[ << ] | [ < ] | [ Up ] | [ > ] | [ >> ] | [Top] | [Contents] | [Index] | [ ? ] |
15.5.2 Nth Root
Integer Nth roots are taken using Newton’s method with the following iteration, where A is the input and n is the root to be taken.
1 A a[i+1] = - * ( --------- + (n-1)*a[i] ) n a[i]^(n-1)
The initial approximation a[1] is generated bitwise by successively powering a trial root with or without new 1 bits, aiming to be just above the true root. The iteration converges quadratically when started from a good approximation. When n is large more initial bits are needed to get good convergence. The current implementation is not particularly well optimized.
This document was generated on March 31, 2014 using texi2html 5.0.