numpy
2.0.0
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00001 #ifndef __NPY_MATH_C99_H_ 00002 #define __NPY_MATH_C99_H_ 00003 00004 #ifdef __cplusplus 00005 extern "C" { 00006 #endif 00007 00008 #include <math.h> 00009 #ifdef __SUNPRO_CC 00010 #include <sunmath.h> 00011 #endif 00012 #ifdef HAVE_NPY_CONFIG_H 00013 #include <npy_config.h> 00014 #endif 00015 #include <numpy/npy_common.h> 00016 00017 00018 /* 00019 * NAN and INFINITY like macros (same behavior as glibc for NAN, same as C99 00020 * for INFINITY) 00021 * 00022 * XXX: I should test whether INFINITY and NAN are available on the platform 00023 */ 00024 NPY_INLINE static float __npy_inff(void) 00025 { 00026 const union { npy_uint32 __i; float __f;} __bint = {0x7f800000UL}; 00027 return __bint.__f; 00028 } 00029 00030 NPY_INLINE static float __npy_nanf(void) 00031 { 00032 const union { npy_uint32 __i; float __f;} __bint = {0x7fc00000UL}; 00033 return __bint.__f; 00034 } 00035 00036 NPY_INLINE static float __npy_pzerof(void) 00037 { 00038 const union { npy_uint32 __i; float __f;} __bint = {0x00000000UL}; 00039 return __bint.__f; 00040 } 00041 00042 NPY_INLINE static float __npy_nzerof(void) 00043 { 00044 const union { npy_uint32 __i; float __f;} __bint = {0x80000000UL}; 00045 return __bint.__f; 00046 } 00047 00048 #define NPY_INFINITYF __npy_inff() 00049 #define NPY_NANF __npy_nanf() 00050 #define NPY_PZEROF __npy_pzerof() 00051 #define NPY_NZEROF __npy_nzerof() 00052 00053 #define NPY_INFINITY ((npy_double)NPY_INFINITYF) 00054 #define NPY_NAN ((npy_double)NPY_NANF) 00055 #define NPY_PZERO ((npy_double)NPY_PZEROF) 00056 #define NPY_NZERO ((npy_double)NPY_NZEROF) 00057 00058 #define NPY_INFINITYL ((npy_longdouble)NPY_INFINITYF) 00059 #define NPY_NANL ((npy_longdouble)NPY_NANF) 00060 #define NPY_PZEROL ((npy_longdouble)NPY_PZEROF) 00061 #define NPY_NZEROL ((npy_longdouble)NPY_NZEROF) 00062 00063 /* 00064 * Useful constants 00065 */ 00066 #define NPY_E 2.718281828459045235360287471352662498 /* e */ 00067 #define NPY_LOG2E 1.442695040888963407359924681001892137 /* log_2 e */ 00068 #define NPY_LOG10E 0.434294481903251827651128918916605082 /* log_10 e */ 00069 #define NPY_LOGE2 0.693147180559945309417232121458176568 /* log_e 2 */ 00070 #define NPY_LOGE10 2.302585092994045684017991454684364208 /* log_e 10 */ 00071 #define NPY_PI 3.141592653589793238462643383279502884 /* pi */ 00072 #define NPY_PI_2 1.570796326794896619231321691639751442 /* pi/2 */ 00073 #define NPY_PI_4 0.785398163397448309615660845819875721 /* pi/4 */ 00074 #define NPY_1_PI 0.318309886183790671537767526745028724 /* 1/pi */ 00075 #define NPY_2_PI 0.636619772367581343075535053490057448 /* 2/pi */ 00076 #define NPY_EULER 0.577215664901532860606512090082402431 /* Euler constant */ 00077 #define NPY_SQRT2 1.414213562373095048801688724209698079 /* sqrt(2) */ 00078 #define NPY_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */ 00079 00080 #define NPY_Ef 2.718281828459045235360287471352662498F /* e */ 00081 #define NPY_LOG2Ef 1.442695040888963407359924681001892137F /* log_2 e */ 00082 #define NPY_LOG10Ef 0.434294481903251827651128918916605082F /* log_10 e */ 00083 #define NPY_LOGE2f 0.693147180559945309417232121458176568F /* log_e 2 */ 00084 #define NPY_LOGE10f 2.302585092994045684017991454684364208F /* log_e 10 */ 00085 #define NPY_PIf 3.141592653589793238462643383279502884F /* pi */ 00086 #define NPY_PI_2f 1.570796326794896619231321691639751442F /* pi/2 */ 00087 #define NPY_PI_4f 0.785398163397448309615660845819875721F /* pi/4 */ 00088 #define NPY_1_PIf 0.318309886183790671537767526745028724F /* 1/pi */ 00089 #define NPY_2_PIf 0.636619772367581343075535053490057448F /* 2/pi */ 00090 #define NPY_EULERf 0.577215664901532860606512090082402431F /* Euler constant */ 00091 #define NPY_SQRT2f 1.414213562373095048801688724209698079F /* sqrt(2) */ 00092 #define NPY_SQRT1_2f 0.707106781186547524400844362104849039F /* 1/sqrt(2) */ 00093 00094 #define NPY_El 2.718281828459045235360287471352662498L /* e */ 00095 #define NPY_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */ 00096 #define NPY_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */ 00097 #define NPY_LOGE2l 0.693147180559945309417232121458176568L /* log_e 2 */ 00098 #define NPY_LOGE10l 2.302585092994045684017991454684364208L /* log_e 10 */ 00099 #define NPY_PIl 3.141592653589793238462643383279502884L /* pi */ 00100 #define NPY_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */ 00101 #define NPY_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */ 00102 #define NPY_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */ 00103 #define NPY_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */ 00104 #define NPY_EULERl 0.577215664901532860606512090082402431L /* Euler constant */ 00105 #define NPY_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */ 00106 #define NPY_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */ 00107 00108 /* 00109 * C99 double math funcs 00110 */ 00111 double npy_sin(double x); 00112 double npy_cos(double x); 00113 double npy_tan(double x); 00114 double npy_sinh(double x); 00115 double npy_cosh(double x); 00116 double npy_tanh(double x); 00117 00118 double npy_asin(double x); 00119 double npy_acos(double x); 00120 double npy_atan(double x); 00121 00122 double npy_log(double x); 00123 double npy_log10(double x); 00124 double npy_exp(double x); 00125 double npy_sqrt(double x); 00126 double npy_cbrt(double x); 00127 00128 double npy_fabs(double x); 00129 double npy_ceil(double x); 00130 double npy_fmod(double x, double y); 00131 double npy_floor(double x); 00132 00133 double npy_expm1(double x); 00134 double npy_log1p(double x); 00135 double npy_hypot(double x, double y); 00136 double npy_acosh(double x); 00137 double npy_asinh(double xx); 00138 double npy_atanh(double x); 00139 double npy_rint(double x); 00140 double npy_trunc(double x); 00141 double npy_exp2(double x); 00142 double npy_log2(double x); 00143 00144 double npy_atan2(double x, double y); 00145 double npy_pow(double x, double y); 00146 double npy_modf(double x, double* y); 00147 double npy_frexp(double x, int* y); 00148 double npy_ldexp(double n, int y); 00149 00150 double npy_copysign(double x, double y); 00151 