Question for Parisse about CAS floating point

[jte]

(04-12-2015 12:36 PM)Joe Horn Wrote:  

(04-10-2015 07:58 PM)jte Wrote:  My understanding of the CAS semantics for its is inexact numeric values is that they are not exactly equal to any rational or real number.

If by "inexact" you mean "floating-point reals", then you are not correct. In CAS, reals use 48 bits for the mantissa, and are therefore exactly equal to an exact integer divided by an exact power of 2, which is therefore representable as an exact terminating decimal number. For example, the value of approx(1519/99) is stored by CAS as 134962275764989/2^43, which can be written exactly as the terminating decimal number I gave above.

I'm not 100% up to date on the terminology used by the CAS; I hope that isn't confusing matters. I hesitate to use the term "floating-point" as (it is my understanding that) the semantics intended by the author of the CAS does not follow that laid out by IEEE 754. (While the Advanced Graphing app does follow IEEE 754 semantics and views finite floating-point numbers as exact rational / real numbers, it is fairly common to have different interpretations of values produced using floating-point calculations.)

I was wondering exactly where the decimal number you gave above for 1519/99 came from, so I'm glad you clarified that. My intention was to do the same division, but I arrived at a different decimal answer.