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From: Keith Thompson <kst-u@mib.org>
Newsgroups: comp.lang.c
Subject: Re: Big integers
Date: Wed, 05 Dec 2018 13:46:11 -0800
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jacob navia <jacob@jacob.remcomp.fr> writes:
> Le 04/12/2018 à 18:35, Bart a écrit :
> > An extended precision floating 
> > point library would also be intriguing to
> > write. But it can't be arbitrary precision. (How many digits to
> > represent 1/3 exactly in either binary or decimal?)
> I have written one, based on the work of Stephen L Moshier, in x86 asm 
> and arm64 asm. It has aroud the same speed as GMP...
> The layout is as follows:
>
> Each number is 64 bytes, where the first 32 are the sign (I know is 
> wasteful but it is faster than using only one bit) the, the next 32 are 
> the exponent (biased) and then 7 64 bit integers with the mantissa.
>
> All functions of the C standard library are provided using this format

So you have a sign, a 32-bit exponent, and a 448-bit mantissa.

Unless I'm missing something, that still can't represent 1/3 exactly
(though it can approximate it much more closely than smaller formats
can).

To represent 1/3 *exactly*, you need either trinary (which
can't represent 1/5 or 1/7 exactly, or even 1/2) or some kind of
numerator/denominator representation.

-- 
Keith Thompson (The_Other_Keith) kst@mib.org  <http://www.ghoti.net/~kst>
Will write code for food.
"We must do something.  This is something.  Therefore, we must do this."
    -- Antony Jay and Jonathan Lynn, "Yes Minister"