init

.gitignore

@@ -0,0 +1 @@
+pi

Main.c

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+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+double root(double x, int steps) {
+    if(x == 0.0) {
+        return 0.0;
+    }
+    double a = x;
+    x /= 2;
+    for(int i = 0; i < steps; i++) {
+        x = (x + a / x) * 0.5;
+    }
+    return x;
+}
+
+double circle(double x) {
+    return root(1 - x * x, 25);
+}
+
+double monteCarloIntegration() {
+    int amount = 512 * 512;
+    int in = 0;
+    for(int i = 0; i < amount; i++) {
+        double x = rand() / (double)RAND_MAX;
+        double y = rand() / (double)RAND_MAX;
+        in += (x * x + y * y < 1);
+    }
+    return 4.0 * in / amount;
+}
+
+double simpson(double a, double b) {
+    return ((b - a) / 6.0) * (circle(a) + 4 * circle((a + b) * 0.5) + circle(b));
+}
+
+double simpsonIntegration() {
+    double sum = 0.0;
+    for(int i = 0; i < 100; i++) {
+        sum += simpson(i / 100.0, (i + 1) / 100.0);
+    }
+    return 4.0 * sum;
+}
+
+double lineSum() {
+    double sum = 0.0;
+    const int max = 1000000;
+    for(int i = 0; i < max; i++) {
+        double x1 = (double)i / max;
+        double x2 = (i + 1.0) / max;
+        double diffX = x2 - x1;
+        double diffY = circle(x2) - circle(x1);
+        sum += root(diffX * diffX + diffY * diffY, 30);
+    }
+    return sum * 2.0;
+}
+
+double lineRecursion() {
+    double x1 = 0.0;
+    double y1 = 1.0;
+    double x2 = 1.0;
+    double y2 = 0.0;
+    double factor = 2.0;
+    for(int i = 0; i < 24; i++) {
+        double midX = (x1 + x2) * 0.5;
+        double midY = (y1 + y2) * 0.5;
+        double length = root(midX * midX + midY * midY, 10);
+        midX /= length;
+        midY /= length;
+        x2 = midX;
+        y2 = midY;
+        factor *= 2;
+    }
+    double diffX = x2 - x1;
+    double diffY = y2 - y1;
+    return root(diffX * diffX + diffY * diffY, 200) * factor;
+}
+
+void print(double d) {
+    double diff = d - M_PI;
+    printf("%.20lf %.20lf\n", d, diff < 0.0 ? -diff : diff);
+}
+
+int main() {
+    print(monteCarloIntegration());
+    print(simpsonIntegration());
+    print(lineSum());
+    print(lineRecursion());
+    puts("3.14159265358979323846\n");
+    return 0;
+}

Makefile

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+all: pi
+	
+pi: Main.c
+	gcc -o $@ Main.c -Wall -Wextra -Werror -pedantic -O3
+	
+clean:
+	rm -f pi