#ifndef __NPY_MATH_C99_H_ #define __NPY_MATH_C99_H_ #ifdef __cplusplus extern "C" { #endif #include #ifdef __SUNPRO_CC #include #endif #ifdef HAVE_NPY_CONFIG_H #include #endif #include /* By adding static inline specifiers to npy_math function definitions when appropriate, compiler is given the opportunity to optimize */ #if NPY_INLINE_MATH #define NPY_INPLACE NPY_INLINE static #else #define NPY_INPLACE #endif /* * NAN and INFINITY like macros (same behavior as glibc for NAN, same as C99 * for INFINITY) * * XXX: I should test whether INFINITY and NAN are available on the platform */ NPY_INLINE static float __npy_inff(void) { const union { npy_uint32 __i; float __f;} __bint = {0x7f800000UL}; return __bint.__f; } NPY_INLINE static float __npy_nanf(void) { const union { npy_uint32 __i; float __f;} __bint = {0x7fc00000UL}; return __bint.__f; } NPY_INLINE static float __npy_pzerof(void) { const union { npy_uint32 __i; float __f;} __bint = {0x00000000UL}; return __bint.__f; } NPY_INLINE static float __npy_nzerof(void) { const union { npy_uint32 __i; float __f;} __bint = {0x80000000UL}; return __bint.__f; } #define NPY_INFINITYF __npy_inff() #define NPY_NANF __npy_nanf() #define NPY_PZEROF __npy_pzerof() #define NPY_NZEROF __npy_nzerof() #define NPY_INFINITY ((npy_double)NPY_INFINITYF) #define NPY_NAN ((npy_double)NPY_NANF) #define NPY_PZERO ((npy_double)NPY_PZEROF) #define NPY_NZERO ((npy_double)NPY_NZEROF) #define NPY_INFINITYL ((npy_longdouble)NPY_INFINITYF) #define NPY_NANL ((npy_longdouble)NPY_NANF) #define NPY_PZEROL ((npy_longdouble)NPY_PZEROF) #define NPY_NZEROL ((npy_longdouble)NPY_NZEROF) /* * Useful constants */ #define NPY_E 2.718281828459045235360287471352662498 /* e */ #define NPY_LOG2E 1.442695040888963407359924681001892137 /* log_2 e */ #define NPY_LOG10E 0.434294481903251827651128918916605082 /* log_10 e */ #define NPY_LOGE2 0.693147180559945309417232121458176568 /* log_e 2 */ #define NPY_LOGE10 2.302585092994045684017991454684364208 /* log_e 10 */ #define NPY_PI 3.141592653589793238462643383279502884 /* pi */ #define NPY_PI_2 1.570796326794896619231321691639751442 /* pi/2 */ #define NPY_PI_4 0.785398163397448309615660845819875721 /* pi/4 */ #define NPY_1_PI 0.318309886183790671537767526745028724 /* 1/pi */ #define NPY_2_PI 0.636619772367581343075535053490057448 /* 2/pi */ #define NPY_EULER 0.577215664901532860606512090082402431 /* Euler constant */ #define NPY_SQRT2 1.414213562373095048801688724209698079 /* sqrt(2) */ #define NPY_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */ #define NPY_Ef 2.718281828459045235360287471352662498F /* e */ #define NPY_LOG2Ef 1.442695040888963407359924681001892137F /* log_2 e */ #define NPY_LOG10Ef 0.434294481903251827651128918916605082F /* log_10 e */ #define NPY_LOGE2f 0.693147180559945309417232121458176568F /* log_e 2 */ #define NPY_LOGE10f 2.302585092994045684017991454684364208F /* log_e 10 */ #define NPY_PIf 3.141592653589793238462643383279502884F /* pi */ #define NPY_PI_2f 1.570796326794896619231321691639751442F /* pi/2 */ #define NPY_PI_4f 0.785398163397448309615660845819875721F /* pi/4 */ #define NPY_1_PIf 0.318309886183790671537767526745028724F /* 1/pi */ #define NPY_2_PIf 0.636619772367581343075535053490057448F /* 2/pi */ #define NPY_EULERf 0.577215664901532860606512090082402431F /* Euler constant */ #define NPY_SQRT2f 1.414213562373095048801688724209698079F /* sqrt(2) */ #define NPY_SQRT1_2f 0.707106781186547524400844362104849039F /* 1/sqrt(2) */ #define