[Axiom-developer] [#167 Infinite Floats Domain] Float and DFloat

[wyscc]

Changes 
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
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??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.
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-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.

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