算数平方根计算

阅读量： 46

最近更新于 2022-04-05 12:37

测试环境

gcc 9.4.0 – 64位

-no-pie -std=c17 -Wall -Werror=return-type -Werror=address -Werror=sequence-point -Werror=format-security -Wextra -pedantic -Wimplicit-fallthrough -Wsequence-point -Wswitch-unreachable -Wswitch-enum -Wstringop-truncation -Wbool-compare -Wtautological-compare -Wfloat-equal -Wshadow=global -Wpointer-arith -Wpointer-compare -Wcast-align -Wcast-qual -Wwrite-strings -Wdangling-else -Wlogical-op -Wconversion -g -O0 -lm

方法一：牛顿迭代法

#include <stdio.h>
#include <math.h>


double my_abs(double num)
{
    if (num < 0)
    {
        return -num;
    }
    return num;
}


double my_sqrt(double num)
{
    double epsilon = 0.000001;  // 精度要求
    double guess = 1.0;  // 初始估计值
    while (my_abs(guess * guess - num) > epsilon)
    {
        guess = ((num / guess) + guess) / 2;
    }
    return guess;
}


int main()
{
    printf("my_sqrt\t\tsqrt\n");
    printf("%lf\t%lf\n", my_sqrt(2), sqrt(2));
    printf("%lf\t%lf\n", my_sqrt(3), sqrt(3));
    printf("%lf\t%lf\n", my_sqrt(4), sqrt(4));
    printf("%lf\t%lf\n", my_sqrt(5), sqrt(5));
    printf("%lf\t%lf\n", my_sqrt(6), sqrt(6));
    printf("%lf\t%lf\n", my_sqrt(7), sqrt(7));
    printf("%lf\t%lf\n", my_sqrt(8), sqrt(8));
    printf("%lf\t%lf\n", my_sqrt(9), sqrt(9));
    printf("%lf\t%lf\n", my_sqrt(10), sqrt(10));
}

方法二：二分法

#include <stdio.h>
#include <math.h>


double my_abs(double num)
{
    if (num < 0)
    {
        return -num;
    }
    return num;
}


double my_sqrt(double num)
{
    double epsilon = 0.000001;  // 精度
    double low = 0;
    double high = num;
    double mid = (low + high) / 2;
    while (my_abs(mid * mid - num) > epsilon)
    {
        if (mid * mid > num)
        {
            high = mid;
        }
        else
        {
            low = mid;
        }
        mid = (high + low) / 2;
    }
    return mid;
}


int main()
{
    printf("my_sqrt\t\tsqrt\n");
    printf("%lf\t%lf\n", my_sqrt(2), sqrt(2));
    printf("%lf\t%lf\n", my_sqrt(3), sqrt(3));
    printf("%lf\t%lf\n", my_sqrt(4), sqrt(4));
    printf("%lf\t%lf\n", my_sqrt(5), sqrt(5));
    printf("%lf\t%lf\n", my_sqrt(6), sqrt(6));
    printf("%lf\t%lf\n", my_sqrt(7), sqrt(7));
    printf("%lf\t%lf\n", my_sqrt(8), sqrt(8));
    printf("%lf\t%lf\n", my_sqrt(9), sqrt(9));
    printf("%lf\t%lf\n", my_sqrt(10), sqrt(10));
}