NPY_El 2.718281828459045235360287471352662498L /* e */ #define NPY_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */ #define NPY_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */ #define NPY_LOGE2l 0.693147180559945309417232121458176568L /* log_e 2 */ #define NPY_LOGE10l 2.302585092994045684017991454684364208L /* log_e 10 */ #define NPY_PIl 3.141592653589793238462643383279502884L /* pi */ #define NPY_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */ #define NPY_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */ #define NPY_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */ #define NPY_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */ #define NPY_EULERl 0.577215664901532860606512090082402431L /* Euler constant */ #define NPY_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */ #define NPY_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */ /* * C99 double math funcs */ NPY_INPLACE double npy_sin(double x); NPY_INPLACE double npy_cos(double x); NPY_INPLACE double npy_tan(double x); NPY_INPLACE double npy_sinh(double x); NPY_INPLACE double npy_cosh(double x); NPY_INPLACE double npy_tanh(double x); NPY_INPLACE double npy_asin(double x); NPY_INPLACE double npy_acos(double x); NPY_INPLACE double npy_atan(double x); NPY_INPLACE double npy_log(double x); NPY_INPLACE double npy_log10(double x); NPY_INPLACE double npy_exp(double x); NPY_INPLACE double npy_sqrt(double x); NPY_INPLACE double npy_cbrt(double x); NPY_INPLACE double npy_fabs(double x); NPY_INPLACE double npy_ceil(double x); NPY_INPLACE double npy_fmod(double x, double y); NPY_INPLACE double npy_floor(double x); NPY_INPLACE double npy_expm1(double x); NPY_INPLACE double npy_log1p(double x); NPY_INPLACE double npy_hypot(double x, double y); NPY_INPLACE double npy_acosh(double x); NPY_INPLACE double npy_asinh(double xx); NPY_INPLACE double npy_atanh(double x); NPY_INPLACE double npy_rint(double x); NPY_INPLACE double npy_trunc(double x); NPY_INPLACE double npy_exp2(double x); NPY_INPLACE double npy_log2(double x); NPY_INPLACE double npy_atan2(double x, double y); NPY_INPLACE double npy_pow(double x, double y); NPY_INPLACE double npy_modf(double x, double* y); NPY_INPLACE double npy_frexp(double x, int* y); NPY_INPLACE double npy_ldexp(double n, int y); NPY_INPLACE double npy_copysign(double x, double y); double npy_nextafter(double x, double y); double npy_spacing(double x); /* * IEEE 754 fpu handling. Those are guaranteed to be macros */ /* use builtins to avoid function calls in tight loops * only available if npy_config.h is available (= numpys own build) */ #if HAVE___BUILTIN_ISNAN #define npy_isnan(x) __builtin_isnan(x) #else #ifndef NPY_HAVE_DECL_ISNAN #define npy_isnan(x) ((x) != (x)) #else #if defined(_MSC_VER) && (_MSC_VER < 1900) #define npy_isnan(x) _isnan((x)) #else #define npy_isnan(x) isnan(x) #endif #endif #endif /* only available if npy_config.h is available (= numpys own build) */ #if HAVE___BUILTIN_ISFINITE #define npy_isfinite(x) __builtin_isfinite(x) #else #ifndef NPY_HAVE_DECL_ISFINITE #ifdef _MSC_VER #define npy_isfinite(x) _finite((x)) #else #define npy_isfinite(x) !npy_isnan((x) + (-x)) #endif #else #define npy_isfinite(x) isfinite((x)) #endif #endif /* only available if npy_config.h is available (= numpys own build) */ #if HAVE___BUILTIN_ISINF #define npy_isinf(x) __builtin_isinf(x) #else #ifndef NPY_HAVE_DECL_ISINF #define npy_isinf(x) (!npy_isfinite(x) && !npy_isnan(x)) #else #if defined(_MSC_VER) && (_MSC_VER < 1900) #define npy_isinf(x) (!