| Copyright | (c) 2011 Bryan O'Sullivan |
|---|---|
| License | BSD3 |
| Maintainer | bos@serpentine.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Numeric.MathFunctions.Comparison
Description
Functions for approximate comparison of floating point numbers.
Approximate floating point comparison, based on Bruce Dawson's "Comparing floating point numbers": http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
Synopsis
- relativeError :: Double -> Double -> Double
- eqRelErr :: Double -> Double -> Double -> Bool
- addUlps :: Int -> Double -> Double
- ulpDistance :: Double -> Double -> Word64
- ulpDelta :: Double -> Double -> Int64
- within :: Int -> Double -> Double -> Bool
Relative erros
relativeError :: Double -> Double -> Double #
Calculate relative error of two numbers:
\[ \frac{|a - b|}{\max(|a|,|b|)} \]
It lies in [0,1) interval for numbers with same sign and (1,2] for numbers with different sign. If both arguments are zero or negative zero function returns 0. If at least one argument is transfinite it returns NaN
Arguments
| :: Double | eps relative error should be in [0,1) range |
| -> Double | a |
| -> Double | b |
| -> Bool |
Check that relative error between two numbers a and b. If
relativeError returns NaN it returns False.
Ulps-based comparison
ulpDistance :: Double -> Double -> Word64 #
Measure distance between two Doubles in ULPs (units of least
precision). Note that it's different from abs (ulpDelta a b)
since it returns correct result even when ulpDelta overflows.
ulpDelta :: Double -> Double -> Int64 #
Measure signed distance between two Doubles in ULPs (units of least
precision). Note that unlike ulpDistance it can overflow.
>>> ulpDelta 1 (1 + m_epsilon) 1
Arguments
| :: Int | Number of ULPs of accuracy desired. |
| -> Double | |
| -> Double | |
| -> Bool |
Compare two Double values for approximate equality, using
Dawson's method.
The required accuracy is specified in ULPs (units of least
precision). If the two numbers differ by the given number of ULPs
or less, this function returns True.