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+
+cdef extern from "<cmath>" namespace "std" nogil:
+ # all C99 functions
+ float acos(float x) except +
+ double acos(double x) except +
+ long double acos(long double x) except +
+ float acosf(float x) except +
+ long double acosl(long double x) except +
+
+ float asin(float x) except +
+ double asin(double x) except +
+ long double asin(long double x) except +
+ float asinf(float x) except +
+ long double asinl(long double x) except +
+
+ float atan(float x) except +
+ double atan(double x) except +
+ long double atan(long double x) except +
+ float atanf(float x) except +
+ long double atanl(long double x) except +
+
+ float atan2(float y, float x) except +
+ double atan2(double y, double x) except +
+ long double atan2(long double y, long double x) except +
+ float atan2f(float y, float x) except +
+ long double atan2l(long double y, long double x) except +
+
+ float cos(float x) except +
+ double cos(double x) except +
+ long double cos(long double x) except +
+ float cosf(float x) except +
+ long double cosl(long double x) except +
+
+ float sin(float x) except +
+ double sin(double x) except +
+ long double sin(long double x) except +
+ float sinf(float x) except +
+ long double sinl(long double x) except +
+
+ float tan(float x) except +
+ double tan(double x) except +
+ long double tan(long double x) except +
+ float tanf(float x) except +
+ long double tanl(long double x) except +
+
+ float acosh(float x) except +
+ double acosh(double x) except +
+ long double acosh(long double x) except +
+ float acoshf(float x) except +
+ long double acoshl(long double x) except +
+
+ float asinh(float x) except +
+ double asinh(double x) except +
+ long double asinh(long double x) except +
+ float asinhf(float x) except +
+ long double asinhl(long double x) except +
+
+ float atanh(float x) except +
+ double atanh(double x) except +
+ long double atanh(long double x) except +
+ float atanhf(float x) except +
+ long double atanhl(long double x) except +
+
+ float cosh(float x) except +
+ double cosh(double x) except +
+ long double cosh(long double x) except +
+ float coshf(float x) except +
+ long double coshl(long double x) except +
+
+ float sinh(float x) except +
+ double sinh(double x) except +
+ long double sinh(long double x) except +
+ float sinhf(float x) except +
+ long double sinhl(long double x) except +
+
+ float tanh(float x) except +
+ double tanh(double x) except +
+ long double tanh(long double x) except +
+ float tanhf(float x) except +
+ long double tanhl(long double x) except +
+
+ float exp(float x) except +
+ double exp(double x) except +
+ long double exp(long double x) except +
+ float expf(float x) except +
+ long double expl(long double x) except +
+
+ float exp2(float x) except +
+ double exp2(double x) except +
+ long double exp2(long double x) except +
+ float exp2f(float x) except +
+ long double exp2l(long double x) except +
+
+ float expm1(float x) except +
+ double expm1(double x) except +
+ long double expm1(long double x) except +
+ float expm1f(float x) except +
+ long double expm1l(long double x) except +
+
+ float frexp(float value, int* exp) except +
+ double frexp(double value, int* exp) except +
+ long double frexp(long double value, int* exp) except +
+ float frexpf(float value, int* exp) except +
+ long double frexpl(long double value, int* exp) except +
+
+ int ilogb(float x) except +
+ int ilogb(double x) except +
+ int ilogb(long double x) except +
+ int ilogbf(float x) except +
+ int ilogbl(long double x) except +
+
+ float ldexp(float x, int exp) except +
+ double ldexp(double x, int exp) except +
+ long double ldexp(long double x, int exp) except +
+ float ldexpf(float x, int exp) except +
+ long double ldexpl(long double x, int exp) except +
+
+ float log(float x) except +
+ double log(double x) except +
+ long double log(long double x) except +
+ float logf(float x) except +
+ long double logl(long double x) except +
+
+ float log10(float x) except +
+ double log10(double x) except +
+ long double log10(long double x) except +
+ float log10f(float x) except +
+ long double log10l(long double x) except +
+
+ float log1p(float x) except +
+ double log1p(double x) except +
+ long double log1p(long double x) except +
+ float log1pf(float x) except +
+ long double log1pl(long double x) except +
+
+ float log2(float x) except +
+ double log2(double x) except +
+ long double log2(long double x) except +
+ float log2f(float x) except +
+ long double log2l(long double x) except +
+
+ float logb(float x) except +
+ double logb(double x) except +
+ long double logb(long double x) except +
+ float logbf(float x) except +
+ long double logbl(long double x) except +
+
