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## GMP Inputs

**From**: |
Hans Aberg |

**Subject**: |
GMP Inputs |

**Date**: |
Wed, 25 Apr 2001 22:33:05 +0200 |

Here are some inputs about multi-precision numbers in general:
- Apart from the data types "integer", "rational", and "floating", I have
identified a data type "fixed" for fixed point numbers. This would be like
quotient pairs (p, q), where p, q are integers, and q > 0 is held fixed,
and 1/q is the precision. For example, to be used for computations with
money, time.
Perhaps exotic, but I mention it anyhow.
- As for the inaccuracy (inverted value of precision) of floating and fixed
point numbers, I think that a fairly correct mathematical way would be to
use differentials of the operations involved to compute the new inaccuracy.
That is, unless the user specifically requests a round-off.
For the floating type, one would use logarithmic differentials dlog f :=
(df)/f, and for the fixed point type regular differentials. For example,
floating multiplication gives the new inaccuracy dlog(x*y) = dlog x + log
y, which is no worse than max(dlog x, log y), or the minimum precision of x
and y.
Hans Aberg

**Re: GMP MacOS PPC assembler**, *(continued)*
**Re: GMP MacOS PPC assembler**, *Linus Nordberg*, `2001/04/26`
**Re: GMP MacOS PPC assembler**, *Hans Aberg*, `2001/04/26`
**Re: GMP MacOS PPC assembler**, *Torbjorn Granlund*, `2001/04/27`
**Re: GMP MacOS PPC assembler**, *Hans Aberg*, `2001/04/27`
**Re: GMP MacOS PPC assembler**, *Kevin Ryde*, `2001/04/29`
**Re: GMP MacOS PPC assembler**, *Hans Aberg*, `2001/04/30`
**GMP parser**, *Hans Aberg*, `2001/04/26`
**Re: GMP parser**, *Kevin Ryde*, `2001/04/29`
**Re: GMP parser**, *Hans Aberg*, `2001/04/30`
**GMP C++ wrap**, *Hans Aberg*, `2001/04/25`
**GMP Inputs**,
*Hans Aberg* **<=**
**Re: GMP Inputs**, *Kevin Ryde*, `2001/04/25`
**Re: GMP Inputs**, *Hans Aberg*, `2001/04/26`

**GMP ceil/floor/trunc**, *Hans Aberg*, `2001/04/24`