power_spectrum

std.seq.power_spectrum · Level L4

The power spectrum of a real signal: |yₖ|² for its discrete Fourier transform y, the energy at each frequency.

Pₖ = |Σⱼ xⱼ·e^(−2πi·jk/n)|²

Signature

power_spectrum(x: f64[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.
Agrees with the reference np.abs(np.fft.fft(x))**2 to 80 digits (100-digit arithmetic), on all 40 test cases.
All 166 float64 results inside the running error bound; the closest uses 12% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 49%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 98

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

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Called by

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sha256:8073d1ff1a6b6fe52eac4938e0f14adb0f51396f71e41e0419efbb965a42d70e

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.power_spectrum · Ω:power_spectrum
Pins: sha256:04d228dbe587c3c250bed89e7949f0733e8c84d799f3218fece2ccefcab28aa8this graph alone
Evidence: sha256:4d7f3315ecdec79226585109051791b89848037f4fb7df66e74d24d59ee3790cthe 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.