double npy_nextafter(double x, double y); 00152 double npy_spacing(double x); 00153 00154 /* 00155 * IEEE 754 fpu handling. Those are guaranteed to be macros 00156 */ 00157 00158 /* use builtins to avoid function calls in tight loops 00159 * only available if npy_config.h is available (= numpys own build) */ 00160 #if HAVE___BUILTIN_ISNAN 00161 #define npy_isnan(x) __builtin_isnan(x) 00162 #else 00163 #ifndef NPY_HAVE_DECL_ISNAN 00164 #define npy_isnan(x) ((x) != (x)) 00165 #else 00166 #if defined(_MSC_VER) && (_MSC_VER < 1900) 00167 #define npy_isnan(x) _isnan((x)) 00168 #else 00169 #define npy_isnan(x) isnan(x) 00170 #endif 00171 #endif 00172 #endif 00173 00174 00175 /* only available if npy_config.h is available (= numpys own build) */ 00176 #if HAVE___BUILTIN_ISFINITE 00177 #define npy_isfinite(x) __builtin_isfinite(x) 00178 #else 00179 #ifndef NPY_HAVE_DECL_ISFINITE 00180 #ifdef _MSC_VER 00181 #define npy_isfinite(x) _finite((x)) 00182 #else 00183 #define npy_isfinite(x) !npy_isnan((x) + (-x)) 00184 #endif 00185 #else 00186 #define npy_isfinite(x) isfinite((x)) 00187 #endif 00188 #endif 00189 00190 /* only available if npy_config.h is available (= numpys own build) */ 00191 #if HAVE___BUILTIN_ISINF 00192 #define npy_isinf(x) __builtin_isinf(x) 00193 #else 00194 #ifndef NPY_HAVE_DECL_ISINF 00195 #define npy_isinf(x) (!npy_isfinite(x) && !npy_isnan(x)) 00196 #else 00197 #if defined(_MSC_VER) && (_MSC_VER < 1900) 00198 #define npy_isinf(x) (!_finite((x)) && !_isnan((x))) 00199 #else 00200 #define npy_isinf(x) isinf((x)) 00201 #endif 00202 #endif 00203 #endif 00204 00205 #ifndef NPY_HAVE_DECL_SIGNBIT 00206 int _npy_signbit_f(float x); 00207 int _npy_signbit_d(double x); 00208 int _npy_signbit_ld(long double x); 00209 #define npy_signbit(x) \ 00210 (sizeof (x) == sizeof (long double) ? _npy_signbit_ld (x) \ 00211 : sizeof (x) == sizeof (double) ? _npy_signbit_d (x) \ 00212 : _npy_signbit_f (x)) 00213 #else 00214 #define npy_signbit(x) signbit((x)) 00215 #endif 00216 00217 /* 00218 * float C99 math functions 00219 */ 00220 00221 float npy_sinf(float x); 00222 float npy_cosf(float x); 00223 float npy_tanf(float x); 00224 float npy_sinhf(float x); 00225 float npy_coshf(float x); 00226 float npy_tanhf(float x); 00227 float npy_fabsf(float x); 00228 float npy_floorf(float x); 00229 float npy_ceilf(float x); 00230 float npy_rintf(float x); 00231 float npy_truncf(float x); 00232 float npy_sqrtf(float x); 00233 float npy_cbrtf(float x); 00234 float npy_log10f(float x); 00235 float npy_logf(float x); 00236 float npy_expf(float x); 00237 float npy_expm1f(float x); 00238 float npy_asinf(float x); 00239 float npy_acosf(float x); 00240 float npy_atanf(float x); 00241 float npy_asinhf(float x); 00242 float npy_acoshf(float x); 00243 float npy_atanhf(float x); 00244 float npy_log1pf(float x); 00245 float npy_exp2f(float x); 00246 float npy_log2f(float x); 00247 00248 float npy_atan2f(float x, float y); 00249 float npy_hypotf(float x, float y); 00250 float npy_powf(float x, float y); 00251 float npy_fmodf(float x, float y); 00252 00253 float npy_modff(float