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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.
330 lines
10 KiB
C
330 lines
10 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: atnat.c */
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/* */
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/* FUNCTIONS: uatan */
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/* atanMp */
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/* signArctan */
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/* */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
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/* mpatan.c mpatan2.c mpsqrt.c */
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/* uatan.tbl */
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/* */
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/* An ultimate atan() routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of atan(x). */
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/* */
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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 <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include "uatan.tbl"
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#include "atnat.h"
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#include <fenv.h>
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#include <float.h>
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#include <libm-alias-double.h>
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#include <math.h>
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#include <math_private.h>
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#include <stap-probe.h>
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void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */
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static double atanMp (double, const int[]);
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/* Fix the sign of y and return */
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static double
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__signArctan (double x, double y)
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{
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return __copysign (y, x);
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}
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/* An ultimate atan() routine. Given an IEEE double machine number x, */
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/* routine computes the correctly rounded (to nearest) value of atan(x). */
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double
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__atan (double x)
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{
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double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
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v, vv, w, ww, y, yy, z, zz;
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#ifndef DLA_FMS
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double t4, t5, t6;
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#endif
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int i, ux, dx;
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static const int pr[M] = { 6, 8, 10, 32 };
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number num;
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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/* x=NaN */
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if (((ux & 0x7ff00000) == 0x7ff00000)
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&& (((ux & 0x000fffff) | dx) != 0x00000000))
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return x + x;
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/* Regular values of x, including denormals +-0 and +-INF */
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SET_RESTORE_ROUND (FE_TONEAREST);
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u = (x < 0) ? -x : x;
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if (u < C)
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{
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if (u < B)
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{
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if (u < A)
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{
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math_check_force_underflow_nonneg (u);
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return x;
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}
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else
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{ /* A <= u < B */
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v = x * x;
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yy = d11.d + v * d13.d;
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yy = d9.d + v * yy;
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yy = d7.d + v * yy;
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yy = d5.d + v * yy;
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yy = d3.d + v * yy;
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yy *= x * v;
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if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
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return y;
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EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */
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s1 = f17.d + v * f19.d;
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s1 = f15.d + v * s1;
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s1 = f13.d + v * s1;
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s1 = f11.d + v * s1;
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s1 *= v;
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ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
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t8);
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ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
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if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
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return y;
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return atanMp (x, pr);
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}
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}
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else
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{ /* B <= u < C */
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i = (TWO52 + TWO8 * u) - TWO52;
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i -= 16;
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z = u - cij[i][0].d;
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yy = cij[i][5].d + z * cij[i][6].d;
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yy = cij[i][4].d + z * yy;
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yy = cij[i][3].d + z * yy;
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yy = cij[i][2].d + z * yy;
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yy *= z;
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t1 = cij[i][1].d;
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if (i < 112)
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{
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if (i < 48)
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u2 = U21; /* u < 1/4 */
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else
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u2 = U22;
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} /* 1/4 <= u < 1/2 */
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else
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{
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if (i < 176)
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u2 = U23; /* 1/2 <= u < 3/4 */
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else
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u2 = U24;
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} /* 3/4 <= u <= 1 */
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if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
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return __signArctan (x, y);
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z = u - hij[i][0].d;
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s1 = hij[i][14].d + z * hij[i][15].d;
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s1 = hij[i][13].d + z * s1;
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s1 = hij[i][12].d + z * s1;
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s1 = hij[i][11].d + z * s1;
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s1 *= z;
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ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
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MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
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if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
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return __signArctan (x, y);
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return atanMp (x, pr);
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}
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}
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else
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{
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if (u < D)
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{ /* C <= u < D */
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w = 1 / u;
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EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
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ww = w * ((1 - t1) - t2);
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i = (TWO52 + TWO8 * w) - TWO52;
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i -= 16;
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z = (w - cij[i][0].d) + ww;
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yy = cij[i][5].d + z * cij[i][6].d;
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yy = cij[i][4].d + z * yy;
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yy = cij[i][3].d + z * yy;
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yy = cij[i][2].d + z * yy;
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yy = HPI1 - z * yy;
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t1 = HPI - cij[i][1].d;
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if (i < 112)
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u3 = U31; /* w < 1/2 */
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else
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u3 = U32; /* w >= 1/2 */
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if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
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return __signArctan (x, y);
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DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9,
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t10);
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t1 = w - hij[i][0].d;
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EADD (t1, ww, z, zz);
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s1 = hij[i][14].d + z * hij[i][15].d;
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s1 = hij[i][13].d + z * s1;
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s1 = hij[i][12].d + z * s1;
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s1 = hij[i][11].d + z * s1;
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s1 *= z;
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ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
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MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
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SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
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if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
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return __signArctan (x, y);
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return atanMp (x, pr);
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}
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else
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{
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if (u < E)
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{ /* D <= u < E */
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w = 1 / u;
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v = w * w;
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EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
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yy = d11.d + v * d13.d;
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yy = d9.d + v * yy;
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yy = d7.d + v * yy;
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yy = d5.d + v * yy;
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yy = d3.d + v * yy;
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yy *= w * v;
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ww = w * ((1 - t1) - t2);
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ESUB (HPI, w, t3, cor);
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yy = ((HPI1 + cor) - ww) - yy;
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if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
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return __signArctan (x, y);
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DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8,
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t9, t10);
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MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
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s1 = f17.d + v * f19.d;
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s1 = f15.d + v * s1;
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s1 = f13.d + v * s1;
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s1 = f11.d + v * s1;
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s1 *= v;
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ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
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SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);
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if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
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return __signArctan (x, y);
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return atanMp (x, pr);
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}
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else
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{
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/* u >= E */
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if (x > 0)
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return HPI;
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else
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return MHPI;
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}
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}
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}
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}
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/* Final stages. Compute atan(x) by multiple precision arithmetic */
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static double
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atanMp (double x, const int pr[])
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{
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mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
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double y1, y2;
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int i, p;
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for (i = 0; i < M; i++)
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{
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p = pr[i];
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__dbl_mp (x, &mpx, p);
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__mpatan (&mpx, &mpy, p);
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__dbl_mp (u9[i].d, &mpt1, p);
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__mul (&mpy, &mpt1, &mperr, p);
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__add (&mpy, &mperr, &mpy1, p);
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__sub (&mpy, &mperr, &mpy2, p);
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__mp_dbl (&mpy1, &y1, p);
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__mp_dbl (&mpy2, &y2, p);
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if (y1 == y2)
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{
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LIBC_PROBE (slowatan, 3, &p, &x, &y1);
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return y1;
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}
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}
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LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
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return y1; /*if impossible to do exact computing */
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}
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#ifndef __atan
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libm_alias_double (__atan, atan)
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#endif
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