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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c | 328 |
1 files changed, 328 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c new file mode 100644 index 0000000000..3641a35ce1 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/s_atan.c @@ -0,0 +1,328 @@ +/* + * 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 |