| Integer Square Root |
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| number theoretic algorithms | |
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Positive Integer ''n'' is the positive integer ''m'' which is the greatest integer less than or equal to the square root of ''n'', :
ALGORITHM To calculate √''n'', and in particular, isqrt(''n''), one can use Newton's Method for the equation ''x''2 - ''n'' = 0, which gives us the Recursive formula : One can choose for example ''x''0 = ''n'' as initial guess. The Sequence {''x k''} Converges Quadratically to √''n'' as ''k''→∞. It can be proved (the proof is not trivial) that one can stop as soon as |
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