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5a82c74822
glibc/sysdeps/ieee754/dbl-64/e_asin.c
Paul Eggert 5a82c74822 Prefer https to http for gnu.org and fsf.org URLs 
Also, change sources.redhat.com to sourceware.org.
This patch was automatically generated by running the following shell
script, which uses GNU sed, and which avoids modifying files imported
from upstream:

sed -ri '
  s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g
  s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g
' \
  $(find $(git ls-files) -prune -type f \
      ! -name '*.po' \
      ! -name 'ChangeLog*' \
      ! -path COPYING ! -path COPYING.LIB \
      ! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \
      ! -path manual/texinfo.tex ! -path scripts/config.guess \
      ! -path scripts/config.sub ! -path scripts/install-sh \
      ! -path scripts/mkinstalldirs ! -path scripts/move-if-change \
      ! -path INSTALL ! -path  locale/programs/charmap-kw.h \
      ! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \
      ! '(' -name configure \
            -execdir test -f configure.ac -o -f configure.in ';' ')' \
      ! '(' -name preconfigure \
            -execdir test -f preconfigure.ac ';' ')' \
      -print)

and then by running 'make dist-prepare' to regenerate files built
from the altered files, and then executing the following to cleanup:

  chmod a+x sysdeps/unix/sysv/linux/riscv/configure
  # Omit irrelevant whitespace and comment-only changes,
  # perhaps from a slightly-different Autoconf version.
  git checkout -f \
    sysdeps/csky/configure \
    sysdeps/hppa/configure \
    sysdeps/riscv/configure \
    sysdeps/unix/sysv/linux/csky/configure
  # Omit changes that caused a pre-commit check to fail like this:
  # remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines
  git checkout -f \
    sysdeps/powerpc/powerpc64/ppc-mcount.S \
    sysdeps/unix/sysv/linux/s390/s390-64/syscall.S
  # Omit change that caused a pre-commit check to fail like this:
  # remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline
  git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
2019-09-07 02:43:31 -07:00

