Module stability 

Numerical stability improvements

Numerical Stability Improvements

This module provides numerically stable implementations of common algorithms that are prone to precision loss, overflow, or catastrophic cancellation.

Features

• Stable summation algorithms (Kahan, pairwise, compensated)
• Robust variance and standard deviation calculations
• Overflow-resistant multiplication and exponentiation
• Stable trigonometric range reduction
• Robust normalization techniques
• Improved root finding with bracketing
• Stable matrix condition number estimation

Structs

KahanSum

Kahan summation algorithm for accurate floating-point summation

WelfordVariance

Welford’s online algorithm for computing variance

Enums

MatrixNorm

Matrix norm types

Traits

StableComputation

Trait for numerically stable computations

Functions

binomial_stable

Stable computation of binomial coefficients

condition_number_estimate

Condition number estimation using 1-norm

cross_entropy_stable

Cross entropy loss with numerical stability

expm1_stable

Stable computation of exp(x) - 1 for small x

factorial_stable

Numerically stable factorial computation

hypot_stable

Stable computation of sqrt(x² + y²) avoiding overflow

log1p_stable

Stable computation of log(1 + x) for small x

log_sigmoid_stable

Numerically stable log-sigmoid function

log_sum_exp

Log-sum-exp trick for stable computation of log(sum(exp(x)))

mulmod_stable

Stable computation of (a*b) % m avoiding overflow

neumaier_sum

Neumaier summation algorithm (improved Kahan summation)

pairwise_sum

Pairwise summation algorithm

reduce_angle

Stable angle reduction for trigonometric functions

sigmoid_stable

Numerically stable sigmoid function

stable_mean

Stable mean calculation using compensated summation

stable_norm_2

Stable L2 norm computation avoiding overflow/underflow

stable_softmax

Stable softmax computation

stable_variance

Stable two-pass algorithm for variance calculation

stablematrix_norm

Stable matrix norm computation