ipow
std.elementwise.ipow · Level L4xᵏ for a real x and an integer k ≥ 0, elementwise, by binary exponentiation: at most 2·log₂k + 1 multiplications. x⁰ = 1, 0⁰ included.
Signature
ipow(x: f64[n], k: i64[n]) → f64[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
x ** kin exact rational arithmetic, on all 40 test cases. - All 171 float64 results inside the running error bound; the closest uses 72% 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 53% of it.
- correctly rounded (the float64 nearest the exact value)
- 54%
- bit-equal to the NumPy formula in float64
- 54%
- largest error, in units in the last place
- 12
Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.
Identity
sha256:da7ab54fee3c040cb45881b564c526ce06dff9ed2b0384e63fb97eefa67e2ec0The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.elementwise.ipow · Ω:ipow
- Pins
sha256:e31af51a805b8eeec9167015d10d96de7f04324338b9a3aac2f9013c71b0a5a4this graph and the 2 it reaches through calls- Evidence
sha256:b7c3db7c6d28e2b42763b5761f289e0d7efc13206e38f33ffc27429b597b65ccthe 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.