_finite((x)) && !_isnan((x))) #else #define npy_isinf(x) isinf((x)) #endif #endif #endif #ifndef NPY_HAVE_DECL_SIGNBIT int _npy_signbit_f(float x); int _npy_signbit_d(double x); int _npy_signbit_ld(long double x); #define npy_signbit(x) \ (sizeof (x) == sizeof (long double) ? _npy_signbit_ld (x) \ : sizeof (x) == sizeof (double) ? _npy_signbit_d (x) \ : _npy_signbit_f (x)) #else #define npy_signbit(x) signbit((x)) #endif /* * float C99 math functions */ NPY_INPLACE float npy_sinf(float x); NPY_INPLACE float npy_cosf(float x); NPY_INPLACE float npy_tanf(float x); NPY_INPLACE float npy_sinhf(float x); NPY_INPLACE float npy_coshf(float x); NPY_INPLACE float npy_tanhf(float x); NPY_INPLACE float npy_fabsf(float x); NPY_INPLACE float npy_floorf(float x); NPY_INPLACE float npy_ceilf(float x); NPY_INPLACE float npy_rintf(float x); NPY_INPLACE float npy_truncf(float x); NPY_INPLACE float npy_sqrtf(float x); NPY_INPLACE float npy_cbrtf(float x); NPY_INPLACE float npy_log10f(float x); NPY_INPLACE float npy_logf(float x); NPY_INPLACE float npy_expf(float x); NPY_INPLACE float npy_expm1f(float x); NPY_INPLACE float npy_asinf(float x); NPY_INPLACE float npy_acosf(float x); NPY_INPLACE float npy_atanf(float x); NPY_INPLACE float npy_asinhf(float x); NPY_INPLACE float npy_acoshf(float x); NPY_INPLACE float npy_atanhf(float x); NPY_INPLACE float npy_log1pf(float x); NPY_INPLACE float npy_exp2f(float x); NPY_INPLACE float npy_log2f(float x); NPY_INPLACE float npy_atan2f(float x, float y); NPY_INPLACE float npy_hypotf(float x, float y); NPY_INPLACE float npy_powf(float x, float y); NPY_INPLACE float npy_fmodf(float x, float y); NPY_INPLACE float npy_modff(float x, float* y); NPY_INPLACE float npy_frexpf(float x, int* y); NPY_INPLACE float npy_ldexpf(float x, int y); NPY_INPLACE float npy_copysignf(float x, float y); float npy_nextafterf(float x, float y); float npy_spacingf(float x); /* * long double C99 math functions */ NPY_INPLACE npy_longdouble npy_sinl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_cosl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_tanl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_sinhl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_coshl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_tanhl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_fabsl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_floorl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_ceill(npy_longdouble x); NPY_INPLACE npy_longdouble npy_rintl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_truncl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_sqrtl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_cbrtl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_log10l(npy_longdouble x); NPY_INPLACE npy_longdouble npy_logl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_expl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_expm1l(npy_longdouble x); NPY_INPLACE npy_longdouble npy_asinl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_acosl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_atanl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_asinhl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_acoshl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_atanhl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_log1pl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_exp2l(npy_longdouble x); NPY_INPLACE npy_longdouble