### 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.