File indexing completed on 2024-05-12 03:47:53

 /*
     File                 : nsl_sf_basic.c
     Project              : LabPlot
     Description          : NSL special basic functions
     --------------------------------------------------------------------
     SPDX-FileCopyrightText: 2018-2022 Stefan Gerlach <stefan.gerlach@uni.kn>
     SPDX-License-Identifier: GPL-2.0-or-later
 */
 
 #include "nsl_sf_basic.h"
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_randist.h>
 #include <gsl/gsl_sf.h>
 #include <math.h>
 #include <stdlib.h>
 #ifdef HAVE_LIBCERF
 #include <cerf.h>
 #elif !defined(_MSC_VER)
 #include "Faddeeva.h"
 #endif
 
 double nsl_sf_dummy(double x) {
     return 0 * x; // "use" parameter
 }
 
 double nsl_sf_dummy2(double p, double x) {
     return 0 * p * x; // "use" parameter
 }
 
 /* stdlib.h */
 double nsl_sf_rand(void) {
     return rand();
 }
 #if defined(HAVE_RANDOM_FUNCTION)
 double nsl_sf_random(void) {
     return random();
 }
 double nsl_sf_drand(void) {
     return random() / (double)RAND_MAX;
 }
 #else
 double nsl_sf_random(void) {
     return rand();
 }
 double nsl_sf_drand(void) {
     return rand() / (double)RAND_MAX;
 }
 #endif
 
 double nsl_sf_sgn(double x) {
 #ifndef _WIN32
     return copysign(1.0, x);
 #else
     if (x == 0)
         return 0;
     else
         return GSL_SIGN(x);
 #endif
 }
 
 double nsl_sf_theta(double x) {
     if (x >= 0)
         return 1;
     else
         return 0;
 }
 
 double nsl_sf_exp10(double x) {
 #ifdef __linux__
     return exp10(x);
 #else
     return pow(10., x);
 #endif
 }
 
 /* non-uniform random number generation
  * using a generator chosen by the environment variable GSL_RNG_TYPE
  */
 #define SETUP_GSL_RNG                                                                                                                                          \
     gsl_rng_env_setup();                                                                                                                                       \
     const gsl_rng_type* T = gsl_rng_default;                                                                                                                   \
     gsl_rng* r = gsl_rng_alloc(T);                                                                                                                             \
     gsl_rng_set(r, rand()); /*seed*/
 
 double nsl_sf_ran_gaussian(double sigma) {
     SETUP_GSL_RNG
     return gsl_ran_gaussian_ziggurat(r, sigma);
 }
 double nsl_sf_ran_exponential(double mu) {
     SETUP_GSL_RNG
     return gsl_ran_exponential(r, mu);
 }
 double nsl_sf_ran_laplace(double a) {
     SETUP_GSL_RNG
     return gsl_ran_laplace(r, a);
 }
 double nsl_sf_ran_cauchy(double a) {
     SETUP_GSL_RNG
     return gsl_ran_cauchy(r, a);
 }
 double nsl_sf_ran_rayleigh(double sigma) {
     SETUP_GSL_RNG
     return gsl_ran_rayleigh(r, sigma);
 }
 double nsl_sf_ran_landau(void) {
     SETUP_GSL_RNG
     return gsl_ran_landau(r);
 }
 double nsl_sf_ran_levy(double c, double alpha) {
     SETUP_GSL_RNG
     return gsl_ran_levy(r, c, alpha);
 }
 double nsl_sf_ran_gamma(double a, double b) {
     SETUP_GSL_RNG
     return gsl_ran_gamma(r, a, b);
 }
 double nsl_sf_ran_flat(double a, double b) {
     SETUP_GSL_RNG
     return gsl_ran_flat(r, a, b);
 }
 double nsl_sf_ran_lognormal(double zeta, double sigma) {
     SETUP_GSL_RNG
     return gsl_ran_lognormal(r, zeta, sigma);
 }
 double nsl_sf_ran_chisq(double nu) {
     SETUP_GSL_RNG
     return gsl_ran_chisq(r, nu);
 }
 double nsl_sf_ran_tdist(double nu) {
     SETUP_GSL_RNG
     return gsl_ran_tdist(r, nu);
 }
 double nsl_sf_ran_logistic(double a) {
     SETUP_GSL_RNG
     return gsl_ran_logistic(r, a);
 }
 
