logfloat-0.9.1.3: Log-domain floating point numbers

Data.Number.LogFloat

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

# `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 `LogFloat`s 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!

logFloat :: (Real a, RealToFrac a Double) => a -> LogFloatSource

A constructor which does semantic conversion from normal-domain to log-domain.

logToLogFloat :: (Real a, RealToFrac a Double) => a -> LogFloatSource

Constructor which assumes the argument is already in the log-domain.

fromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> aSource

Return our log-domain value back into normal-domain. Beware of overflow/underflow.

logFromLogFloat :: (Fractional a, Transfinite a, RealToFrac Double a) => LogFloat -> aSource

Return the log-domain value itself without costly conversion