Crate torsh_special 

Special mathematical functions for ToRSh

Re-exports

pub use scirs2_integration::bessel_i0_scirs2;

pub use scirs2_integration::bessel_i1_scirs2;

pub use scirs2_integration::bessel_j0_scirs2;

pub use scirs2_integration::bessel_j1_scirs2;

pub use scirs2_integration::bessel_jn_scirs2;

pub use scirs2_integration::bessel_k0_scirs2;

pub use scirs2_integration::bessel_k1_scirs2;

pub use scirs2_integration::bessel_y0_scirs2;

pub use scirs2_integration::bessel_y1_scirs2;

pub use scirs2_integration::bessel_yn_scirs2;

pub use scirs2_integration::beta;

pub use scirs2_integration::digamma;

pub use scirs2_integration::erf;

pub use scirs2_integration::erfc;

pub use scirs2_integration::erfcx;

pub use scirs2_integration::erfinv;

pub use scirs2_integration::fresnel;

pub use scirs2_integration::fresnel_c;

pub use scirs2_integration::fresnel_s;

pub use scirs2_integration::gamma;

pub use scirs2_integration::lgamma;

pub use scirs2_integration::polygamma;

pub use scirs2_integration::sinc;

pub use elliptic::elliptic_e;

pub use elliptic::elliptic_e_incomplete;

pub use elliptic::elliptic_f;

pub use elliptic::elliptic_k;

pub use elliptic::jacobi_cn;

pub use elliptic::jacobi_dn;

pub use elliptic::jacobi_sn;

pub use elliptic::theta_1;

pub use elliptic::theta_2;

pub use elliptic::theta_3;

pub use elliptic::theta_4;

pub use elliptic::weierstrass_p;

pub use elliptic::weierstrass_sigma;

pub use elliptic::weierstrass_zeta;

pub use exponential_integrals::cosine_integral;

pub use exponential_integrals::exponential_integral_e1;

pub use exponential_integrals::exponential_integral_ei;

pub use exponential_integrals::exponential_integral_en;

pub use exponential_integrals::hyperbolic_cosine_integral;

pub use exponential_integrals::hyperbolic_sine_integral;

pub use exponential_integrals::logarithmic_integral;

pub use exponential_integrals::sine_integral;

pub use hypergeometric::appell_f1;

pub use hypergeometric::hypergeometric_1f1;

pub use hypergeometric::hypergeometric_2f1;

pub use hypergeometric::hypergeometric_pfq;

pub use hypergeometric::hypergeometric_u;

pub use hypergeometric::meijer_g;

pub use orthogonal_polynomials::chebyshev_t;

pub use orthogonal_polynomials::chebyshev_u;

pub use orthogonal_polynomials::gegenbauer_c;

pub use orthogonal_polynomials::hermite_h;

pub use orthogonal_polynomials::hermite_he;

pub use orthogonal_polynomials::jacobi_p;

pub use orthogonal_polynomials::laguerre_l;

pub use orthogonal_polynomials::laguerre_l_associated;

pub use orthogonal_polynomials::legendre_p;

pub use orthogonal_polynomials::legendre_p_associated;

pub use advanced::barnes_g;

pub use advanced::dirichlet_eta;

pub use advanced::hurwitz_zeta;

pub use advanced::polylogarithm;

pub use advanced::riemann_zeta;

pub use advanced_special::dawson;

pub use advanced_special::kelvin_bei;

pub use advanced_special::kelvin_ber;

pub use advanced_special::kelvin_kei;

pub use advanced_special::kelvin_ker;

pub use advanced_special::parabolic_cylinder_d;

pub use advanced_special::spence;

pub use advanced_special::struve_h;

pub use advanced_special::struve_l;

pub use advanced_special::voigt_profile;

pub use airy::airy_ai;

pub use airy::airy_ai_prime;

pub use airy::airy_bi;

pub use airy::airy_bi_prime;

pub use coulomb::coulomb_f;

pub use coulomb::coulomb_g;

pub use coulomb::coulomb_sigma;

pub use lommel::lommel_S;

pub use lommel::lommel_s;

pub use lommel::lommel_u;

pub use lommel::lommel_v;

pub use mathieu::mathieu_Ce;

pub use mathieu::mathieu_Se;

pub use mathieu::mathieu_a;

