| /* Implementation of the degree trignometric functions COSD, SIND, TAND. |
| Copyright (C) 2020-2021 Free Software Foundation, Inc. |
| Contributed by Steven G. Kargl <kargl@gcc.gnu.org> |
| |
| This file is part of the GNU Fortran runtime library (libgfortran). |
| |
| Libgfortran is free software; you can redistribute it and/or |
| modify it under the terms of the GNU General Public |
| License as published by the Free Software Foundation; either |
| version 3 of the License, or (at your option) any later version. |
| |
| Libgfortran 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. |
| |
| Under Section 7 of GPL version 3, you are granted additional |
| permissions described in the GCC Runtime Library Exception, version |
| 3.1, as published by the Free Software Foundation. |
| |
| You should have received a copy of the GNU General Public License and |
| a copy of the GCC Runtime Library Exception along with this program; |
| see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #include "libgfortran.h" |
| |
| #include <math.h> |
| |
| /* Body of library functions which are cannot be implemented on the current |
| * platform because it lacks a capability, such as an underlying trigonometric |
| * function (sin, cos, tan) or C99 floating-point function (fabs, fmod). */ |
| #define STRINGIFY_EXPAND(x) #x |
| #define ERROR_RETURN(f, k, x) runtime_error (#f " is unavailable for" \ |
| " REAL(KIND=" STRINGIFY_EXPAND(k) ") because the system math library" \ |
| " lacks support for it"); \ |
| RETURN(x) |
| |
| /* |
| For real x, let {x}_P or x_P be the closest representible number in the |
| floating point representation which uses P binary bits of fractional |
| precision (with IEEE rounding semantics). |
| |
| Similarly, let f_P(x) be shorthand for {f(x)}_P. |
| |
| Let ulp_P(x) be the unit of least precision for x: in other words the |
| maximal value of |a_P - b_P| where a_P <= x <= b_P and a_P != b_P. |
| |
| Let x ~= y <-> | x - y | < ulp_P(x - y). |
| |
| Let deg(x) be the value of x radians in degrees. |
| |
| Values for each precision P were selected as follows. |
| |
| |
| COSD_SMALL = 2**{-N} such that for all x <= COSD_SMALL: |
| |
| * cos(deg(x)) ~= 1, or equivalently: |
| |
| | 1 - cos(deg(x)) | < ulp_P(1). |
| |
| Unfortunately for SIND (and therefore TAND) a similar relation is only |
| possible for REAL(4) and REAL(8). With REAL(10) and REAL(16), enough |
| precision is available such that sin_P(x) != x_P for some x less than any |
| value. (There are values where this equality holds, but the distance has |
| inflection points.) |
| |
| For REAL(4) and REAL(8), we can select SIND_SMALL such that: |
| |
| * sin(deg(x)) ~= deg(x), or equivalently: |
| |
| | deg(x) - sin(deg(x)) | < ulp_P(deg(x)). |
| |
| */ |
| |
| #ifdef HAVE_GFC_REAL_4 |
| |
| /* Build _gfortran_sind_r4, _gfortran_cosd_r4, and _gfortran_tand_r4 */ |
| |
| #define KIND 4 |
| #define TINY 0x1.p-100 /* ~= 7.889e-31 */ |
| #define COSD_SMALL 0x1.p-7 /* = 7.8125e-3 */ |
| #define SIND_SMALL 0x1.p-5 /* = 3.125e-2 */ |
| #define COSD30 8.66025388e-01 |
| #define PIO180H 1.74560547e-02 /* high 12 bits. */ |
| #define PIO180L -2.76216747e-06 /* Next 24 bits. */ |
| |
| #if defined(HAVE_FABSF) && defined(HAVE_FMODF) && defined(HAVE_COPYSIGNF) |
| |
| #ifdef HAVE_SINF |
| #define ENABLE_SIND |
| #endif |
| |
| #ifdef HAVE_COSF |
| #define ENABLE_COSD |
| #endif |
| |
| #ifdef HAVE_TANF |
| #define ENABLE_TAND |
| #endif |
| |
| #endif /* HAVE_FABSF && HAVE_FMODF && HAVE_COPYSIGNF */ |
| |
| #ifdef GFC_REAL_4_INFINITY |
| #define HAVE_INFINITY_KIND |
| #endif |
| |
| #include "trigd_lib.inc" |
| |
| #undef KIND |
| #undef TINY |
| #undef COSD_SMALL |
| #undef SIND_SMALL |
| #undef COSD30 |
| #undef PIO180H |
| #undef PIO180L |
| #undef ENABLE_SIND |
| #undef ENABLE_COSD |
| #undef ENABLE_TAND |
| #undef HAVE_INFINITY_KIND |
| |
| #endif /* HAVE_GFC_REAL_4... */ |
| |
| |
| #ifdef HAVE_GFC_REAL_8 |
| |
| /* Build _gfortran_sind_r8, _gfortran_cosd_r8, and _gfortran_tand_r8 */ |
