synth_step
std.seq.synth_step · Level L0One coefficient of a synthetic-division pass: out = cⱼ + mⱼ·a·(the previous output), where the mask mⱼ says whether this coefficient takes part in the pass. The body taylor_pass scans.
outⱼ = cⱼ + mⱼ·a·outⱼ₋₁
Signature
synth_step(prev: f64[], cj: f64[], mj: f64[], a: f64[]) → f64[]
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
cj + mj*a*previn exact rational arithmetic, on all 40 test cases. - All 40 float64 results inside the running error bound; the closest uses 46% 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 45% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 90%
- bit-equal to the NumPy formula in float64
- 100%
- largest error, in units in the last place
- 3.80
Identity
sha256:4766a32f25e250e4614adb1500359c7a296b4b9edd14ee805a7e09888991f43cThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.synth_step · Ω:synth_step
- Pins
sha256:3f9c7145dc0ac11691abf397bea11af2a8ee010a648e1b928f0cdfd907a69b31this graph alone- Evidence
sha256:b09a56e67350ead6c86cbdca08daba16e68264af7d59e0878540278ecd388dbcthe 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.