+ float modf(float value, float* iptr) except +
+ double modf(double value, double* iptr) except +
+ long double modf(long double value, long double* iptr) except +
+ float modff(float value, float* iptr) except +
+ long double modfl(long double value, long double* iptr) except +
+
+ float scalbn(float x, int n) except +
+ double scalbn(double x, int n) except +
+ long double scalbn(long double x, int n) except +
+ float scalbnf(float x, int n) except +
+ long double scalbnl(long double x, int n) except +
+
+ float scalbln(float x, long int n) except +
+ double scalbln(double x, long int n) except +
+ long double scalbln(long double x, long int n) except +
+ float scalblnf(float x, long int n) except +
+ long double scalblnl(long double x, long int n) except +
+
+ float cbrt(float x) except +
+ double cbrt(double x) except +
+ long double cbrt(long double x) except +
+ float cbrtf(float x) except +
+ long double cbrtl(long double x) except +
+
+ # absolute values
+ int abs(int j) except +
+ long int abs(long int j) except +
+ long long int abs(long long int j) except +
+ float abs(float j) except +
+ double abs(double j) except +
+ long double abs(long double j) except +
+
+ float fabs(float x) except +
+ double fabs(double x) except +
+ long double fabs(long double x) except +
+ float fabsf(float x) except +
+ long double fabsl(long double x) except +
+
+ float hypot(float x, float y) except +
+ double hypot(double x, double y) except +
+ long double hypot(long double x, long double y) except +
+ float hypotf(float x, float y) except +
+ long double hypotl(long double x, long double y) except +
+
+ # C++17 three-dimensional hypotenuse
+ float hypot(float x, float y, float z) except +
+ double hypot(double x, double y, double z) except +
+ long double hypot(long double x, long double y, long double z) except +
+
+ float pow(float x, float y) except +
+ double pow(double x, double y) except +
+ long double pow(long double x, long double y) except +
+ float powf(float x, float y) except +
+ long double powl(long double x, long double y) except +
+
+ float sqrt(float x) except +
+ double sqrt(double x) except +
+ long double sqrt(long double x) except +
+ float sqrtf(float x) except +
+ long double sqrtl(long double x) except +
+
+ float erf(float x) except +
+ double erf(double x) except +
+ long double erf(long double x) except +
+ float erff(float x) except +
+ long double erfl(long double x) except +
+
+ float erfc(float x) except +
+ double erfc(double x) except +
+ long double erfc(long double x) except +
+ float erfcf(float x) except +
+ long double erfcl(long double x) except +
+
+ float lgamma(float x) except +
+ double lgamma(double x) except +
+ long double lgamma(long double x) except +
+ float lgammaf(float x) except +
+ long double lgammal(long double x) except +
+
+ float tgamma(float x) except +
+ double tgamma(double x) except +
+ long double tgamma(long double x) except +
+ float tgammaf(float x) except +
+ long double tgammal(long double x) except +
+
+ float ceil(float x) except +
+ double ceil(double x) except +
+ long double ceil(long double x) except +
+ float ceilf(float x) except +
+ long double ceill(long double x) except +
+
+ float floor(float x) except +
+ double floor(double x) except +
+ long double floor(long double x) except +
+ float floorf(float x) except +
+ long double floorl(long double x) except +
+
+ float nearbyint(float x) except +
+ double nearbyint(double x) except +
+ long double nearbyint(long double x) except +
+ float nearbyintf(float x) except +
+ long double nearbyintl(long double x) except +
+
+ float rint(float x) except +
+ double rint(double x) except +
+ long double rint(long double x) except +
+ float rintf(float x) except +
+ long double rintl(long double x) except +
+
+ long int lrint(float x) except +
+ long int lrint(double x) except +
+ long int lrint(long double x) except +
+ long int lrintf(float x) except +
+ long int lrintl(long double x) except +
+
+ long long int llrint(float x) except +
+ long long int llrint(double x) except +
+ long long int llrint(long double x) except +
+ long long int llrintf(float x) except +
+ long long int llrintl(long double x) except +
+
+ float round(float x) except +
+ double round(double x) except +
+ long double round(long double x) except +
+ float roundf(float x) except +
+ long double roundl(long double x) except +
+
+ long int lround(float x) except +
+ long int lround(double x) except +
+ long int lround(long double x) except +
+ long int lroundf(float x) except +
+ long int lroundl(long double x) except +
+
+ long long int llround(float x) except +
+ long long int llround(double x) except +
+ long long int llround(long double x) except +
+ long long int llroundf(float x) except +