pub use mathieu::mathieu_b;

pub use mathieu::mathieu_ce;

pub use mathieu::mathieu_se;

pub use spheroidal::oblate_angular;

pub use spheroidal::oblate_angular_tensor;

pub use spheroidal::oblate_radial;

pub use spheroidal::oblate_radial_tensor;

pub use spheroidal::prolate_angular;

pub use spheroidal::prolate_angular_tensor;

pub use spheroidal::prolate_radial;

pub use spheroidal::prolate_radial_tensor;

pub use spheroidal::spheroidal_eigenvalue;

pub use lambert_w::lambert_w;

pub use lambert_w::lambert_w_complex;

pub use lambert_w::lambert_w_derivative;

pub use lambert_w::lambert_w_principal;

pub use lambert_w::lambert_w_secondary;

pub use lambert_w::applications::solve_exponential_equation;

pub use lambert_w::applications::solve_x_to_x_equals_c;

pub use lambert_w::applications::tree_function;

pub use lambert_w::applications::wright_omega;

pub use statistical::chi_squared_cdf;

pub use statistical::f_distribution_cdf;

pub use statistical::incomplete_beta;

pub use statistical::normal_cdf;

pub use statistical::normal_cdf_general;

pub use statistical::normal_pdf;

pub use statistical::normal_pdf_general;

pub use statistical::student_t_cdf;

pub use complex::complex_airy_ai_c64;

pub use complex::complex_airy_bi_c64;

pub use complex::complex_bessel_j_c32;

pub use complex::complex_bessel_j_c64;

pub use complex::complex_bessel_y_c32;

pub use complex::complex_bessel_y_c64;

pub use complex::complex_beta_c32;

pub use complex::complex_beta_c64;

pub use complex::complex_erf_c32;

pub use complex::complex_erf_c64;

pub use complex::complex_erfc_c32;

pub use complex::complex_erfc_c64;

pub use complex::complex_gamma_c32;

pub use complex::complex_gamma_c64;

pub use complex::complex_incomplete_gamma_c64;

pub use complex::complex_log_principal;

pub use complex::complex_polygamma_c32;

pub use complex::complex_polygamma_c64;

pub use complex::complex_pow_principal;

pub use complex::complex_sqrt_principal;

pub use complex::complex_zeta_c32;

pub use complex::complex_zeta_c64;

pub use error_handling::error_recovery::clamp_to_finite;

pub use error_handling::error_recovery::gradual_clamp;

pub use error_handling::error_recovery::replace_problematic_values;

pub use error_handling::safe_functions::safe_bessel_j0;

pub use error_handling::safe_functions::safe_bessel_j1;

pub use error_handling::safe_functions::safe_bessel_y0;

pub use error_handling::safe_functions::safe_bessel_y1;

pub use error_handling::safe_functions::safe_erf;

pub use error_handling::safe_functions::safe_erfc;

pub use error_handling::safe_functions::safe_gamma;

pub use error_handling::safe_functions::safe_lgamma;

pub use error_handling::DomainConstraints;

pub use error_handling::InputValidation;

pub use fast_approximations::atanh_fast;

pub use fast_approximations::bessel_j0_fast;

pub use fast_approximations::cos_fast;

pub use fast_approximations::cosh_fast;

pub use fast_approximations::erf_fast;

pub use fast_approximations::erfc_fast;

pub use fast_approximations::exp_fast;

pub use fast_approximations::gamma_fast;

pub use fast_approximations::log_fast;

pub use fast_approximations::sin_fast;

pub use fast_approximations::sinh_fast;

pub use fast_approximations::tanh_fast;

pub use lookup_tables::bessel_j0_optimized;

pub use lookup_tables::erf_optimized;

pub use lookup_tables::factorial;

pub use lookup_tables::gamma_optimized;

pub use lookup_tables::POLY_COEFFS;

pub use simd_optimizations::erf_simd;

pub use simd_optimizations::exp_family_simd;

pub use simd_optimizations::gamma_simd;

pub use simd_optimizations::ExpVariant;

pub use smart_caching::cache_stats;

pub use smart_caching::cached_compute;

pub use smart_caching::clear_cache;

pub use smart_caching::function_ids;

pub use smart_caching::CacheStats;

pub use smart_caching::FloatKey;

pub use smart_caching::SmartCache;

