Numeric.IEEE

Approximate comparison of floating point numbers based on the algorithm in Section 4.2.2 of Knuth's _Seminumerical Algorithms_ and NaN-aware minimum and maximum.

Relative accuracy within eps is measured using an interval of size 2*r, where r = 2^k eps, and k is the maximum exponent of x and y. If x and y lie within this interval, they are considered approximately equal.

Note that x and y are compared to relative accuracy, so these functions are not suitable for testing whether a value is approximately zero.

The implementation is based on the GNU Scientific Library implementation, which is based on the package fcmp by T.C. Belding.

NaN-aware minimum and maximum

maxF :: RealFloat a => a -> a -> a

A version of max that returns NaN if either argument is NaN.

minF :: RealFloat a => a -> a -> a

A version of min that returns NaN if either argument is NaN.

Relative comparisons

delta :: RealFloat a => a

A value suitable for relative comparisons when half of of the digits of precision are important. For Doubles this value is 7.450580596923828e-9.

epsilon :: RealFloat a => a

The smallest positive floating-point number x such that 1 + x != 1. Suitable for relative comparisons when all but the least significant digit of precision are important. For Doubles this value is 2.220446049250313e-16.

epsilon' :: RealFloat a => a

The smallest positive floating-point number x such that 1 - x != 1. Suitable for relative comparisons when one number is exact and all but the least significant digit of precision in the other number are important. For Doubles this value is 1.1102230246251565e-16.

eqRel :: RealFloat a => a -> a -> a -> Bool

eqRel eps x y. Relative equality comparator. Returns False if either argument is NaN.

neqRel :: RealFloat a => a -> a -> a -> Bool

neqRel eps x y. Relative inequality comparator. Returns False if either argument is NaN.

ltRel :: RealFloat a => a -> a -> a -> Bool

ltRel eps x y. Relative less-than comparator. Returns False if either argument is NaN.

lteRel :: RealFloat a => a -> a -> a -> Bool

lteRel eps x y. Relative less-than-or-equal-to comparator. Returns False if either argument is NaN.

gtRel :: RealFloat a => a -> a -> a -> Bool

gtRel eps x y. Relative greater-than comparator. Returns False if either argument is NaN.

gteRel :: RealFloat a => a -> a -> a -> Bool

gteRel eps x y. Relative greater-than-or-equal-to comparator. Returns False if either argument is NaN.

compareRel :: RealFloat a => a -> a -> a -> Ordering

compareRel eps x y gives an ordering of x and y based on a relative comparison of accuracy eps. This will call error if either argument is NaN.