reach_step
std.linalg.reach_step · Level L1One more edge of reachability: R ← min(1, R + R·A), so R picks up every vertex one step further along an edge. The body reachability scans; it does not read its sequence element.
R′ = min(1, R + R·A)
Signature
reach_step(R: f64[n, n], t: f64[], A: f64[n, n]) → f64[n, 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
np.minimum(1, R + R @ A)in exact rational arithmetic, on all 40 test cases. - All 917 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
sha256:0a96cd6691a5d1168d0d28df98c0bfdc6d0e9e6217d75db5a65d0c0c08ec59a9The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.reach_step · Ω:reach_step
- Pins
sha256:458c01a18d1ac716f21dbc91099e992acb8d937e6fe396262d3fcf0d4946bdbdthis graph alone- Evidence
sha256:28030a64e92e5fa783a8a90aacd6d821ce306923130a562ef2b28f4c3b8bf4b1the 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.