 double nsl_sf_ran_poisson(double mu) {
     SETUP_GSL_RNG
     return (double)gsl_ran_poisson(r, mu);
 }
 double nsl_sf_ran_bernoulli(double p) {
     SETUP_GSL_RNG
     return (double)gsl_ran_bernoulli(r, p);
 }
 double nsl_sf_ran_binomial(double p, double n) {
     SETUP_GSL_RNG
     return (double)gsl_ran_binomial(r, p, (unsigned int)round(n));
 }
 
 /*
  * source: https://stackoverflow.com/questions/11376288/fast-computing-of-log2-for-64-bit-integers
  * source: https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup
  */
 int nsl_sf_log2_int(unsigned int x) {
 #ifdef _MSC_VER
     return nsl_sf_log2_int2(x);
 #else
     return nsl_sf_log2_int0(x);
 #endif
 }
 int nsl_sf_log2_int0(unsigned int x) {
 #ifdef _MSC_VER
     return 0; /* not implemented yet */
 #else
     return (int)(8 * sizeof(unsigned int) - __builtin_clz(x) - 1);
 #endif
 }
 int nsl_sf_log2_int2(int x) {
     const signed char LogTable256[256] = {-1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5,
                                           5,  5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
                                           6,  6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
                                           6,  6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                                           7,  7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                                           7,  7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                                           7,  7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7};
 
     unsigned int r; // r will be lg(v)
     unsigned int t, tt; // temporaries
     if ((tt = x >> 16))
         r = (t = tt >> 8) ? 24 + LogTable256[t] : 16 + LogTable256[tt];
     else
         r = (t = x >> 8) ? 8 + LogTable256[t] : LogTable256[x];
 
     return r;
 }
 int nsl_sf_log2_int3(uint64_t value) {
     const int tab64[64] = {63, 0,  58, 1,  59, 47, 53, 2,  60, 39, 48, 27, 54, 33, 42, 3,  61, 51, 37, 40, 49, 18, 28, 20, 55, 30, 34, 11, 43, 14, 22, 4,
                            62, 57, 46, 52, 38, 26, 32, 41, 50, 36, 17, 19, 29, 10, 13, 21, 56, 45, 25, 31, 35, 16, 9,  12, 44, 24, 15, 8,  23, 7,  6,  5};
 
     value |= value >> 1;
     value |= value >> 2;
     value |= value >> 4;
     value |= value >> 8;
     value |= value >> 16;
     value |= value >> 32;
 
     return tab64[((uint64_t)((value - (value >> 1)) * 0x07EDD5E59A4E28C2)) >> 58];
 }
 int nsl_sf_log2p1_int(int x) {
     // fastest method
     return nsl_sf_log2_int(x) + 1;
     // TODO: why is this so slow
     // return (int)log2(x) + 1;
 }
 int nsl_sf_log2_longlong(unsigned long long x) {
 #ifdef _MSC_VER
     return 0; /* not implemented yet */
 #else
     return (int)(8 * sizeof(unsigned long long) - __builtin_clzll(x) - 1);
 #endif
 }
 
 double nsl_sf_sec(double x) {
     return 1. / cos(x);
 }
 double nsl_sf_csc(double x) {
     return 1. / sin(x);
 }
 double nsl_sf_cot(double x) {
     return 1. / tan(x);
 }
 double nsl_sf_asec(double x) {
     return acos(1. / x);
 }
 double nsl_sf_acsc(double x) {
     return asin(1. / x);
 }
 double nsl_sf_acot(double x) {
     if (x > 0)
         return atan(1. / x);
     else
         return atan(1. / x) + M_PI;
 }
 double nsl_sf_sech(double x) {
     return 1. / cosh(x);
 }
 double nsl_sf_csch(double x) {
     return 1. / sinh(x);
 }
 double nsl_sf_coth(double x) {
     return 1. / tanh(x);
 }
 double nsl_sf_asech(double x) {
     return gsl_acosh(1. / x);
 }
 double nsl_sf_acsch(double x) {
     return gsl_asinh(1. / x);
 }
 double nsl_sf_acoth(double x) {
     return gsl_atanh(1. / x);
 }
 
