Three-way comparison

In computer science, a three-way comparison takes two values A and B belonging to a type with a total order and determines whether A < B, A = B, or A > B in a single operation, in accordance with the mathematical law of trichotomy. In computer science, a three-way comparison takes two values A and B belonging to a type with a total order and determines whether A < B, A = B, or A > B in a single operation, in accordance with the mathematical law of trichotomy. Many processors have instruction sets that support such an operation on primitive types.Some machines have signed integers based on a sign-and-magnitude or one's complement representation (see signed number representations), both of which allow a differentiated positive and negative zero. This does not violate trichotomy as long as a consistent total order is adopted: either −0 = +0 or −0 < +0 is valid. Common floating point types, however, have an exception to trichotomy: there is a special value 'NaN' (Not a Number) such that x < NaN, x > NaN, and x = NaN are all false for all floating-point values x (including NaN itself). In C, the functions strcmp and memcmp perform a three-way comparison between strings and memory buffers, respectively. They return a negative number when the first argument is lexicographically smaller than the second, zero when the arguments are equal, and a positive number otherwise. This convention of returning the 'sign of the difference' is extended to arbitrary comparison functions by the standard sorting function qsort, which takes a comparison function as an argument and requires it to abide by it. C++20 adds the 'spaceship operator' <=>, which similarly returns the sign of the difference and can also return different types (convertible to signed integers) depending on the strictness of the comparison. In Perl (for numeric comparisons only, the cmp operator is used for string lexical comparisons), PHP (since version 7), Ruby, and Apache Groovy, the 'spaceship operator' <=> returns the values −1, 0, or 1 depending on whether A < B, A = B, or A > B, respectively. In Python 2.x cmp (removed in 3.x), OCaml and Kotlin, the cmp, compare and compareTo functions compute the same thing, respectively. In the Haskell standard library, the three-way comparison function compare is defined for all types in the Ord class; it returns type Ordering, whose values are LT (less than), EQ (equal), and GT (greater than): Many object-oriented languages have a three-way comparison method, which performs a three-way comparison between the object and another given object. For example, in Java, any class that implements the Comparable interface has a compareTo method which either returns a negative integer, zero, or a positive integer, or throws a NullPointerException (if one or both objects are null). Similarly, in the .NET Framework, any class that implements the IComparable interface has such a CompareTo method. Since Java version 1.5, the same can be computed using the Math.signum static method if the difference can be known without computational problems such as arithmetic overflow mentioned below. Many computer languages allow the definition of functions so a compare(A,B) could be devised appropriately, but the question is whether or not its internal definition can employ some sort of three-way syntax or else must fall back on repeated tests.