Xref: utzoo comp.arch:14422 comp.lang.lisp:2866 comp.lang.misc:4340 comp.lang.smalltalk:1735
Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!yale!cmcl2!lanl!lambda!jlg
From: jlg@lambda.UUCP (Jim Giles)
Newsgroups: comp.arch,comp.lang.lisp,comp.lang.misc,comp.lang.smalltalk
Subject: Re: heaps of numbers (tagged immediate float formats & float usage)
Message-ID: <14261@lambda.UUCP>
Date: 5 Mar 90 23:36:42 GMT
References: <1990Mar5.220724.3718@Neon.Stanford.EDU>
Lines: 13

From article <1990Mar5.220724.3718@Neon.Stanford.EDU>, by wilson@carcoar.Stanford.EDU (Paul Wilson):
> [...]
> I don't get this.  It seems to me that if 8 bits gives you a range of 10**-38
> to 10**+38, then 4 bits ought to give you half as many orders of magnitude,
> or about 10**-19 to 10**+19.  [...]

Exponent range scales as the _LOG_ (base 2) of the number of bits in
the exponent.  So, 8 bits gives an exponent range of (about) 2^-127 thru
2^127 - that is, about 10^-39 thru 10^39.  A 4 bit exponent only gives
an exponent range of about 2^-15 thru 2^15 - that is, a little more than
10^-5 thru 10^5.

J. Giles