From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-0.3 required=5.0 tests=BAYES_00,HK_RANDOM_FROM, INVALID_MSGID autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,a0f1b3fbaa361b4 X-Google-Attributes: gid103376,public From: bglbv@my-dejanews.com Subject: Re: Very big Integers Date: 1999/04/29 Message-ID: <87vhefjhgw.fsf@bglbv.my-dejanews.com>#1/1 X-Deja-AN: 472482891 References: <7fq44c$16m1@news1.newsguy.com> <87676lsl2h.fsf@bglbv.my-dejanews.com> <7fuc3k$gv4$1@nnrp1.dejanews.com> X-Complaints-To: abuse@freeuk.net X-Trace: nnrp2.clara.net 925427522 212.126.148.209 (Fri, 30 Apr 1999 00:12:02 BST) NNTP-Posting-Date: Fri, 30 Apr 1999 00:12:02 BST Newsgroups: comp.lang.ada Date: 1999-04-29T00:00:00+00:00 List-Id: Robert Dewar writes: > > 128-bit floating point may come close to the > > required 100 bits of mantissa. (In fact, on an IEEE > > machine it > > should have slightly more than that. But the "100" > > probably wasn't meant literally.) > > There is no such requirement or recommendation in either > IEEE754 or IEEE854. For example, a format which was > 80-bit Intel expanded to 128 bits by adding 48 bits > required to be all zeroes would be a legitimate > implementation of extended, and in any case extended > precision is not required! I said "should", not "ought to" or "must". The intended connotation was one of mere likelihood. It is customary (whether it's actually mandated/recommended by the IEEE standards is besides my point) to have: 32-bit FP: 8-bit exponent, 24-bit mantissa (including implicit leading 1) 64-bit : 11-bit exponent, 53-bit mantissa A reasonable extrapolation *for those platforms that provide an effective 128-bit floating point type* (that excludes "80-bit with padding", and I'll grant you that not all platforms support 128-bit FP), either in hardware or in software, is for such a data type to have approximately 2*53=106 bits of mantissa (give or take a few bits). That's all I meant by my remark. If the requirement is for 100-bit integers, then a typical 128-bit floating point format is likely to fit the bill. Such a format is not available on all platforms, and atypical formats are certainly possible. Note that my extrapolation is more conservative than "14-bit exponent, 114-bit mantissa" because vendors have been known to sacrifice a few bits for the added simplicity of using a pair of standard 64-bit floats and the hardware instructions that go with them.