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38722448c6
This patch makes the dbl-64 atan and tan implementations use libm_alias_double, removing the corresponding ldbl-opt wrappers. Tested for x86_64, and with build-many-glibcs.py. Installed stripped shared libraries are unchanged on non-ldbl-opt platforms. For ldbl-opt configurations, the patch has the effect of causing compat_symbol to define atanl and tanl in terms of __atan and __tan instead of in terms of atan and tan, which is enough to change the installed stripped libm.so. * sysdeps/ieee754/dbl-64/s_atan.c: Include <libm-alias-double.h>. (atan): Define using libm_alias_double. * sysdeps/ieee754/dbl-64/s_tan.c: Include <libm-alias-double.h>. (tan): Define using libm_alias_double. * sysdeps/ieee754/ldbl-opt/s_atan.c: Remove file. * sysdeps/ieee754/ldbl-opt/s_tan.c: Likewise.
850 lines
22 KiB
C
850 lines
22 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) 2001-2017 Free Software Foundation, Inc.
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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 2.1 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, see <http://www.gnu.org/licenses/>.
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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 <errno.h>
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#include <float.h>
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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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#include <math_private.h>
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#include <libm-alias-double.h>
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#include <fenv.h>
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#include <stap-probe.h>
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#ifndef SECTION
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# define SECTION
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#endif
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static double tanMp (double);
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void __mptan (double, mp_no *, int);
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double
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SECTION
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__tan (double x)
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{
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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,
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s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya,
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yya, z0, z, zz, z2, zz2;
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#ifndef DLA_FMS
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double t5, t6;
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#endif
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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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double retval;
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int __branred (double, double *, double *);
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int __mpranred (double, mp_no *, int);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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/* x=+-INF, x=NaN */
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num.d = x;
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ux = num.i[HIGH_HALF];
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if ((ux & 0x7ff00000) == 0x7ff00000)
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{
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if ((ux & 0x7fffffff) == 0x7ff00000)
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__set_errno (EDOM);
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retval = x - x;
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goto ret;
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}
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w = (x < 0.0) ? -x : x;
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/* (I) The case abs(x) <= 1.259e-8 */
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if (w <= g1.d)
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{
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math_check_force_underflow_nonneg (w);
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retval = x;
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goto ret;
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}
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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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{
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/* First stage */
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x2 = x * x;
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t2 = d9.d + x2 * d11.d;
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t2 = d7.d + x2 * t2;
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t2 = d5.d + x2 * t2;
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t2 = d3.d + x2 * t2;
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t2 *= x * x2;
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if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
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{
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retval = y;
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goto ret;
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}
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/* Second stage */
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c1 = a25.d + x2 * a27.d;
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c1 = a23.d + x2 * c1;
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c1 = a21.d + x2 * c1;
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c1 = a19.d + x2 * c1;
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c1 = a17.d + x2 * c1;
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c1 = a15.d + x2 * c1;
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c1 *= x2;
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EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5);
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ADD2 (a13.d, aa13.d, c1, 0.0, 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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
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if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
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{
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retval = y;
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goto ret;
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}
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retval = tanMp (x);
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goto ret;
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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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{
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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;
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z2 = z * z;
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s = (x < 0.0) ? -1 : 1;
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pz = z + z * z2 * (e0.d + z2 * e1.d);
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fi = xfg[i][1].d;
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gi = xfg[i][2].d;
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t2 = pz * (gi + fi) / (gi - pz);
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if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d))
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{
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retval = (s * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = fi * ua3.d + t3 * ub3.d;
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if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
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{
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retval = (s * y);
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goto ret;
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}
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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, 0.0, 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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (z, 0.0, 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 (1.0, 0.0, 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,
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t10);
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if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
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{
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retval = (s * y);
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goto ret;
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}
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retval = tanMp (x);
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goto ret;
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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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{
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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 < 0.0)
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{
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ya = -a;
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yya = -da;
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sy = -1;
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}
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else
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{
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ya = a;
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yya = da;
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sy = 1;
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}
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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)
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{
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retval = tanMp (x);
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goto ret;
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}
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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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{
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a2 = a * a;
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t2 = d9.d + a2 * d11.d;
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t2 = d7.d + a2 * t2;
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t2 = d5.d + a2 * t2;
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t2 = d3.d + a2 * t2;
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t2 = da + a * a2 * t2;
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if (n)
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{
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/* First stage -cot */
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EADD (a, t2, b, db);
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DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8,
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t9, t10);
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if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c))
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{
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retval = (-y);
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goto ret;
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}
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}
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else
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{
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/* First stage tan */
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if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a))
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{
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retval = y;
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goto ret;
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}
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}
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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);
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a = t1;
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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 = a25.d + x2 * a27.d;
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c1 = a23.d + x2 * c1;
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c1 = a21.d + x2 * c1;
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c1 = a19.d + x2 * c1;
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c1 = a17.d + x2 * c1;
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c1 = a15.d + x2 * c1;
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c1 *= x2;
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ADD2 (a13.d, aa13.d, c1, 0.0, 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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{
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/* Second stage -cot */
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DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7,
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t8, t9, t10);
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if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
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{
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retval = (-y);
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goto ret;
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}
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}
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else
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{
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/* Second stage tan */
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if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1))
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{
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retval = y;
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goto ret;
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}
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}
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retval = tanMp (x);
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goto ret;
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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;
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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;
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gi = xfg[i][2].d;
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if (n)
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{
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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))
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{
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retval = (-sy * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = gi * ua10.d + t3 * ub10.d;
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if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
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{
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retval = (-sy * y);
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goto ret;
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}
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}
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else
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{
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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))
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{
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retval = (sy * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = fi * ua9.d + t3 * ub9.d;
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if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
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{
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retval = (sy * y);
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goto ret;
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}
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}
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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, 0.0, 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);
|
|
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;
|
|
}
|
|
|
|
/* (---) 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 < 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 */
|
|
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;
|
|
}
|
|
|
|
/* (---) 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 < 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)
|
|
{
|
|
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 = 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))
|
|
{
|
|
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, 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
|
|
SECTION
|
|
tanMp (double x)
|
|
{
|
|
int p;
|
|
double y;
|
|
mp_no mpy;
|
|
p = 32;
|
|
__mptan (x, &mpy, p);
|
|
__mp_dbl (&mpy, &y, p);
|
|
LIBC_PROBE (slowtan, 2, &x, &y);
|
|
return y;
|
|
}
|
|
|
|
#ifndef __tan
|
|
libm_alias_double (__tan, tan)
|
|
#endif
|