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From: rwallace@vax1.tcd.ie
Newsgroups: comp.arch
Subject: Re: F.P. vs. arbitrary-precision
Message-ID: <6837.26e7ee92@vax1.tcd.ie>
Date: 7 Sep 90 19:01:37 GMT
References: <3755@osc.COM> <4513@taux01.nsc.com> <119244@linus.mitre.org>
Organization: Computer Laboratory, Trinity College Dublin
Lines: 32

> :If they have a good FPU, using it for integer multiplication *is* a "reasonable
> :way".  Besides, a bad implementation doesn't prove anything about the basic
> :idea of FP.
>  
> Having a good FPU just isn't good enough. Even with IEEE 64-bit, there are
> only 53 bits of a mantissa. So just how does one multiply two 32 bit integers
> together using floating point? The answer is: one can't without losing bits.
> (or by doing several multiplies on the low/high halves and combining things)
> Futhermore, if I should need to multiply integers in this way, they must
> first be converted to floating point, then the product must be converted back.
> Can you say expensive???
> 
> The four basic operations of arithmetic are +, -, x, /. Any computer that
> can't perform them on its atomic data units [whatever the word size is]
> is a joke.

First, why do you need 32 x 32 -> 64? OK in principle 32 x 32 can give a 64
bit answer but in practice 99% of the time you're going to be working in 32
bits all the way and you don't want 64 bit answers (which is why C has
int x int -> int not int x int -> long).

Second, there is a huge amount of processing done which depends on integer +
and - and fp +, -, * and / being fast, so there is hardware support for these.
There is practically no processing done which depends on integer * and / being
fast (accessing an array of structures doesn't count because a smart compiler
can use shifts and adds), and don't bother giving anecdotal cases because it's
still less than 1% of the total. Therefore chip space was not wasted on making
these fast.
-- 
"To summarize the summary of the summary: people are a problem"
Russell Wallace, Trinity College, Dublin
rwallace@vax1.tcd.ie