 double nsl_sf_harmonic(double x) {
     // check if x is a negative integer
     if (x < 0 && !gsl_fcmp(round(x) - x, 0., 1.e-16))
         return GSL_POSINF;
 
     return gsl_sf_psi(x + 1) + M_EULER;
 }
 
 /* error functions and related */
 double nsl_sf_erfcx(double x) {
 #ifdef HAVE_LIBCERF
     return erfcx(x);
 #elif defined(_MSC_VER)
     return 0.; // not supported yet
 #else
     return Faddeeva_erfcx_re(x);
 #endif
 }
 
 double nsl_sf_erfi(double x) {
 #ifdef HAVE_LIBCERF
     return erfi(x);
 #elif defined(_MSC_VER)
     return 0.; // not supported yet
 #else
     return Faddeeva_erfi_re(x);
 #endif
 }
 
 double nsl_sf_im_w_of_x(double x) {
 #ifdef HAVE_LIBCERF
     return im_w_of_x(x);
 #elif defined(_MSC_VER)
     return 0.; // not supported yet
 #else
     return Faddeeva_w_im(x);
 #endif
 }
 
 #if !defined(_MSC_VER)
 double nsl_sf_im_w_of_z(COMPLEX z) {
 #ifdef HAVE_LIBCERF
     return cimag(w_of_z(z));
 #else
     return cimag(Faddeeva_w(z, 0));
 #endif
 }
 #endif
 
 double nsl_sf_dawson(double x) {
 #ifdef HAVE_LIBCERF
     return dawson(x);
 #elif defined(_MSC_VER)
     return 0.; // not supported yet
 #else
     return Faddeeva_Dawson_re(x);
 #endif
 }
 
 double nsl_sf_voigt(double x, double sigma, double gamma) {
 #ifdef HAVE_LIBCERF
     return voigt(x, sigma, gamma);
 #elif defined(_MSC_VER)
     return 0.; // not supported yet
 #else
     COMPLEX z = (x + I * gamma) / (M_SQRT2 * sigma);
     return creal(Faddeeva_w(z, 0)) / (M_SQRT2 * M_SQRTPI * sigma);
 #endif
 }
 
 double nsl_sf_pseudovoigt(double x, double eta, double sigma, double gamma) {
     if (sigma == 0 || gamma == 0)
         return 0;
     // TODO: what if eta < 0 or > 1?
 
     return (1. - eta) * gsl_ran_gaussian_pdf(x, sigma) + eta * gsl_ran_cauchy_pdf(x, gamma);
 }
 
 double nsl_sf_pseudovoigt1(double x, double eta, double w) {
     // 2w - FWHM, sigma_G = w/sqrt(2ln(2))
     return nsl_sf_pseudovoigt(x, eta, w / sqrt(2. * M_LN2), w);
 }
 
 /* wrapper for GSL functions with integer parameters */
 #define MODE GSL_PREC_DOUBLE
 /* mathematical functions */
 double nsl_sf_ldexp(double x, double expo) {
     return gsl_ldexp(x, (int)round(expo));
 }
 double nsl_sf_powint(double x, double n) {
     return gsl_sf_pow_int(x, (int)round(n));
 }
 /* Airy functions */
 double nsl_sf_airy_Ai(double x) {
     return gsl_sf_airy_Ai(x, MODE);
 }
 double nsl_sf_airy_Bi(double x) {
     return gsl_sf_airy_Bi(x, MODE);
 }
 double nsl_sf_airy_Ais(double x) {
     return gsl_sf_airy_Ai_scaled(x, MODE);
 }
 double nsl_sf_airy_Bis(double x) {
     return gsl_sf_airy_Bi_scaled(x, MODE);
 }
 double nsl_sf_airy_Aid(double x) {
     return gsl_sf_airy_Ai_deriv(x, MODE);
 }
 double nsl_sf_airy_Bid(double x) {
     return gsl_sf_airy_Bi_deriv(x, MODE);
 }
 double nsl_sf_airy_Aids(double x) {
     return gsl_sf_airy_Ai_deriv_scaled(x, MODE);
 }
 double nsl_sf_airy_Bids(double x) {
     return gsl_sf_airy_Bi_deriv_scaled(x, MODE);
 }
 double nsl_sf_airy_0_Ai(double s) {
     return gsl_sf_airy_zero_Ai((unsigned int)round(s));
 }
 double nsl_sf_airy_0_Bi(double s) {
     return gsl_sf_airy_zero_Bi((unsigned int)round(s));
 }
 double nsl_sf_airy_0_Aid(double s) {
     return gsl_sf_airy_zero_Ai_deriv((unsigned int)round(s));
 }
 double nsl_sf_airy_0_Bid(double s) {
     return gsl_sf_airy_zero_Bi_deriv((unsigned int)round(s));
 }
 /* Bessel functions */
 double nsl_sf_bessel_Jn(double n, double x) {
     return gsl_sf_bessel_Jn((int)round(n), x);
 }
 double nsl_sf_bessel_Yn(double n, double x) {
     return gsl_sf_bessel_Yn((int)round(n), x);
 }
 double nsl_sf_bessel_In(double n, double x) {
     return gsl_sf_bessel_In((int)round(n), x);
 }
 double nsl_sf_bessel_Ins(double n, double x) {
     return gsl_sf_bessel_In_scaled((int)round(n), x);
 }
 double nsl_sf_bessel_Kn(double n, double x) {
     return gsl_sf_bessel_Kn((int)round(n), x);
 }
 double nsl_sf_bessel_Kns(double n, double x) {
     return gsl_sf_bessel_Kn_scaled((int)round(n), x);
 }
 double nsl_sf_bessel_jl(double l, double x) {
     return gsl_sf_bessel_jl((int)round(l), x);
 }
 double nsl_sf_bessel_yl(double l, double x) {
     return gsl_sf_bessel_yl((int)round(l), x);
 }
 double nsl_sf_bessel_ils(double l, double x) {
     return gsl_sf_bessel_il_scaled((int)round(l), x);
 }
 double nsl_sf_bessel_kls(double l, double x) {
     return gsl_sf_bessel_kl_scaled((int)round(l), x);
 }
 double nsl_sf_bessel_0_J0(double s) {
     return gsl_sf_bessel_zero_J0((unsigned int)round(s));
 }
 double nsl_sf_bessel_0_J1(double s) {
     return gsl_sf_bessel_zero_J1((unsigned int)round(s));
 }
 double nsl_sf_bessel_0_Jnu(double nu, double s) {
     return gsl_sf_bessel_zero_Jnu(nu, (unsigned int)round(s));
 }
 
 double nsl_sf_hydrogenicR(double n, double l, double z, double r) {
     return gsl_sf_hydrogenicR((int)round(n), (int)round(l), z, r);
 }
 /* elliptic integrals */
 double nsl_sf_ellint_Kc(double x) {
     return gsl_sf_ellint_Kcomp(x, MODE);
 }
 double nsl_sf_ellint_Ec(double x) {
     return gsl_sf_ellint_Ecomp(x, MODE);
 }
 double nsl_sf_ellint_Pc(double x, double n) {
     return gsl_sf_ellint_Pcomp(x, n, MODE);
 }
 double nsl_sf_ellint_F(double phi, double k) {
     return gsl_sf_ellint_F(phi, k, MODE);
 }
 double nsl_sf_ellint_E(double phi, double k) {
     return gsl_sf_ellint_E(phi, k, MODE);
 }
 double nsl_sf_ellint_P(double phi, double k, double n) {
     return gsl_sf_ellint_P(phi, k, n, MODE);
 }
 double nsl_sf_ellint_D(double phi, double k) {
 #if GSL_MAJOR_VERSION >= 2
     return gsl_sf_ellint_D(phi, k, MODE);
 #else
     return gsl_sf_ellint_D(phi, k, 0.0, MODE);
 #endif
 }
 double nsl_sf_ellint_RC(double x, double y) {
     return gsl_sf_ellint_RC(x, y, MODE);
 }
 double nsl_sf_ellint_RD(double x, double y, double z) {
     return gsl_sf_ellint_RD(x, y, z, MODE);
 }
 double nsl_sf_ellint_RF(double x, double y, double z) {
     return gsl_sf_ellint_RF(x, y, z, MODE);
 }
 double nsl_sf_ellint_RJ(double x, double y, double z, double p) {
     return gsl_sf_ellint_RJ(x, y, z, p, MODE);
 }
 
