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-rw-r--r--sysdeps/ieee754/dbl-64/s_tan.c533
1 files changed, 466 insertions, 67 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index 714cf27dd2..2db8673389 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -1,81 +1,480 @@
-/* @(#)s_tan.c 5.1 93/09/24 */
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * IBM Accurate Mathematical Library
+ * Copyright (c) International Business Machines Corp., 2001
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $";
-#endif
-
-/* tan(x)
- * Return tangent function of x.
- *
- * kernel function:
- * __kernel_tan ... tangent function on [-pi/4,pi/4]
- * __ieee754_rem_pio2 ... argument reduction routine
- *
- * Method.
- * Let S,C and T denote the sin, cos and tan respectively on
- * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
- * in [-pi/4 , +pi/4], and let n = k mod 4.
- * We have
- *
- * n sin(x) cos(x) tan(x)
- * ----------------------------------------------------------
- * 0 S C T
- * 1 C -S -1/T
- * 2 -S -C T
- * 3 -C S -1/T
- * ----------------------------------------------------------
+ * 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 of the License, or
+ * (at your option) any later version.
*
- * Special cases:
- * Let trig be any of sin, cos, or tan.
- * trig(+-INF) is NaN, with signals;
- * trig(NaN) is that NaN;
+ * 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 General Public License for more details.
*
- * Accuracy:
- * TRIG(x) returns trig(x) nearly rounded
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
+/*********************************************************************/
+/* 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 "endian.h"
+#include "dla.h"
+#include "mpa.h"
+#include "MathLib.h"
+static double tanMp(double);
+void __mptan(double, mp_no *, int);
-#include "math.h"
-#include "math_private.h"
+double tan(double x) {
+#include "utan.h"
+#include "utan.tbl"
-#ifdef __STDC__
- double __tan(double x)
-#else
- double __tan(x)
- double x;
-#endif
-{
- double y[2],z=0.0;
- int32_t n, ix;
+ 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,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
+ int p;
+ number num,v;
+ mp_no mpa,mpy,mpt1,mpt2;
+
+ int branred(double, double *, double *);
+ int mpranred(double, mp_no *, int);
+
+ /* x=+-INF, x=NaN */
+ num.d = x; ux = num.i[HIGH_HALF];
+ if ((ux&0x7ff00000)==0x7ff00000) return x-x;
+
+ w=(x<ZERO) ? -x : x;
+
+ /* (I) The case abs(x) <= 1.259e-8 */
+ if (w<=g1.d) return x;
+
+ /* (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)) return y;
+
+ /* 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)) return y;
+ return tanMp(x);
+ }
+
+ /* (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)) return (s*y);
+ t3 = (t2<ZERO) ? -t2 : t2;
+ if ((y=fi+(t2-(t4=fi*ua3.d+t3*ub3.d)))==fi+(t2+t4)) return (s*y);
+
+ /* 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)) return (s*y);
+ return tanMp(x);
+ }
+
+ /* (---) 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) return tanMp(x);
+
+ /* (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)) return (-y); }
+ else {
+ /* First stage tan */
+ if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) return y; }
+ /* 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)) return (-y); }
+ else {
+ /* Second stage tan */
+ if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) return y; }
+ return tanMp(x);
+ }
+
+ /* (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;
- /* High word of x. */
- GET_HIGH_WORD(ix,x);
+ if (n) {
+ /* -cot */
+ t2 = pz*(fi+gi)/(fi+pz);
+ if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) return (-sy*y);
+ t3 = (t2<ZERO) ? -t2 : t2;
+ if ((y=gi-(t2-(t4=gi*ua10.d+t3*ub10.d)))==gi-(t2+t4)) return (-sy*y); }
+ else {
+ /* tan */
+ t2 = pz*(gi+fi)/(gi-pz);
+ if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) return (sy*y);
+ t3 = (t2<ZERO) ? -t2 : t2;
+ if ((y=fi+(t2-(t4=fi*ua9.d+t3*ub9.d)))==fi+(t2+t4)) return (sy*y); }
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
+ /* 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)
- /* tan(Inf or NaN) is NaN */
- else if (ix>=0x7ff00000) return x-x; /* NaN */
+ 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)
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2(x,y);
- return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
- -1 -- n odd */
- }
+ 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)) 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-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;
}
-weak_alias (__tan, tan)
+
#ifdef NO_LONG_DOUBLE
-strong_alias (__tan, __tanl)
-weak_alias (__tan, tanl)
+weak_alias (tan, tanl)
#endif
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-10 03:44:11 +0000