npy_log2l(npy_longdouble x); NPY_INPLACE npy_longdouble npy_atan2l(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_hypotl(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_powl(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_fmodl(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_modfl(npy_longdouble x, npy_longdouble* y); NPY_INPLACE npy_longdouble npy_frexpl(npy_longdouble x, int* y); NPY_INPLACE npy_longdouble npy_ldexpl(npy_longdouble x, int y); NPY_INPLACE npy_longdouble npy_copysignl(npy_longdouble x, npy_longdouble y); npy_longdouble npy_nextafterl(npy_longdouble x, npy_longdouble y); npy_longdouble npy_spacingl(npy_longdouble x); /* * Non standard functions */ NPY_INPLACE double npy_deg2rad(double x); NPY_INPLACE double npy_rad2deg(double x); NPY_INPLACE double npy_logaddexp(double x, double y); NPY_INPLACE double npy_logaddexp2(double x, double y); NPY_INPLACE double npy_divmod(double x, double y, double *modulus); NPY_INPLACE double npy_heaviside(double x, double h0); NPY_INPLACE float npy_deg2radf(float x); NPY_INPLACE float npy_rad2degf(float x); NPY_INPLACE float npy_logaddexpf(float x, float y); NPY_INPLACE float npy_logaddexp2f(float x, float y); NPY_INPLACE float npy_divmodf(float x, float y, float *modulus); NPY_INPLACE float npy_heavisidef(float x, float h0); NPY_INPLACE npy_longdouble npy_deg2radl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_rad2degl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_logaddexpl(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_logaddexp2l(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_divmodl(npy_longdouble x, npy_longdouble y, npy_longdouble *modulus); NPY_INPLACE npy_longdouble npy_heavisidel(npy_longdouble x, npy_longdouble h0); #define npy_degrees npy_rad2deg #define npy_degreesf npy_rad2degf #define npy_degreesl npy_rad2degl #define npy_radians npy_deg2rad #define npy_radiansf npy_deg2radf #define npy_radiansl npy_deg2radl /* * Complex declarations */ /* * C99 specifies that complex numbers have the same representation as * an array of two elements, where the first element is the real part * and the second element is the imaginary part. */ #define __NPY_CPACK_IMP(x, y, type, ctype) \ union { \ ctype z; \ type a[2]; \ } z1;; \ \ z1.a[0] = (x); \ z1.a[1] = (y); \ \ return z1.z; static NPY_INLINE npy_cdouble npy_cpack(double x, double y) { __NPY_CPACK_IMP(x, y, double, npy_cdouble); } static NPY_INLINE npy_cfloat npy_cpackf(float x, float y) { __NPY_CPACK_IMP(x, y, float, npy_cfloat); } static NPY_INLINE npy_clongdouble npy_cpackl(npy_longdouble x, npy_longdouble y) { __NPY_CPACK_IMP(x, y, npy_longdouble, npy_clongdouble); } #undef __NPY_CPACK_IMP /* * Same remark as above, but in the other direction: extract first/second * member of complex number, assuming a C99-compatible representation * * Those are defineds as static inline, and such as a reasonable compiler would * most likely compile this to one or two instructions (on CISC at least) */ #define __NPY_CEXTRACT_IMP(z, index, type, ctype) \ union { \ ctype z; \ type a[2]; \ } __z_repr; \ __z_repr.z = z; \ \ return __z_repr.a[index]; static NPY_INLINE double npy_creal(npy_cdouble z) { __NPY_CEXTRACT_IMP(z, 0, double, npy_cdouble); } static NPY_INLINE double npy_cimag(npy_cdouble z) { __NPY_CEXTRACT_IMP(z, 1, double, npy_cdouble); } static NPY_INLINE float npy_crealf(npy_cfloat z) { __NPY_CEXTRACT_IMP(z, 0, float, npy_cfloat); } static NPY_INLINE float npy_cimagf(npy_cfloat