Stable Numerics Subroutine Library
Programming Reference Manual
Version 1.2 DD-00006-012

3.5.1 Empty Triplex

An empty triplex value T= ∅ for T ∈TR is defined as a degenerate case where all components are undefined or null:

        -       -
T ={[x,x,x]| x =x =x =∅}= ∅.

This represents the absence of a valid triplex value, analogous to the empty set in interval arithmetic.

In computational implementations, the empty triplex is typically represented using qNaN (Quiet-Not-a-Number) values. Any arithmetic operation involving a qNaN will propagate the qNaN, ensuring that invalid or undefined operations do not yield misleading results.