*gawk:* Floating point summary

15.8 Summary
============
* Most computer arithmetic is done using either integers or
floating-point values. Standard 'awk' uses double-precision
floating-point values.
* In the early 1990s Barbie mistakenly said, "Math class is tough!"
Although math isn't tough, floating-point arithmetic isn't the same
as pencil-and-paper math, and care must be taken:
- Not all numbers can be represented exactly.
- Comparing values should use a delta, instead of being done
directly with '==' and '!='.
- Errors accumulate.
- Operations are not always truly associative or distributive.
* Increasing the accuracy can help, but it is not a panacea.
* Often, increasing the accuracy and then rounding to the desired
number of digits produces reasonable results.
* Use '-M' (or '--bignum') to enable MPFR arithmetic. Use 'PREC' to
set the precision in bits, and 'ROUNDMODE' to set the IEEE 754
rounding mode.
* With '-M', 'gawk' performs arbitrary-precision integer arithmetic
using the GMP library. This is faster and more space-efficient
than using MPFR for the same calculations.
* There are several areas with respect to floating-point numbers
where 'gawk' disagrees with the POSIX standard. It pays to be
aware of them.
* Overall, there is no need to be unduly suspicious about the results
from floating-point arithmetic. The lesson to remember is that
floating-point arithmetic is always more complex than arithmetic
using pencil and paper. In order to take advantage of the power of
floating-point arithmetic, you need to know its limitations and
work within them. For most casual use of floating-point
arithmetic, you will often get the expected result if you simply
round the display of your final results to the correct number of
significant decimal digits.
* As general advice, avoid presenting numerical data in a manner that
implies better precision than is actually the case.