Data commit

Task/Continued-fraction/Maxima/continued-fraction.maxima

@@ -0,0 +1,23 @@
+cfeval(x) := block([a, b, n, z], a: x[1], b: x[2], n: length(a), z: 0,
+   for i from n step -1 thru 2 do z: b[i]/(a[i] + z), a[1] + z)$
+
+cf_sqrt2(n) := [cons(1, makelist(2, i, 2, n)), cons(0, makelist(1, i, 2, n))]$
+
+cf_e(n) := [cons(2, makelist(i, i, 1, n - 1)), append([0, 1], makelist(i, i, 1, n - 2))]$
+
+cf_pi(n) := [cons(3, makelist(6, i, 2, n)), cons(0, makelist((2*i - 1)^2, i, 1, n - 1))]$
+
+cfeval(cf_sqrt2(20)), numer;   /* 1.414213562373097 */
+% - sqrt(2), numer;            /* 1.3322676295501878*10^-15 */
+
+cfeval(cf_e(20)), numer;       /* 2.718281828459046 */
+% - %e, numer;                 /* 4.4408920985006262*10^-16 */
+
+cfeval(cf_pi(20)), numer;      /* 3.141623806667839 */
+% - %pi, numer;                /* 3.115307804568701*10^-5 */
+
+
+/* convergence is much slower for pi */
+fpprec: 20$
+x: cfeval(cf_pi(10000))$
+bfloat(x - %pi);               /* 2.4999999900104930006b-13 */