bareiss_step

std.linalg.bareiss_step · Level L4

One column of fraction-free Gaussian elimination (Bareiss) on an integer matrix: if some row at or below r has a nonzero entry in column c, swap the first such row into row r and replace each later row by (p·row − M[i, c]·row r)/prev, which is exact (p the new pivot, prev the one before), then r ← r + 1; otherwise nothing changes. The body rank_exact scans.

row_i ← (p·row_i − M[i, c]·row_r)/prev

Signature

bareiss_step(M: f64[m, n], r: f64[], prev: f64[], c: f64[]) → f64[m, n], f64[], f64[]

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 the same elimination on Python integers in exact rational arithmetic, on all 40 test cases.
All 536 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

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

—

Called by

rank_exact

sha256:8b3c4aa62f342bb9c1443891e86f81d795a226f117286160203874501a029cb8

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

Control handle

Symbol: Ω:std.linalg.bareiss_step · Ω:bareiss_step
Pins: sha256:4ec0eff335748de59bdc4085f110bed7305b7bdb316a4bb2fa06a7ff1205f943this graph alone
Evidence: sha256:ae82c0787535f6956fe123ae75427887b33cb7fcaa4adabeb9a53f9fee9d6080the 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.