Improve accuracy of divide and reciprocal

[muzimuzhi]

Brief outline of the bug

Without fpu library, currently the accuracy of math functions divide and reciprocal are not so good. eTeX's \dimexpr might help, by using

‘scaling’ operations (a multiplication immediately followed by a division) which are performed as one combined operation with a 64-bit product as intermediate value.
_{excerpted from the eTeX manual, sec. 3.5 "Expressions"}

Existing discussions

• divide: Symbol 1's analysis on TeX-SX, Henri's attempt hmenke@5077895
• reciprocal: Wrong position of a point using the "scale" option #1146, related TeX-SX questions

Minimal working example (MWE)

\documentclass{article}
\usepackage{pgfmath}

\begin{document}
\pgfmathprint{38.89993/38.9}, % = 1.2, should be less than 1
\pgfmathprint{38.8999/38.9}   % = 1.1

\pgfmathreciprocal{1.25}\pgfmathresult % = 0.80019, 0.8 expected
\end{document}

[hmenke]

I think you are conflating a few different things here. There are a number of orthogonal issues with the divide and reciprocal functions:

1. Loss of precision (\pgfmathreciprocal{1.25})
2. Dimension too large (\pgfmathdivide{1000.0}{0.001})
3. Bogus results (\pgfmathdivide{38.89993}{38.9})

The most pressing issue is fixing the bogus results. Eventually we should find workarounds for the other two issues as well, but as of now they just reflect the nature and limitations of TeX's fixed-point arithmetic.