poly_hash

std.seq.poly_hash · Level L4

A polynomial rolling hash of a sequence of byte codes: a Scan of hash_step from 0, keeping the last value. Equal sequences hash equally; it is not a cryptographic hash.

h = Σᵢ cᵢ·131ⁿ⁻¹⁻ⁱ mod 1 000 000 007

Signature

poly_hash(codes: i64[n]) → i64[]

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.

codesi64[n]0Scan·hash_steppartialSlicelastReshapehhi64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference h = (h * 131 + c) % p, over the codes in exact rational arithmetic, on all 40 test cases.
  • All 40 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
hash_step
Called by
—
sha256:15bb647d8da6ccffe0a5743a97ab6e82d9ec90914a5d7a023fdbc080cf221ebf

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.poly_hash · Ω:poly_hash
Pins
sha256:dfdfceaf5ba69cf5ca9d2ecd076653470ab645f5f4f276d41544d499142035dathis graph and the 1 it reaches through calls
Evidence
sha256:fed59903d1f2ce33d39fd37c520ddab8a57e3ae1b9bd923aa4c1af9ae36fec9cthe 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.