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c6c6dd4803
* manual/contrib.texi: Removed licenses, added acknowledgements
for contributions by Intel, IBM, Craig Metz.
* LICENSES: New file, contains the text of all non-FSF licenses in the
distribution that require putting the notice in the accompanying
documentation.
* README.template, README: Mention LICENSES.
* sysdeps/mach/hurd/net/if_ppp.h: Replaced CMU license with a
new one modelled on the modern BSD license, per recent letter
of permission from CMU.
* sysdeps/unix/sysv/linux/net/if_ppp.h: Likewise.
* sysdeps/ieee754/dbl-64/MathLib.h: Changed the copyright holder
from IBM to FSF, per the recent Software Letter. Changed the
distribution terms from GPL to LGPL.
* sysdeps/ieee754/dbl-64/asincos.tbl: Added FSF copyright and
copying permission notice (Lesser GPL), per recent IBM Software Letter.
* sysdeps/ieee754/dbl-64/powtwo.tbl: Likewise.
* sysdeps/ieee754/dbl-64/root.tbl: Likewise.
* sysdeps/ieee754/dbl-64/sincos.tbl: Likewise.
* sysdeps/ieee754/dbl-64/uatan.tbl: Likewise.
* sysdeps/ieee754/dbl-64/uexp.tbl: Likewise.
* sysdeps/ieee754/dbl-64/ulog.tbl: Likewise.
* sysdeps/ieee754/dbl-64/upow.tbl: Likewise.
* sysdeps/ieee754/dbl-64/utan.tbl: Likewise.
* sysdeps/ieee754/dbl-64/atnat.h: Changed the copyright holder
from IBM to FSF, per the recent Software Letter. Corrected the
text of the copying permission notice to say Lesser GPL instead
of GPL in warranty disclaimer paragraph.
* sysdeps/ieee754/dbl-64/atnat2.h: Likewise.
* sysdeps/ieee754/dbl-64/branred.h: Likewise.
* sysdeps/ieee754/dbl-64/dla.h: Likewise.
* sysdeps/ieee754/dbl-64/doasin.h: Likewise.
* sysdeps/ieee754/dbl-64/dosincos.h: Likewise.
* sysdeps/ieee754/dbl-64/mpa.h: Likewise.
* sysdeps/ieee754/dbl-64/mpa2.h: Likewise.
* sysdeps/ieee754/dbl-64/mpatan.h: Likewise.
* sysdeps/ieee754/dbl-64/mpexp.h: Likewise.
* sysdeps/ieee754/dbl-64/mplog.h: Likewise.
* sysdeps/ieee754/dbl-64/mpsqrt.h: Likewise.
* sysdeps/ieee754/dbl-64/mydefs.h: Likewise.
* sysdeps/ieee754/dbl-64/sincos32.h: Likewise.
* sysdeps/ieee754/dbl-64/uasncs.h: Likewise.
* sysdeps/ieee754/dbl-64/uexp.h: Likewise.
* sysdeps/ieee754/dbl-64/ulog.h: Likewise.
* sysdeps/ieee754/dbl-64/upow.h: Likewise.
* sysdeps/ieee754/dbl-64/urem.h: Likewise.
* sysdeps/ieee754/dbl-64/uroot.h: Likewise.
* sysdeps/ieee754/dbl-64/usncs.h: Likewise.
* sysdeps/ieee754/dbl-64/utan.h: Likewise.
* sysdeps/ieee754/dbl-64/branred.c: Corrected the text of the copying
permission notice to say Lesser GPL instead of GPL in warranty
disclaimer paragraph.
* sysdeps/ieee754/dbl-64/doasin.c: Likewise.
* sysdeps/ieee754/dbl-64/dosincos.c: Likewise.
* sysdeps/ieee754/dbl-64/e_asin.c: Likewise.
* sysdeps/ieee754/dbl-64/e_atan2.c: Likewise.
* sysdeps/ieee754/dbl-64/e_exp.c: Likewise.
* sysdeps/ieee754/dbl-64/e_log.c: Likewise.
* sysdeps/ieee754/dbl-64/e_pow.c: Likewise.
* sysdeps/ieee754/dbl-64/e_remainder.c: Likewise.
* sysdeps/ieee754/dbl-64/e_sqrt.c: Likewise.
* sysdeps/ieee754/dbl-64/halfulp.c: Likewise.
* sysdeps/ieee754/dbl-64/mpa.c: Likewise.
* sysdeps/ieee754/dbl-64/mpatan.c: Likewise.
* sysdeps/ieee754/dbl-64/mpatan2.c: Likewise.
* sysdeps/ieee754/dbl-64/mpexp.c: Likewise.
