Minkowski question-mark function: Difference between revisions

=={{header|Nim}}==

{{trans|Go}}

<lang Nim>import math, strformat

const MaxIter = 151

func minkowski(x: float): float =

if x notin 0.0..1.0:

return floor(x) + minkowski(x - floor(x))

var

p = x.uint64

r = p + 1

q, s = 1u64

d = 1.0

y = p.float

while true:

d /= 2

if y + d == y: break

let m = p + r

if m < 0 or p < 0: break

let n = q + s

if n < 0: break

if x < m.float / n.float:

r = m

s = n

else:

y += d

p = m

q = n

result = y + d

func minkowskiInv(x: float): float =

if x notin 0.0..1.0:

return floor(x) + minkowskiInv(x - floor(x))

if x == 1 or x == 0:

return x

var

contFrac: seq[uint32]

curr = 0u32

count = 1u32

i = 0

x = x

while true:

x *= 2

if curr == 0:

if x < 1:

inc count

else:

inc i

contFrac.setLen(i + 1)

contFrac[i - 1] = count

count = 1

curr = 1

x -= 1

else:

if x > 1:

inc count

x -= 1

else:

inc i

contFrac.setLen(i + 1)

contFrac[i - 1] = count

count = 1

curr = 0

if x == floor(x):

contFrac[i] = count

break

if i == MaxIter:

break

var ret = 1 / contFrac[i].float

for j in countdown(i - 1, 0):

ret = contFrac[j].float + 1 / ret

result = 1 / ret

echo &"{minkowski(0.5*(1+sqrt(5.0))):19.16f}, {5/3:19.16f}"

echo &"{minkowskiInv(-5/9):19.16f}, {(sqrt(13.0)-7)/6:19.16f}"

echo &"{minkowski(minkowskiInv(0.718281828)):19.16f}, " &

&"{minkowskiInv(minkowski(0.1213141516171819)):19.16f}"</lang>

{{out}}

<pre> 1.6666666666696983, 1.6666666666666667

-0.5657414540893351, -0.5657414540893352

0.7182818280000092, 0.1213141516171819</pre>