1*0bfacb9bSmrg /* Implementation of the degree trignometric functions COSD, SIND, TAND. 2*0bfacb9bSmrg Copyright (C) 2020 Free Software Foundation, Inc. 3*0bfacb9bSmrg Contributed by Steven G. Kargl <kargl@gcc.gnu.org> 4*0bfacb9bSmrg 5*0bfacb9bSmrg This file is part of the GNU Fortran runtime library (libgfortran). 6*0bfacb9bSmrg 7*0bfacb9bSmrg Libgfortran is free software; you can redistribute it and/or 8*0bfacb9bSmrg modify it under the terms of the GNU General Public 9*0bfacb9bSmrg License as published by the Free Software Foundation; either 10*0bfacb9bSmrg version 3 of the License, or (at your option) any later version. 11*0bfacb9bSmrg 12*0bfacb9bSmrg Libgfortran is distributed in the hope that it will be useful, 13*0bfacb9bSmrg but WITHOUT ANY WARRANTY; without even the implied warranty of 14*0bfacb9bSmrg MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15*0bfacb9bSmrg GNU General Public License for more details. 16*0bfacb9bSmrg 17*0bfacb9bSmrg Under Section 7 of GPL version 3, you are granted additional 18*0bfacb9bSmrg permissions described in the GCC Runtime Library Exception, version 19*0bfacb9bSmrg 3.1, as published by the Free Software Foundation. 20*0bfacb9bSmrg 21*0bfacb9bSmrg You should have received a copy of the GNU General Public License and 22*0bfacb9bSmrg a copy of the GCC Runtime Library Exception along with this program; 23*0bfacb9bSmrg see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 24*0bfacb9bSmrg <http://www.gnu.org/licenses/>. */ 25*0bfacb9bSmrg 26*0bfacb9bSmrg #include "libgfortran.h" 27*0bfacb9bSmrg 28*0bfacb9bSmrg #include <math.h> 29*0bfacb9bSmrg 30*0bfacb9bSmrg /* Body of library functions which are cannot be implemented on the current 31*0bfacb9bSmrg * platform because it lacks a capability, such as an underlying trigonometric 32*0bfacb9bSmrg * function (sin, cos, tan) or C99 floating-point function (fabs, fmod). */ 33*0bfacb9bSmrg #define STRINGIFY_EXPAND(x) #x 34*0bfacb9bSmrg #define ERROR_RETURN(f, k, x) runtime_error (#f " is unavailable for" \ 35*0bfacb9bSmrg " REAL(KIND=" STRINGIFY_EXPAND(k) ") because the system math library" \ 36*0bfacb9bSmrg " lacks support for it"); \ 37*0bfacb9bSmrg RETURN(x) 38*0bfacb9bSmrg 39*0bfacb9bSmrg /* 40*0bfacb9bSmrg For real x, let {x}_P or x_P be the closest representible number in the 41*0bfacb9bSmrg floating point representation which uses P binary bits of fractional 42*0bfacb9bSmrg precision (with IEEE rounding semantics). 43*0bfacb9bSmrg 44*0bfacb9bSmrg Similarly, let f_P(x) be shorthand for {f(x)}_P. 45*0bfacb9bSmrg 46*0bfacb9bSmrg Let ulp_P(x) be the unit of least precision for x: in other words the 47*0bfacb9bSmrg maximal value of |a_P - b_P| where a_P <= x <= b_P and a_P != b_P. 48*0bfacb9bSmrg 49*0bfacb9bSmrg Let x ~= y <-> | x - y | < ulp_P(x - y). 50*0bfacb9bSmrg 51*0bfacb9bSmrg Let deg(x) be the value of x radians in degrees. 52*0bfacb9bSmrg 53*0bfacb9bSmrg Values for each precision P were selected as follows. 