[Random, Alignment] Refactor np.random.* to match NumPy parity

[Nucs]

Overview

Major refactor of NumSharp's random sampling module to achieve 1-to-1 parity with NumPy 2.x. This includes replacing the RNG engine, implementing 25 missing distributions, and standardizing the API surface.

Problem

NumSharp's np.random.* had several critical misalignments with NumPy:

1. Different RNG algorithm — NumSharp used .NET's Subtractive Generator (Knuth), while NumPy uses Mersenne Twister (MT19937). Same seed produced completely different sequences.

2. Missing distributions — Only ~10 of NumPy's 35+ distributions were implemented.

3. Inconsistent API — Size parameters, scalar returns, and validation differed from NumPy behavior.

4. No long indexing — Size parameters used int instead of long, limiting array sizes.

Proposal

RNG Engine Replacement

• Implement MT19937 (Mersenne Twister) to match NumPy's random state
• Add NextGaussian() for Box-Muller transform (normal distribution)
• Verify seed compatibility: np.random.seed(42) produces identical sequences

Missing Distributions (25 new)

• weibull, standard_cauchy, vonmises, f, logseries
• standard_normal, standard_t, triangular
• dirichlet, gumbel, hypergeometric, laplace, logistic
• multinomial, multivariate_normal, negative_binomial
• noncentral_chisquare, noncentral_f, pareto, power
• rayleigh, standard_exponential, standard_gamma
• wald, zipf

API Standardization

• Migrate all distributions to UnmanagedMemoryBlock
• Standardize size parameter overloads: int[] + params long[]
• Align scalar returns (0D arrays) with NumPy
• Fix size/axis/seed validation to match NumPy

Multivariate Normal Fix

• Implement SVD-based algorithm for covariance decomposition
• Match NumPy's eigenvector sign convention

Evidence

Before (seed=42, first value):

Function	NumPy	NumSharp (old)
rand()	0.3745401188	0.6681064659 ❌
randn()	0.4967141530	Different ❌
randint(0,10)	6	Different ❌

After:
All functions produce identical sequences to NumPy given the same seed.

Scope / Non-goals

In scope:

• Legacy np.random.* API (RandomState-style)
• All distributions available in NumPy 2.x legacy API

Not in scope:

• NumPy's new Generator API (np.random.default_rng())
• BitGenerator architecture
• PCG64/Philox/SFC64 generators

Breaking Changes

Change	Impact	Migration
RNG sequences differ	Code relying on specific random values with fixed seeds	Re-generate expected values or remove seed-dependent assertions
params int[] removed	rand(5, 10) no longer compiles	Use rand(5L, 10L) or rand(new Shape(5, 10))
Scalar returns are 0D	rand().GetDouble() → rand().GetDouble(0)	Add index [0] or use .GetValue()

Benchmark / Performance

• MT19937 performance is comparable to .NET's RNG
• UnmanagedMemoryBlock migration eliminates managed array allocations
• No measurable regression in distribution sampling

Related Issues

• Depends on longindexing branch for long array indexing support
• Enables future work on Generator API (NumPy 1.17+ style)

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Summary

• 49 commits, 100 files changed, +20,930 / -666 lines
• 25 new distributions implemented
• MT19937 RNG engine for NumPy seed compatibility
• Comprehensive test coverage
• Documentation: NUMPY_RANDOM.md, RANDOM_MIGRATION_PLAN.md