mulhilo32

std.seq.mulhilo32 · Level L4

The 64-bit product of two 32-bit words, as its high and low halves: [⌊a·b/2³²⌋, a·b mod 2³²]. Composed from 16-bit halves, so every intermediate stays below 2³⁴ and int64 holds it exactly; a·b itself would not fit.

[⌊a·b / 2³²⌋, a·b mod 2³²]

Signature

mulhilo32(a: i64[n], b: i64[n]) → i64[2, 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 [(a*b) >> 32, (a*b) & 0xFFFFFFFF] on Python ints in exact rational arithmetic, on all 40 test cases.
All 292 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

philox4x32_round

sha256:7ed3bf9b5cb9095f83ca2d8c10f2a6ca6303ef8c8781f8ced677e50fb968a4ec

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.mulhilo32 · Ω:mulhilo32
Pins: sha256:41f52129b121d7db9f8e721a15bebd9e2f482ece74ce99415f3ff10e3d193858this graph alone
Evidence: sha256:1830390600593f17550556700666b9c4cf2e049c230de0385d7733c1f68294a4the 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.