| |
| #define KIND 8 |
| #define TINY 0x1.p-1000 /* ~= 9.33e-302 (min exp -1074) */ |
| #define COSD_SMALL 0x1.p-21 /* ~= 4.768e-7 */ |
| #define SIND_SMALL 0x1.p-19 /* ~= 9.537e-7 */ |
| #define COSD30 8.6602540378443860e-01 |
| #define PIO180H 1.7453283071517944e-02 /* high 21 bits. */ |
| #define PIO180L 9.4484253514332993e-09 /* Next 53 bits. */ |
| |
| #if defined(HAVE_FABS) && defined(HAVE_FMOD) && defined(HAVE_COPYSIGN) |
| |
| #ifdef HAVE_SIN |
| #define ENABLE_SIND |
| #endif |
| |
| #ifdef HAVE_COS |
| #define ENABLE_COSD |
| #endif |
| |
| #ifdef HAVE_TAN |
| #define ENABLE_TAND |
| #endif |
| |
| #endif /* HAVE_FABS && HAVE_FMOD && HAVE_COPYSIGN */ |
| |
| #ifdef GFC_REAL_8_INFINITY |
| #define HAVE_INFINITY_KIND |
| #endif |
| |
| #include "trigd_lib.inc" |
| |
| #undef KIND |
| #undef TINY |
| #undef COSD_SMALL |
| #undef SIND_SMALL |
| #undef COSD30 |
| #undef PIO180H |
| #undef PIO180L |
| #undef ENABLE_SIND |
| #undef ENABLE_COSD |
| #undef ENABLE_TAND |
| #undef HAVE_INFINITY_KIND |
| |
| #endif /* HAVE_GFC_REAL_8... */ |
| |
| |
| #ifdef HAVE_GFC_REAL_10 |
| |
| /* Build _gfortran_sind_r10, _gfortran_cosd_r10, and _gfortran_tand_r10 */ |
| |
| #define KIND 10 |
| #define TINY 0x1.p-16400 /* ~= 1.28e-4937 (min exp -16494) */ |
| #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */ |
| #undef SIND_SMALL /* not precise */ |
| #define COSD30 8.66025403784438646787e-01 |
| #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */ |
| #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */ |
| |
| #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL) |
| |
| #ifdef HAVE_SINL |
| #define ENABLE_SIND |
| #endif |
| |
| #ifdef HAVE_COSL |
| #define ENABLE_COSD |
| #endif |
| |
| #ifdef HAVE_TANL |
| #define ENABLE_TAND |
| #endif |
| |
| #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */ |
| |
| #ifdef GFC_REAL_10_INFINITY |
| #define HAVE_INFINITY_KIND |
| #endif |
| |
| #include "trigd_lib.inc" |
| |
| #undef KIND |
| #undef TINY |
| #undef COSD_SMALL |
| #undef SIND_SMALL |
| #undef COSD30 |
| #undef PIO180H |
| #undef PIO180L |
| #undef ENABLE_SIND |
| #undef ENABLE_COSD |
| #undef ENABLE_TAND |
| #undef HAVE_INFINITY_KIND |
| |
| #endif /* HAVE_GFC_REAL_10 */ |
| |
| |
| #ifdef HAVE_GFC_REAL_16 |
| |
| /* Build _gfortran_sind_r16, _gfortran_cosd_r16, and _gfortran_tand_r16 */ |
| |
| #define KIND 16 |
| #define TINY 0x1.p-16400 /* ~= 1.28e-4937 */ |
| #undef SIND_SMALL /* not precise */ |
| |
| #if GFC_REAL_16_DIGITS == 64 |
| /* 80 bit precision, use constants from REAL(10). */ |
| #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */ |
| #define COSD30 8.66025403784438646787e-01 |
| #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */ |
| #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */ |
| |
| #else |
| /* Proper float128 precision. */ |
| #define COSD_SMALL 0x1.p-51 /* ~= 4.441e-16 */ |
| #define COSD30 8.66025403784438646763723170752936183e-01 |
| #define PIO180H 1.74532925199433197605003442731685936e-02 |
| #define PIO180L -2.39912634365882824665106671063098954e-17 |
| #endif |
| |
| #ifdef GFC_REAL_16_IS_LONG_DOUBLE |
| |
| #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL) |
| |
| #ifdef HAVE_SINL |
| #define ENABLE_SIND |
| #endif |
| |
| #ifdef HAVE_COSL |
| #define ENABLE_COSD |
| #endif |
| |
| #ifdef HAVE_TANL |
| #define ENABLE_TAND |
| #endif |
| |
| #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */ |
| |
| #else |
| |
| /* libquadmath: HAVE_*Q are never defined. They must be available. */ |
| #define ENABLE_SIND |
| #define ENABLE_COSD |
| #define ENABLE_TAND |
| |
| #endif /* GFC_REAL_16_IS_LONG_DOUBLE */ |
| |
| #ifdef GFC_REAL_16_INFINITY |
| #define HAVE_INFINITY_KIND |
| #endif |
| |
| #include "trigd_lib.inc" |
| |
| #undef KIND |
| #undef TINY |
| #undef COSD_SMALL |
| #undef SIND_SMALL |
| #undef COSD30 |
| #undef PIO180H |
| #undef PIO180L |
| #undef ENABLE_SIND |
| #undef ENABLE_COSD |
| #undef ENABLE_TAND |
| #undef HAVE_INFINITY_KIND |
| |
| #endif /* HAVE_GFC_REAL_16 */ |