54*0bfacb9bSmrg 55*0bfacb9bSmrg 56*0bfacb9bSmrg COSD_SMALL = 2**{-N} such that for all x <= COSD_SMALL: 57*0bfacb9bSmrg 58*0bfacb9bSmrg * cos(deg(x)) ~= 1, or equivalently: 59*0bfacb9bSmrg 60*0bfacb9bSmrg | 1 - cos(deg(x)) | < ulp_P(1). 61*0bfacb9bSmrg 62*0bfacb9bSmrg Unfortunately for SIND (and therefore TAND) a similar relation is only 63*0bfacb9bSmrg possible for REAL(4) and REAL(8). With REAL(10) and REAL(16), enough 64*0bfacb9bSmrg precision is available such that sin_P(x) != x_P for some x less than any 65*0bfacb9bSmrg value. (There are values where this equality holds, but the distance has 66*0bfacb9bSmrg inflection points.) 67*0bfacb9bSmrg 68*0bfacb9bSmrg For REAL(4) and REAL(8), we can select SIND_SMALL such that: 69*0bfacb9bSmrg 70*0bfacb9bSmrg * sin(deg(x)) ~= deg(x), or equivalently: 71*0bfacb9bSmrg 72*0bfacb9bSmrg | deg(x) - sin(deg(x)) | < ulp_P(deg(x)). 73*0bfacb9bSmrg 74*0bfacb9bSmrg */ 75*0bfacb9bSmrg 76*0bfacb9bSmrg #ifdef HAVE_GFC_REAL_4 77*0bfacb9bSmrg 78*0bfacb9bSmrg /* Build _gfortran_sind_r4, _gfortran_cosd_r4, and _gfortran_tand_r4 */ 79*0bfacb9bSmrg 80*0bfacb9bSmrg #define KIND 4 81*0bfacb9bSmrg #define TINY 0x1.p-100 /* ~= 7.889e-31 */ 82*0bfacb9bSmrg #define COSD_SMALL 0x1.p-7 /* = 7.8125e-3 */ 83*0bfacb9bSmrg #define SIND_SMALL 0x1.p-5 /* = 3.125e-2 */ 84*0bfacb9bSmrg #define COSD30 8.66025388e-01 85*0bfacb9bSmrg #define PIO180H 1.74560547e-02 /* high 12 bits. */ 86*0bfacb9bSmrg #define PIO180L -2.76216747e-06 /* Next 24 bits. */ 87*0bfacb9bSmrg 88*0bfacb9bSmrg #if defined(HAVE_FABSF) && defined(HAVE_FMODF) && defined(HAVE_COPYSIGNF) 89*0bfacb9bSmrg 90*0bfacb9bSmrg #ifdef HAVE_SINF 91*0bfacb9bSmrg #define ENABLE_SIND 92*0bfacb9bSmrg #endif 93*0bfacb9bSmrg 94*0bfacb9bSmrg #ifdef HAVE_COSF 95*0bfacb9bSmrg #define ENABLE_COSD 96*0bfacb9bSmrg #endif 97*0bfacb9bSmrg 98*0bfacb9bSmrg #ifdef HAVE_TANF 99*0bfacb9bSmrg #define ENABLE_TAND 100*0bfacb9bSmrg #endif 101*0bfacb9bSmrg 102*0bfacb9bSmrg #endif /* HAVE_FABSF && HAVE_FMODF && HAVE_COPYSIGNF */ 103*0bfacb9bSmrg 104*0bfacb9bSmrg #ifdef GFC_REAL_4_INFINITY 105*0bfacb9bSmrg #define HAVE_INFINITY_KIND 106*0bfacb9bSmrg #endif 107*0bfacb9bSmrg 108*0bfacb9bSmrg #include "trigd_lib.inc" 109*0bfacb9bSmrg 110*0bfacb9bSmrg #undef KIND 111*0bfacb9bSmrg #undef TINY 112*0bfacb9bSmrg #undef COSD_SMALL 113*0bfacb9bSmrg #undef SIND_SMALL 114*0bfacb9bSmrg #undef COSD30 115*0bfacb9bSmrg #undef PIO180H 116*0bfacb9bSmrg #undef PIO180L 117*0bfacb9bSmrg #undef ENABLE_SIND 118*0bfacb9bSmrg #undef ENABLE_COSD 119*0bfacb9bSmrg #undef ENABLE_TAND 120*0bfacb9bSmrg #undef HAVE_INFINITY_KIND 121*0bfacb9bSmrg 122*0bfacb9bSmrg #endif /* HAVE_GFC_REAL_4... */ 123*0bfacb9bSmrg 124*0bfacb9bSmrg 125*0bfacb9bSmrg #ifdef HAVE_GFC_REAL_8 126*0bfacb9bSmrg 127*0bfacb9bSmrg /* Build _gfortran_sind_r8, _gfortran_cosd_r8, and _gfortran_tand_r8 */ 128*0bfacb9bSmrg 129*0bfacb9bSmrg #define KIND 8 130*0bfacb9bSmrg #define TINY 0x1.p-1000 /* ~= 9.33e-302 (min exp -1074) */ 131*0bfacb9bSmrg #define COSD_SMALL 0x1.p-21 /* ~= 4.768e-7 */ 132*0bfacb9bSmrg #define SIND_SMALL 0x1.p-19 /* ~= 9.537e-7 */ 133*0bfacb9bSmrg #define COSD30 8.6602540378443860e-01 134*0bfacb9bSmrg #define PIO180H 1.7453283071517944e-02 /* high 21 bits. */ 135*0bfacb9bSmrg #define PIO180L 9.4484253514332993e-09 /* Next 53 bits. */ 136*0bfacb9bSmrg 137*0bfacb9bSmrg #if defined(HAVE_FABS) && defined(HAVE_FMOD) && defined(HAVE_COPYSIGN) 138*0bfacb9bSmrg 139*0bfacb9bSmrg #ifdef HAVE_SIN 140*0bfacb9bSmrg #define ENABLE_SIND 141*0bfacb9bSmrg #endif 142*0bfacb9bSmrg 143*0bfacb9bSmrg #ifdef HAVE_COS 144*0bfacb9bSmrg #define ENABLE_COSD 145*0bfacb9bSmrg #endif 146*0bfacb9bSmrg 147*0bfacb9bSmrg #ifdef HAVE_TAN 148*0bfacb9bSmrg #define ENABLE_TAND 149*0bfacb9bSmrg #endif 150*0bfacb9bSmrg 151*0bfacb9bSmrg #endif /* HAVE_FABS && HAVE_FMOD && HAVE_COPYSIGN */ 152*0bfacb9bSmrg 153*0bfacb9bSmrg #ifdef GFC_REAL_8_INFINITY 154*0bfacb9bSmrg #define HAVE_INFINITY_KIND 155*0bfacb9bSmrg #endif 156*0bfacb9bSmrg 157*0bfacb9bSmrg #include "trigd_lib.inc" 158*0bfacb9bSmrg 159*0bfacb9bSmrg #undef KIND 160*0bfacb9bSmrg #undef TINY 161*0bfacb9bSmrg #undef COSD_SMALL 162*0bfacb9bSmrg #undef SIND_SMALL 163*0bfacb9bSmrg #undef COSD30 164*0bfacb9bSmrg #undef PIO180H 165*0bfacb9bSmrg #undef PIO180L 166*0bfacb9bSmrg #undef ENABLE_SIND 167*0bfacb9bSmrg #undef ENABLE_COSD 168*0bfacb9bSmrg #undef ENABLE_TAND 169*0bfacb9bSmrg #undef HAVE_INFINITY_KIND 170*0bfacb9bSmrg 171*0bfacb9bSmrg #endif /* HAVE_GFC_REAL_8... */ 172*0bfacb9bSmrg 173*0bfacb9bSmrg 174*0bfacb9bSmrg #ifdef HAVE_GFC_REAL_10 175*0bfacb9bSmrg 176*0bfacb9bSmrg /* Build _gfortran_sind_r10, _gfortran_cosd_r10, and _gfortran_tand_r10 */ 177*0bfacb9bSmrg 178*0bfacb9bSmrg #define KIND 10 179*0bfacb9bSmrg #define TINY 0x1.p-16400 /* ~= 1.28e-4937 (min exp -16494) */ 180*0bfacb9bSmrg #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */ 181*0bfacb9bSmrg #undef SIND_SMALL /* not precise */ 182*0bfacb9bSmrg #define COSD30 8.66025403784438646787e-01 183*0bfacb9bSmrg #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */ 184*0bfacb9bSmrg #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */ 185*0bfacb9bSmrg 186*0bfacb9bSmrg #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL) 187*0bfacb9bSmrg 188*0bfacb9bSmrg #ifdef HAVE_SINL 189*0bfacb9bSmrg #define ENABLE_SIND 190*0bfacb9bSmrg #endif 191*0bfacb9bSmrg 192*0bfacb9bSmrg #ifdef HAVE_COSL 193*0bfacb9bSmrg #define ENABLE_COSD 194*0bfacb9bSmrg #endif 195*0bfacb9bSmrg 196*0bfacb9bSmrg #ifdef HAVE_TANL 197*0bfacb9bSmrg #define ENABLE_TAND 198*0bfacb9bSmrg #endif 199*0bfacb9bSmrg 200*0bfacb9bSmrg #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */ 201*0bfacb9bSmrg 202*0bfacb9bSmrg #ifdef GFC_REAL_10_INFINITY 203*0bfacb9bSmrg #define HAVE_INFINITY_KIND 204*0bfacb9bSmrg #endif 205*0bfacb9bSmrg 206*0bfacb9bSmrg #include "trigd_lib.inc" 207*0bfacb9bSmrg 208*0bfacb9bSmrg #undef KIND 209*0bfacb9bSmrg #undef TINY 210*0bfacb9bSmrg #undef COSD_SMALL 211*0bfacb9bSmrg #undef SIND_SMALL 212*0bfacb9bSmrg #undef COSD30 213*0bfacb9bSmrg #undef PIO180H 