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Minkowski question-mark function: Difference between revisions

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Minkowski question-mark function (view source)

Revision as of 14:55, 30 January 2022

14,438 bytes added ,  2 years ago
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→‎{{header|Phix}}: added (proper) syntax colouring, marked p2js compatible
(→‎{{header|Haskell}}: simplifed and rewrote the solution.)
m (→‎{{header|Phix}}: added (proper) syntax colouring, marked p2js compatible)
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=={{header|Phix}}==
{{trans|FreeBASIC}}
<!--<lang Phix>(phixonline)-->
<lang Euphoria>constant MAXITER = 151
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">MAXITER</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">151</span>
function minkowski(atom x)
atom p = floor(x)
<span style="color: #008080;">function</span> <span style="color: #000000;">minkowski</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
if x>1 or x<0 then return p+minkowski(x-p) end if
<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
atom q = 1, r = p + 1, s = 1, m, n, d = 1, y = p
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">minkowski</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
while true do
<span style="color: #004080;">atom</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span>
d = d/2
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
if y + d = y then exit end if
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span>
m = p + r
<span style="color: #008080;">if</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if m < 0 or p < 0 then exit end if
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">r</span>
n = q + s
<span style="color: #008080;">if</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if n < 0 then exit end if
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">s</span>
if x < m/n then
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
r = m
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">/</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
s = n
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span>
else
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
y = y + d
<span p style="color: m#008080;">else</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">d</span>
q = n
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span>
end if
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return y + d
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">d</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function minkowski_inv(atom x)
if x>1 or x<0 then return floor(x)+minkowski_inv(x-floor(x)) end if
<span style="color: #008080;">function</span> <span style="color: #000000;">minkowski_inv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
if x=1 or x=0 then return x end if
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">minkowski_inv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
sequence contfrac = {}
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
integer curr = 0, count = 1
<span style="color: #004080;">sequence</span> <span style="color: #000000;">contfrac</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
while true do
<span style="color: #004080;">integer</span> <span style="color: #000000;">curr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
x *= 2
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
if curr = 0 then
<span style="color: #000000;">x</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
if x<1 then
<span style="color: #008080;">if</span> <span style="color: #000000;">curr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
count += 1
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
else
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
contfrac &= count
<span count style="color: 1#008080;">else</span>
<span style="color: #000000;">contfrac</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">count</span>
curr = 1
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
x -= 1
<span style="color: #000000;">curr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
end if
<span style="color: #000000;">x</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
else
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if x>1 then
<span count +style="color: 1#008080;">else</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
x -= 1
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
else
<span style="color: #000000;">x</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
contfrac &= count
<span count style="color: 1#008080;">else</span>
<span style="color: #000000;">contfrac</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">count</span>
curr = 0
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
end if
<span style="color: #000000;">curr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if x = floor(x) then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
contfrac &= count
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
exit
<span style="color: #000000;">contfrac</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">count</span>
end if
<span style="color: #008080;">exit</span>
if length(contfrac)=MAXITER then exit end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">contfrac</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">MAXITER</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
atom ret = 1/contfrac[$]
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
for i = length(contfrac)-1 to 1 by -1 do
<span style="color: #004080;">atom</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">contfrac</span><span style="color: #0000FF;">[$]</span>
ret = contfrac[i] + 1.0/ret
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">contfrac</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">contfrac</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1.0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">ret</span>
return 1/ret
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">ret</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
printf(1,"%20.16f %20.16f\n",{minkowski(0.5*(1+sqrt(5))), 5/3})
printf(1,"%20.16f %20.16f\n",{minkowski_inv(-5/9), (sqrt(13)-7)/6})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%20.16f %20.16f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">minkowski</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">))),</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">})</span>
printf(1,"%20.16f %20.16f\n",{minkowski(minkowski_inv(0.718281828)),
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%20.16f %20.16f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">minkowski_inv</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">5</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">6</span><span style="color: #0000FF;">})</span>
minkowski_inv(minkowski(0.1213141516171819))})</lang>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%20.16f %20.16f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">minkowski</span><span style="color: #0000FF;">(</span><span style="color: #000000;">minkowski_inv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.718281828</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">minkowski_inv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">minkowski</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.1213141516171819</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
{{out}}
<pre>
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