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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2019 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <https://www.gnu.org/licenses/>.
*/
/******************************************************************/
/* MODULE_NAME:uasncs.c */
/* */
/* FUNCTIONS: uasin */
/* uacos */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
/* doasin.c sincos32.c dosincos.c mpa.c */
/* sincos.tbl asincos.tbl powtwo.tbl root.tbl */
/* */
/* Ultimate asin/acos routines. Given an IEEE double machine */
/* number x, compute the correctly rounded value of */
/* arcsin(x)or arccos(x) according to the function called. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/******************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "asincos.tbl"
#include "root.tbl"
#include "powtwo.tbl"
#include "MathLib.h"
#include "uasncs.h"
#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#ifndef SECTION
# define SECTION
#endif
void __doasin(double x, double dx, double w[]);
void __dubsin(double x, double dx, double v[]);
void __dubcos(double x, double dx, double v[]);
void __docos(double x, double dx, double v[]);
double __sin32(double x, double res, double res1);
double __cos32(double x, double res, double res1);
/***************************************************************************/
/* An ultimate asin routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of arcsin(x) */
/***************************************************************************/
double
SECTION
__ieee754_asin(double x){
double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2];
mynumber u,v;
int4 k,m,n;
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff&m; /* no sign */
if (k < 0x3e500000)
{
math_check_force_underflow (x);
return x; /* for x->0 => sin(x)=x */
}
/*----------------------2^-26 <= |x| < 2^ -3 -----------------*/
else
if (k < 0x3fc00000) {
x2 = x*x;
t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
res = x+t; /* res=arcsin(x) according to Taylor series */
cor = (x-res)+t;
if (res == res+1.025*cor) return res;
else {
x1 = x+big;
xx = x*x;
x1 -= big;
x2 = x - x1;
p = x1*x1*x1;
s1 = a1.x*p;
s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
res1 = x+s1;
s2 = ((x-res1)+s1)+s2;
res = res1+s2;
cor = (res1-res)+s2;
if (res == res+1.00014*cor) return res;
else {
__doasin(x,0,w);
if (w[0]==(w[0]+1.00000001*w[1])) return w[0];
else {
y=fabs(x);
res=fabs(w[0]);
res1=fabs(w[0]+1.1*w[1]);
return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
}
}
}
}
/*---------------------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;
res =asncs.x[n+8] +t;
cor = (asncs.x[n+8]-res)+t;
if (res == res+1.05*cor) return (m>0)?res:-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]);
res = r+t;
cor = (r-res)+t;
if (res == res+1.0005*cor) return (m>0)?res:-res;
else {
res1=res+1.1*cor;
z=0.5*(res1-res);
__dubsin(res,z,w);
z=(w[0]-fabs(x))+w[1];
if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
else {
y=fabs(x);
return (m>0)?__sin32(y,res,res1):-__sin32(y,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];
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]+xx*asncs.x[n+7])))))+asncs.x[n+8];
t+=p;
res =asncs.x[n+9] +t;
cor = (asncs.x[n+9]-res)+t;
if (res == res+1.01*cor) return (m>0)?res:-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]);
res = r+t;
cor = (r-res)+t;
if (res == res+1.0005*cor) return (m>0)?res:-res;
else {
res1=res+1.1*cor;
z=0.5*(res1-res);
__dubsin(res,z,w);
z=(w[0]-fabs(x))+w[1];
if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
else {
y=fabs(x);
return (m>0)?__sin32(y,res,res1):-__sin32(y,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];
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]+xx*(asncs.x[n+7]+xx*asncs.x[n+8]))))))+asncs.x[n+9];
t+=p;
res =asncs.x[n+10] +t;
cor = (asncs.x[n+10]-res)+t;
if (res == res+1.01*cor) return (m>0)?res:-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]);
res = r+t;
cor = (r-res)+t;
if (res == res+1.0008*cor) return (m>0)?res:-res;
else {
res1=res+1.1*cor;
z=0.5*(res1-res);
y=hp0.x-res;
z=((hp0.x-y)-res)+(hp1.x-z);
__dubcos(y,z,w);
z=(w[0]-fabs(x))+w[1];
if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
else {
y=fabs(x);
return (m>0)?__sin32(y,res,res1):-__sin32(y,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];
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]
+xx*(asncs.x[n+7]+xx*(asncs.x[n+8]+
xx*asncs.x[n+9])))))))+asncs.x[n+10];
t+=p;
res =asncs.x[n+11] +t;
cor = (asncs.x[n+11]-res)+t;
if (res == res+1.01*cor) return (m>0)?res:-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]);
res = r+t;
cor = (r-res)+t;
if (res == res+1.0007*cor) return (m>0)?res:-res;
else {
res1=res+1.1*cor;
z=0.5*(res1-res);
y=(hp0.x-res)-z;
z=y+hp1.x;
y=(y-z)+hp1.x;
__dubcos(z,y,w);
z=(w[0]-fabs(x))+w[1];
if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
else {
y=fabs(x);
return (m>0)?__sin32(y,res,res1):-__sin32(y,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];
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]
+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;
res =asncs.x[n+12] +t;
cor = (asncs.x[n+12]-res)+t;
if (res == res+1.01*cor) return (m>0)?res:-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]);
res = r+t;
cor = (r-res)+t;
if (res == res+1.0007*cor) return (m>0)?res:-res;
else {
res1=res+1.1*cor;
z=0.5*(res1-res);
y=(hp0.x-res)-z;
z=y+hp1.x;
y=(y-z)+hp1.x;
__dubcos(z,y,w);
z=(w[0]-fabs(x))+w[1];
if (z>1.0e-27) return (m>0)?min(res,res1):-min(res,res1);
else if (z<-1.0e-27) return (m>0)?max(res,res1):-max(res,res1);
else {
y=fabs(x);
return (m>0)?__sin32(y,res,res1):-__sin32(y,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=(c+t24)-t24;
cc = (z-y*y)/(t+y);
p=(((((f6*z+f5)*z+f4)*z+f3)*z+f2)*z+f1)*z;
cor = (hp1.x - 2.0*cc)-2.0*(y+cc)*p;
res1 = hp0.x - 2.0*y;
res =res1 + cor;
if (res == res+1.003*((res1-res)+cor)) return (m>0)?res:-res;
else {
c=y+cc;
cc=(y-c)+cc;
__doasin(c,cc,w);
res1=hp0.x-2.0*w[0];
cor=((hp0.x-res1)-2.0*w[0])+(hp1.x-2.0*w[1]);
res = res1+cor;
cor = (res1-res)+cor;
if (res==(res+1.0000001*cor)) return (m>0)?res:-res;
else {
y=fabs(x);
res1=res+1.1*cor;
return (m>0)?__sin32(y,res,res1):-__sin32(y,res,res1);
}
}
} /* else if (k < 0x3ff00000) */
/*---------------------------- |x|>=1 -------------------------------*/
else if (k==0x3ff00000 && u.i[LOW_HALF]==0) return (m>0)?hp0.x:-hp0.x;
else
if (k>0x7ff00000 || (k == 0x7ff00000 && u.i[LOW_HALF] != 0)) return x + 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; /* NaN */
}
}
#ifndef __ieee754_asin
strong_alias (__ieee754_asin, __asin_finite)
#endif
/*******************************************************************/
/* */
/* End of arcsine, below is arccosine */
/* */
/*******************************************************************/
double
SECTION
__ieee754_acos(double x)
{
double x1,x2,xx,s1,s2,res1,p,t,res,r,cor,cc,y,c,z,w[2],eps;
mynumber u,v;
int4 k,m,n;
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff&m;
/*------------------- |x|<2.77556*10^-17 ----------------------*/
if (k < 0x3c880000) return hp0.x;
/*----------------- 2.77556*10^-17 <= |x| < 2^-3 --------------*/
else
if (k < 0x3fc00000) {
x2 = x*x;
t = (((((f6*x2 + f5)*x2 + f4)*x2 + f3)*x2 + f2)*x2 + f1)*(x2*x);
r=hp0.x-x;
cor=(((hp0.x-r)-x)+hp1.x)-t;
res = r+cor;
cor = (r-res)+cor;
if (res == res+1.004*cor) return res;
else {
x1 = x+big;
xx = x*x;
x1 -= big;
x2 = x - x1;
p = x1*x1*x1;
s1 = a1.x*p;
s2 = ((((((c7*xx + c6)*xx + c5)*xx + c4)*xx + c3)*xx + c2)*xx*xx*x +
((a1.x+a2.x)*x2*x2+ 0.5*x1*x)*x2) + a2.x*p;
res1 = x+s1;
s2 = ((x-res1)+s1)+s2;
r=hp0.x-res1;
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 + 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;
}
}
#ifndef __ieee754_acos
strong_alias (__ieee754_acos, __acos_finite)
#endif
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