Biobase.Types.NumericalExtremes

For some values, we want to have different kind of extreme values. Consider a Double representing an energy. We want near infinities that do not lead to numeric problems.

TODO benchmark different extremes and their interplay with algebraic operations.

TODO consider the ieee754 package

Documentation

class NumericalExtremes x where

Very large and small numbers with some numerical safety to 1/0 or maxBound (depending on if we are Integral or RealFloat.

We have:

maxFinite >= extremelyLarge >= veryLarge

veryLarge >= verySmall

verySmall >= extremelySmall >= minFinite.

TODO the small stuff should actually be around zero, but positive and go into NumericalEpsilon. Here we should actually use other names.

Methods

maxFinite :: x

Largest finite number

minFinite :: x

Smallest finite number

veryLarge :: x

Around 1/100 of the largest finite number

verySmall :: x

Around 1/100 of the smallest finite number

extremelyLarge :: x

Around 1/ 10 of the largest finite number

extremelySmall :: x

Around 1/ 10 of the smallest finite number

Instances

NumericalExtremes Double

NumericalExtremes Int

NumericalExtremes DeltaGibbs

NumericalExtremes DeltaDekaGibbs

class NumericalEpsilon x where

Small numbers.

Methods

epsilon :: x

Smallest positive number /= 0.0.

Instances

NumericalEpsilon Double

NumericalEpsilon DeltaGibbs