How can I define NaN in LaTeX3

Question

LaTeX3 l3fp offers a way to check if a variable has a an infinite value. The following code defines a number and then sets its value to π/2. It then calculates tan(π/2) to get a large result.

\ExplSyntaxOn
  \fp_new:N \mynumber
  \fp_new:N \pi_half
  \fp_div:Nn \pi_half{\c_pi_fp/2}
  \fp_tan:Nn  \mynumber{\pi_half}
  \texttt{\mynumber}\\

  \fp_if_infinity:NTF \c_infinity_fp {NaN}{Do~something~with~\number}\\

\ExplSyntaxOff

In many languages the indeterminate form is normally indicated by NaN what would be a good strategy to define a macro to test for this in expl3 for all cases of NaN, such as division by zero etc?

Answer 1

The FPU for LaTeX3 has undergone some major changes. Up to the version included in the DVD of TeX Live 2012 (mid-June 2012) the 'old' FPU worked one way. The improved FPU, available from the development repository and scheduled for release to CTAN some time in late June 2012, is expandable and features a number of improvements.

Updated (expandable) FPU answer

The new FPU recognises the 'not a number' concept

\fp_set:Nn \l_tmpa_fp { nan }

NaN is not equal to any value, not even another NaN: this is the standard approach in many languages. Thus

\fp_compare:nNnTF { nan } = { nan } { \TRUE } { \FALSE }

is FALSE.

Original (non-expandable) FPU answer

There are currently special markers in expl3 for infinite and undefined results, \c_infinite_fp and \c_undefined_fp. Division by exactly zero is undefined:

\fp_div:Nn \l_my_fp { 0 }
\fp_if_undefined:NTF \l_my_fp { TRUE } { FALSE }

gives TRUE.

Thinking about this again, I notice that the tangent of π/2 should not actually be infinite as it does not have a limit (thinking about the various tests for limits of series). I suspect this should be altered: expect the next expl3 update to improve in this area.