x, float* y); 00254 float npy_frexpf(float x, int* y); 00255 float npy_ldexpf(float x, int y); 00256 00257 float npy_copysignf(float x, float y); 00258 float npy_nextafterf(float x, float y); 00259 float npy_spacingf(float x); 00260 00261 /* 00262 * long double C99 math functions 00263 */ 00264 00265 npy_longdouble npy_sinl(npy_longdouble x); 00266 npy_longdouble npy_cosl(npy_longdouble x); 00267 npy_longdouble npy_tanl(npy_longdouble x); 00268 npy_longdouble npy_sinhl(npy_longdouble x); 00269 npy_longdouble npy_coshl(npy_longdouble x); 00270 npy_longdouble npy_tanhl(npy_longdouble x); 00271 npy_longdouble npy_fabsl(npy_longdouble x); 00272 npy_longdouble npy_floorl(npy_longdouble x); 00273 npy_longdouble npy_ceill(npy_longdouble x); 00274 npy_longdouble npy_rintl(npy_longdouble x); 00275 npy_longdouble npy_truncl(npy_longdouble x); 00276 npy_longdouble npy_sqrtl(npy_longdouble x); 00277 npy_longdouble npy_cbrtl(npy_longdouble x); 00278 npy_longdouble npy_log10l(npy_longdouble x); 00279 npy_longdouble npy_logl(npy_longdouble x); 00280 npy_longdouble npy_expl(npy_longdouble x); 00281 npy_longdouble npy_expm1l(npy_longdouble x); 00282 npy_longdouble npy_asinl(npy_longdouble x); 00283 npy_longdouble npy_acosl(npy_longdouble x); 00284 npy_longdouble npy_atanl(npy_longdouble x); 00285 npy_longdouble npy_asinhl(npy_longdouble x); 00286 npy_longdouble npy_acoshl(npy_longdouble x); 00287 npy_longdouble npy_atanhl(npy_longdouble x); 00288 npy_longdouble npy_log1pl(npy_longdouble x); 00289 npy_longdouble npy_exp2l(npy_longdouble x); 00290 npy_longdouble npy_log2l(npy_longdouble x); 00291 00292 npy_longdouble npy_atan2l(npy_longdouble x, npy_longdouble y); 00293 npy_longdouble npy_hypotl(npy_longdouble x, npy_longdouble y); 00294 npy_longdouble npy_powl(npy_longdouble x, npy_longdouble y); 00295 npy_longdouble npy_fmodl(npy_longdouble x, npy_longdouble y); 00296 00297 npy_longdouble npy_modfl(npy_longdouble x, npy_longdouble* y); 00298 npy_longdouble npy_frexpl(npy_longdouble x, int* y); 00299 npy_longdouble npy_ldexpl(npy_longdouble x, int y); 00300 00301 npy_longdouble npy_copysignl(npy_longdouble x, npy_longdouble y); 00302 npy_longdouble npy_nextafterl(npy_longdouble x, npy_longdouble y); 00303 npy_longdouble npy_spacingl(npy_longdouble x); 00304 00305 /* 00306 * Non standard functions 00307 */ 00308 double npy_deg2rad(double x); 00309 double npy_rad2deg(double x); 00310 double npy_logaddexp(double x, double y); 00311 double npy_logaddexp2(double x, double y); 00312 double npy_divmod(double x, double y, double *modulus); 00313 00314 float npy_deg2radf(float x); 00315 float npy_rad2degf(float x); 00316 float npy_logaddexpf(float x, float y); 00317 float npy_logaddexp2f(float x, float y); 00318 float npy_divmodf(float x, float y, float *modulus); 00319 00320 npy_longdouble npy_deg2radl(npy_longdouble x); 00321 npy_longdouble npy_rad2degl(npy_longdouble x); 00322 npy_longdouble npy_logaddexpl(npy_longdouble x, npy_longdouble y); 00323 npy_longdouble npy_logaddexp2l(npy_longdouble x, npy_longdouble y); 00324 npy_longdouble npy_divmodl(npy_longdouble x, npy_longdouble