On 2013-09-12, at 8:18 AM, Dmitry Nadezhin <dmitry.nadez...@gmail.com> wrote:
> The reason while binary and decimal digits are mixed can be ullustrated by > such example. > It is necessary 3 decimal fraction digits to represent exactly pbinary > power pow(2,-3) : > pow(2,-3)=1/8=0.125 > > > On Thu, Sep 12, 2013 at 3:57 PM, David Chase <david.r.ch...@oracle.com>wrote: > >> This explanation seems to combine numbers of binary digits (1075) >> and numbers of decimal digits (17), and therefore makes me a little >> nervous, though I think 1100 is a conservative choice that, even if not >> 100% correct, will be 99.(over 700 9s)% correct. >> >> David Yes, but you are adding them. It is as if you took two lengths, 1075 feet and 17 yards, added them, rounded up, and said that 1100 yards will be adequate (which is entirely true, though perhaps overconservative). Overconservative is okay. 2^-1075 is the binary ulp, give or take a fencepost, not the decimal ulp. David
