sinc

std.elementwise.sinc · Level L5

The normalized sinc function, sin(πx)/(πx), and 1 at x = 0: the Fourier transform of a box, zero at every other integer. π is computed as arccos(−1), so in exact arithmetic the graph means π itself.

sinc x = sin(πx)/(πx), sinc 0 = 1

Signature

sinc(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 1 if x == 0 else np.sin(np.pi * x) / (np.pi * x) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 185 float64 results inside the running error bound; the closest uses 11% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 11% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 35%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 53

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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sha256:3158efc7e81aae50444476df5d7e36c3c0fba0293ce7009601d2afc37b7e952f

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.sinc · Ω:sinc
Pins: sha256:d3d51c803ef833b272a70d9c9e8239a57d577bf70cb89d0c4e51c436c70b2d7fthis graph alone
Evidence: sha256:c0ad6e61165da83aa8195b0f8de9501fd8c46e971dca21f1d4da653d0beeb6b0the 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.