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| 1 #ifndef _TGMATH_H |
| 2 #define _TGMATH_H |
| 3 |
| 4 /* |
| 5 the return types are only correct with gcc (__GNUC__) |
| 6 otherwise they are long double or long double complex |
| 7 |
| 8 the long double version of a function is never chosen when |
| 9 sizeof(double) == sizeof(long double) |
| 10 (but the return type is set correctly with gcc) |
| 11 */ |
| 12 |
| 13 #include <math.h> |
| 14 #include <complex.h> |
| 15 |
| 16 #define __IS_FP(x) (sizeof((x)+1ULL) == sizeof((x)+1.0f)) |
| 17 #define __IS_CX(x) (__IS_FP(x) && sizeof(x) == sizeof((x)+I)) |
| 18 #define __IS_REAL(x) (__IS_FP(x) && 2*sizeof(x) == sizeof((x)+I)) |
| 19 |
| 20 #define __FLT(x) (__IS_REAL(x) && sizeof(x) == sizeof(float)) |
| 21 #define __LDBL(x) (__IS_REAL(x) && sizeof(x) == sizeof(long double) && sizeof(lo
ng double) != sizeof(double)) |
| 22 |
| 23 #define __FLTCX(x) (__IS_CX(x) && sizeof(x) == sizeof(float complex)) |
| 24 #define __DBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(double complex)) |
| 25 #define __LDBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(long double complex) && s
izeof(long double) != sizeof(double)) |
| 26 |
| 27 /* return type */ |
| 28 |
| 29 #ifdef __GNUC__ |
| 30 /* |
| 31 the result must be casted to the right type |
| 32 (otherwise the result type is determined by the conversion |
| 33 rules applied to all the function return types so it is long |
| 34 double or long double complex except for integral functions) |
| 35 |
| 36 this cannot be done in c99, so the typeof gcc extension is |
| 37 used and that the type of ?: depends on wether an operand is |
| 38 a null pointer constant or not |
| 39 (in c11 _Generic can be used) |
| 40 |
| 41 the c arguments below must be integer constant expressions |
| 42 so they can be in null pointer constants |
| 43 (__IS_FP above was carefully chosen this way) |
| 44 */ |
| 45 /* if c then t else void */ |
| 46 #define __type1(c,t) __typeof__(*(0?(t*)0:(void*)!(c))) |
| 47 /* if c then t1 else t2 */ |
| 48 #define __type2(c,t1,t2) __typeof__(*(0?(__type1(c,t1)*)0:(__type1(!(c),t2)*)0)) |
| 49 /* cast to double when x is integral, otherwise use typeof(x) */ |
| 50 #define __RETCAST(x) ( \ |
| 51 __type2(__IS_FP(x), __typeof__(x), double)) |
| 52 /* 2 args case, should work for complex types (cpow) */ |
| 53 #define __RETCAST_2(x, y) ( \ |
| 54 __type2(__IS_FP(x) && __IS_FP(y), \ |
| 55 __typeof__((x)+(y)), \ |
| 56 __typeof__((x)+(y)+1.0))) |
| 57 /* 3 args case (fma only) */ |
| 58 #define __RETCAST_3(x, y, z) ( \ |
| 59 __type2(__IS_FP(x) && __IS_FP(y) && __IS_FP(z), \ |
| 60 __typeof__((x)+(y)+(z)), \ |
| 61 __typeof__((x)+(y)+(z)+1.0))) |
| 62 /* drop complex from the type of x */ |
| 63 /* TODO: wrong when sizeof(long double)==sizeof(double) */ |
| 64 #define __RETCAST_REAL(x) ( \ |
| 65 __type2(__IS_FP(x) && sizeof((x)+I) == sizeof(float complex), float, \ |
| 66 __type2(sizeof((x)+1.0+I) == sizeof(double complex), double, \ |
| 67 long double))) |
| 68 /* add complex to the type of x */ |
| 69 #define __RETCAST_CX(x) (__typeof__(__RETCAST(x)0+I)) |
| 70 #else |
| 71 #define __RETCAST(x) |
| 72 #define __RETCAST_2(x, y) |
| 73 #define __RETCAST_3(x, y, z) |
| 74 #define __RETCAST_REAL(x) |
| 75 #define __RETCAST_CX(x) |
| 76 #endif |
| 77 |
| 78 /* function selection */ |
| 79 |
| 80 #define __tg_real_nocast(fun, x) ( \ |
| 81 __FLT(x) ? fun ## f (x) : \ |
