c++ - Efficient way to compute p^q (exponentiation), where q is an integer -

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what efficient way compute pq, q integer?

exponentiation squaring uses o(lg q) multiplications.

template <typename t> t expt(t p, unsigned q) {     t r(1);      while (q != 0) {         if (q % 2 == 1) {    // q odd             r *= p;             q--;         }         p *= p;         q /= 2;     }      return r; }

this should work on monoid (t, operator*) t constructed 1 identity element. includes numeric types.

extending signed q easy: divide 1 result of above absolute value of q (but usual, careful when computing absolute value).


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