214*0bfacb9bSmrg #undef PIO180L 215*0bfacb9bSmrg #undef ENABLE_SIND 216*0bfacb9bSmrg #undef ENABLE_COSD 217*0bfacb9bSmrg #undef ENABLE_TAND 218*0bfacb9bSmrg #undef HAVE_INFINITY_KIND 219*0bfacb9bSmrg 220*0bfacb9bSmrg #endif /* HAVE_GFC_REAL_10 */ 221*0bfacb9bSmrg 222*0bfacb9bSmrg 223*0bfacb9bSmrg #ifdef HAVE_GFC_REAL_16 224*0bfacb9bSmrg 225*0bfacb9bSmrg /* Build _gfortran_sind_r16, _gfortran_cosd_r16, and _gfortran_tand_r16 */ 226*0bfacb9bSmrg 227*0bfacb9bSmrg #define KIND 16 228*0bfacb9bSmrg #define TINY 0x1.p-16400 /* ~= 1.28e-4937 */ 229*0bfacb9bSmrg #undef SIND_SMALL /* not precise */ 230*0bfacb9bSmrg 231*0bfacb9bSmrg #if GFC_REAL_16_DIGITS == 64 232*0bfacb9bSmrg /* 80 bit precision, use constants from REAL(10). */ 233*0bfacb9bSmrg #define COSD_SMALL 0x1.p-26 /* ~= 1.490e-8 */ 234*0bfacb9bSmrg #define COSD30 8.66025403784438646787e-01 235*0bfacb9bSmrg #define PIO180H 1.74532925229868851602e-02 /* high 32 bits */ 236*0bfacb9bSmrg #define PIO180L -3.04358939097084072823e-12 /* Next 64 bits */ 237*0bfacb9bSmrg 238*0bfacb9bSmrg #else 239*0bfacb9bSmrg /* Proper float128 precision. */ 240*0bfacb9bSmrg #define COSD_SMALL 0x1.p-51 /* ~= 4.441e-16 */ 241*0bfacb9bSmrg #define COSD30 8.66025403784438646763723170752936183e-01 242*0bfacb9bSmrg #define PIO180H 1.74532925199433197605003442731685936e-02 243*0bfacb9bSmrg #define PIO180L -2.39912634365882824665106671063098954e-17 244*0bfacb9bSmrg #endif 245*0bfacb9bSmrg 246*0bfacb9bSmrg #ifdef GFC_REAL_16_IS_LONG_DOUBLE 247*0bfacb9bSmrg 248*0bfacb9bSmrg #if defined(HAVE_FABSL) && defined(HAVE_FMODL) && defined(HAVE_COPYSIGNL) 249*0bfacb9bSmrg 250*0bfacb9bSmrg #ifdef HAVE_SINL 251*0bfacb9bSmrg #define ENABLE_SIND 252*0bfacb9bSmrg #endif 253*0bfacb9bSmrg 254*0bfacb9bSmrg #ifdef HAVE_COSL 255*0bfacb9bSmrg #define ENABLE_COSD 256*0bfacb9bSmrg #endif 257*0bfacb9bSmrg 258*0bfacb9bSmrg #ifdef HAVE_TANL 259*0bfacb9bSmrg #define ENABLE_TAND 260*0bfacb9bSmrg #endif 261*0bfacb9bSmrg 262*0bfacb9bSmrg #endif /* HAVE_FABSL && HAVE_FMODL && HAVE_COPYSIGNL */ 263*0bfacb9bSmrg 264*0bfacb9bSmrg #else 265*0bfacb9bSmrg 266*0bfacb9bSmrg /* libquadmath: HAVE_*Q are never defined. They must be available. */ 267*0bfacb9bSmrg #define ENABLE_SIND 268*0bfacb9bSmrg #define ENABLE_COSD 269*0bfacb9bSmrg #define ENABLE_TAND 270*0bfacb9bSmrg 271*0bfacb9bSmrg #endif /* GFC_REAL_16_IS_LONG_DOUBLE */ 272*0bfacb9bSmrg 273*0bfacb9bSmrg #ifdef GFC_REAL_16_INFINITY 274*0bfacb9bSmrg #define HAVE_INFINITY_KIND 275*0bfacb9bSmrg #endif 276*0bfacb9bSmrg 277*0bfacb9bSmrg #include "trigd_lib.inc" 278*0bfacb9bSmrg 279*0bfacb9bSmrg #undef KIND 280*0bfacb9bSmrg #undef TINY 281*0bfacb9bSmrg #undef COSD_SMALL 282*0bfacb9bSmrg #undef SIND_SMALL 283*0bfacb9bSmrg #undef COSD30 284*0bfacb9bSmrg #undef PIO180H 285*0bfacb9bSmrg #undef PIO180L 286*0bfacb9bSmrg #undef ENABLE_SIND 287*0bfacb9bSmrg #undef ENABLE_COSD 288*0bfacb9bSmrg #undef ENABLE_TAND 289*0bfacb9bSmrg #undef HAVE_INFINITY_KIND 290*0bfacb9bSmrg 291*0bfacb9bSmrg #endif /* HAVE_GFC_REAL_16 */ 292