用牛顿迭代法计算整数的平方根到任意精度

DESCRIPTION This program to call GMP big integer functions to calculate the square root of single precision integer, it can get the result up to arbitrary accuracy.This program only use GMP big integer functions, it never call GMP Floating-point Functions to do it. The following GMP functions was used. mpz_init mpz_clear mpz_set_ui mpz_sizeinbase mpz_cmp mpz_add mpz_sub mpz_mul mpz_mul_ui mpz_pow_ui mpz_tdiv_q mpz_get_str Arithmetic The main Arithmetic is Newton's method. It first gets an approximate value of square root of a given integer. The Initial value was expressed with a fraction. Then it calls Newton's method to the value with more precise over and over. Final, it converts the value of square root of the integer from fraction format to a decimal string. How to use it 1. Build it in Windows You can build this project with VC6 or VC2008. You can open workspace file (sqrt_withGMP.dsw is for VC6 and sqrt_withGMP.sln is for VC2008) with VC6 or VC2008 to build it, in release mode, the executable file will be copied to ./bin folder. You can run it in "bin" folder directly. 2. Build it in Linux Please make sure that you have installed GMP in your Linux PC first, then you can run below command to create an executable in source code folder. gcc -lm -lgmp sqrt_withGMP.c -o sqrt_withGMP Performance Basically, the Performance is very good. The following data is time cost for calculating sqrt(2) to 10000,100000,1000000 digital Result Digital Calculate time (ms) print time (ms) 10000 3 2.6 100000 47 31 1000000 986 894 AUTHOR Baocheng Liang (liangbch@263.net), Feb-17, 2012