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Math class is tough!

— *Teen Talk Barbie, July 1992*

This section provides a high-level overview of the issues
involved when doing lots of floating-point arithmetic.^{99}
The discussion applies to both hardware and arbitrary-precision
floating-point arithmetic.

CAUTION:The material here is purposely general. If you need to do serious computer arithmetic, you should do some research first, and not rely just on what we tell you.

• Inexactness of computations: | Floating point math is not exact. | |

• Getting Accuracy: | Getting more accuracy takes some work. | |

• Try To Round: | Add digits and round. | |

• Setting precision: | How to set the precision. | |

• Setting the rounding mode: | How to set the rounding mode. |

There
is a very nice paper on floating-point arithmetic by David Goldberg, “What Every
Computer Scientist Should Know About Floating-Point Arithmetic,”
ACM Computing Surveys **23**, 1 (1991-03): 5-48. This is
worth reading if you are interested in the details, but it does require
a background in computer science.