Minkowski question-mark function: Difference between revisions

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 =={{header|Julia}}==
-{{trans|FreeBASIC}}
-<syntaxhighlight lang="julia">function minkowski(x)
+<syntaxhighlight lang="julia">function questionmark(x)
-    p = Int(floor(x))
+    y, p = fldmod(x, 1)
-    (x > 1 || x < 0) && return p + minkowski(x)
+    q, d = 1 - p, .5
-    q, r, s, m, n = 1, p + 1, 1, 0, 0
+    while y + d > y
-    d, y = 1.0, Float64(p)
+        if p < q
-    while true
+            q -= p
-        d /= 2.0
-        y + d == y && break
-        m = p + r
-        (m < 0 || p < 0) && break
-        n = q + s
-        n < 0 && break
-        if x < (m / n)
-            r, s = m, n
         else
-            y, p, q = y + d, m, n
+            p -= q
+            y += d
         end
+        d /= 2
     end
-    return y + d
+    y
 end
-function minkowski_inv(x, maxiter=151)
+function questionmark_inv(x)
-    p = Int(floor(x))
+    y, bits = fldmod(x, 1)
+    lo, hi = [0, 1], [1, 1]
-    (x > 1 || x < 0) && return p + minkowski_inv(x - p, maxiter)
-    (x == 1 || x == 0) && return x
+    while (y + /(lo...)) != (y + /(hi...))
+        bit, bits = fldmod(2*bits, 1)
-    contfrac = [0]
+        bit > 0 ? (lo .+= hi) : (hi .+= lo)
-    curr, coun, i = 0, 1, 0
-    while i < maxiter
-        x *= 2
-        if curr == 0
-            if x < 1
-                coun += 1
-            else
-                i += 1
-                push!(contfrac, 0)
-                contfrac[i] = coun
-                coun = 1
-                curr = 1
-                x -= 1
-            end
-        else
-            if x > 1
-                coun += 1
-                x -= 1
-            else
-                i += 1
-                push!(contfrac, 0)
-                contfrac[i] = coun
-                coun = 1
-                curr = 0
-            end
-        end
-        if x == Int(floor(x))
-            contfrac[i + 1] = coun
-            break
-        end
     end
-    ret = 1.0 / contfrac[i + 1]
+    y + /((lo .+ hi)...)
-    for j in i:-1:1
-        ret = contfrac[j] + 1.0 / ret
-    end
-    return 1.0 / ret
 end
+x, y = 0.718281828, 0.1213141516171819
-println(" ", minkowski((1 + sqrt(5)) / 2), "   ", 5 / 3)
+for (a, b) ∈ [
-println(minkowski_inv(-5/9), "   ", (sqrt(13) - 7) / 6)
+        (5/3, questionmark((1 + √5)/2)),
-println(" ", minkowski(minkowski_inv(0.718281828)), "   ",
+        ((√13-7)/6, questionmark_inv(-5/9)),
-    minkowski_inv(minkowski(0.1213141516171819)))
+        (x, questionmark_inv(questionmark(x))),
+        (y, questionmark(questionmark_inv(y)))]
+    println(a, a ≈ b ? " ≈ " : " != ", b)
+end
 </syntaxhighlight>{{out}}
 <pre>
+.6666666666666667 ≈ 1.666666666667894
-.6666666666696983   1.6666666666666667
+-0.5657414540893352 ≈ -0.5657414540893351
--0.5657414540893351   -0.5657414540893352
+.718281828 ≈ 0.7182818279999971
-.7182818280000092   0.12131415161718191
+.1213141516171819 ≈ 0.12131415161718095
 </pre>