Three-way Comparison - Machine-level Computation

Machine-level Computation

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 we adopt a consistent total order: 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).

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