11]);
|
|
if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0004; }
|
|
else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0002; }
|
|
res = p+t;
|
|
cor = (p-res)+t;
|
|
if (res == (res+eps*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
z=0.5*(res1-res);
|
|
__docos(res,z,w);
|
|
z=(w[0]-x)+w[1];
|
|
if (z>1.0e-27) return max(res,res1);
|
|
else if (z<-1.0e-27) return min(res,res1);
|
|
else return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fe80000) */
|
|
|
|
/*------------------------- 0.75 <= |x| < 0.921875 -------------*/
|
|
else
|
|
if (k < 0x3fed8000) {
|
|
n = 992+((k&0x000fe000)>>13)*13;
|
|
if (m>0) {xx = x - asncs.x[n]; eps = 1.04; }
|
|
else {xx = -x - asncs.x[n]; eps = 1.01; }
|
|
t = asncs.x[n+1]*xx;
|
|
p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
|
|
xx*(asncs.x[n+5]+xx*(asncs.x[n+6]+xx*(asncs.x[n+7]+
|
|
xx*asncs.x[n+8]))))))+asncs.x[n+9];
|
|
t+=p;
|
|
y = (m>0)?(hp0.x-asncs.x[n+10]):(hp0.x+asncs.x[n+10]);
|
|
t = (m>0)?(hp1.x-t):(hp1.x+t);
|
|
res = y+t;
|
|
if (res == res+eps*((y-res)+t)) return res;
|
|
else {
|
|
r=asncs.x[n+10]+xx*asncs.x[n+11];
|
|
t=((asncs.x[n+10]-r)+xx*asncs.x[n+11])+(p+xx*asncs.x[n+12]);
|
|
if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0032; }
|
|
else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0008; }
|
|
res = p+t;
|
|
cor = (p-res)+t;
|
|
if (res == (res+eps*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
z=0.5*(res1-res);
|
|
__docos(res,z,w);
|
|
z=(w[0]-x)+w[1];
|
|
if (z>1.0e-27) return max(res,res1);
|
|
else if (z<-1.0e-27) return min(res,res1);
|
|
else return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fed8000) */
|
|
|
|
/*-------------------0.921875 <= |x| < 0.953125 ------------------*/
|
|
else
|
|
if (k < 0x3fee8000) {
|
|
n = 884+((k&0x000fe000)>>13)*14;
|
|
if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
|
|
else {xx = -x - asncs.x[n]; eps =1.005; }
|
|
t = asncs.x[n+1]*xx;
|
|
p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
|
|
xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
|
|
+xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
|
|
xx*asncs.x[n+9])))))))+asncs.x[n+10];
|
|
t+=p;
|
|
y = (m>0)?(hp0.x-asncs.x[n+11]):(hp0.x+asncs.x[n+11]);
|
|
t = (m>0)?(hp1.x-t):(hp1.x+t);
|
|
res = y+t;
|
|
if (res == res+eps*((y-res)+t)) return res;
|
|
else {
|
|
r=asncs.x[n+11]+xx*asncs.x[n+12];
|
|
t=((asncs.x[n+11]-r)+xx*asncs.x[n+12])+(p+xx*asncs.x[n+13]);
|
|
if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; }
|
|
else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; }
|
|
res = p+t;
|
|
cor = (p-res)+t;
|
|
if (res == (res+eps*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
z=0.5*(res1-res);
|
|
__docos(res,z,w);
|
|
z=(w[0]-x)+w[1];
|
|
if (z>1.0e-27) return max(res,res1);
|
|
else if (z<-1.0e-27) return min(res,res1);
|
|
else return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fee8000) */
|
|
|
|
