modes

std.stats.modes · Level L2

The modes of a finite list of observations: the values that occur most often. Returned as the sorted observations with a 0/1 mark on the first occurrence of each mode, so the mode set is the marked values in increasing order. When every value occurs once, every value is a mode.

modes = {v : #{i : xᵢ = v} = max}

Signature

modes(x: f64[n]) → 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.
Equal to the reference sorted(x); mark the first occurrence of each value of maximal frequency 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:ddc7cb2ab0a728eeca0f517301ee5606208d55d126563e54dacc1840126890c4

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

Control handle

Symbol: Ω:std.stats.modes · Ω:modes
Pins: sha256:f7503c018b3ce692add46d4294cbdc244edefeadb98ffb3ee4954b63a4330122this graph alone
Evidence: sha256:8a770d858a54e8be5ba80bfa11b845c2e49ab37d58d166572c9ff74b70ac58b4the 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.