java - Calculate the power with multithreads -

i'm working on calculator calculates number power of number. happens code:

public biginteger generate(long power, long base){      biginteger result = biginteger.valueof(base),      = biginteger.valueof(base);     int j=0;      while(j!=power-1){         result = result.multiply(a);         j++;     }      return result; } 

i know if there mathematical way split type of calculation multiple threads, program calculate things 987654321 ^ 987654321 faster. cpu have 6 cores if there way use them @ once stuff great.

the first thing comes mind factorization, i.e., write base number product

base = a_1 * ... * a_n 

and compute a_i^b on separate threads, , multiply results. need computational effort finding factorization, first check if numbers ´big enough´ bother multiple cores, , if are, start standard checks if factorization possible. or divide first 100 prime numbers, should not take long.

especially, if number factorizes several times same factor, have compute power once, i.e.,

(24)^5 = (3*2*2*2)^5 = 3^5 * 2^5 * 2^5 * 2^5 

and compute r_1 = 3^5 , r_2 = 2^5 , multiply result r = r_1 * r_2 * r_2 * r_2.

you can factorize exponents, algorithm tad more complicated.