inverse_permutation

std.seq.inverse_permutation · Level L3

The inverse of a permutation: inv[perm[i]] = i. Each position is scattered to where it came from, then Cast back to integers.

inv[permᵢ] = i

Signature

inverse_permutation(perm: i64[n]) → i64[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.

permi64[n]Iotapos0.0MultiplyblankScatterAddplacedCastinvinvi64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.argsort(perm) in exact rational arithmetic, on all 40 test cases.
  • All 178 int64 results are exact: the error is zero.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the int64 nearest the exact value)
100%
bit-equal to the NumPy formula in int64
100%
largest error, in units in the last place
0

Identity

Calls
—
Called by
—
sha256:c754fdcea214e333b904f5b11a8183b000e38989146fbc4b9e6dc941fb5e1e61

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.inverse_permutation · Ω:inverse_permutation
Pins
sha256:5c45caf603188ad453754a87dcb92e8b47d43d0eaa1542b04e55de7191cd3a30this graph alone
Evidence
sha256:bfe84fe36f858b639b5f229f7bbfb6181d0872cb7c320e8f87b317def4fade05the 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.