Module scalar 

Scalar Distribution Utilities Module - High-Precision Scalar Statistical Functions

Fundamental scalar mathematical functions providing the computational building blocks for statistical distribution calculations with optimal numerical precision and SIMD acceleration. These utilities form the foundation for all distribution PDF, CDF, and quantile computations.

Constants

W8

Auto-generated SIMD lane widths from build.rs SIMD lane count for 8-bit elements (u8, i8). Determined at build time based on target architecture capabilities, or overridden via SIMD_LANES_OVERRIDE.

W16

SIMD lane count for 16-bit elements (u16, i16). Determined at build time based on target architecture capabilities, or overridden via SIMD_LANES_OVERRIDE.

W32

SIMD lane count for 32-bit elements (u32, i32, f32). Determined at build time based on target architecture capabilities, or overridden via SIMD_LANES_OVERRIDE.

W64

SIMD lane count for 64-bit elements (u64, i64, f64). Determined at build time based on target architecture capabilities, or overridden via SIMD_LANES_OVERRIDE.

Functions

binomial_cdf_scalar

Scalar binomial CDF

binomial_quantile_cornish_fisher

Compute the Cornish–Fisher-based binomial quantile for a single pi. Returns f64::NAN for any out-of-range or non-finite input. Does not handle nulls; caller is responsible.

chi2_newton_refine

Standard Newton refinement for chi-squared quantile computation.

chi2_newton_refine_extreme

Specialised Newton refinement for extreme chi-squared quantile computation.

gamma_func

Special cases:

gamma_pdf_scalar

Scalar gamma PDF for Newton refinement

half_integer_gamma

Evaluates gamma function at half-integer arguments using closed-form expression.

incomplete_beta

Regularised incomplete beta I_x(a, b).

incomplete_beta_inv

Inverse regularised incomplete beta I_x(a, b)

inv_reg_lower_gamma

Inverse of the regularised lower incomplete gamma: finds x such that P(a, x) = p (a>0, 0≤p≤1).

inv_reg_upper_gamma

Inverse of the regularised upper incomplete gamma: finds x such that Q(a, x) = q (a>0, 0≤q≤1), Q=1-P.

inv_std_normal

Computes the inverse standard normal cumulative distribution function (quantile function).

inv_std_normal_core

Core inverse standard normal function for left tail probabilities.

ln_choose

Computes logarithmic binomial coefficient for integer arguments with validation.

ln_choose_simd

Generic SIMD logarithmic binomial coefficient with compile-time lane count.

ln_choose_v

High-performance vectorised logarithmic binomial coefficient computation.

ln_gamma

Natural log of the absolute value of the Gamma function, ln|Γ(x)|.

ln_gamma_plus1

ln(k!) = ln_gamma(k+1)

ln_gamma_simd

Vectorised Lanczos ln Γ for x >= 1.0 (reflection not needed in binomial) Helper due to missing simd helpers in std_lib

normal_cdf_scalar

Evaluates standard normal cumulative distribution function with high accuracy.

normal_pdf_scalar

Evaluates standard normal probability density function at given point.

normal_quantile_scalar

Inverse CDF Φ⁻¹(q) for the normal distribution.

reg_lower_gamma

Regularised lower incomplete gamma P(a, x)

regularised_gamma_p

Regularised lower incomplete gamma (series + continued fraction).