Data.Number.LogFloat
 Portability portable Stability provisional Maintainer wren@community.haskell.org
 Contents Exceptional numeric values LogFloat data type and conversion functions
Description

This module presents a type for storing numbers in the log-domain. The main reason for doing this is to prevent underflow when multiplying many small probabilities as is done in Hidden Markov Models and other statistical models often used for natural language processing. The log-domain also helps prevent overflow when multiplying many large numbers. In rare cases it can speed up numerical computation (since addition is faster than multiplication, though logarithms are exceptionally slow), but the primary goal is to improve accuracy of results. A secondary goal has been to maximize efficiency since these computations are frequently done within a O(n^3) loop.

The LogFloat of this module is restricted to non-negative numbers for efficiency's sake, see the forthcoming Data.Number.LogFloat.Signed for doing signed log-domain calculations.

Synopsis
 module Data.Number.Transfinite data LogFloat logFloat :: (Real a, RealToFrac a Double) => a -> LogFloat logToLogFloat :: (Real a, RealToFrac a Double) => a -> LogFloat fromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> a logFromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> a
Exceptional numeric values
module Data.Number.Transfinite
LogFloat data type and conversion functions
 data LogFloat Source

A LogFloat is just a Double with a special interpretation. The logFloat function is presented instead of the constructor, in order to ensure semantic conversion. At present the Show instance will convert back to the normal-domain, and so will underflow at that point. This behavior may change in the future.

Performing operations in the log-domain is cheap, prevents underflow, and is otherwise very nice for dealing with miniscule probabilities. However, crossing into and out of the log-domain is expensive and should be avoided as much as possible. In particular, if you're doing a series of multiplications as in lp * logFloat q * logFloat r it's faster to do lp * logFloat (q * r) if you're reasonably sure the normal-domain multiplication won't underflow, because that way you enter the log-domain only once, instead of twice.

Even more particularly, you should avoid addition whenever possible. Addition is provided because it's necessary at times and the proper implementation is not immediately transparent. However, between two LogFloats addition requires crossing the exp/log boundary twice; with a LogFloat and a regular number it's three times since the regular number needs to enter the log-domain first. This makes addition incredibly slow. Again, if you can parenthesize to do plain operations first, do it! Instances
 Eq LogFloat Fractional LogFloat Num LogFloat Ord LogFloat Real LogFloat Show LogFloat PartialOrd LogFloat
 logFloat :: (Real a, RealToFrac a Double) => a -> LogFloat Source
 logToLogFloat :: (Real a, RealToFrac a Double) => a -> LogFloat Source
 fromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> a Source
 logFromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> a Source