pf_random_normal_at Interface

public interface pf_random_normal_at

One standard normal draw: value draw (default 1) of stream i under seed.

i is integer(int32) or integer(int64); seed and draw are integer(int64). Mean 0, variance 1, and the whole real line is reachable up to what the tail algorithm can produce.

Ziggurat over 256 equal-area layers (parquet_ziggurat), which accepts 98.5 % of draws after one 64-bit read and falls back to a wedge test or a tail walk otherwise. Bit-identical for a given libm: the wedge test needs exp and the tail needs log. pf_random_normal_portable_at is the same distribution through a frozen logarithm, identical on every platform.

This does NOT equal %normal at the same coordinate, and that is deliberate. A rejection algorithm consumes a number of words that depends on the values it drew, so no caller can say where value k of a stream walk begins without having drawn the preceding k-1 -- which would make a chunked or threaded fill impossible. The coordinate-addressed forms sidestep that by giving each (i, draw) its own derived sub-stream, so this value is a pure function of its coordinates and a bulk fill splits anywhere. The stream walk cannot do that, because being a walk is its purpose. See pf_normal_algorithm, and pf_random_exp_at for the one distribution where the two DO agree.

Independent of pf_random_normal_portable_at at the same coordinate, by construction: the two derive their sub-streams through different labels, so they are two normals rather than two functions of one uniform. Same for either one against its own stream walk.

Module Procedures