ie_step
std.sets.ie_step · Level L4One term of inclusion-exclusion: for the index set I given by the bits of c, (−1)^(|I|+1)·|∩_{i ∈ I} S_i|, added to the running total (the empty I adds nothing). The body inclusion_exclusion runs.
(−1)^(|I|+1) |∩_{i∈I} S_i|
Signature
ie_step(c: f64[], total: f64[], S: f64[s, m], pow2: f64[s], count: f64[]) → 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
the bits of c, the intersection of the chosen rows, the sign of |I|in exact rational arithmetic, on all 40 test cases. - All 80 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
sha256:50186f7e31bcb14acfb10490b47545f99e204da9a23789f3edd24ba745e8ec3eThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.sets.ie_step · Ω:ie_step
- Pins
sha256:27ec2310b54029786d19c1a7f422e71a3394e4a364cf6f97ec7c816288904ffbthis graph alone- Evidence
sha256:2e7ca772b73ccd925c73c88bceebb5d0c76e23f40d726bc90e8df8999099794fthe 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.