normal_draws

std.stats.normal_draws · Level L5

One standard normal number for each element of x, by inverse-transform sampling: Φ⁻¹ of the Wichmann–Hill uniform draws. Reproducible from its state.

Φ⁻¹(uniform_draws(state, x))

Signature

normal_draws(state: i64[3], x: f64[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.

statei64[3]xf64[n]uniform_drawsuNdtrizzf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference Φ⁻¹ of the exact Wichmann–Hill draws to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 128 float64 results inside the running error bound; the closest uses 45% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
11%
bit-equal to the NumPy formula in float64
33%
largest error, in units in the last place
50

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

Calls
uniform_draws
Called by
—
sha256:b461e3982e95e6739c503f0b4477183be34553b32126eb6f9de23016b3ebde2d

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