IEEE Arithmetic

Abstract

The aims of this chapter are to look in more depth at arithmetic and in particular at the support that Fortran provides for the IEEE 754 and later standards. There is a coverage of:

• hardware support for arithmetic.

• integer formats.

• floating point formats: single and double.

• special values: denormal, infinity and not a number — nan.

• exceptions and flags: divide by zero, inexact, invalid, overflow, underflow.

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.

Godel, First incompleteness theorem