/*--------------------0.953125 <= |x| < 0.96875 ----------------*/
|
|
else
|
|
if (k < 0x3fef0000) {
|
|
n = 768+((k&0x000fe000)>>13)*15;
|
|
if (m>0) {xx = x - asncs.x[n]; eps=1.04; }
|
|
else {xx = -x - asncs.x[n]; eps=1.005;}
|
|
t = asncs.x[n+1]*xx;
|
|
p=xx*xx*(asncs.x[n+2]+xx*(asncs.x[n+3]+xx*(asncs.x[n+4]+
|
|
xx*(asncs.x[n+5]+xx*(asncs.x[n+6]
|
|
+xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+xx*(asncs.x[n+9]+
|
|
xx*asncs.x[n+10]))))))))+asncs.x[n+11];
|
|
t+=p;
|
|
y = (m>0)?(hp0.x-asncs.x[n+12]):(hp0.x+asncs.x[n+12]);
|
|
t = (m>0)?(hp1.x-t):(hp1.x+t);
|
|
res = y+t;
|
|
if (res == res+eps*((y-res)+t)) return res;
|
|
else {
|
|
r=asncs.x[n+12]+xx*asncs.x[n+13];
|
|
t=((asncs.x[n+12]-r)+xx*asncs.x[n+13])+(p+xx*asncs.x[n+14]);
|
|
if (m>0) {p = hp0.x-r; t = (((hp0.x-p)-r)-t)+hp1.x; eps=1.0030; }
|
|
else {p = hp0.x+r; t = ((hp0.x-p)+r)+(hp1.x+t); eps=1.0005; }
|
|
res = p+t;
|
|
cor = (p-res)+t;
|
|
if (res == (res+eps*cor)) return res;
|
|
else {
|
|
res1=res+1.1*cor;
|
|
z=0.5*(res1-res);
|
|
__docos(res,z,w);
|
|
z=(w[0]-x)+w[1];
|
|
if (z>1.0e-27) return max(res,res1);
|
|
else if (z<-1.0e-27) return min(res,res1);
|
|
else return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
} /* else if (k < 0x3fef0000) */
|
|
/*-----------------0.96875 <= |x| < 1 ---------------------------*/
|
|
|
|
else
|
|
if (k<0x3ff00000) {
|
|
z = 0.5*((m>0)?(1.0-x):(1.0+x));
|
|
v.x=z;
|
|
k=v.i[HIGH_HALF];
|
|
t=inroot[(k&0x001fffff)>>14]*powtwo[511-(k>>21)];
|
|
r=1.0-t*t*z;
|
|
t = t*(rt0+r*(rt1+r*(rt2+r*rt3)));
|
|
c=t*z;
|
|
t=c*(1.5-0.5*t*c);
|
|
y = (t27*c+c)-t27*c;
|
|
cc = (z-y*y)/(t+y);
|
|
p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z;
|
|
if (m<0) {
|
|
cor = (hp1.x - cc)-(y+cc)*p;
|
|
res1 = hp0.x - y;
|
|
res =res1 + cor;
|
|
if (res == res+1.002*((res1-res)+cor)) return (res+res);
|
|
else {
|
|
c=y+cc;
|
|
cc=(y-c)+cc;
|
|
__doasin(c,cc,w);
|
|
res1=hp0.x-w[0];
|
|
cor=((hp0.x-res1)-w[0])+(hp1.x-w[1]);
|
|
res = res1+cor;
|
|
cor = (res1-res)+cor;
|
|
if (res==(res+1.000001*cor)) return (res+res);
|
|
else {
|
|
res=res+res;
|
|
res1=res+1.2*cor;
|
|
return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
cor = cc+p*(y+cc);
|
|
res = y + cor;
|
|
if (res == res+1.03*((y-res)+cor)) return (res+res);
|
|
else {
|
|
c=y+cc;
|
|
cc=(y-c)+cc;
|
|
__doasin(c,cc,w);
|
|
res = w[0];
|
|
cor=w[1];
|
|
if (res==(res+1.000001*cor)) return (res+res);
|
|
else {
|
|
res=res+res;
|
|
res1=res+1.2*cor;
|
|
return __cos32(x,res,res1);
|
|
}
|
|
}
|
|
}
|
|
} /* else if (k < 0x3ff00000) */
|
|
|
|
/*---------------------------- |x|>=1 -----------------------*/
|
|
else
|
|
if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?0:2.0*hp0.x;
|
|
else
|
|
if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x;
|
|
else {
|
|
u.i[HIGH_HALF]=0x7ff00000;
|
|
v.i[HIGH_HALF]=0x7ff00000;
|
|
u.i[LOW_HALF]=0;
|
|
v.i[LOW_HALF]=0;
|
|
return u.x/v.x;
|
|
}
|
|
}
|