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On Feb 13 2013, Hossam A. H. Fahmy wrote:
On Tue, 2013-02-12 at 21:30 -0800, Richard Fateman wrote:It is amusing to consider that [1/3, 0.1d0] could either be converted, with some loss, to two floats [0.3333...3, 0.1d0]or without loss to two rationals,[1/3, 3602879701896397/ 2^55]In fact, 3602879701896397/ 2^55 = 0.1000000000000000055511151231257827021181583404541015625and not 0.1.It is impossible to get an exact rational representation of the vast majority of decimal fractions using only a power of 2 denominator. That is the mathematical reason that lead to the inclusion of decimalfloating point specification in IEEE 754-2008.
I am sorry, but that misuse of the word "mathematical" sticks in my gullet. The fact that a fixed size of decimal floating-point can represent a wider range of decimal fractions than binary (and a stronger statement does not hold) is no different from the fact that a binary one can represent a wider range of binary fractions than decimal. There was and is no mathematical reason that ten is a preferred base over two, or even three. The claims of extra accuracy for decimal floating-point are polemic, pure and simple, and precisely the converse can be argued with rather more reference to mathematics. Please leave it out of this discussion. Regards, Nick Maclaren.