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- /* Implementation of the degree trignometric functions COSD, SIND, TAND.
- Copyright (C) 2020-2022 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 */
- #ifdef HAVE_GFC_REAL_17
- /* Build _gfortran_sind_r17, _gfortran_cosd_r17, and _gfortran_tand_r17 */
- #define KIND 17
- #define TINY 0x1.p-16400 /* ~= 1.28e-4937 */
- #undef SIND_SMALL /* not precise */
- /* 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
- /* libquadmath or glibc 2.32+: HAVE_*Q are never defined. They must be available. */
- #define ENABLE_SIND
- #define ENABLE_COSD
- #define ENABLE_TAND
- #ifdef GFC_REAL_17_INFINITY
- #define HAVE_INFINITY_KIND
- #endif
- #ifdef POWER_IEEE128
- #define COPYSIGN __copysignieee128
- #define FMOD __fmodieee128
- #define FABS __fabsieee128
- #define FMA __fmaieee128
- #define SIN __sinieee128
- #define COS __cosieee128
- #define TAN __tanieee128
- #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_17 */
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