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npy_math.h
#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_ #define NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_ #include <numpy/npy_common.h> #include <math.h> /* 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 static inline #else #define NPY_INPLACE #endif #ifdef __cplusplus extern "C" { #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 */ static inline float __npy_inff(void) { const union { npy_uint32 __i; float __f;} __bint = {0x7f800000UL}; return __bint.__f; } static inline float __npy_nanf(void) { const union { npy_uint32 __i; float __f;} __bint = {0x7fc00000UL}; return __bint.__f; } static inline float __npy_pzerof(void) { const union { npy_uint32 __i; float __f;} __bint = {0x00000000UL}; return __bint.__f; } static inline 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) */ /* * Integer functions. */ NPY_INPLACE npy_uint npy_gcdu(npy_uint a, npy_uint b); NPY_INPLACE npy_uint npy_lcmu(npy_uint a, npy_uint b); NPY_INPLACE npy_ulong npy_gcdul(npy_ulong a, npy_ulong b); NPY_INPLACE npy_ulong npy_lcmul(npy_ulong a, npy_ulong b); NPY_INPLACE npy_ulonglong npy_gcdull(npy_ulonglong a, npy_ulonglong b); NPY_INPLACE npy_ulonglong npy_lcmull(npy_ulonglong a, npy_ulonglong b); NPY_INPLACE npy_int npy_gcd(npy_int a, npy_int b); NPY_INPLACE npy_int npy_lcm(npy_int a, npy_int b); NPY_INPLACE npy_long npy_gcdl(npy_long a, npy_long b); NPY_INPLACE npy_long npy_lcml(npy_long a, npy_long b); NPY_INPLACE npy_longlong npy_gcdll(npy_longlong a, npy_longlong b); NPY_INPLACE npy_longlong npy_lcmll(npy_longlong a, npy_longlong b); NPY_INPLACE npy_ubyte npy_rshiftuhh(npy_ubyte a, npy_ubyte b); NPY_INPLACE npy_ubyte npy_lshiftuhh(npy_ubyte a, npy_ubyte b); NPY_INPLACE npy_ushort npy_rshiftuh(npy_ushort a, npy_ushort b); NPY_INPLACE npy_ushort npy_lshiftuh(npy_ushort a, npy_ushort b); NPY_INPLACE npy_uint npy_rshiftu(npy_uint a, npy_uint b); NPY_INPLACE npy_uint npy_lshiftu(npy_uint a, npy_uint b); NPY_INPLACE npy_ulong npy_rshiftul(npy_ulong a, npy_ulong b); NPY_INPLACE npy_ulong npy_lshiftul(npy_ulong a, npy_ulong b); NPY_INPLACE npy_ulonglong npy_rshiftull(npy_ulonglong a, npy_ulonglong b); NPY_INPLACE npy_ulonglong npy_lshiftull(npy_ulonglong a, npy_ulonglong b); NPY_INPLACE npy_byte npy_rshifthh(npy_byte a, npy_byte b); NPY_INPLACE npy_byte npy_lshifthh(npy_byte a, npy_byte b); NPY_INPLACE npy_short npy_rshifth(npy_short a, npy_short b); NPY_INPLACE npy_short npy_lshifth(npy_short a, npy_short b); NPY_INPLACE npy_int npy_rshift(npy_int a, npy_int b); NPY_INPLACE npy_int npy_lshift(npy_int a, npy_int b); NPY_INPLACE npy_long npy_rshiftl(npy_long a, npy_long b); NPY_INPLACE npy_long npy_lshiftl(npy_long a, npy_long b); NPY_INPLACE npy_longlong npy_rshiftll(npy_longlong a, npy_longlong b); NPY_INPLACE npy_longlong npy_lshiftll(npy_longlong a, npy_longlong b); NPY_INPLACE uint8_t npy_popcountuhh(npy_ubyte a); NPY_INPLACE uint8_t npy_popcountuh(npy_ushort a); NPY_INPLACE uint8_t npy_popcountu(npy_uint a); NPY_INPLACE uint8_t npy_popcountul(npy_ulong a); NPY_INPLACE uint8_t npy_popcountull(npy_ulonglong a); NPY_INPLACE uint8_t npy_popcounthh(npy_byte a); NPY_INPLACE uint8_t npy_popcounth(npy_short a); NPY_INPLACE uint8_t npy_popcount(npy_int a); NPY_INPLACE uint8_t npy_popcountl(npy_long a); NPY_INPLACE uint8_t npy_popcountll(npy_longlong a); /* * C99 double math funcs that need fixups or are blocklist-able */ 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_hypot(double x, double y); NPY_INPLACE double npy_log2(double x); NPY_INPLACE double npy_atan2(double x, double y); /* Mandatory C99 double math funcs, no blocklisting or fixups */ /* defined for legacy reasons, should be deprecated at some point */ #define npy_sinh sinh #define npy_cosh cosh #define npy_tanh tanh #define npy_asin asin #define npy_acos acos #define npy_atan atan #define npy_log log #define npy_log10 log10 #define npy_cbrt cbrt #define npy_fabs fabs #define npy_ceil ceil #define npy_fmod fmod #define npy_floor floor #define npy_expm1 expm1 #define npy_log1p log1p #define npy_acosh acosh #define npy_asinh asinh #define npy_atanh atanh #define npy_rint rint #define npy_trunc trunc #define npy_exp2 exp2 #define npy_frexp frexp #define npy_ldexp ldexp #define npy_copysign copysign #define npy_exp exp #define npy_sqrt sqrt #define