* sysdeps/ieee754/dbl-64/mplog.c: Likewise.
* sysdeps/ieee754/dbl-64/mpsqrt.c: Likewise.
* sysdeps/ieee754/dbl-64/mptan.c: Likewise.
* sysdeps/ieee754/dbl-64/s_atan.c: Likewise.
* sysdeps/ieee754/dbl-64/s_sin.c: Likewise.
* sysdeps/ieee754/dbl-64/s_tan.c: Likewise.
* sysdeps/ieee754/dbl-64/sincos32.c: Likewise.
* sysdeps/ieee754/dbl-64/slowexp.c: Likewise.
* sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
487 lines
17 KiB
C
487 lines
17 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001 Free Software Foundation
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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 Lesser 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: utan.c */
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/* */
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/* FUNCTIONS: utan */
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/* tanMp */
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/* */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */
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/* branred.c sincos32.c mptan.c */
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/* utan.tbl */
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/* */
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/* An ultimate tan routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of tan(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 "dla.h"
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#include "mpa.h"
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#include "MathLib.h"
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#include "math.h"
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static double tanMp(double);
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void __mptan(double, mp_no *, int);
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double tan(double x) {
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#include "utan.h"
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#include "utan.tbl"
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int ux,i,n;
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double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy,
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t,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
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int p;
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number num,v;
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mp_no mpa,mpt1,mpt2;
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#if 0
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mp_no mpy;
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#endif
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int __branred(double, double *, double *);
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int __mpranred(double, mp_no *, int);
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/* x=+-INF, x=NaN */
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num.d = x; ux = num.i[HIGH_HALF];
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if ((ux&0x7ff00000)==0x7ff00000) return x-x;
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w=(x<ZERO) ? -x : x;
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/* (I) The case abs(x) <= 1.259e-8 */
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if (w<=g1.d) return x;
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/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
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if (w<=g2.d) {
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/* First stage */
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x2 = x*x;
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t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d))));
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if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2)) return y;
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/* Second stage */
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c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
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x2*a27.d))))));
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EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5)
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ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(x ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(x ,zero.d,c2,cc2,c1,cc1,t1,t2)
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if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1)) return y;
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return tanMp(x);
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}
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/* (III) The case 0.0608 < abs(x) <= 0.787 */
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if (w<=g3.d) {
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/* First stage */
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i = ((int) (mfftnhf.d+TWO8*w));
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z = w-xfg[i][0].d; z2 = z*z; s = (x<ZERO) ? MONE : ONE;
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pz = z+z*z2*(e0.d+z2*e1.d);
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fi = xfg[i][1].d; gi = xfg[i][2].d; t2 = pz*(gi+fi)/(gi-pz);
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if ((y=fi+(t2-fi*u3.d))==fi+(t2+fi*u3.d)) return (s*y);
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t3 = (t2<ZERO) ? -t2 : t2;
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if ((y=fi+(t2-(t4=fi*ua3.d+t3*ub3.d)))==fi+(t2+t4)) return (s*y);
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/* Second stage */
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ffi = xfg[i][3].d;
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c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
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EMULV(z,z,z2,zz2,t1,t2,t3,t4,t5)
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ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(z ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(z ,zero.d,c2,cc2,c1,cc1,t1,t2)
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ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
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MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
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SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
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DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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if ((y=c3+(cc3-u4.d*c3))==c3+(cc3+u4.d*c3)) return (s*y);
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return tanMp(x);
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}
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/* (---) The case 0.787 < abs(x) <= 25 */
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if (w<=g4.d) {
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/* Range reduction by algorithm i */
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t = (x*hpinv.d + toint.d);
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xn = t - toint.d;
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v.d = t;
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t1 = (x - xn*mp1.d) - xn*mp2.d;
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n =v.i[LOW_HALF] & 0x00000001;
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da = xn*mp3.d;
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a=t1-da;
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da = (t1-a)-da;
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if (a<ZERO) {ya=-a; yya=-da; sy=MONE;}
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else {ya= a; yya= da; sy= ONE;}
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/* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
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if (ya<=gy1.d) return tanMp(x);
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/* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
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if (ya<=gy2.d) {
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a2 = a*a;
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t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
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if (n) {
