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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