 double nsl_sf_exprel_n(double n, double x) {
     return gsl_sf_exprel_n((int)round(n), x);
 }
 double nsl_sf_fermi_dirac_int(double j, double x) {
     return gsl_sf_fermi_dirac_int((int)round(j), x);
 }
 /* Gamma */
 double nsl_sf_fact(double n) {
     return gsl_sf_fact((unsigned int)round(n));
 }
 double nsl_sf_doublefact(double n) {
     return gsl_sf_doublefact((unsigned int)round(n));
 }
 double nsl_sf_lnfact(double n) {
     return gsl_sf_lnfact((unsigned int)round(n));
 }
 double nsl_sf_lndoublefact(double n) {
     return gsl_sf_lndoublefact((unsigned int)round(n));
 }
 double nsl_sf_choose(double n, double m) {
     return gsl_sf_choose((unsigned int)round(n), (unsigned int)round(m));
 }
 double nsl_sf_lnchoose(double n, double m) {
     return gsl_sf_lnchoose((unsigned int)round(n), (unsigned int)round(m));
 }
 double nsl_sf_taylorcoeff(double n, double x) {
     return gsl_sf_taylorcoeff((int)round(n), x);
 }
 
 double nsl_sf_gegenpoly_n(double n, double l, double x) {
     return gsl_sf_gegenpoly_n((int)round(n), l, x);
 }
 
 /* Hermite polynomials and functions since GSL 2.4 */
 #if (GSL_MAJOR_VERSION > 2) || (GSL_MAJOR_VERSION == 2) && (GSL_MINOR_VERSION >= 4)
 double nsl_sf_hermite_prob(double n, double x) {
     return gsl_sf_hermite_prob((int)round(n), x);
 }
 double nsl_sf_hermite_func(double n, double x) {
     return gsl_sf_hermite_func((int)round(n), x);
 }
 double nsl_sf_hermite_func_der(double m, double n, double x) {
     return gsl_sf_hermite_func_der((int)round(m), (int)round(n), x);
 }
 #if (GSL_MAJOR_VERSION == 2) && (GSL_MINOR_VERSION < 6)
 double nsl_sf_hermite(double n, double x) {
     return gsl_sf_hermite_phys((int)round(n), x);
 }
 double nsl_sf_hermite_deriv(double m, double n, double x) {
     return gsl_sf_hermite_phys_der((int)round(m), (int)round(n), x);
 }
 double nsl_sf_hermite_prob_deriv(double m, double n, double x) {
     return gsl_sf_hermite_prob_der((int)round(m), (int)round(n), x);
 }
 #else /* renamed and added func_fast in GSL 2.6 */
 double nsl_sf_hermite(double n, double x) {
     return gsl_sf_hermite((int)round(n), x);
 }
 double nsl_sf_hermite_deriv(double m, double n, double x) {
     return gsl_sf_hermite_deriv((int)round(m), (int)round(n), x);
 }
 double nsl_sf_hermite_prob_deriv(double m, double n, double x) {
     return gsl_sf_hermite_prob_deriv((int)round(m), (int)round(n), x);
 }
 double nsl_sf_hermite_func_fast(double n, double x) {
     return gsl_sf_hermite_func_fast((int)round(n), x);
 }
 #endif
 #endif
 
 double nsl_sf_hyperg_1F1i(double m, double n, double x) {
     return gsl_sf_hyperg_1F1_int((int)round(m), (int)round(n), x);
 }
 double nsl_sf_hyperg_Ui(double m, double n, double x) {
     return gsl_sf_hyperg_U_int((int)round(m), (int)round(n), x);
 }
 double nsl_sf_laguerre_n(double n, double a, double x) {
     return gsl_sf_laguerre_n((int)round(n), a, x);
 }
 
