GlossaryΒΆ

transdouble

An implementation of transreal floating point numbers on top of IEEE 754 double precision numbers. Transdoubles are one of the number classes implemented in Ginger.

Ginger uses transdoubles in preference to plain old doubles because they are more straightforward to understand, have less surprises for programmers and make maths programs more robust.

transreal

Transreal numbers are a simple extension to real arithmetic with the aim of making all arithmetic functions total. There are three special ‘transreal’ numbers +infinity, -infinity and nullity that help with this. In contrast to plain old floating point arithmetic these are perfectly respectable values (e.g. nullity equals nullity.)

There are practical advantages to using total arithmetic as the basis for programming languages: base cases are simplified and the need for reasoning about exceptional situations is eliminated.