+ long long int llroundl(long double x) except +
+
+ float trunc(float x) except +
+ double trunc(double x) except +
+ long double trunc(long double x) except +
+ float truncf(float x) except +
+ long double truncl(long double x) except +
+
+ float fmod(float x, float y) except +
+ double fmod(double x, double y) except +
+ long double fmod(long double x, long double y) except +
+ float fmodf(float x, float y) except +
+ long double fmodl(long double x, long double y) except +
+
+ float remainder(float x, float y) except +
+ double remainder(double x, double y) except +
+ long double remainder(long double x, long double y) except +
+ float remainderf(float x, float y) except +
+ long double remainderl(long double x, long double y) except +
+
+ float remquo(float x, float y, int* quo) except +
+ double remquo(double x, double y, int* quo) except +
+ long double remquo(long double x, long double y, int* quo) except +
+ float remquof(float x, float y, int* quo) except +
+ long double remquol(long double x, long double y, int* quo) except +
+
+ float copysign(float x, float y) except +
+ double copysign(double x, double y) except +
+ long double copysign(long double x, long double y) except +
+ float copysignf(float x, float y) except +
+ long double copysignl(long double x, long double y) except +
+
+ double nan(const char* tagp) except +
+ float nanf(const char* tagp) except +
+ long double nanl(const char* tagp) except +
+
+ float nextafter(float x, float y) except +
+ double nextafter(double x, double y) except +
+ long double nextafter(long double x, long double y) except +
+ float nextafterf(float x, float y) except +
+ long double nextafterl(long double x, long double y) except +
+
+ float nexttoward(float x, long double y) except +
+ double nexttoward(double x, long double y) except +
+ long double nexttoward(long double x, long double y) except +
+ float nexttowardf(float x, long double y) except +
+ long double nexttowardl(long double x, long double y) except +
+
+ float fdim(float x, float y) except +
+ double fdim(double x, double y) except +
+ long double fdim(long double x, long double y) except +
+ float fdimf(float x, float y) except +
+ long double fdiml(long double x, long double y) except +
+
+ float fmax(float x, float y) except +
+ double fmax(double x, double y) except +
+ long double fmax(long double x, long double y) except +
+ float fmaxf(float x, float y) except +
+ long double fmaxl(long double x, long double y) except +
+
+ float fmin(float x, float y) except +
+ double fmin(double x, double y) except +
+ long double fmin(long double x, long double y) except +
+ float fminf(float x, float y) except +
+ long double fminl(long double x, long double y) except +
+
+ float fma(float x, float y, float z) except +
+ double fma(double x, double y, double z) except +
+ long double fma(long double x, long double y, long double z) except +
+ float fmaf(float x, float y, float z) except +
+ long double fmal(long double x, long double y, long double z) except +
+
+ # C++20 linear interpolation
+ float lerp(float a, float b, float t)
+ double lerp(double a, double b, double t)
+ long double lerp(long double a, long double b, long double t)
+
+ # classification / comparison functions
+ int fpclassify(float x) except +
+ int fpclassify(double x) except +
+ int fpclassify(long double x) except +
+
+ bint isfinite(float x) except +
+ bint isfinite(double x) except +
+ bint isfinite(long double x) except +
+
+ bint isinf(float x) except +
+ bint isinf(double x) except +
+ bint isinf(long double x) except +
+
+ bint isnan(float x) except +
+ bint isnan(double x) except +
+ bint isnan(long double x) except +
+
+ bint isnormal(float x) except +
+ bint isnormal(double x) except +
+ bint isnormal(long double x) except +
+
+ bint signbit(float x) except +
+ bint signbit(double x) except +
+ bint signbit(long double x) except +
+
+ bint isgreater(float x, float y) except +
+ bint isgreater(double x, double y) except +
+ bint isgreater(long double x, long double y) except +
+
+ bint isgreaterequal(float x, float y) except +
+ bint isgreaterequal(double x, double y) except +
+ bint isgreaterequal(long double x, long double y) except +
+
+ bint isless(float x, float y) except +
+ bint isless(double x, double y) except +
+ bint isless(long double x, long double y) except +
+
+ bint islessequal(float x, float y) except +
+ bint islessequal(double x, double y) except +
+ bint islessequal(long double x, long double y) except +
+
+ bint islessgreater(float x, float y) except +
+ bint islessgreater(double x, double y) except +
+ bint islessgreater(long double x, long double y) except +
+
+ bint isunordered(float x, float y) except +
+ bint isunordered(double x, double y) except +
