bisect_cube_step

std.seq.bisect_cube_step · Level L2

One bisection step for x³ = a: halve the bracket [lo, hi], keeping the half where x³ − a changes sign. The body that cbrt_bisect runs.

mid = (lo + hi)/2; mid³ > a ? [lo, mid] : [mid, hi]

Signature

bisect_cube_step(lohi: f64[2], a: f64[]) → f64[2]

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.

lohif64[2]af64[]SliceloSlicehiAddsum0.5MultiplymidMultiplym2Multiplym30.0SubtractfGreaterupWherenew_loWherenew_hiConcatnextnextf64[2]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference mid = (lo + hi)/2; [lo, mid] if mid**3 > a else [mid, hi] in exact rational arithmetic, on all 40 test cases.
  • All 80 float64 results inside the running error bound; the closest uses 49% of it.
  • Interpreter and NumPy backend return bit-identical results.
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
0.50

Identity

Calls
—
Called by
cbrt_bisect
sha256:67d3646d7cd8b0d833f4da0e1e055b5d0deb39bc5dcbf0871ab4b61f8fb26c6a

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol
Ω:std.seq.bisect_cube_step · Ω:bisect_cube_step
Pins
sha256:188f95821ff771dc41ffc5a1b1c74454352fdecd8e71ce710f6bd9505e9e44d6this graph alone
Evidence
sha256:26cd03e86de8a542c947c0022ea7adfb8c098af4d818570b33958a3179039137the 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.