Function smoothing_width 

fn smoothing_width(prox: f64, n: f64, sigma: f64) -> f64

The Gaussian width SDF smooths a voxel with: sigma*round(prox^n, 2), as sdf_curvature.m computes it.

Rounding to two decimals makes the width a discrete choice, which has to come out the same on every target (or the browser and qsmxt run smooth a voxel on a rounding boundary with different widths, and the inner inversion spreads the difference) and the same as MATLAB’s:

• prox^n comes from portable_math::pow, and the proximity map it is computed from uses only portable functions too (the Gaussian kernels here and the curvature’s angles). The platform’s powf differs between targets in the last bit for about one input in ten, and a one-ulp difference flips the rounding whenever the value sits within an ulp of a hundredth’s midpoint.
• The operations are MATLAB’s, in MATLAB’s order: round(x, 2) is round(x*100)/100, with halves rounded away from zero (as f64::round does), then multiplied by sigma. With QSMART’s own proximity map (prox.nii from its 3 T reference run) as input, this gives its alpha.nii bit for bit, for both stages. sigma*round(x*100)/100 evaluated left to right (as before) differs in the last bit in a quarter of the brain.

No libm is correctly rounded, MATLAB’s included, so a value within an ulp of a midpoint can still round differently from MATLAB; away from midpoints every pow within an ulp of the exact value gives MATLAB’s width.