y, 00325 npy_longdouble *modulus); 00326 00327 #define npy_degrees npy_rad2deg 00328 #define npy_degreesf npy_rad2degf 00329 #define npy_degreesl npy_rad2degl 00330 00331 #define npy_radians npy_deg2rad 00332 #define npy_radiansf npy_deg2radf 00333 #define npy_radiansl npy_deg2radl 00334 00335 /* 00336 * Complex declarations 00337 */ 00338 00339 /* 00340 * C99 specifies that complex numbers have the same representation as 00341 * an array of two elements, where the first element is the real part 00342 * and the second element is the imaginary part. 00343 */ 00344 #define __NPY_CPACK_IMP(x, y, type, ctype) \ 00345 union { \ 00346 ctype z; \ 00347 type a[2]; \ 00348 } z1;; \ 00349 \ 00350 z1.a[0] = (x); \ 00351 z1.a[1] = (y); \ 00352 \ 00353 return z1.z; 00354 00355 static NPY_INLINE npy_cdouble npy_cpack(double x, double y) 00356 { 00357 __NPY_CPACK_IMP(x, y, double, npy_cdouble); 00358 } 00359 00360 static NPY_INLINE npy_cfloat npy_cpackf(float x, float y) 00361 { 00362 __NPY_CPACK_IMP(x, y, float, npy_cfloat); 00363 } 00364 00365 static NPY_INLINE npy_clongdouble npy_cpackl(npy_longdouble x, npy_longdouble y) 00366 { 00367 __NPY_CPACK_IMP(x, y, npy_longdouble, npy_clongdouble); 00368 } 00369 #undef __NPY_CPACK_IMP 00370 00371 /* 00372 * Same remark as above, but in the other direction: extract first/second 00373 * member of complex number, assuming a C99-compatible representation 00374 * 00375 * Those are defineds as static inline, and such as a reasonable compiler would 00376 * most likely compile this to one or two instructions (on CISC at least) 00377 */ 00378 #define __NPY_CEXTRACT_IMP(z, index, type, ctype) \ 00379 union { \ 00380 ctype z; \ 00381 type a[2]; \ 00382 } __z_repr; \ 00383 __z_repr.z = z; \ 00384 \ 00385 return __z_repr.a[index]; 00386 00387 static NPY_INLINE double npy_creal(npy_cdouble z) 00388 { 00389 __NPY_CEXTRACT_IMP(z, 0, double, npy_cdouble); 00390 } 00391 00392 static NPY_INLINE double npy_cimag(npy_cdouble z) 00393 { 00394 __NPY_CEXTRACT_IMP(z, 1, double, npy_cdouble); 00395 } 00396 00397 static NPY_INLINE float npy_crealf(npy_cfloat z) 00398 { 00399 __NPY_CEXTRACT_IMP(z, 0, float, npy_cfloat); 00400 } 00401 00402 static NPY_INLINE float npy_cimagf(npy_cfloat z) 00403 { 00404 __NPY_CEXTRACT_IMP(z, 1, float, npy_cfloat); 00405 } 00406 00407 static NPY_INLINE npy_longdouble npy_creall(npy_clongdouble z) 00408 { 00409 __NPY_CEXTRACT_IMP(z, 0, npy_longdouble, npy_clongdouble); 00410 } 00411 00412 static NPY_INLINE npy_longdouble npy_cimagl(npy_clongdouble z) 00413 { 00414 __NPY_CEXTRACT_IMP(z, 1, npy_longdouble, npy_clongdouble); 00415 } 00416 #undef __NPY_CEXTRACT_IMP 00417 00418 /* 00419 * Double precision complex functions 00420 */ 00421 double npy_cabs(npy_cdouble z); 00422 double npy_carg(npy_cdouble z); 00423 00424 npy_cdouble npy_cexp(npy_cdouble z); 00425 npy_cdouble npy_clog(npy_cdouble z); 00426 npy_cdouble npy_cpow(npy_cdouble x, npy_cdouble y); 00427 00428 npy_cdouble npy_csqrt(npy_cdouble z); 00429 00430 npy_cdouble npy_ccos(npy_cdouble z); 00431 npy_cdouble npy_csin(npy_cdouble z); 00432 npy_cdouble