philox_uniform

std.seq.philox_uniform · Level L5

Uniform draws in (0, 1) from Philox4x32-10, one per counter, under a key: 52 bits, the high 20 of the first word and all 32 of the second, as (v + ½)/2⁵². Exact in float64, and never 0 or 1. A key is a stream; counters 0, 1, 2, … are its draws, reproducible on every backend.

u = (⌊w₀/2¹²⌋·2³² + w₁ + ½) / 2⁵², (w₀, w₁, …) = Philox4x32-10((c, 0, 0, 0), key)

Signature

philox_uniform(counter: i64[n], key: i64[2]) → f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference (v + 1/2)/2^52 exactly, v from Philox4x32-10 on Python ints in exact rational arithmetic, on all 40 test cases.
All 171 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

philox4x32_10

Called by

philox_normal

sha256:6a9d9d0dc374932c2c2abeef3c73d4f85db77b3917dfb86ace79e5c4435c80bf

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.seq.philox_uniform · Ω:philox_uniform
Pins: sha256:b477a374240d7884d0b9f90d7d7c41e36ab330e74d9fbc8020446f513ff4f5abthis graph and the 3 it reaches through calls
Evidence: sha256:3d59431766cdbc5f2c0065f849d43c877295d4adc5dfb311c0d67ca791cfd9d4the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.