On Mar 12, 7:20 am, Piet van Oostrum <[EMAIL PROTECTED]> wrote: > But if the answer is incorrect (in the float calculation) the error is > limited. IEEE 754 prescribes that the error should be at most 1 LSB, IIRC. > And then the number of errors is the proper measure.
There are two operations here, both of which can introduce error of up to 0.5 ulp (ulp = unit in the last place). Moreover, the second operation (the multiplication) can magnify the error introduced by the first (the division). You're correct that for IEEE 754 binary floating-point arithmetic, (x/y)*y and x will either be equal or differ by exactly 1ulp (except perhaps in rarely-occurring corner cases). But for decimal numbers, (x/y)*y and x could be as much as 5 ulps apart. Mark > -- > Piet van Oostrum <[EMAIL PROTECTED]> > URL:http://pietvanoostrum.com[PGP 8DAE142BE17999C4] > Private email: [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
