fraction_equal

std.elementwise.fraction_equal · Level L3

Whether the fractions p/q and r/s (integers, q and s nonzero) are equal, as 1 or 0: ps = rq, exactly, without dividing. The same test decides a proportion a : b = c : d, ad = bc.

p/q = r/s ⇔ ps = rq

Signature

fraction_equal(p: i64[n], q: i64[n], r: i64[n], s: i64[n]) → 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.
Equal to the reference p·s == r·q in Python integers in exact rational arithmetic, on all 40 test cases.
All 156 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

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Called by

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sha256:8dbbc8cd9f97d3a2e8a45e5cbf2d538f17b288226000f473eed2101ff456e28f

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

Control handle

Symbol: Ω:std.elementwise.fraction_equal · Ω:fraction_equal
Pins: sha256:37873baa1544d5b9421dcac139d29e05b41e5a758e4f3b342bc6994fa53760cbthis graph alone
Evidence: sha256:74a7c2e3c1c09767973166008b16892cd67385bbf625d53c2443e271e8ca56ddthe 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.