mdeale@algol.acs.calpoly.edu (Myron Deale) (06/30/89)
Hello, IEEE 754 is the floating point standard for binary radix. Is p854 intended for "arbitrary" radix? or higher-powers-of-two radix? In Cody and Waite's "... Elementary Functions" it is noted that radices higher than two are more subject to wobbling precision. In this light, what is the purpose of p854? Myron // mdeale@cosmos.acs.calpoly.edu
dick@ucsfccb..ucsf.edu (Dick Karpinski) (07/11/89)
In article <12194@polyslo.CalPoly.EDU> mdeale@algol.acs.calpoly.edu (Myron Deale) writes: > IEEE 754 is the floating point standard for binary radix. Is p854 >intended for "arbitrary" radix? or higher-powers-of-two radix? > > In Cody and Waite's "... Elementary Functions" it is noted that radices >higher than two are more subject to wobbling precision. In this light, what >is the purpose of p854? The committee was quite clear that their purpose was to extend the benefits of a carefully thought out set of precision and exception rules to other formats of binary floating-point (and to decimal floating-point) arithmetic. Specific sizes of exponent and significand in 754 give way to formulas relating the two parts of a floating-point number. Other radices were considered but there was no support for base 8 or 16 since they are inferior to base 2 and lose the hidden bit trick. Base 10 is inferior to base 2 but has the distinct advantage that human readable representations do not suffer any conversion roundoff on the way in and out. Dick Dick Karpinski Manager of Minicomputer Services, UCSF Computer Center Domain: dick@cca.ucsf.edu (415) 476-4529 (11-7) BITNET: dick@ucsfcca or dick@ucsfvm (415) 658-6803 (Home) USPS: U-76 UCSF, San Francisco, CA 94143-0704 (415) 658-3797 (ans)
gideony@microsoft.UUCP (Gideon Yuvall) (07/12/89)
In article <2194@ucsfcca.ucsf.edu> dick@ucsfccb.UUCP (Dick Karpinski) writes: >a floating-point number. Other radices were considered but there >was no support for base 8 or 16 since they are inferior to base 2 >and lose the hidden bit trick. Base 10 is inferior to base 2 but >has the distinct advantage that human readable representations do >not suffer any conversion roundoff on the way in and out. W. Kahan says base-16 fell off the standard when it became clear IBM wasn't interested: nobody in his right mind would put hex floating-point on a new architecture, and the old 360/370/... architecture was not going to be changed. -- Gideon Yuval, gideony@microsof.UUCP, 206-882-8080 (fax:206-883-8101;TWX:160520)