npy_pow pow #define npy_modf modf #define npy_nextafter nextafter double npy_spacing(double x); /* * IEEE 754 fpu handling */ /* use builtins to avoid function calls in tight loops * only available if npy_config.h is available (= numpys own build) */ #ifdef HAVE___BUILTIN_ISNAN #define npy_isnan(x) __builtin_isnan(x) #else #define npy_isnan(x) isnan(x) #endif /* only available if npy_config.h is available (= numpys own build) */ #ifdef HAVE___BUILTIN_ISFINITE #define npy_isfinite(x) __builtin_isfinite(x) #else #define npy_isfinite(x) isfinite((x)) #endif /* only available if npy_config.h is available (= numpys own build) */ #ifdef HAVE___BUILTIN_ISINF #define npy_isinf(x) __builtin_isinf(x) #else #define npy_isinf(x) isinf((x)) #endif #define npy_signbit(x) signbit((x)) /* * float C99 math funcs that need fixups or are blocklist-able */ 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_expf(float x); NPY_INPLACE float npy_sqrtf(float x); NPY_INPLACE float npy_hypotf(float x, float y); NPY_INPLACE float npy_log2f(float x); NPY_INPLACE float npy_atan2f(float x, float y); NPY_INPLACE float npy_powf(float x, float y); NPY_INPLACE float npy_modff(float x, float* y); /* Mandatory C99 float math funcs, no blocklisting or fixups */ /* defined for legacy reasons, should be deprecated at some point */ #define npy_sinhf sinhf #define npy_coshf coshf #define npy_tanhf tanhf #define npy_asinf asinf #define npy_acosf acosf #define npy_atanf atanf #define npy_logf logf #define npy_log10f log10f #define npy_cbrtf cbrtf #define npy_fabsf fabsf #define npy_ceilf ceilf #define npy_fmodf fmodf #define npy_floorf floorf #define npy_expm1f expm1f #define npy_log1pf log1pf #define npy_asinhf asinhf #define npy_acoshf acoshf #define npy_atanhf atanhf #define npy_rintf rintf #define npy_truncf truncf #define npy_exp2f exp2f #define npy_frexpf frexpf #define npy_ldexpf ldexpf #define npy_copysignf copysignf #define npy_nextafterf nextafterf float npy_spacingf(float x); /* * long double C99 double math funcs that need fixups or are blocklist-able */ 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_expl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_sqrtl(npy_longdouble x); NPY_INPLACE npy_longdouble npy_hypotl(npy_longdouble x, npy_longdouble y); 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_powl(npy_longdouble x, npy_longdouble y); NPY_INPLACE npy_longdouble npy_modfl(npy_longdouble x, npy_longdouble* y); /* Mandatory C99 double math funcs, no blocklisting or fixups */ /* defined for legacy reasons, should be deprecated at some point */ #define npy_sinhl sinhl #define npy_coshl coshl #define npy_tanhl tanhl #define npy_fabsl fabsl #define npy_floorl floorl #define npy_ceill ceill #define npy_rintl rintl #define npy_truncl truncl #define npy_cbrtl cbrtl #define npy_log10l log10l #define npy_logl logl #define npy_expm1l expm1l #define npy_asinl asinl #define npy_acosl acosl #define npy_atanl atanl #define npy_asinhl asinhl #define npy_acoshl acoshl #define npy_atanhl atanhl #define npy_log1pl log1pl #define npy_exp2l exp2l #define npy_fmodl fmodl #define npy_frexpl frexpl #define npy_ldexpl ldexpl #define npy_copysignl copysignl #define npy_nextafterl nextafterl 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 inline npy_cdouble npy_cpack(double x, double y) { __NPY_CPACK_IMP(x, y, double, npy_cdouble); } static inline npy_cfloat npy_cpackf(float x, float y) { __NPY_CPACK_IMP(x, y, float, npy_cfloat); } static 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 inline double npy_creal(npy_cdouble z) { __NPY_CEXTRACT_IMP(z, 0, double, npy_cdouble); } static inline double npy_cimag(npy_cdouble z) { __NPY_CEXTRACT_IMP(z, 1, double, npy_cdouble); } static inline float npy_crealf(npy_cfloat z) { __NPY_CEXTRACT_IMP(z, 0, float, npy_cfloat); } static inline float npy_cimagf(npy_cfloat z) { __NPY_CEXTRACT_IMP(z, 1, float, npy_cfloat); } static inline npy_longdouble npy_creall(npy_clongdouble z) { __NPY_CEXTRACT_IMP(z, 0, npy_longdouble, npy_clongdouble); } static 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. The _barrier * form of the call is preferable, where the argument is * (char*)&local_variable */ 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 /* NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_ */
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