newton_unconverged
std.func.newton_unconverged · Level L1Whether any residual |f(x) − y| is still above tol, as 1 or 0. The condition newton loops on. A template over f.
[ maxᵢ |f(xᵢ) − yᵢ| > tol ]
Signature
newton_unconverged(x: f64[n], y: f64[n], tol: 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.
- Agrees with the reference
witness f = softplus: float(np.max(np.abs(softplus(x) - y)) > tol)to 80 digits (100-digit arithmetic), on all 40 test cases. - All 40 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
sha256:95b9ff16de676dac45fcf456ed03458872c6463f3b9835c069a531824eea21eaThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.func.newton_unconverged[f=std.elementwise.softplus]
- Pins
sha256:daf740754aa47662108f17ec22b0768f0ece60f721ac3bdf2c250b23fec9a0aathis graph and the 2 it reaches through calls- Evidence
sha256:a684a671605813232a1ddbfbfb8f128c28c638d844eabbeac92c916e372419ccthe 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.