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/* First stage -cot */
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EADD(a,t2,b,db)
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DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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if ((y=c+(dc-u6.d*c))==c+(dc+u6.d*c)) return (-y); }
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else {
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/* First stage tan */
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if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) return y; }
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/* Second stage */
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/* Range reduction by algorithm ii */
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t = (x*hpinv.d + toint.d);
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xn = t - toint.d;
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v.d = t;
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t1 = (x - xn*mp1.d) - xn*mp2.d;
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n =v.i[LOW_HALF] & 0x00000001;
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da = xn*pp3.d;
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t=t1-da;
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da = (t1-t)-da;
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t1 = xn*pp4.d;
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a = t - t1;
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da = ((t-a)-t1)+da;
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/* Second stage */
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EADD(a,da,t1,t2) a=t1; da=t2;
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MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
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c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
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x2*a27.d))))));
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ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
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if (n) {
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/* Second stage -cot */
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DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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if ((y=c2+(cc2-u8.d*c2)) == c2+(cc2+u8.d*c2)) return (-y); }
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else {
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/* Second stage tan */
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if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) return y; }
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return tanMp(x);
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}
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/* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */
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/* First stage */
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i = ((int) (mfftnhf.d+TWO8*ya));
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z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
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pz = z+z*z2*(e0.d+z2*e1.d);
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fi = xfg[i][1].d; gi = xfg[i][2].d;
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if (n) {
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/* -cot */
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t2 = pz*(fi+gi)/(fi+pz);
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if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) return (-sy*y);
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t3 = (t2<ZERO) ? -t2 : t2;
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if ((y=gi-(t2-(t4=gi*ua10.d+t3*ub10.d)))==gi-(t2+t4)) return (-sy*y); }
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else {
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/* tan */
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t2 = pz*(gi+fi)/(gi-pz);
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if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) return (sy*y);
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t3 = (t2<ZERO) ? -t2 : t2;
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if ((y=fi+(t2-(t4=fi*ua9.d+t3*ub9.d)))==fi+(t2+t4)) return (sy*y); }
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/* Second stage */
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ffi = xfg[i][3].d;
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EADD(z0,yya,z,zz)
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MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
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c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
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ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
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ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
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MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
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SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
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if (n) {
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/* -cot */
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DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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if ((y=c3+(cc3-u12.d*c3))==c3+(cc3+u12.d*c3)) return (-sy*y); }
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else {
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/* tan */
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DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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if ((y=c3+(cc3-u11.d*c3))==c3+(cc3+u11.d*c3)) return (sy*y); }
|
|
|
|
return tanMp(x);
|
|
}
|
|
|
|
/* (---) 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) return tanMp(x);
|
|
|
|
/* (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)) return (-y); }
|
|
else {
|
|
/* First stage tan */
|
|
if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a)) return y; }
|
|
|
|
/* 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)) return (-y); }
|
|
else {
|
|
/* Second stage tan */
|
|
if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) return (y); }
|
|
return tanMp(x);
|
|
}
|
|
|
|
/* (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)) return (-sy*y);
|
|
t3 = (t2<ZERO) ? -t2 : t2;
|
|
if ((y=gi-(t2-(t4=gi*ua18.d+t3*ub18.d)))==gi-(t2+t4)) return (-sy*y); }
|
|
else {
|
|
/* tan */
|
|
t2 = pz*(gi+fi)/(gi-pz);
|
|
if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d)) return (sy*y);
|
|
t3 = (t2<ZERO) ? -t2 : t2;
|
|
if ((y=fi+(t2-(t4=fi*ua17.d+t3*ub17.d)))==fi+(t2+t4)) return (sy*y); }
|
|
|
|
/* 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)) return (-sy*y); }
|
|
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)) return (sy*y); }
|
|
return tanMp(x);
|
|
}
|
|
|
|
/* (---) 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) return tanMp(x);
|
|
|
|
/* (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)) return (-y); }
|
|
else {
|
|
/* First stage tan */
|
|
if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a)) return y; }
|
|
|
|
/* 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)) return (-y); }
|
|
else {
|
|
/* Second stage tan */
|
|
if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1)) return y; }
|
|
return tanMp(x);
|
|
}
|
|
|
|
/* (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)) return (-sy*y);
|
|
t3 = (t2<ZERO) ? -t2 : t2;
|
|
if ((y=gi-(t2-(t4=gi*ua26.d+t3*ub26.d)))==gi-(t2+t4)) return (-sy*y); }
|
|
else {
|
|
/* tan */
|
|
t2 = pz*(gi+fi)/(gi-pz);
|
|
if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d)) return (sy*y);
|
|
t3 = (t2<ZERO) ? -t2 : t2;
|
|
if ((y=fi+(t2-(t4=fi*ua25.d+t3*ub25.d)))==fi+(t2+t4)) return (sy*y); }
|
|
|
|
/* 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)) return (-sy*y); }
|
|
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)) return (sy*y); }
|
|
return tanMp(x);
|
|
}
|
|
|
|
|
|
/* multiple precision stage */
|
|
/* Convert x to multi precision number,compute tan(x) by mptan() routine */
|
|
/* and converts result back to double */
|
|
static double 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
|