add approximation for pi by gauss-legendre

src/reihen.c

@@ -28,4 +28,19 @@ double exponential(double x){
 
 double euler(){
     return exponential(1);
+}
+
+double pi(double eps){
+    double a = 1, b = 1/powerD(0.5, 2), t = 0.25, p = 1;
+    double aNew, piold, pi = 1;
+    do{
+        aNew = .5 * (a + b);
+        b = powerD(0.5 , a * b);
+        t -= p * (a - aNew) * (a - aNew);
+        a = aNew;
+        p *= 2;
+        piold = pi;
+        pi = (a + b) * (a + b) / (4 * t);
+    } while (absD(pi - piold) > eps);
+    return pi;
 }

src/reihen.h

@@ -3,5 +3,6 @@
 
 double exponential(double x);
 double euler();
+double pi();
 
 #endif // reihen.h

test/test_reihen.c

@@ -36,4 +36,12 @@ void test_Exponent_with_negative_number(void){
     TEST_ASSERT_DOUBLE_WITHIN(0.000001, 0.135335, r2);
 }
 
+void test_pi(void){
+    double r1;
+
+    r1 = pi(1e-8);
+    
+    TEST_ASSERT_DOUBLE_WITHIN(0.0000001, 3.14159265, r1);
+}
+
 #endif // TEST