npy_ctan(npy_cdouble z); 00433 00434 npy_cdouble npy_ccosh(npy_cdouble z); 00435 npy_cdouble npy_csinh(npy_cdouble z); 00436 npy_cdouble npy_ctanh(npy_cdouble z); 00437 00438 npy_cdouble npy_cacos(npy_cdouble z); 00439 npy_cdouble npy_casin(npy_cdouble z); 00440 npy_cdouble npy_catan(npy_cdouble z); 00441 00442 npy_cdouble npy_cacosh(npy_cdouble z); 00443 npy_cdouble npy_casinh(npy_cdouble z); 00444 npy_cdouble npy_catanh(npy_cdouble z); 00445 00446 /* 00447 * Single precision complex functions 00448 */ 00449 float npy_cabsf(npy_cfloat z); 00450 float npy_cargf(npy_cfloat z); 00451 00452 npy_cfloat npy_cexpf(npy_cfloat z); 00453 npy_cfloat npy_clogf(npy_cfloat z); 00454 npy_cfloat npy_cpowf(npy_cfloat x, npy_cfloat y); 00455 00456 npy_cfloat npy_csqrtf(npy_cfloat z); 00457 00458 npy_cfloat npy_ccosf(npy_cfloat z); 00459 npy_cfloat npy_csinf(npy_cfloat z); 00460 npy_cfloat npy_ctanf(npy_cfloat z); 00461 00462 npy_cfloat npy_ccoshf(npy_cfloat z); 00463 npy_cfloat npy_csinhf(npy_cfloat z); 00464 npy_cfloat npy_ctanhf(npy_cfloat z); 00465 00466 npy_cfloat npy_cacosf(npy_cfloat z); 00467 npy_cfloat npy_casinf(npy_cfloat z); 00468 npy_cfloat npy_catanf(npy_cfloat z); 00469 00470 npy_cfloat npy_cacoshf(npy_cfloat z); 00471 npy_cfloat npy_casinhf(npy_cfloat z); 00472 npy_cfloat npy_catanhf(npy_cfloat z); 00473 00474 00475 /* 00476 * Extended precision complex functions 00477 */ 00478 npy_longdouble npy_cabsl(npy_clongdouble z); 00479 npy_longdouble npy_cargl(npy_clongdouble z); 00480 00481 npy_clongdouble npy_cexpl(npy_clongdouble z); 00482 npy_clongdouble npy_clogl(npy_clongdouble z); 00483 npy_clongdouble npy_cpowl(npy_clongdouble x, npy_clongdouble y); 00484 00485 npy_clongdouble npy_csqrtl(npy_clongdouble z); 00486 00487 npy_clongdouble npy_ccosl(npy_clongdouble z); 00488 npy_clongdouble npy_csinl(npy_clongdouble z); 00489 npy_clongdouble npy_ctanl(npy_clongdouble z); 00490 00491 npy_clongdouble npy_ccoshl(npy_clongdouble z); 00492 npy_clongdouble npy_csinhl(npy_clongdouble z); 00493 npy_clongdouble npy_ctanhl(npy_clongdouble z); 00494 00495 npy_clongdouble npy_cacosl(npy_clongdouble z); 00496 npy_clongdouble npy_casinl(npy_clongdouble z); 00497 npy_clongdouble npy_catanl(npy_clongdouble z); 00498 00499 npy_clongdouble npy_cacoshl(npy_clongdouble z); 00500 npy_clongdouble npy_casinhl(npy_clongdouble z); 00501 npy_clongdouble npy_catanhl(npy_clongdouble z); 00502 00503 00504 /* 00505 * Functions that set the floating point error 00506 * status word. 00507 */ 00508 00509 /* 00510 * platform-dependent code translates floating point 00511 * status to an integer sum of these values 00512 */ 00513 #define NPY_FPE_DIVIDEBYZERO 1 00514 #define NPY_FPE_OVERFLOW 2 00515 #define NPY_FPE_UNDERFLOW 4 00516 #define NPY_FPE_INVALID 8 00517 00518 int npy_get_floatstatus(void); 00519 int npy_clear_floatstatus(void); 00520 void npy_set_floatstatus_divbyzero(void); 00521 void npy_set_floatstatus_overflow(void); 00522 void npy_set_floatstatus_underflow(void); 00523 void npy_set_floatstatus_invalid(void); 00524 00525 #ifdef __cplusplus 00526 } 00527 #endif 00528 00529 #endif