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Re^2: 64-bit division anomolies (Solved.)

by Discipulus (Canon)
on Feb 17, 2015 at 09:42 UTC ( [id://1116955]=note: print w/replies, xml ) Need Help??


in reply to Re: 64-bit division anomolies (Solved.)
in thread 64-bit division anomolies (Solved.)

oh.. well.. If you have time, can i ask you to comment a bit more your code?
just to make it more appreciable by people with low mathfu as me.. ;=)?

L*
There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

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Re^3: 64-bit division anomolies (Solved.)
by salva (Canon) on Feb 17, 2015 at 10:07 UTC
    My method, first builds an approximation of the solution of a/b as... 
    s1 = ((a / 2) / b) * 2;

    [download]
    a / 2 is done using the bug-free shift-right operator (>>) and results always in a number with bit 64 unset, so we can divide it by b without incurring in the convert-to-NV bug. Again multiplying by 2 is done with the shift-left operator (<<).

    Then, we use the approximation to build the exact solution as: 

    s = s1 + (a - s1 * b) / b

    [download]

    Well, actually, in order to do everything using bug-free operations, the code uses the following equivalence: 

    s2 = (a / 2) / b
s1 = s2 * 2
s = s1 + (a - s1 * b) / b
s = s2 * 2 + (a - (s2 * b) * 2) / b

    [download]
    where $d is s2, and $e is (a - (s2 * b) * 2).
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