File: gawk.info,  Node: Floating point summary,  Prev: POSIX Floating Point Problems,  Up: Arbitrary Precision Arithmetic

16.8 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.