| 82 __LDBL(x) ? fun ## l (x) : \ |
| 83 fun(x) ) |
| 84 |
| 85 #define __tg_real(fun, x) (__RETCAST(x)__tg_real_nocast(fun, x)) |
| 86 |
| 87 #define __tg_real_2_1(fun, x, y) (__RETCAST(x)( \ |
| 88 __FLT(x) ? fun ## f (x, y) : \ |
| 89 __LDBL(x) ? fun ## l (x, y) : \ |
| 90 fun(x, y) )) |
| 91 |
| 92 #define __tg_real_2(fun, x, y) (__RETCAST_2(x, y)( \ |
| 93 __FLT(x) && __FLT(y) ? fun ## f (x, y) : \ |
| 94 __LDBL((x)+(y)) ? fun ## l (x, y) : \ |
| 95 fun(x, y) )) |
| 96 |
| 97 #define __tg_complex(fun, x) (__RETCAST_CX(x)( \ |
| 98 __FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \ |
| 99 __LDBLCX((x)+I) ? fun ## l (x) : \ |
| 100 fun(x) )) |
| 101 |
| 102 #define __tg_complex_retreal(fun, x) (__RETCAST_REAL(x)( \ |
| 103 __FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \ |
| 104 __LDBLCX((x)+I) ? fun ## l (x) : \ |
| 105 fun(x) )) |
| 106 |
| 107 #define __tg_real_complex(fun, x) (__RETCAST(x)( \ |
| 108 __FLTCX(x) ? c ## fun ## f (x) : \ |
| 109 __DBLCX(x) ? c ## fun (x) : \ |
| 110 __LDBLCX(x) ? c ## fun ## l (x) : \ |
| 111 __FLT(x) ? fun ## f (x) : \ |
| 112 __LDBL(x) ? fun ## l (x) : \ |
| 113 fun(x) )) |
| 114 |
| 115 /* special cases */ |
| 116 |
| 117 #define __tg_real_remquo(x, y, z) (__RETCAST_2(x, y)( \ |
| 118 __FLT(x) && __FLT(y) ? remquof(x, y, z) : \ |
| 119 __LDBL((x)+(y)) ? remquol(x, y, z) : \ |
| 120 remquo(x, y, z) )) |
| 121 |
| 122 #define __tg_real_fma(x, y, z) (__RETCAST_3(x, y, z)( \ |
| 123 __FLT(x) && __FLT(y) && __FLT(z) ? fmaf(x, y, z) : \ |
| 124 __LDBL((x)+(y)+(z)) ? fmal(x, y, z) : \ |
| 125 fma(x, y, z) )) |
| 126 |
| 127 #define __tg_real_complex_pow(x, y) (__RETCAST_2(x, y)( \ |
| 128 __FLTCX((x)+(y)) && __IS_FP(x) && __IS_FP(y) ? cpowf(x, y) : \ |
| 129 __FLTCX((x)+(y)) ? cpow(x, y) : \ |
| 130 __DBLCX((x)+(y)) ? cpow(x, y) : \ |
| 131 __LDBLCX((x)+(y)) ? cpowl(x, y) : \ |
| 132 __FLT(x) && __FLT(y) ? powf(x, y) : \ |
| 133 __LDBL((x)+(y)) ? powl(x, y) : \ |
| 134 pow(x, y) )) |
| 135 |
| 136 #define __tg_real_complex_fabs(x) (__RETCAST_REAL(x)( \ |
| 137 __FLTCX(x) ? cabsf(x) : \ |
| 138 __DBLCX(x) ? cabs(x) : \ |
| 139 __LDBLCX(x) ? cabsl(x) : \ |
| 140 __FLT(x) ? fabsf(x) : \ |
| 141 __LDBL(x) ? fabsl(x) : \ |
| 142 fabs(x) )) |
| 143 |
| 144 /* suppress any macros in math.h or complex.h */ |
| 145 |
| 146 #undef acos |
| 147 #undef acosh |
| 148 #undef asin |
| 149 #undef asinh |
| 150 #undef atan |
| 151 #undef atan2 |
| 152 #undef atanh |
| 153 #undef carg |
| 154 #undef cbrt |
| 155 #undef ceil |
| 156 #undef cimag |
| 157 #undef conj |
| 158 #undef copysign |
| 159 #undef cos |
| 160 #undef cosh |
| 161 #undef cproj |
| 162 #undef creal |
| 163 #undef erf |
| 164 #undef erfc |
| 165 #undef exp |
| 166 #undef exp2 |
| 167 #undef expm1 |
| 168 #undef fabs |
| 169 #undef fdim |
| 170 #undef floor |
| 171 #undef fma |
| 172 #undef fmax |
| 173 #undef fmin |
| 174 #undef fmod |
| 175 #undef frexp |
| 176 #undef hypot |
| 177 #undef ilogb |
| 178 #undef ldexp |
| 179 #undef lgamma |
| 180 #undef llrint |
| 181 #undef llround |
| 182 #undef log |
| 183 #undef log10 |
| 184 #undef log1p |
| 185 #undef log2 |
| 186 #undef logb |
| 187 #undef lrint |
| 188 #undef lround |
| 189 #undef nearbyint |
| 190 #undef nextafter |
| 191 #undef nexttoward |
| 192 #undef pow |
| 193 #undef remainder |
| 194 #undef remquo |
| 195 #undef rint |
| 196 #undef round |
| 197 #undef scalbln |
| 198 #undef scalbn |
