Modulemath-functions-0.3.4.4Haskell2010

Numeric.MathFunctions.Comparison

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

6 values

Packagemath-functions-0.3.4.4
Exports6
LanguageHaskell2010
LicenceBSD-2-Clause
SourceComparison.hs

Relative erros

2 declarations

valuerelativeError :: 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

valueeqRelErr

:: 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

4 declarations

valueaddUlps :: Int -> Double -> Double

Add N ULPs (units of least precision) to Double number.

valueulpDistance :: 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.

valueulpDelta :: 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

valuewithin

:: 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.