z) { __NPY_CEXTRACT_IMP(z, 1, float, npy_cfloat); } static NPY_INLINE npy_longdouble npy_creall(npy_clongdouble z) { __NPY_CEXTRACT_IMP(z, 0, npy_longdouble, npy_clongdouble); } static NPY_INLINE npy_longdouble npy_cimagl(npy_clongdouble z) { __NPY_CEXTRACT_IMP(z, 1, npy_longdouble, npy_clongdouble); } #undef __NPY_CEXTRACT_IMP /* * Double precision complex functions */ double npy_cabs(npy_cdouble z); double npy_carg(npy_cdouble z); npy_cdouble npy_cexp(npy_cdouble z); npy_cdouble npy_clog(npy_cdouble z); npy_cdouble npy_cpow(npy_cdouble x, npy_cdouble y); npy_cdouble npy_csqrt(npy_cdouble z); npy_cdouble npy_ccos(npy_cdouble z); npy_cdouble npy_csin(npy_cdouble z); npy_cdouble npy_ctan(npy_cdouble z); npy_cdouble npy_ccosh(npy_cdouble z); npy_cdouble npy_csinh(npy_cdouble z); npy_cdouble npy_ctanh(npy_cdouble z); npy_cdouble npy_cacos(npy_cdouble z); npy_cdouble npy_casin(npy_cdouble z); npy_cdouble npy_catan(npy_cdouble z); npy_cdouble npy_cacosh(npy_cdouble z); npy_cdouble npy_casinh(npy_cdouble z); npy_cdouble npy_catanh(npy_cdouble z); /* * Single precision complex functions */ float npy_cabsf(npy_cfloat z); float npy_cargf(npy_cfloat z); npy_cfloat npy_cexpf(npy_cfloat z); npy_cfloat npy_clogf(npy_cfloat z); npy_cfloat npy_cpowf(npy_cfloat x, npy_cfloat y); npy_cfloat npy_csqrtf(npy_cfloat z); npy_cfloat npy_ccosf(npy_cfloat z); npy_cfloat npy_csinf(npy_cfloat z); npy_cfloat npy_ctanf(npy_cfloat z); npy_cfloat npy_ccoshf(npy_cfloat z); npy_cfloat npy_csinhf(npy_cfloat z); npy_cfloat npy_ctanhf(npy_cfloat z); npy_cfloat npy_cacosf(npy_cfloat z); npy_cfloat npy_casinf(npy_cfloat z); npy_cfloat npy_catanf(npy_cfloat z); npy_cfloat npy_cacoshf(npy_cfloat z); npy_cfloat npy_casinhf(npy_cfloat z); npy_cfloat npy_catanhf(npy_cfloat z); /* * Extended precision complex functions */ npy_longdouble npy_cabsl(npy_clongdouble z); npy_longdouble npy_cargl(npy_clongdouble z); npy_clongdouble npy_cexpl(npy_clongdouble z); npy_clongdouble npy_clogl(npy_clongdouble z); npy_clongdouble npy_cpowl(npy_clongdouble x, npy_clongdouble y); npy_clongdouble npy_csqrtl(npy_clongdouble z); npy_clongdouble npy_ccosl(npy_clongdouble z); npy_clongdouble npy_csinl(npy_clongdouble z); npy_clongdouble npy_ctanl(npy_clongdouble z); npy_clongdouble npy_ccoshl(npy_clongdouble z); npy_clongdouble npy_csinhl(npy_clongdouble z); npy_clongdouble npy_ctanhl(npy_clongdouble z); npy_clongdouble npy_cacosl(npy_clongdouble z); npy_clongdouble npy_casinl(npy_clongdouble z); npy_clongdouble npy_catanl(npy_clongdouble z); npy_clongdouble npy_cacoshl(npy_clongdouble z); npy_clongdouble npy_casinhl(npy_clongdouble z); npy_clongdouble npy_catanhl(npy_clongdouble z); /* * Functions that set the floating point error * status word. */ /* * platform-dependent code translates floating point * status to an integer sum of these values */ #define NPY_FPE_DIVIDEBYZERO 1 #define NPY_FPE_OVERFLOW 2 #define NPY_FPE_UNDERFLOW 4 #define NPY_FPE_INVALID 8 int npy_clear_floatstatus_barrier(char*); int npy_get_floatstatus_barrier(char*); /* * use caution with these - clang and gcc8.1 are known to reorder calls * to this form of the function which can defeat the check */ int npy_clear_floatstatus(void); int npy_get_floatstatus(void); void npy_set_floatstatus_divbyzero(void); void npy_set_floatstatus_overflow(void); void npy_set_floatstatus_underflow(void); void npy_set_floatstatus_invalid(void); #ifdef __cplusplus } #endif #if NPY_INLINE_MATH #include "npy_math_internal.h" #endif #endif