pub use trigonometric::sinc as sinc_unnormalized;

pub use visualization::analyze_function_behavior;

pub use visualization::benchmark_optimization_levels;

pub use visualization::compare_function_accuracy;

pub use visualization::generate_ascii_plot;

pub use visualization::print_accuracy_report;

pub use visualization::print_analysis_report;

pub use visualization::AccuracyComparison;

pub use visualization::FunctionAnalysis;

pub use visualization::Monotonicity;

pub use visualization::PlotData;

pub use constants::APERY;

pub use constants::CATALAN;

pub use constants::DOTTIE;

pub use constants::EULER_GAMMA;

pub use constants::FEIGENBAUM_ALPHA;

pub use constants::FEIGENBAUM_DELTA;

pub use constants::GLAISHER_KINKELIN;

pub use constants::GOLDEN_RATIO;

pub use constants::GOLDEN_RATIO_RECIPROCAL;

pub use constants::KHINCHIN;

pub use constants::LEVY;

pub use constants::LN_2PI;

pub use constants::LN_PI;

pub use constants::MILLS;

pub use constants::PI_SQUARED_OVER_6;

pub use constants::PLASTIC_NUMBER;

pub use constants::RAMANUJAN;

pub use constants::SQRT_2PI;

pub use constants::utility::HALF_LN_2PI;

pub use constants::utility::INV_2PI;

pub use constants::utility::INV_SQRT_2PI;

pub use constants::utility::LN_4PI;

pub use constants::utility::LOG_SQRT_2PI;

pub use constants::utility::PI_OVER_4;

pub use constants::utility::SQRT_PI_OVER_2;

pub use constants::utility::SQRT_PI_OVER_8;

pub use constants::utility::STIRLING_CONSTANT;

pub use constants::utility::THREE_PI_OVER_4;

pub use constants::utility::TWO_OVER_SQRT_PI;

pub use constants::bernoulli;

pub use constants::fractions;

pub use constants::physics;

pub use constants::zeta_values;

pub use utils::chebyshev_expansion;

pub use utils::chebyshev_expansion_tensor;

pub use utils::continued_fraction;

pub use utils::continued_fraction_tensor;

pub use utils::double_factorial;

pub use utils::factorial_safe;

pub use utils::pade_approximant;

pub use utils::pade_approximant_tensor;

pub use bessel::*;

Modules

advanced

Advanced Mathematical Functions

advanced_special

Advanced Special Functions

airy

Airy Functions

bessel

Bessel functions

complex

Complex special functions module

constants

Mathematical constants for special functions

coulomb

Coulomb Wave Functions

elliptic

Elliptic Functions and Integrals

error_functions

Error functions

error_handling

Enhanced error handling and edge case coverage for special functions

exponential_integrals

Exponential Integrals

fast_approximations

Fast Approximations for Special Functions

gamma

Gamma and related functions

hypergeometric

Hypergeometric Functions

lambert_w

Lambert W Function Implementation

lommel

Lommel Functions

lookup_tables

Lookup Tables for Special Functions

mathieu

Mathieu Functions

numerical_accuracy_tests

Comprehensive numerical accuracy tests for special functions

orthogonal_polynomials

Orthogonal Polynomials

prelude

Prelude module for convenient imports

scirs2_integration

SciRS2 Special Functions Integration

simd_optimizations

SIMD Optimizations for Special Functions

smart_caching

Smart caching for expensive special function computations

spheroidal

Spheroidal Wave Functions

statistical

Statistical Functions

trigonometric

Special trigonometric functions

utils

Utility Functions for Special Mathematical Operations

visualization

Visualization tools for function behavior and accuracy analysis

Constants

VERSION

VERSION_MAJOR

VERSION_MINOR

VERSION_PATCH

Functions

acosh

Inverse hyperbolic cosine

asinh

Inverse hyperbolic sine

atanh

Inverse hyperbolic tangent

cosh

Hyperbolic cosine (using existing implementation)

expm1

Exponential minus one (exp(x) - 1) for better numerical stability

log1p

Natural logarithm of one plus x (log(1 + x)) for better numerical stability

sinh

Hyperbolic sine (using existing implementation)

tanh_special

Hyperbolic tangent (using existing implementation)

Type Aliases

TorshResult

Convenience type alias for Results in this crate