Overview of Floating-Point Ordering

Quxlang's built-in comparison operators give floating-point values a stable total order. This is useful when floats are keys, sorted values, or fields in a larger value:

VAR values [3]F32 :[0.0, -2.0, 5.0];

IF (values[0] < values[2])
{
  // The comparison participates in the same ordering model as other values.
}

The order distinguishes negative zero from positive zero and treats canonical NaN values as equal to each other. Generic comparison and serialization code can therefore use the same three-way ordering as other types.

IEEE predicates for numerical comparisons

Some algorithms require IEEE behavior instead. In particular, IEEE comparison treats both signed zeros as equal and treats every comparison with NaN as unordered:

VAR zero F32 := 0.0;
VAR negative_zero F32 := zero * (zero - 1.0);
VAR nan F32 := zero / zero;

ASSERT(zero != negative_zero);
ASSERT(IEEE_EQUALS(zero, negative_zero));

ASSERT(nan == nan);
ASSERT(IEEE_NOTEQUALS(nan, nan));

The built-in operators provide value identity and ordering for containers and generated structural operations. IEEE_EQUALS, IEEE_NOTEQUALS, IEEE_LESS, and IEEE_GREATER provide IEEE predicate semantics for numerical algorithms. Both forms use primitive floating-point comparisons and require no allocation.

The Floating-Point Ordering Reference specifies the complete special-value behavior and intrinsic requirements.