/* Implementation of the degree trignometric functions COSD, SIND, TAND. Copyright (C) 2020-2022 Free Software Foundation, Inc. Contributed by Steven G. Kargl 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 . */ #include "libgfortran.h" #include /* 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 */