complex_conj

std.elementwise.complex_conj · Level L2

The conjugate a − bi of each element of a complex vector stored as a [2, n] array. z·z̄ = |z|², a real number.

conj(a + bi) = a − bi

Signature

complex_conj(z: f64[2, n]) → f64[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 [z[0], -z[1]] in exact rational arithmetic, on all 40 test cases.
All 356 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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sha256:8eb5f115ca05cb9a95384b0e0be4dedb2c417167b5a239d6d764e81ccee96a79

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.complex_conj · Ω:complex_conj
Pins: sha256:53fa730dc4faeddd01c39f44cec85d796e5779db7b147071b02aa88071aa22aathis graph alone
Evidence: sha256:6b79c5d5c91360d6df476915b84edadf0b1ebe3554e810c919ec0a3ddc7881b3the 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.