floatinf

Floatinf is a term sometimes used to denote the positive infinity value in floating-point arithmetic. It is not a formal standard name, but it appears in codebases and documentation as a shorthand for an unbounded numeric value represented within floating-point formats such as IEEE 754.

Representation and semantics

In IEEE 754 floating-point systems, positive infinity is encoded as an exponent of all ones with a zero fraction, while negative infinity has the sign bit set. These values behave as idealized bounds: they are greater than every finite number, and they propagate through arithmetic as defined by the standard. For example, with positive infinity:

- inf plus any finite number yields inf; inf plus inf yields inf.

- inf minus a finite number yields inf; inf minus inf yields NaN.

- inf times a positive finite number yields inf; inf times a negative finite number yields -inf.

- finite divided by inf yields 0; inf divided by finite yields inf; inf divided by inf yields NaN.

- zero times inf yields NaN.

Comparisons

Positive infinity compares greater than all finite numbers. inf equals itself (inf == inf is true). Comparisons involving NaN are distinct: any comparison with NaN is typically false, except that NaN != NaN is true.

Language examples

Many languages provide explicit constants for infinity:

- Python: float('inf') or math.inf

- JavaScript: Infinity

- Java: Double.POSITIVE_INFINITY

- C/C++: INFINITY or std::numeric_limits<double>::infinity()

Uses and limitations

Infinity serves as a sentinel for unbounded results, overflow handling, or uninitialized yet-reached limits in algorithms. It helps avoid immediate overflow in calculations but requires careful handling to avoid misleading results, especially when combined with NaN or when signaling errors.