crdistr: crdist for Python

The normal distribution over NumPy arrays, from crnumerics' C library libcrdist: erfinv, erfcinv, probit (the standard normal quantile: R's qnorm, SciPy's ndtri), ndtr, log_ndtr, normpdf and logit, correctly rounded to nearest in binary32, binary16 and bfloat16, every input of each checked against MPFR on x86-64 and aarch64; and samplers on a Philox4x32-10 stream. The results are the same bits on every machine, in any floating-point environment.

import numpy as np, crdistr
crdistr.probit(np.float32(0.975))                  # 1.959964, the float32 nearest the exact quantile
u = np.random.default_rng(1).random(10, dtype=np.float32)
z = crdistr.probit(u)                              # normal draws: the same everywhere for the same u
crdistr.erfinv(np.array([0.1, 0.5], np.float16))   # binary16 in, binary16 out, rounded once
crdistr.log_ndtr(np.float32(-40))                  # log Phi(-40) = -804.6084, where Phi underflows binary64
s = crdistr.Stream(seed=42)                        # Philox4x32-10, (seed, substream, index)
g = s.gamma(1000, shape=2.5)                      # the same bits on every machine

Also ndtr (Phi), normpdf and logit, correctly rounded like the inverses; and Stream's uniform, normal, exponential, gamma, beta, chisquared, student_t, poisson, binomial (int64) and words, whose bits are fixed by the specification in crdist.h (the tests check the binding against its recorded fingerprints).

The format follows the input. float16 arrays use binary16, and ml_dtypes' bfloat16 arrays use bfloat16; for bfloat16 bit patterns given as uint16, use erfinv_bf16, erfcinv_bf16 and probit_bf16. float32 uses binary32. Anything else is converted to float32 first, rounded to nearest, so a float64 0.1 becomes float32's 0.1 before the function sees it.

The library is libcrdist.so.0, from crnumerics' make install (or CRDIST_LIBRARY naming it). The tests (make crdist-python-check at crnumerics' root) compare results with mpmath, rounded once to each format. Linux (x86-64, aarch64) and macOS (Apple Silicon). pip install crdistr, then import crdistr: the name is crdistr on PyPI and as a module, "crdist" on PyPI being an unrelated project (the C library is still crdist: libcrdist, crdist.h).