Changes http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff --
??changed: -$m$ has 53 bits stored in a 52 bit field (not including sign, note that in base 2, the most significant digit normalized must be 1, so no need to store it!) and $e$ has 11 bits (including sign, ranging from $-1075$ to $971$ which accounts for an offset of 53 because the base point location). This is exactly equivalent to the IEEE-754 standard for 64 bit floating point. The actual arithmetics is done via Lisp, which I assume calls the hardware. - -In 'FLOAT', conceptually the infinite precision floating point system, is basically also finite precision floating point system, with the ability to increase precision as requested. However, this promotion is not automatic. In other words, every 'FLOAT' number has its own precision, implicit in the length of its mantissa. In effect, 'FLOAT' is the union of floating point systems with various precisions, but without any coercion between them. So Tim is not entirely wrong is saying we don't have infinite precision floating point in the spirit of INT. The real question for the developers is then: $m$ has 53 bits stored in a 52 bit field (not including sign, note that in base 2, the most significant digit normalized must be 1, so no need to store it!) and $e$ has 11 bits (including sign, ranging from $-1075$ to $971$ which accounts for an offset of 53 because the base point location). This is exactly equivalent to the IEEE-754 standard for 64 bit floating point. The actual arithmetic operations are done via Lisp, which I assume calls the hardware. In 'FLOAT', conceptually the infinite precision floating point system, is basically also finite precision floating point system, with the ability to increase precision as requested. However, this promotion is not automatic. In other words, every 'FLOAT' number has its own precision, implicit in the length of its mantissa. In effect, 'FLOAT' is the union of floating point systems with various precisions, but without exact arithmetic. So Tim is not entirely wrong in saying we don't have infinite precision floating point in the spirit of INT. The real question for the developers is then: ??changed: -Example. Addition of two 'FLOAT' with different orders of magnitude will not lead to a higher precision answer. What should be the right answer depends on your point of view: if the precision of the number is important, then this is correct. If exact arithmetic with floating point is what you want, this is not correct. Example. Addition of two 'FLOAT' with different orders of magnitude will not lead to a higher precision answer. What should be the right answer depends on your point of view: if the precision of the numbers are important, then this example is correctly handled in Axiom. If exact arithmetic with floating point is what you want, this is not correct. -- forwarded from http://page.axiom-developer.org/zope/mathaction/[EMAIL PROTECTED] _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
