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/* 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 */
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