wichmann_hill_step

std.seq.wichmann_hill_step · Level L4

One step of the Wichmann–Hill generator (AS 183, 1982): three small multiplicative congruential generators side by side, each sᵢ ↦ aᵢ·sᵢ mod mᵢ. It is the body uniform_draws scans; the element it is handed only sets how many steps there are.

sᵢ′ = aᵢ·sᵢ mod mᵢ, a = (171, 172, 170), m = (30269, 30307, 30323)

Signature

wichmann_hill_step(state: i64[3], x: f64[]) → i64[3]

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 (171·s₁ mod 30269, 172·s₂ mod 30307, 170·s₃ mod 30323) in exact rational arithmetic, on all 40 test cases.
All 120 int64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the int64 nearest the exact value): 100%
bit-equal to the NumPy formula in int64: 100%
largest error, in units in the last place: 0

Identity

Calls

—

Called by

uniform_draws

sha256:7636adf5fff65dc1feb3e0a0237a9e7c5d72421ef1e7e14439e3737d525ea0be

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.wichmann_hill_step · Ω:wichmann_hill_step
Pins: sha256:3cee394fad425303e81f7e470b6625340edc93a70910e186cfa14395d870ca38this graph alone
Evidence: sha256:842223b2da0793fcddcb3bc40c14c20dfaa33a49a41f93e6c9d98379bf023fe0the 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.