[fractionalhare]

This is a good explanation of range reduction with respect to floating point. I use a similar (but not quite identical) techniue in the article; I may expand it with more information about what's happening with the exponent and mantissa bits like you did here.

That reminds me, I'm using the domain [-1, 1] for range reduction. But by symmetry of e^x, I can actually use [0, 1]. Thank you!

[dietrichepp]

Depending on the particular architecture you may prefer [-0.5, +0.5].