Data commit

Task/Eulers-constant-0.5772.../Processing/eulers-constant-0.5772....processing

@@ -0,0 +1,145 @@
+/*********************************************
+ Subject: Comparing five methods for
+ computing Euler's constant 0.5772...
+ // https://rosettacode.org/wiki/Euler%27s_constant_0.5772...
+ --------------------------------------------*/
+double a, b, h, n2, r, u, v;
+float floatA, floatB, floatN2;
+int k, k2, m, n;
+double eps = 1e-6;
+
+void setup() {
+  size(100, 100);
+  noLoop();
+}
+
+void draw() {
+  println("From the definition, err. 3e-10\n");
+
+  n = 400;
+
+  h = 1;
+
+  for (int k = 2; k <= n; k++) {
+    h += 1.0 / k;
+  }
+  //faster convergence: Negoi, 1997
+  a = log(n +.5 + 1.0 / (24*n));
+
+  println("Hn    ", h);
+  println("gamma ", h - a);
+  println("k = ", n);
+  println("");
+
+
+  println("Sweeney, 1963, err. idem");
+  n = 21;
+
+  double s[] = {0, n};
+  r = n;
+  k = 1;
+  while (r > eps) {
+    k ++;
+    r *= (double) n / k;
+    s[k & 1] = s[k & 1] + r / k;
+  }
+
+  // println("gamma %.16f\nk = %d\n\n", s[1] - s[0] - log(n), k);
+
+  println("Hn    ", h);
+  println("gamma ", s[1] - s[0] - log(n));
+  println("k = ", k);
+  println("");
+
+  println("Bailey, 1988");
+  n = 5;
+  floatA = 1;
+  h = 1;
+  floatN2 = pow(2, n);
+  r = 1;
+  k = 1;
+  while (abs(floatB - floatA) > eps) {
+    k += 1;
+    r *= floatN2 / k;
+    h += 1.0 / k;
+    floatB = floatA;
+    floatA += r * h;
+  }
+  floatA *= floatN2 / exp(floatN2);
+
+  println("gamma ", floatA - n * log(2));
+  println("k = ", k);
+  println("");
+
+  println("Brent-McMillan, 1980");
+
+  n = 13;
+
+  floatA = -log(n);
+  floatB = 1;
+  u = a;
+  v = b;
+  n2 = n * n;
+  k2 = 0;
+  k = 0;
+
+
+  while (abs(floatA) > eps) {
+    k2 += 2*k + 1;
+    k += 1;
+    floatA *= n2 / k;
+    floatB *= n2 / k2;
+    floatA = (floatA + floatB) / k;
+    u += floatA;
+    v += floatB;
+  }
+  println("gamma  ", u / v);
+  println("k      ", k);
+
+
+
+  println("How Euler did it in 1735\n");
+  //Bernoulli numbers with even indices
+
+  double[] B2 = new double[11];
+
+  B2[1] = 1.0;
+  B2[2] = 1.0/6;
+  B2[3] = -1.0/30;
+  B2[4] = 1.0/42;
+  B2[5] = -1.0/30;
+  B2[6] = 5.0/66;
+  B2[7] = -691.0/2730;
+  B2[8] = 7.0/6;
+  B2[9] = -3617.0/510;
+  B2[10]= 43867.0/798;
+
+  m = 7;
+  n = 10;
+
+  //n-th harmonic number
+  h = 1;
+  for (k = 2; k <= n; k++) {
+    h += 1.0 / k;
+  }
+  println("Hn    ", h);
+
+  h -= log(n);
+  println("  -ln ", h);
+
+  //expansion C = -digamma(1)
+  a = -1.0 / (2*n);
+  n2 = n * n;
+  r = 1;
+  for (k = 1; k <= m; k++) {
+    r *= n2;
+    a += B2[k] / (2*k * r);
+  }
+
+  println("");
+  println("err  ", a);
+  println("gamma ", h + a );
+  println("k = ", n + m);
+  println("");
+  println("C  =  0.57721566490153286...\n");
+}