/*
* IBM Accurate Mathematical Library
- * Copyright (c) International Business Machines Corp., 2001
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001-2015 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 of the License, or
+ * 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 General Public License for more details.
+ * 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, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+ * along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/*********************************************************************/
/* MODULE_NAME: utan.c */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
+
+#include <errno.h>
#include "endian.h"
-#include "dla.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>
+#include <fenv.h>
+#include <stap-probe.h>
+
+#ifndef SECTION
+# define SECTION
+#endif
+
+static double tanMp (double);
+void __mptan (double, mp_no *, int);
-double tan(double x) {
+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,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
+ 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,mpy,mpt1,mpt2;
+ number num, v;
+ mp_no mpa, mpt1, mpt2;
+
+ double retval;
- int branred(double, double *, double *);
- int mpranred(double, mp_no *, int);
+ 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) return x-x;
+ 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;
+ w = (x < 0.0) ? -x : x;
/* (I) The case abs(x) <= 1.259e-8 */
- if (w<=g1.d) return x;
+ 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)) 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);
- }
+ if (w <= g2.d)
+ {
+ /* First stage */
+ x2 = x * x;
+
+ t2 = d9.d + x2 * d11.d;
+ t2 = d7.d + x2 * t2;
+ t2 = d5.d + x2 * t2;
+ t2 = d3.d + x2 * t2;
+ t2 *= x * x2;
+
+ if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
+ {
+ retval = y;
+ goto ret;
+ }
+
+ /* Second stage */
+ c1 = a25.d + x2 * a27.d;
+ c1 = a23.d + x2 * c1;
+ c1 = a21.d + x2 * c1;
+ c1 = a19.d + x2 * c1;
+ c1 = a17.d + x2 * c1;
+ c1 = a15.d + x2 * c1;
+ c1 *= x2;
+
+ EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5);
+ ADD2 (a13.d, aa13.d, c1, 0.0, 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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (x, 0.0, 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)) 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);
- }
+ if (w <= g3.d)
+ {
+ /* First stage */
+ i = ((int) (mfftnhf.d + TWO8 * w));
+ z = w - xfg[i][0].d;
+ z2 = z * z;
+ s = (x < 0.0) ? -1 : 1;
+ 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 < 0.0) ? -t2 : t2;
+ t4 = fi * ua3.d + t3 * ub3.d;
+ if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
+ {
+ retval = (s * y);
+ 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) 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);
+ 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, 0.0, 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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (z, 0.0, 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 (1.0, 0.0, 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*pp3.d;
- t=t1-da;
- da = (t1-t)-da;
- t1 = xn*pp4.d;
- a = t - t1;
- da = ((t-a)-t1)+da;
+ 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 < 0.0)
+ {
+ ya = -a;
+ yya = -da;
+ sy = -1;
+ }
+ else
+ {
+ ya = a;
+ yya = da;
+ sy = 1;
+ }
+
+ /* (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 = d9.d + a2 * d11.d;
+ t2 = d7.d + a2 * t2;
+ t2 = d5.d + a2 * t2;
+ t2 = d3.d + a2 * t2;
+ t2 = da + a * a2 * t2;
+
+ if (n)
+ {
+ /* First stage -cot */
+ EADD (a, t2, b, db);
+ DIV2 (1.0, 0.0, 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 = a25.d + x2 * a27.d;
+ c1 = a23.d + x2 * c1;
+ c1 = a21.d + x2 * c1;
+ c1 = a19.d + x2 * c1;
+ c1 = a17.d + x2 * c1;
+ c1 = a15.d + x2 * c1;
+ c1 *= x2;
+
+ ADD2 (a13.d, aa13.d, c1, 0.0, 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 (1.0, 0.0, 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 < 0.0) ? -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 < 0.0) ? -t2 : t2;
+ t4 = fi * ua9.d + t3 * ub9.d;
+ if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
+ {
+ retval = (sy * y);
+ goto ret;
+ }
+ }
/* 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);
+ 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, 0.0, 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 (1.0, 0.0, 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;
}
- /* (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)) 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); }
-
- /* 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)) 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; }
+ 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 < 0.0)
+ {
+ ya = -a;
+ yya = -da;
+ sy = -1;
+ }
+ else
+ {
+ ya = a;
+ yya = da;
+ sy = 1;
+ }
+
+ /* (+++) 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 = d9.d + a2 * d11.d;
+ t2 = d7.d + a2 * t2;
+ t2 = d5.d + a2 * t2;
+ t2 = d3.d + a2 * t2;
+ t2 = da + a * a2 * t2;
+
+ if (n)
+ {
+ /* First stage -cot */
+ EADD (a, t2, b, db);
+ DIV2 (1.0, 0.0, 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 = a25.d + x2 * a27.d;
+ c1 = a23.d + x2 * c1;
+ c1 = a21.d + x2 * c1;
+ c1 = a19.d + x2 * c1;
+ c1 = a17.d + x2 * c1;
+ c1 = a15.d + x2 * c1;
+ c1 *= x2;
+
+ ADD2 (a13.d, aa13.d, c1, 0.0, 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 (1.0, 0.0, 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 < 0.0) ? -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 < 0.0) ? -t2 : t2;
+ t4 = fi * ua17.d + t3 * ub17.d;
+ if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
+ {
+ retval = (sy * 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)) return (-y); }
- else {
- /* Second stage tan */
- if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) return (y); }
- return tanMp(x);
+ 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, 0.0, 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 (1.0, 0.0, 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;
}
- /* (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;}
+ n = (__branred (x, &a, &da)) & 0x00000001;
+ EADD (a, da, t1, t2);
+ a = t1;
+ da = t2;
+ if (a < 0.0)
+ {
+ ya = -a;
+ yya = -da;
+ sy = -1;
+ }
+ else
+ {
+ ya = a;
+ yya = da;
+ sy = 1;
+ }
/* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */
- if (ya<=gy1.d) return tanMp(x);
+ 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)) 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);
- }
+ if (ya <= gy2.d)
+ {
+ a2 = a * a;
+ t2 = d9.d + a2 * d11.d;
+ t2 = d7.d + a2 * t2;
+ t2 = d5.d + a2 * t2;
+ t2 = d3.d + a2 * t2;
+ t2 = da + a * a2 * t2;
+ if (n)
+ {
+ /* First stage -cot */
+ EADD (a, t2, b, db);
+ DIV2 (1.0, 0.0, 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 = a25.d + x2 * a27.d;
+ c1 = a23.d + x2 * c1;
+ c1 = a21.d + x2 * c1;
+ c1 = a19.d + x2 * c1;
+ c1 = a17.d + x2 * c1;
+ c1 = a15.d + x2 * c1;
+ c1 *= x2;
+
+ ADD2 (a13.d, aa13.d, c1, 0.0, 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 (1.0, 0.0, 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)) 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); }
+ 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 < 0.0) ? -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 < 0.0) ? -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)) 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);
-}
+ 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, 0.0, 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 (1.0, 0.0, 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 tanMp(double x)
+static double
+SECTION
+tanMp (double x)
{
int p;
double y;
mp_no mpy;
- p=32;
- __mptan(x, &mpy, p);
- __mp_dbl(&mpy,&y,p);
+ p = 32;
+ __mptan (x, &mpy, p);
+ __mp_dbl (&mpy, &y, p);
+ LIBC_PROBE (slowtan, 2, &x, &y);
return y;
}
projects / thirdparty / glibc.git / blobdiff