+ bint isunordered(long double x, long double y) except +
+
+ # C++17 mathematical special functions
+
+ # associated Laguerre polynomials
+ double assoc_laguerre(unsigned int n, unsigned int m, double x) except +
+ float assoc_laguerref(unsigned int n, unsigned int m, float x) except +
+ long double assoc_laguerrel(unsigned int n, unsigned int m, long double x) except +
+
+ # associated Legendre functions
+ double assoc_legendre(unsigned int l, unsigned int m, double x) except +
+ float assoc_legendref(unsigned int l, unsigned int m, float x) except +
+ long double assoc_legendrel(unsigned int l, unsigned int m, long double x) except +
+
+ # beta function
+ double beta(double x, double y) except +
+ float betaf(float x, float y) except +
+ long double betal(long double x, long double y) except +
+
+ # complete elliptic integral of the first kind
+ double comp_ellint_1(double k) except +
+ float comp_ellint_1f(float k) except +
+ long double comp_ellint_1l(long double k) except +
+
+ # complete elliptic integral of the second kind
+ double comp_ellint_2(double k) except +
+ float comp_ellint_2f(float k) except +
+ long double comp_ellint_2l(long double k) except +
+
+ # complete elliptic integral of the third kind
+ double comp_ellint_3(double k, double nu) except +
+ float comp_ellint_3f(float k, float nu) except +
+ long double comp_ellint_3l(long double k, long double nu) except +
+
+ # regular modified cylindrical Bessel functions
+ double cyl_bessel_i(double nu, double x) except +
+ float cyl_bessel_if(float nu, float x) except +
+ long double cyl_bessel_il(long double nu, long double x) except +
+
+ # cylindrical Bessel functions of the first kind
+ double cyl_bessel_j(double nu, double x) except +
+ float cyl_bessel_jf(float nu, float x) except +
+ long double cyl_bessel_jl(long double nu, long double x) except +
+
+ # irregular modified cylindrical Bessel functions
+ double cyl_bessel_k(double nu, double x) except +
+ float cyl_bessel_kf(float nu, float x) except +
+ long double cyl_bessel_kl(long double nu, long double x) except +
+
+ # cylindrical Neumann functions
+ # cylindrical Bessel functions of the second kind
+ double cyl_neumann(double nu, double x) except +
+ float cyl_neumannf(float nu, float x) except +
+ long double cyl_neumannl(long double nu, long double x) except +
+
+ # incomplete elliptic integral of the first kind
+ double ellint_1(double k, double phi) except +
+ float ellint_1f(float k, float phi) except +
+ long double ellint_1l(long double k, long double phi) except +
+
+ # incomplete elliptic integral of the second kind
+ double ellint_2(double k, double phi) except +
+ float ellint_2f(float k, float phi) except +
+ long double ellint_2l(long double k, long double phi) except +
+
+ # incomplete elliptic integral of the third kind
+ double ellint_3(double k, double nu, double phi) except +
+ float ellint_3f(float k, float nu, float phi) except +
+ long double ellint_3l(long double k, long double nu, long double phi) except +
+
+ # exponential integral
+ double expint(double x) except +
+ float expintf(float x) except +
+ long double expintl(long double x) except +
+
+ # Hermite polynomials
+ double hermite(unsigned int n, double x) except +
+ float hermitef(unsigned int n, float x) except +
+ long double hermitel(unsigned int n, long double x) except +
+
+ # Laguerre polynomials
+ double laguerre(unsigned int n, double x) except +
+ float laguerref(unsigned int n, float x) except +
+ long double laguerrel(unsigned int n, long double x) except +
+
+ # Legendre polynomials
+ double legendre(unsigned int l, double x) except +
+ float legendref(unsigned int l, float x) except +
+ long double legendrel(unsigned int l, long double x) except +
+
+ # Riemann zeta function
+ double riemann_zeta(double x) except +
+ float riemann_zetaf(float x) except +
+ long double riemann_zetal(long double x) except +
+
+ # spherical Bessel functions of the first kind
+ double sph_bessel(unsigned int n, double x) except +
+ float sph_besself(unsigned int n, float x) except +
+ long double sph_bessell(unsigned int n, long double x) except +
+
+ # spherical associated Legendre functions
+ double sph_legendre(unsigned int l, unsigned int m, double theta) except +
+ float sph_legendref(unsigned int l, unsigned int m, float theta) except +
+ long double sph_legendrel(unsigned int l, unsigned int m, long double theta) except +
+
+ # spherical Neumann functions
+ # spherical Bessel functions of the second kind
+ double sph_neumann(unsigned int n, double x) except +
+ float sph_neumannf(unsigned int n, float x) except +
+ long double sph_neumannl(unsigned int n, long double x) except +
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