Objective-C で 積分(台形則)して π を求める

πの求め方

積分(台形則)

#import <Foundation/Foundation.h>
#import <math.h>

double f(double x)
{
    return 4 / (1 + x * x); 
}

int main()
{
    const double a = 0;
    const double b = 1;

    // 台形則で積分
    int n = 2;
    int i, j;
    for (j = 1; j <= 10; j++)
    {
        double h = (b - a) / n;  
        double s = 0;
        double x = a;
        for (i = 1; i <= n - 1; i++)
        {
            x += h;
            s += f(x);
        }
        s = h * ((f(a) + f(b)) / 2 + s);
        n *= 2;

        // 結果を π と比較
        printf("%2d : %13.10f, %13.10f\n", j, s, s - M_PI);
    }

    return 0;
}

xxxxxx@yyyyyy ~/objc
$ gcc -o OC0601 OC0601.m -lobjc -lgnustep-base -I $INCLUDE -L $LIB $CFLAGS

xxxxxx@yyyyyy ~/objc
$ OC0601
 1 :  3.1000000000, -0.0415926536
 2 :  3.1311764706, -0.0104161830
 3 :  3.1389884945, -0.0026041591
 4 :  3.1409416120, -0.0006510415
 5 :  3.1414298932, -0.0001627604
 6 :  3.1415519635, -0.0000406901
 7 :  3.1415824811, -0.0000101725
 8 :  3.1415901105, -0.0000025431
 9 :  3.1415920178, -0.0000006358
10 :  3.1415924946, -0.0000001589

参考文献