 double nsl_sf_legendre_Pl(double l, double x) {
     return gsl_sf_legendre_Pl((int)round(l), x);
 }
 double nsl_sf_legendre_Ql(double l, double x) {
     return gsl_sf_legendre_Ql((int)round(l), x);
 }
 double nsl_sf_legendre_Plm(double l, double m, double x) {
     return gsl_sf_legendre_Plm((int)round(l), (int)round(m), x);
 }
 double nsl_sf_legendre_sphPlm(double l, double m, double x) {
     return gsl_sf_legendre_sphPlm((int)round(l), (int)round(m), x);
 }
 double nsl_sf_conicalP_sphreg(double l, double L, double x) {
     return gsl_sf_conicalP_sph_reg((int)round(l), L, x);
 }
 double nsl_sf_conicalP_cylreg(double m, double l, double x) {
     return gsl_sf_conicalP_sph_reg((int)round(m), l, x);
 }
 double nsl_sf_legendre_H3d(double l, double L, double e) {
     return gsl_sf_legendre_H3d((int)round(l), L, e);
 }
 
 #if (GSL_MAJOR_VERSION >= 2)
 double nsl_sf_mathieu_a(double n, double q) {
     return gsl_sf_mathieu_a((int)round(n), q);
 }
 double nsl_sf_mathieu_b(double n, double q) {
     return gsl_sf_mathieu_b((int)round(n), q);
 }
 double nsl_sf_mathieu_ce(double n, double q, double x) {
     return gsl_sf_mathieu_ce((int)round(n), q, x);
 }
 double nsl_sf_mathieu_se(double n, double q, double x) {
     return gsl_sf_mathieu_se((int)round(n), q, x);
 }
 double nsl_sf_mathieu_Mc(double j, double n, double q, double x) {
     return gsl_sf_mathieu_Mc((int)round(j), (int)round(n), q, x);
 }
 double nsl_sf_mathieu_Ms(double j, double n, double q, double x) {
     return gsl_sf_mathieu_Ms((int)round(j), (int)round(n), q, x);
 }
 #endif
 
 double nsl_sf_psiint(double n) {
     return gsl_sf_psi_int((int)round(n));
 }
 double nsl_sf_psi1int(double n) {
     return gsl_sf_psi_1_int((int)round(n));
 }
 double nsl_sf_psin(double n, double x) {
     return gsl_sf_psi_n((int)round(n), x);
 }
 
 double nsl_sf_zetaint(double n) {
     return gsl_sf_zeta_int((int)round(n));
 }
 double nsl_sf_zetam1int(double n) {
     return gsl_sf_zetam1_int((int)round(n));
 }
 double nsl_sf_etaint(double n) {
     return gsl_sf_eta_int((int)round(n));
 }
 
 /* random number distributions */
 double nsl_sf_poisson(double k, double m) {
     return gsl_ran_poisson_pdf((unsigned int)round(k), m);
 }
 double nsl_sf_bernoulli(double k, double p) {
     return gsl_ran_bernoulli_pdf((unsigned int)round(k), p);
 }
 double nsl_sf_binomial(double k, double p, double n) {
     return gsl_ran_binomial_pdf((unsigned int)round(k), p, (unsigned int)round(n));
 }
 double nsl_sf_negative_binomial(double k, double p, double n) {
     return gsl_ran_negative_binomial_pdf((unsigned int)round(k), p, n);
 }
 double nsl_sf_pascal(double k, double p, double n) {
     return gsl_ran_pascal_pdf((unsigned int)round(k), p, (unsigned int)round(n));
 }
 double nsl_sf_geometric(double k, double p) {
     return gsl_ran_geometric_pdf((unsigned int)round(k), p);
 }
 double nsl_sf_hypergeometric(double k, double n1, double n2, double t) {
     return gsl_ran_hypergeometric_pdf((unsigned int)round(k), (unsigned int)round(n1), (unsigned int)round(n2), (unsigned int)round(t));
 }
 double nsl_sf_logarithmic(double k, double p) {
     return gsl_ran_logarithmic_pdf((unsigned int)round(k), p);
 }