Data.Ord

Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions.

Lexicographic order.

IEEE 754 Double-precision type includes not only numbers, but also positive and negative infinities and a special element called NaN (which can be quiet or signal).

IEEE 754-2008, section 5.11 requires that if at least one of arguments of <=, <, >, >= is NaN then the result of the comparison is False, and instance Ord Double complies with this requirement. This violates the reflexivity: both NaN <= NaN and NaN >= NaN are False.

IEEE 754-2008, section 5.10 defines totalOrder predicate. Unfortunately, compare on Doubles violates the IEEE standard and does not define a total order. More specifically, both compare NaN x and compare x NaN always return GT.

Thus, users must be extremely cautious when using instance Ord Double. For instance, one should avoid ordered containers with keys represented by Double, because data loss and corruption may happen. An IEEE-compliant compare is available in fp-ieee package as TotallyOrdered newtype.

Moving further, the behaviour of min and max with regards to NaN is also non-compliant. IEEE 754-2008, section 5.3.1 defines that quiet NaN should be treated as a missing data by minNum and maxNum functions, for example, minNum(NaN, 1) = minNum(1, NaN) = 1. Some languages such as Java deviate from the standard implementing minNum(NaN, 1) = minNum(1, NaN) = NaN. However, min / max in base are even worse: min NaN 1 is 1, but min 1 NaN is NaN.

IEEE 754-2008 compliant min / max can be found in ieee754 package under minNum / maxNum names. Implementations compliant with minimumNumber / maximumNumber from a newer IEEE 754-2019, section 9.6 are available from fp-ieee package.

See instance Ord Double for discussion of deviations from IEEE 754 standard.

Byte ordering of the internal representation.

Byte ordering of the internal representation.

Scientific numbers can be safely compared for ordering. No magnitude 10^e is calculated so there's no risk of a blowup in space or time when comparing scientific numbers coming from untrusted sources.

Lexicographic ordering. Subject to change between major versions.

Lexicographic ordering. Subject to change between major versions.

Lexicographic ordering. Subject to change between major versions.

The ordering is total and consistent with the Eq instance. However, nothing else about the ordering is specified, and it may change from version to version of either this package or of hashable.

Swaps minBound and maxBound of the underlying type.

Swaps succ and pred of the underlying type.

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed