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From: firth@sei.cmu.edu (Robert Firth)
Newsgroups: comp.arch
Subject: Re: John von Neumann, sqrt instr
Message-ID: <3894@bd.sei.cmu.edu>
Date: 21 Aug 89 12:48:22 GMT
References: <21353@cup.portal.com> <25643@obiwan.mips.COM> <1513@l.cc.purdue.edu> <2376@wyse.wyse.com> <3312@blake.acs.washington.edu> <12640@pur-ee.UUCP>
Reply-To: firth@sei.cmu.edu (Robert Firth)
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Organization: Software Engineering Institute, Pittsburgh, PA
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In article <12640@pur-ee.UUCP> hankd@pur-ee.UUCP (Hank Dietz) writes:
>.. I still haven't been able to find a software technique to make square root
>comparably fast.  Anybody got a screamer of a software technique for
>computing square root?

A fairly good way os to use bit-level hacking to get a first approximation,
and then unroll a few iterations of Newton's method.  When I did sqrt for
the PDP-11, the first approximation was two shifts and an add, and gave
5 bits of accuracy.  Two iterations then yielded 23 bits for a reasonable
single-precision result.  With everything done in registers, the cost
was certainly less than 20 multiplies.