Data commit

Task/Minkowski-question-mark-function/Python/minkowski-question-mark-function.py

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+import math
+
+MAXITER = 151
+
+
+def minkowski(x):
+    if x > 1 or x < 0:
+        return math.floor(x) + minkowski(x - math.floor(x))
+
+    p = int(x)
+    q = 1
+    r = p + 1
+    s = 1
+    d = 1.0
+    y = float(p)
+
+    while True:
+        d /= 2
+        if y + d == y:
+            break
+
+        m = p + r
+        if m < 0 or p < 0:
+            break
+
+        n = q + s
+        if n < 0:
+            break
+
+        if x < m / n:
+            r = m
+            s = n
+        else:
+            y += d
+            p = m
+            q = n
+
+    return y + d
+
+
+def minkowski_inv(x):
+    if x > 1 or x < 0:
+        return math.floor(x) + minkowski_inv(x - math.floor(x))
+
+    if x == 1 or x == 0:
+        return x
+
+    cont_frac = [0]
+    current = 0
+    count = 1
+    i = 0
+
+    while True:
+        x *= 2
+
+        if current == 0:
+            if x < 1:
+                count += 1
+            else:
+                cont_frac.append(0)
+                cont_frac[i] = count
+
+                i += 1
+                count = 1
+                current = 1
+                x -= 1
+        else:
+            if x > 1:
+                count += 1
+                x -= 1
+            else:
+                cont_frac.append(0)
+                cont_frac[i] = count
+
+                i += 1
+                count = 1
+                current = 0
+
+        if x == math.floor(x):
+            cont_frac[i] = count
+            break
+
+        if i == MAXITER:
+            break
+
+    ret = 1.0 / cont_frac[i]
+    for j in range(i - 1, -1, -1):
+        ret = cont_frac[j] + 1.0 / ret
+
+    return 1.0 / ret
+
+
+if __name__ == "__main__":
+    print(
+        "{:19.16f} {:19.16f}".format(
+            minkowski(0.5 * (1 + math.sqrt(5))),
+            5.0 / 3.0,
+        )
+    )
+
+    print(
+        "{:19.16f} {:19.16f}".format(
+            minkowski_inv(-5.0 / 9.0),
+            (math.sqrt(13) - 7) / 6,
+        )
+    )
+
+    print(
+        "{:19.16f} {:19.16f}".format(
+            minkowski(minkowski_inv(0.718281828)),
+            minkowski_inv(minkowski(0.1213141516171819)),
+        )
+    )