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glibc/sysdeps/ieee754/dbl-64/s_tan.c
Richard Henderson eb92c487b3 Create and use SET_RESTORE_ROUND{,_NOEX,_53BIT}{,F,L}.
2012-03-19 06:49:44 -07:00

527 lines
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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001, 2009, 2011 Free Software Foundation
*
* 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 <http://www.gnu.org/licenses/>.
*/
/*********************************************************************/
/* MODULE_NAME: utan.c */
/* */
/* FUNCTIONS: utan */
/* tanMp */
/* */
/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */
/* branred.c sincos32.c mptan.c */
/* utan.tbl */
/* */
/* An ultimate tan routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of tan(x). */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include <errno.h>
#include "endian.h"
#include <dla.h>
#include "mpa.h"
#include "MathLib.h"
#include <math.h>
#include <math_private.h>
#include <fenv.h>
#ifndef SECTION
# define SECTION
#endif
static double tanMp(double);
void __mptan(double, mp_no *, int);
double
SECTION
tan(double x) {
#include "utan.h"
#include "utan.tbl"
int ux,i,n;
double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy,
t,t1,t2,t3,t4,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
#ifndef DLA_FMS
double t5,t6;
#endif
int p;
number num,v;
mp_no mpa,mpt1,mpt2;
#if 0
mp_no mpy;
#endif
double retval;
int __branred(double, double *, double *);
int __mpranred(double, mp_no *, int);
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
/* x=+-INF, x=NaN */
num.d = x; ux = num.i[HIGH_HALF];
if ((ux&0x7ff00000)==0x7ff00000) {
if ((ux&0x7fffffff)==0x7ff00000)
__set_errno (EDOM);
retval = x-x;
goto ret;
}
w=(x<ZERO) ? -x : x;
/* (I) The case abs(x) <= 1.259e-8 */
if (w<=g1.d) { retval = x; goto ret; }
/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
if (w<=g2.d) {
/* First stage */
x2 = x*x;
t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d))));
if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2)) { retval = y; goto ret; }
/* Second stage */
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
x2*a27.d))))));
EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5)
ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(x ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(x ,zero.d,c2,cc2,c1,cc1,t1,t2)
if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1)) { retval = y; goto ret; }
retval = tanMp(x);
goto ret;
}
/* (III) The case 0.0608 < abs(x) <= 0.787 */
if (w<=g3.d) {
/* First stage */
i = ((int) (mfftnhf.d+TWO8*w));
z = w-xfg[i][0].d; z2 = z*z; s = (x<ZERO) ? MONE : ONE;
pz = z+z*z2*(e0.d+z2*e1.d);
fi = xfg[i][1].d; gi = xfg[i][2].d; t2 = pz*(gi+fi)/(gi-pz);
if ((y=fi+(t2-fi*u3.d))==fi+(t2+fi*u3.d)) { retval = (s*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = fi*ua3.d+t3*ub3.d;
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (s*y); goto ret; }
/* Second stage */
ffi = xfg[i][3].d;
c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
EMULV(z,z,z2,zz2,t1,t2,t3,t4,t5)
ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(z ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(z ,zero.d,c2,cc2,c1,cc1,t1,t2)
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u4.d*c3))==c3+(cc3+u4.d*c3)) { retval = (s*y); goto ret; }
retval = tanMp(x);
goto ret;
}
/* (---) The case 0.787 < abs(x) <= 25 */
if (w<=g4.d) {
/* Range reduction by algorithm i */
t = (x*hpinv.d + toint.d);
xn = t - toint.d;
v.d = t;
t1 = (x - xn*mp1.d) - xn*mp2.d;
n =v.i[LOW_HALF] & 0x00000001;
da = xn*mp3.d;
a=t1-da;
da = (t1-a)-da;
if (a<ZERO) {ya=-a; yya=-da; sy=MONE;}
else {ya= a; yya= da; sy= ONE;}
/* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
/* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
if (ya<=gy2.d) {
a2 = a*a;
t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
if (n) {
/* First stage -cot */
EADD(a,t2,b,db)
DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c+(dc-u6.d*c))==c+(dc+u6.d*c)) { retval = (-y); goto ret; } }
else {
/* First stage tan */
if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) { retval = y; goto ret; } }
/* Second stage */
/* Range reduction by algorithm ii */
t = (x*hpinv.d + toint.d);
xn = t - toint.d;
v.d = t;
t1 = (x - xn*mp1.d) - xn*mp2.d;
n =v.i[LOW_HALF] & 0x00000001;
da = xn*pp3.d;
t=t1-da;
da = (t1-t)-da;
t1 = xn*pp4.d;
a = t - t1;
da = ((t-a)-t1)+da;
/* Second stage */
EADD(a,da,t1,t2) a=t1; da=t2;
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
x2*a27.d))))));
ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
if (n) {
/* Second stage -cot */
DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c2+(cc2-u8.d*c2)) == c2+(cc2+u8.d*c2)) { retval = (-y); goto ret; } }
else {
/* Second stage tan */
if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) { retval = y; goto ret; } }
retval = tanMp(x);
goto ret;
}
/* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */
/* First stage */
i = ((int) (mfftnhf.d+TWO8*ya));
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
pz = z+z*z2*(e0.d+z2*e1.d);
fi = xfg[i][1].d; gi = xfg[i][2].d;
if (n) {
/* -cot */
t2 = pz*(fi+gi)/(fi+pz);
if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) { retval = (-sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = gi*ua10.d+t3*ub10.d;
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
t2 = pz*(gi+fi)/(gi-pz);
if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) { retval = (sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = fi*ua9.d+t3*ub9.d;
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
/* Second stage */
ffi = xfg[i][3].d;
EADD(z0,yya,z,zz)
