Am 01.11.14 09:13, schrieb Chris Angelico:
On Sat, Nov 1, 2014 at 7:02 PM, Christian Gollwitzer <aurio...@gmx.de> wrote:
Your above algorithm is obviously doing Heron- or Newton-Raphson iterations,
so the same as with floating point math. The first line before the while
loop computes some approximation to sqrt(n). Instead of doing bit shuffling,
you could compute this by FP math and get closer to the desired result,
unless the integer is too large to be represented by FP. Now, the
terminating condition seems to rely on the fact that the initial estimate
x>=sqrt(n), but I don't really understand it. My guess is that if you do
x=int(sqrt(n)), then do the first iteration, then swap x and y such that
x>y, then enter the loop, you would simply start with a better estimate in
case that the significant bits can be represented by the float.
Part of the point of that algorithm is that it never uses FP, and is
therefore not limited by FP restrictions.
which are???
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