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Postings from July 2001
Philip Newton wrote: > > On the other hand, if a/b==c, then b*c == a. This holds for 10/5==2 --> > 5*2==10, but not if you posit 0/0==0, since 0*0==0, but 5*0==0 as well, > so one could argue that 0/0 should be 5. This argument holds for any > possible result. So if 0/0 has any one value, it has to be one that's > specially defined; NaN makes sense to me for this. > > (And what do you think is 0**0? 0**n == 0 for all positive n, but n**0 > == 1 for all positive n.... Presumably, 0**0 is also NaN, then.) I pulled out "What Every Computer Scientist Should Know About Floating- Point Arithmetic" (ACM Computing Surveys, Vol 23, No 1, March 1991) and checked what it says (based on IEEE 745 & 854): 0/0 == NaN 1/0 == inf -1/0 == -inf -0 == +0 Indeed, there is a discussion of signed zero and its importance in maintaining sign. Only when testing like "if (x==0)" is the sign of zero ignored. For example, IEEE 754 defines: log 0 = -inf and log x is NaN for x < 0 so if x is a small negative number that has underflowed to 0, we can report that log x is NaN because the sign did not disappear when the underflow occurred. As for what 0**0 should be, I can find no mention of it. There is a table of operations that produce NaN's and exponent is not one of them. All of the rules above derive from taking the limit of small numbers going to 0, but I cannot work that out in my head right now (end of the day haze ;~). HTH John -- John Peacock Director of Information Research and Technology Rowman & Littlefield Publishing Group 4720 Boston Way Lanham, MD 20706 301-459-3366 x.5010 fax 301-429-5747Thread Previous | Thread Next