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
if (n) {
/* -cot */
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u12.d*c3))==c3+(cc3+u12.d*c3)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u11.d*c3))==c3+(cc3+u11.d*c3)) { retval = (sy*y); goto ret; } }
retval = tanMp(x);
goto ret;
}
/* (---) The case 25 < abs(x) <= 1e8 */
if (w<=g5.d) {
/* Range reduction by algorithm ii */
t = (x*hpinv.d + toint.d);
xn = t - toint.d;
v.d = t;
t1 = (x - xn*mp1.d) - xn*mp2.d;
n =v.i[LOW_HALF] & 0x00000001;
da = xn*pp3.d;
t=t1-da;
da = (t1-t)-da;
t1 = xn*pp4.d;
a = t - t1;
da = ((t-a)-t1)+da;
EADD(a,da,t1,t2) a=t1; da=t2;
if (a<ZERO) {ya=-a; yya=-da; sy=MONE;}
else {ya= a; yya= da; sy= ONE;}
/* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */
if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
/* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */
if (ya<=gy2.d) {
a2 = a*a;
t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
if (n) {
/* First stage -cot */
EADD(a,t2,b,db)
DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c+(dc-u14.d*c))==c+(dc+u14.d*c)) { retval = (-y); goto ret; } }
else {
/* First stage tan */
if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a)) { retval = y; goto ret; } }
/* Second stage */
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
x2*a27.d))))));
ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
if (n) {
/* Second stage -cot */
DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c2+(cc2-u16.d*c2)) == c2+(cc2+u16.d*c2)) { retval = (-y); goto ret; } }
else {
/* Second stage tan */
if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) { retval = (y); goto ret; } }
retval = tanMp(x);
goto ret;
}
/* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */
/* First stage */
i = ((int) (mfftnhf.d+TWO8*ya));
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
pz = z+z*z2*(e0.d+z2*e1.d);
fi = xfg[i][1].d; gi = xfg[i][2].d;
if (n) {
/* -cot */
t2 = pz*(fi+gi)/(fi+pz);
if ((y=gi-(t2-gi*u18.d))==gi-(t2+gi*u18.d)) { retval = (-sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = gi*ua18.d+t3*ub18.d;
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
t2 = pz*(gi+fi)/(gi-pz);
if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d)) { retval = (sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = fi*ua17.d+t3*ub17.d;
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
/* Second stage */
ffi = xfg[i][3].d;
EADD(z0,yya,z,zz)
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
if (n) {
/* -cot */
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u20.d*c3))==c3+(cc3+u20.d*c3)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u19.d*c3))==c3+(cc3+u19.d*c3)) { retval = (sy*y); goto ret; } }
retval = tanMp(x);
goto ret;
}
/* (---) The case 1e8 < abs(x) < 2**1024 */
/* Range reduction by algorithm iii */
n = (__branred(x,&a,&da)) & 0x00000001;
EADD(a,da,t1,t2) a=t1; da=t2;
if (a<ZERO) {ya=-a; yya=-da; sy=MONE;}
else {ya= a; yya= da; sy= ONE;}
/* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */
if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
/* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */
if (ya<=gy2.d) {
a2 = a*a;
t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
if (n) {
/* First stage -cot */
EADD(a,t2,b,db)
DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c+(dc-u22.d*c))==c+(dc+u22.d*c)) { retval = (-y); goto ret; } }
else {
/* First stage tan */
if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a)) { retval = y; goto ret; } }
/* Second stage */
/* Reduction by algorithm iv */
p=10; n = (__mpranred(x,&mpa,p)) & 0x00000001;
__mp_dbl(&mpa,&a,p); __dbl_mp(a,&mpt1,p);
__sub(&mpa,&mpt1,&mpt2,p); __mp_dbl(&mpt2,&da,p);
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
x2*a27.d))))));
ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
if (n) {
/* Second stage -cot */
DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c2+(cc2-u24.d*c2)) == c2+(cc2+u24.d*c2)) { retval = (-y); goto ret; } }
else {
/* Second stage tan */
if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1)) { retval = y; goto ret; } }
retval = tanMp(x);
goto ret;
}
/* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */
/* First stage */
i = ((int) (mfftnhf.d+TWO8*ya));
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
pz = z+z*z2*(e0.d+z2*e1.d);
fi = xfg[i][1].d; gi = xfg[i][2].d;
if (n) {
/* -cot */
t2 = pz*(fi+gi)/(fi+pz);
if ((y=gi-(t2-gi*u26.d))==gi-(t2+gi*u26.d)) { retval = (-sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = gi*ua26.d+t3*ub26.d;
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
t2 = pz*(gi+fi)/(gi-pz);
if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d)) { retval = (sy*y); goto ret; }
t3 = (t2<ZERO) ? -t2 : t2;
t4 = fi*ua25.d+t3*ub25.d;
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
/* Second stage */
ffi = xfg[i][3].d;
EADD(z0,yya,z,zz)
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
if (n) {
/* -cot */
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u28.d*c3))==c3+(cc3+u28.d*c3)) { retval = (-sy*y); goto ret; } }
else {
/* tan */
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
if ((y=c3+(cc3-u27.d*c3))==c3+(cc3+u27.d*c3)) { retval = (sy*y); goto ret; } }
retval = tanMp(x);
goto ret;
ret:
return retval;
}
/* multiple precision stage */
/* Convert x to multi precision number,compute tan(x) by mptan() routine */
/* and converts result back to double */
static double
SECTION
tanMp(double x)
{
int p;
double y;
mp_no mpy;
p=32;
__mptan(x, &mpy, p);
__mp_dbl(&mpy,&y,p);
return y;
}
#ifdef NO_LONG_DOUBLE
weak_alias (tan, tanl)
#endif
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