AdjacentFloats.jl

Faster versions of nextfloat, prevfloat that work similarly.

Copyright © 2017 by Jeffrey Sarnoff. Released under the MIT License.

Build Status

exports

next_float, prev_float

they run twice as fast as nextfloat, prevfloat (or better)

notes

These routines return +/-Inf when given +/-Inf.

That differs from nextfloat(-Inf) == -realmax(), prevfloat(Inf) == realmax()

  • prevfloat(Inf)==Inf makes more sense to me, and likely is more helpful

They may step as much as two times when given values of very small magnitude (see paper).

references

Siegfried Rump, Paul Zimmermann, Sylvie Boldo, Guillaume Melquiond.

Computing predecessor and successor in rounding to nearest.

BIT Numerical Mathematics, Springer Verlag, 2009, 49 (2), pp.419-431.

http://dx.doi.org/10.1007/s10543-009-0218-z

https://hal.inria.fr/inria-00337537/document

"The routines deliver the exact answer except for a small range near underflow,

in which case the true result is overestimated by eta [the value added/subtracted]."

Siefried M. Rump, Takeshi Ogita, Yusuke Morikura, Shin'ichi Oishi.

Interval arithmetic with fixed rounding mode.

Nonlinear Theory and Its Applications, IEICE, 2016, 7 (3), pp. 362-373

http://dx.doi.org/10.1587/nolta.7.362

http://www.ti3.tu-harburg.de/paper/rump/RuOgMoOi16.pdf