| 199 #undef sin |
| 200 #undef sinh |
| 201 #undef sqrt |
| 202 #undef tan |
| 203 #undef tanh |
| 204 #undef tgamma |
| 205 #undef trunc |
| 206 |
| 207 /* tg functions */ |
| 208 |
| 209 #define acos(x) __tg_real_complex(acos, (x)) |
| 210 #define acosh(x) __tg_real_complex(acosh, (x)) |
| 211 #define asin(x) __tg_real_complex(asin, (x)) |
| 212 #define asinh(x) __tg_real_complex(asinh, (x)) |
| 213 #define atan(x) __tg_real_complex(atan, (x)) |
| 214 #define atan2(x,y) __tg_real_2(atan2, (x), (y)) |
| 215 #define atanh(x) __tg_real_complex(atanh, (x)) |
| 216 #define carg(x) __tg_complex_retreal(carg, (x)) |
| 217 #define cbrt(x) __tg_real(cbrt, (x)) |
| 218 #define ceil(x) __tg_real(ceil, (x)) |
| 219 #define cimag(x) __tg_complex_retreal(cimag, (x)) |
| 220 #define conj(x) __tg_complex(conj, (x)) |
| 221 #define copysign(x,y) __tg_real_2(copysign, (x), (y)) |
| 222 #define cos(x) __tg_real_complex(cos, (x)) |
| 223 #define cosh(x) __tg_real_complex(cosh, (x)) |
| 224 #define cproj(x) __tg_complex(cproj, (x)) |
| 225 #define creal(x) __tg_complex_retreal(creal, (x)) |
| 226 #define erf(x) __tg_real(erf, (x)) |
| 227 #define erfc(x) __tg_real(erfc, (x)) |
| 228 #define exp(x) __tg_real_complex(exp, (x)) |
| 229 #define exp2(x) __tg_real(exp2, (x)) |
| 230 #define expm1(x) __tg_real(expm1, (x)) |
| 231 #define fabs(x) __tg_real_complex_fabs(x) |
| 232 #define fdim(x,y) __tg_real_2(fdim, (x), (y)) |
| 233 #define floor(x) __tg_real(floor, (x)) |
| 234 #define fma(x,y,z) __tg_real_fma((x), (y), (z)) |
| 235 #define fmax(x,y) __tg_real_2(fmax, (x), (y)) |
| 236 #define fmin(x,y) __tg_real_2(fmin, (x), (y)) |
| 237 #define fmod(x,y) __tg_real_2(fmod, (x), (y)) |
| 238 #define frexp(x,y) __tg_real_2_1(frexp, (x), (y)) |
| 239 #define hypot(x,y) __tg_real_2(hypot, (x), (y)) |
| 240 #define ilogb(x) __tg_real_nocast(ilogb, (x)) |
| 241 #define ldexp(x,y) __tg_real_2_1(ldexp, (x), (y)) |
| 242 #define lgamma(x) __tg_real(lgamma, (x)) |
| 243 #define llrint(x) __tg_real_nocast(llrint, (x)) |
| 244 #define llround(x) __tg_real_nocast(llround, (x)) |
| 245 #define log(x) __tg_real_complex(log, (x)) |
| 246 #define log10(x) __tg_real(log10, (x)) |
| 247 #define log1p(x) __tg_real(log1p, (x)) |
| 248 #define log2(x) __tg_real(log2, (x)) |
| 249 #define logb(x) __tg_real(logb, (x)) |
| 250 #define lrint(x) __tg_real_nocast(lrint, (x)) |
| 251 #define lround(x) __tg_real_nocast(lround, (x)) |
| 252 #define nearbyint(x) __tg_real(nearbyint, (x)) |
| 253 #define nextafter(x,y) __tg_real_2(nextafter, (x), (y)) |
| 254 #define nexttoward(x,y) __tg_real_2(nexttoward, (x), (y)) |
| 255 #define pow(x,y) __tg_real_complex_pow((x), (y)) |
| 256 #define remainder(x,y) __tg_real_2(remainder, (x), (y)) |
| 257 #define remquo(x,y,z) __tg_real_remquo((x), (y), (z)) |
| 258 #define rint(x) __tg_real(rint, (x)) |
| 259 #define round(x) __tg_real(round, (x)) |
| 260 #define scalbln(x,y) __tg_real_2_1(scalbln, (x), (y)) |
| 261 #define scalbn(x,y) __tg_real_2_1(scalbn, (x), (y)) |
| 262 #define sin(x) __tg_real_complex(sin, (x)) |
| 263 #define sinh(x) __tg_real_complex(sinh, (x)) |
| 264 #define sqrt(x) __tg_real_complex(sqrt, (x)) |
| 265 #define tan(x) __tg_real_complex(tan, (x)) |
| 266 #define tanh(x) __tg_real_complex(tanh, (x)) |
| 267 #define tgamma(x) __tg_real(tgamma, (x)) |
| 268 #define trunc(x) __tg_real(trunc, (x)) |
| 269 |
| 270 #endif |
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