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Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_atan.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_atan.c | 328 |
1 files changed, 0 insertions, 328 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c deleted file mode 100644 index 3641a35ce1..0000000000 --- a/sysdeps/ieee754/dbl-64/s_atan.c +++ /dev/null @@ -1,328 +0,0 @@ -/* - * IBM Accurate Mathematical Library - * written by International Business Machines Corp. - * Copyright (C) 2001-2017 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 2.1 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 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, see <http://www.gnu.org/licenses/>. - */ -/************************************************************************/ -/* MODULE_NAME: atnat.c */ -/* */ -/* FUNCTIONS: uatan */ -/* atanMp */ -/* signArctan */ -/* */ -/* */ -/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */ -/* mpatan.c mpatan2.c mpsqrt.c */ -/* uatan.tbl */ -/* */ -/* An ultimate atan() routine. Given an IEEE double machine number x */ -/* it computes the correctly rounded (to nearest) value of atan(x). */ -/* */ -/* Assumption: Machine arithmetic operations are performed in */ -/* round to nearest mode of IEEE 754 standard. */ -/* */ -/************************************************************************/ - -#include <dla.h> -#include "mpa.h" -#include "MathLib.h" -#include "uatan.tbl" -#include "atnat.h" -#include <fenv.h> -#include <float.h> -#include <math.h> -#include <math_private.h> -#include <stap-probe.h> - -void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */ -static double atanMp (double, const int[]); - - /* Fix the sign of y and return */ -static double -__signArctan (double x, double y) -{ - return __copysign (y, x); -} - - -/* An ultimate atan() routine. Given an IEEE double machine number x, */ -/* routine computes the correctly rounded (to nearest) value of atan(x). */ -double -atan (double x) -{ - double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3, - v, vv, w, ww, y, yy, z, zz; -#ifndef DLA_FMS - double t4, t5, t6; -#endif - int i, ux, dx; - static const int pr[M] = { 6, 8, 10, 32 }; - number num; - - num.d = x; - ux = num.i[HIGH_HALF]; - dx = num.i[LOW_HALF]; - - /* x=NaN */ - if (((ux & 0x7ff00000) == 0x7ff00000) - && (((ux & 0x000fffff) | dx) != 0x00000000)) - return x + x; - - /* Regular values of x, including denormals +-0 and +-INF */ - SET_RESTORE_ROUND (FE_TONEAREST); - u = (x < 0) ? -x : x; - if (u < C) - { - if (u < B) - { - if (u < A) - { - math_check_force_underflow_nonneg (u); - return x; - } - else - { /* A <= u < B */ - v = x * x; - yy = d11.d + v * d13.d; - yy = d9.d + v * yy; - yy = d7.d + v * yy; - yy = d5.d + v * yy; - yy = d3.d + v * yy; - yy *= x * v; - - if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x)) - return y; - - EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */ - - s1 = f17.d + v * f19.d; - s1 = f15.d + v * s1; - s1 = f13.d + v * s1; - s1 = f11.d + v * s1; - s1 *= v; - - ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, - t8); - ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2); - if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1)) - return y; - - return atanMp (x, pr); - } - } - else - { /* B <= u < C */ - i = (TWO52 + TWO8 * u) - TWO52; - i -= 16; - z = u - cij[i][0].d; - yy = cij[i][5].d + z * cij[i][6].d; - yy = cij[i][4].d + z * yy; - yy = cij[i][3].d + z * yy; - yy = cij[i][2].d + z * yy; - yy *= z; - - t1 = cij[i][1].d; - if (i < 112) - { - if (i < 48) - u2 = U21; /* u < 1/4 */ - else - u2 = U22; - } /* 1/4 <= u < 1/2 */ - else - { - if (i < 176) - u2 = U23; /* 1/2 <= u < 3/4 */ - else - u2 = U24; - } /* 3/4 <= u <= 1 */ - if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1)) - return __signArctan (x, y); - - z = u - hij[i][0].d; - - s1 = hij[i][14].d + z * hij[i][15].d; - s1 = hij[i][13].d + z * s1; - s1 = hij[i][12].d + z * s1; - s1 = hij[i][11].d + z * s1; - s1 *= z; - - ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); - MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); - if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2)) - return __signArctan (x, y); - - return atanMp (x, pr); - } - } - else - { - if (u < D) - { /* C <= u < D */ - w = 1 / u; - EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); - ww = w * ((1 - t1) - t2); - i = (TWO52 + TWO8 * w) - TWO52; - i -= 16; - z = (w - cij[i][0].d) + ww; - - yy = cij[i][5].d + z * cij[i][6].d; - yy = cij[i][4].d + z * yy; - yy = cij[i][3].d + z * yy; - yy = cij[i][2].d + z * yy; - yy = HPI1 - z * yy; - - t1 = HPI - cij[i][1].d; - if (i < 112) - u3 = U31; /* w < 1/2 */ - else - u3 = U32; /* w >= 1/2 */ - if ((y = t1 + (yy - u3)) == t1 + (yy + u3)) - return __signArctan (x, y); - - DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9, - t10); - t1 = w - hij[i][0].d; - EADD (t1, ww, z, zz); - - s1 = hij[i][14].d + z * hij[i][15].d; - s1 = hij[i][13].d + z * s1; - s1 = hij[i][12].d + z * s1; - s1 = hij[i][11].d + z * s1; - s1 *= z; - - ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2); - MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2); - MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2); - SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2); - if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7)) - return __signArctan (x, y); - - return atanMp (x, pr); - } - else - { - if (u < E) - { /* D <= u < E */ - w = 1 / u; - v = w * w; - EMULV (w, u, t1, t2, t3, t4, t5, t6, t7); - - yy = d11.d + v * d13.d; - yy = d9.d + v * yy; - yy = d7.d + v * yy; - yy = d5.d + v * yy; - yy = d3.d + v * yy; - yy *= w * v; - - ww = w * ((1 - t1) - t2); - ESUB (HPI, w, t3, cor); - yy = ((HPI1 + cor) - ww) - yy; - if ((y = t3 + (yy - U4)) == t3 + (yy + U4)) - return __signArctan (x, y); - - DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, - t9, t10); - MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8); - - s1 = f17.d + v * f19.d; - s1 = f15.d + v * s1; - s1 = f13.d + v * s1; - s1 = f11.d + v * s1; - s1 *= v; - - ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2); - MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8); - MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8); - ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2); - SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2); - - if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8)) - return __signArctan (x, y); - - return atanMp (x, pr); - } - else - { - /* u >= E */ - if (x > 0) - return HPI; - else - return MHPI; - } - } - } -} - - /* Final stages. Compute atan(x) by multiple precision arithmetic */ -static double -atanMp (double x, const int pr[]) -{ - mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1; - double y1, y2; - int i, p; - - for (i = 0; i < M; i++) - { - p = pr[i]; - __dbl_mp (x, &mpx, p); - __mpatan (&mpx, &mpy, p); - __dbl_mp (u9[i].d, &mpt1, p); - __mul (&mpy, &mpt1, &mperr, p); - __add (&mpy, &mperr, &mpy1, p); - __sub (&mpy, &mperr, &mpy2, p); - __mp_dbl (&mpy1, &y1, p); - __mp_dbl (&mpy2, &y2, p); - if (y1 == y2) - { - LIBC_PROBE (slowatan, 3, &p, &x, &y1); - return y1; - } - } - LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1); - return y1; /*if impossible to do exact computing */ -} - -#ifdef NO_LONG_DOUBLE -weak_alias (atan, atanl) -#endif |