User:Thebigh/mysandbox: Difference between revisions

The '''Minkowski question-mark function''' converts the continued fraction representation of a number into

<lang freebasic>#define MAXITER 151

function minkowski( x as double ) as double

if x>1 or x<0 then return int(x)+minkowski(x-int(x))

dim as ulongint p = int(x)

dim as ulongint q = 1, r = p + 1, s = 1, m, n

dim as double d = 1, y = p

while true

d = d / 2.0

if y + d = y then exit while

m = p + r

if m < 0 or p < 0 then exit while

n = q + s

if n < 0 then exit while

if x < cast(double,m) / n then

r = m

s = n

else

y = y + d

p = m

q = n

end if

wend

return y + d

end function

function minkowski_inv( byval x as double ) as double

if x>1 or x<0 then return int(x)+minkowski_inv(x-int(x))

if x=1 or x=0 then return x

redim as uinteger contfrac(0 to 0)

dim as uinteger curr=0, count=1, i = 0

do

x *= 2

if curr = 0 then

if x<1 then

count += 1

else

i += 1

redim preserve contfrac(0 to i)

contfrac(i-1)=count

count = 1

curr = 1

x=x-1

endif

else

if x>1 then

count += 1

x=x-1

else

i += 1

redim preserve contfrac(0 to i)

contfrac(i-1)=count

count = 1

curr = 0

endif

end if

if x = int(x) then

contfrac(i)=count

exit do

end if

loop until i = MAXITER

dim as double ret = 1.0/contfrac(i)

for j as integer = i-1 to 0 step -1

ret = contfrac(j) + 1.0/ret

next j

return 1./ret

end function

print minkowski( 0.5*(1+sqr(5)) ), 5./3

print minkowski_inv( -5./9 ), (sqr(13)-7)/6

print minkowski(minkowski_inv(0.718281828)), minkowski_inv(minkowski(0.718281828))