philox_normal

std.seq.philox_normal · Level L5

Standard normal draws from Philox4x32-10, one per counter: Φ⁻¹ of philox_uniform. Inverse-transform sampling; the uniform never reaches 0 or 1, so every draw is finite (|z| < 8.3).

z = Φ⁻¹(philox_uniform(c, key))

Signature

philox_normal(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.
Agrees with the reference Φ⁻¹ of the exact Philox uniform, at 100 digits to 80 digits (100-digit arithmetic), on all 40 test cases.
All 126 float64 results inside the running error bound; the closest uses 25% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 42%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 69

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

philox_uniform

Called by

—

sha256:81d052c7232d09b5671b5a56e8945c18fc83bd06a302d486ab02837d88dbbab0

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_normal · Ω:philox_normal
Pins: sha256:a4f5bc18fe99d2352bf824b306a5e1c0f03358a550bfe6e1d63be8931b32c585this graph and the 4 it reaches through calls
Evidence: sha256:674f115d4d1e60329c4dcd04012f6a3a09fc7af302aa49f92a489854966c0633the 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.