gawk: Floating point summary

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1 15.8 Summary
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1    * Most computer arithmetic is done using either integers or
1      floating-point values.  Standard 'awk' uses double-precision
1      floating-point values.
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1    * In the early 1990s Barbie mistakenly said, "Math class is tough!"
1      Although math isn't tough, floating-point arithmetic isn't the same
1      as pencil-and-paper math, and care must be taken:
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1         - Not all numbers can be represented exactly.
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1         - Comparing values should use a delta, instead of being done
1           directly with '==' and '!='.
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1         - Errors accumulate.
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1         - Operations are not always truly associative or distributive.
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1    * Increasing the accuracy can help, but it is not a panacea.
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1    * Often, increasing the accuracy and then rounding to the desired
1      number of digits produces reasonable results.
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1    * Use '-M' (or '--bignum') to enable MPFR arithmetic.  Use 'PREC' to
1      set the precision in bits, and 'ROUNDMODE' to set the IEEE 754
1      rounding mode.
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1    * With '-M', 'gawk' performs arbitrary-precision integer arithmetic
1      using the GMP library.  This is faster and more space-efficient
1      than using MPFR for the same calculations.
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1    * There are several areas with respect to floating-point numbers
1      where 'gawk' disagrees with the POSIX standard.  It pays to be
1      aware of them.
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1    * Overall, there is no need to be unduly suspicious about the results
1      from floating-point arithmetic.  The lesson to remember is that
1      floating-point arithmetic is always more complex than arithmetic
1      using pencil and paper.  In order to take advantage of the power of
1      floating-point arithmetic, you need to know its limitations and
1      work within them.  For most casual use of floating-point
1      arithmetic, you will often get the expected result if you simply
1      round the display of your final results to the correct number of
1      significant decimal digits.
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1    * As general advice, avoid presenting numerical data in a manner that
1      implies better precision than is actually the case.
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