/* Implementation of the degree trignometric functions COSD, SIND, TAND. Copyright (C) 2020 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 */