philox4x32_round

std.seq.philox4x32_round · Level L5

One round of Philox4x32 on every counter at once: with the round key k = key + r·W mod 2³² and (hi, lo) the halves of M·x, the words (x₀, x₁, x₂, x₃) become (hi₁ ⊕ x₁ ⊕ k₀, lo₁, hi₀ ⊕ x₃ ⊕ k₁, lo₀). The body that philox4x32_10 scans, once per round r.

(x₀, x₁, x₂, x₃) ← (hi(M₁x₂) ⊕ x₁ ⊕ k₀, lo(M₁x₂), hi(M₀x₀) ⊕ x₃ ⊕ k₁, lo(M₀x₀)), k = key + r·W mod 2³²

Signature

philox4x32_round(ctr: i64[4, n], r: i64[], key: i64[2]) → i64[4, 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 one Philox4x32 round on Python ints, with M = (0xD2511F53, 0xCD9E8D57), W = (0x9E3779B9, 0xBB67AE85) in exact rational arithmetic, on all 40 test cases.
All 516 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

mulhilo32

Called by

philox4x32_10

sha256:58e53cd53c400a2ae3ee2365431f3e442093a21e12a70e00e8e43262e0e4e6fc

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.philox4x32_round · Ω:philox4x32_round
Pins: sha256:4aa14e00ab9a72f5b5f906514699a910d4632ebb05f87dfa75ce93d0b1093811this graph and the 1 it reaches through calls
Evidence: sha256:a98df37898c5761e39b1d72956ad4a01703cafd4ffdf917ecbbf92015ba69f58the 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.