June 2018 Update

Task/Continued-fraction/Julia/continued-fraction.julia

@@ -0,0 +1,36 @@
+function _sqrt(a::Bool, n)
+    if a
+        return n > 0 ? 2.0 : 1.0
+    else
+        return 1.0
+    end
+end
+
+function _napier(a::Bool, n)
+    if a
+        return n > 0 ? Float64(n) : 2.0
+    else
+        return n > 1 ? n - 1.0 : 1.0
+    end
+end
+
+function _pi(a::Bool, n)
+    if a
+        return n > 0 ? 6.0 : 3.0
+    else
+        return (2.0 * n - 1.0) ^ 2.0 # exponentiation operator
+    end
+end
+
+function calc(f::Function, expansions::Integer)
+    a, b = true, false
+    r = 0.0
+    for i in expansions:-1:1
+        r = f(b, i) / (f(a, i) + r)
+    end
+    return f(a, 0) + r
+end
+
+for (v, f) in (("√2", _sqrt), ("e", _napier), ("π", _pi))
+    @printf("%3s = %f\n", v, calc(f, 1000))
+end

Task/Continued-fraction/Ring/continued-fraction.ring

@@ -0,0 +1,21 @@
+# Project : Continued fraction
+# Date    : 2018/03/17
+# Author : Gal Zsolt [~ CalmoSoft ~]
+# Email   : <calmosoft@gmail.com>
+
+see "SQR(2) = " + contfrac(1, 1, "2", "1") + nl
+see "        e = " + contfrac(2, 1, "n", "n") + nl
+see "       PI = " + contfrac(3, 1, "6", "(2*n+1)^2") + nl
+
+func contfrac(a0, b1, a, b)
+        expr = ""
+        n = 0
+        while len(expr) < (700 - n)
+                 n = n + 1
+                 eval("temp1=" + a)
+                 eval("temp2=" + b)
+                 expr = expr + string(temp1) + char(43) + string(temp2) + "/("
+        end
+        str = copy(")",n)
+        eval("temp3=" + expr + "1" + str)
+        return a0 + b1 / temp3

Task/Continued-fraction/Scheme/continued-fraction-1.ss

@@ -0,0 +1,50 @@
+#!r6rs
+(import (rnrs base (6))
+        (srfi :41 streams))
+
+(define nats (stream-cons 0 (stream-map (lambda (x) (+ x 1)) nats)))
+
+(define (build-stream fn) (stream-map fn nats))
+
+(define (stream-cycle s . S)
+  (cond
+    ((stream-null? (car S)) stream-null)
+    (else (stream-cons (stream-car s)
+                       (apply stream-cycle (append S (list (stream-cdr s))))))))
+
+(define (cf-floor cf) (stream-car cf))
+(define (cf-num cf) (stream-car (stream-cdr cf)))
+(define (cf-denom cf) (stream-cdr (stream-cdr cf)))
+
+(define (cf-integer? x) (stream-null? (stream-cdr x)))
+
+(define (cf->real x)
+  (let refine ((x x) (n 65536))
+    (cond
+      ((= n 0) +inf.0)
+      ((cf-integer? x) (cf-floor x))
+      (else (+ (cf-floor x)
+               (/ (cf-num x)
+                  (refine (cf-denom x) (- n 1))))))))
+
+(define (real->cf x)
+  (let-values (((integer-part fractional-part) (div-and-mod x 1)))
+    (if (= fractional-part 0.0)
+        (stream (exact integer-part))
+        (stream-cons
+         (exact integer-part)
+         (stream-cons
+          1
+          (real->cf (/ fractional-part)))))))
+
+
+(define sqrt2 (stream-cons 1 (stream-constant 1 2)))
+
+(define napier
+  (stream-append (stream 2 1)
+                 (stream-cycle (stream-cdr nats) (stream-cdr nats))))
+
+(define pi
+  (stream-cons 3
+               (stream-cycle (build-stream (lambda (n) (expt (- (* 2 (+ n 1)) 1) 2)))
+                             (stream-constant 6))))

Task/Continued-fraction/Scheme/continued-fraction-2.ss

@@ -0,0 +1,6 @@
+> (cf->real sqrt2)
+1.4142135623730951
+> (cf->real napier)
+2.7182818284590455
+> (cf->real pi)
+3.141592653589794