Minkowski question-mark function: Difference between revisions

</pre>

=={{header|Python}}==

{{trans|Go}}

<lang python>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)),

)

)

</lang>

{{out}}

<pre>

1.6666666666696983 1.6666666666666667

-0.5657414540893351 -0.5657414540893352

0.7182818280000092 0.1213141516171819