Arithmetic/Rational: Difference between revisions
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m (→{{header|Phix}}: added syntax colouring the hard way) |
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{Trans|Tcl}} |
{{Trans|Tcl}} |
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Phix does not support operator overloading (I am strongly opposed to such nonsense), nor does it have a fraction library, but it might look a bit like this. |
Phix does not support operator overloading (I am strongly opposed to such nonsense), nor does it have a native fraction library, but it might look a bit like this. |
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<!--<lang Phix>(phixonline)--> |
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<lang Phix>without warning -- (several unused routines in this code) |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #008080;">without</span> <span style="color: #000000;">warning</span> <span style="color: #000080;font-style:italic;">-- (several unused routines in this code)</span> |
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constant NUM = 1, DEN = 2 |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">NUM</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DEN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span> |
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type frac(object r) |
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return sequence(r) and integer(r[NUM]) and integer(r[DEN]) and length(r)=2 |
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<span style="color: #008080;">type</span> <span style="color: #000000;">frac</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> |
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end type |
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<span style="color: #008080;">return</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">2</span> <span style="color: #008080;">and</span> <span style="color: #004080;">integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">and</span> <span style="color: #004080;">integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DEN</span><span style="color: #0000FF;">])</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">type</span> |
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function normalise(object n, atom d=0) |
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atom g |
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<span style="color: #008080;">function</span> <span style="color: #000000;">normalise</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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if sequence(n) then |
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<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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{n,d} = n |
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<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: #0000FF;">=</span> <span style="color: #000000;">n</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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if d<0 then |
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<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
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n = -n |
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">n</span> |
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d = -d |
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<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">d</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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g = gcd(n,d) |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">gcd</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> |
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return {n/g,d/g} |
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">/</span><span style="color: #000000;">g</span><span style="color: #0000FF;">}</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_new(integer n,d=1) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_new</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</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> |
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return normalise(n,d) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">normalise</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> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_abs(frac r) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> |
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return {abs(r[NUM]),r[DEN]} |
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">DEN</span><span style="color: #0000FF;">]}</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_inv(frac r) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_inv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> |
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return reverse(r) |
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_add(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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integer {an,ad} = a, |
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<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">an</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> |
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{bn,bd} = b |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> |
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return normalise(an*bd+bn*ad,ad*bd) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">normalise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">an</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">+</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ad</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">)</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_sub(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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integer {an,ad} = a, |
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<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">an</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> |
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{bn,bd} = b |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> |
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return normalise(an*bd-bn*ad,ad*bd) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">normalise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">an</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">-</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ad</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">)</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_mul(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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integer {an,ad} = a, |
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<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">an</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> |
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{bn,bd} = b |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> |
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return normalise(an*bn,ad*bd) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">normalise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">an</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ad</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">)</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_div(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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integer {an,ad} = a, |
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<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">an</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> |
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{bn,bd} = b |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span> |
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return normalise(an*bd,ad*bn) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">normalise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">an</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bd</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ad</span><span style="color: #0000FF;">*</span><span style="color: #000000;">bn</span><span style="color: #0000FF;">)</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_eq(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_eq</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return a==b |
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">==</span><span style="color: #000000;">b</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_ne(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_ne</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return a!=b |
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">b</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_lt(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_lt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return frac_sub(a,b)[NUM]<0 |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">0</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_gt(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_gt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return frac_sub(a,b)[NUM]>0 |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">]></span><span style="color: #000000;">0</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_le(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return frac_sub(a,b)[NUM]<=0 |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">]<=</span><span style="color: #000000;">0</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function frac_ge(frac a, frac b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">frac_ge</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frac</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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return frac_sub(a,b)[NUM]>=0 |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">NUM</span><span style="color: #0000FF;">]>=</span><span style="color: #000000;">0</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function is_perfect(integer num) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">num</span><span style="color: #0000FF;">)</span> |
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frac sum = frac_new(0) |
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<span style="color: #000000;">frac</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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sequence f = factors(num,1) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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for i=1 to length(f) do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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sum = frac_add(sum,frac_new(1,f[i])) |
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<span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">frac_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">total</span><span style="color: #0000FF;">,</span><span style="color: #000000;">frac_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]))</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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return frac_eq(sum,frac_new(2)) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">frac_eq</span><span style="color: #0000FF;">(</span><span style="color: #000000;">total</span><span style="color: #0000FF;">,</span><span style="color: #000000;">frac_new</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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procedure get_perfect_numbers() |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">get_perfect_numbers</span><span style="color: #0000FF;">()</span> |
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atom t0 = time() |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> |
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for i=2 to power(2,19) do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">13</span><span style="color: #0000FF;">:</span><span style="color: #000000;">19</span><span style="color: #0000FF;">))</span> |
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if is_perfect(i) then |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
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printf(1,"perfect: %d\n",i) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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end if |
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<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;">"perfect: %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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printf(1,"elapsed: %3.2f seconds\n",time()-t0) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<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;">"elapsed: %3.2f seconds\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> |
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integer pn5 = power(2,12)*(power(2,13)-1) -- 5th perfect number |
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if is_perfect(pn5) then |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">pn5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)*(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 5th perfect number</span> |
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printf(1,"perfect: %d\n",pn5) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn5</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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end if |
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<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;">"perfect: %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pn5</span><span style="color: #0000FF;">)</span> |
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end procedure |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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get_perfect_numbers()</lang> |
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<span style="color: #000000;">get_perfect_numbers</span><span style="color: #0000FF;">()</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Line 3,339: | Line 3,342: | ||
Turned out to be slightly slower than native, but worth it for large number support.<br> |
Turned out to be slightly slower than native, but worth it for large number support.<br> |
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See also [[Bernoulli_numbers#Phix|Bernoulli_numbers]] for another example of mpqs in action. |
See also [[Bernoulli_numbers#Phix|Bernoulli_numbers]] for another example of mpqs in action. |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">/</span><span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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function is_perfect(integer num) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">num</span><span style="color: #0000FF;">)</span> |
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mpq tot = mpq_init(), |
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<span style="color: #004080;">mpq</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_init</span><span style="color: #0000FF;">(),</span> |
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fth = mpq_init() |
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<span style="color: #000000;">fth</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_init</span><span style="color: #0000FF;">()</span> |
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sequence f = factors(num,1) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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for i=1 to length(f) do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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mpq_set_si(fth,1,f[i]) |
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<span style="color: #7060A8;">mpq_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
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mpq_add(tot,tot,fth) |
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<span style="color: #7060A8;">mpq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fth</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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return mpq_cmp_si(tot,2,1)=0 |
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">mpq_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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procedure get_perfect_numbers() |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">get_perfect_numbers</span><span style="color: #0000FF;">()</span> |
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atom t0 = time() |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> |
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for i=2 to power(2,19) do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">13</span><span style="color: #0000FF;">:</span><span style="color: #000000;">19</span><span style="color: #0000FF;">))</span> |
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if is_perfect(i) then |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
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printf(1,"perfect: %d\n",i) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
|||
end if |
|||
<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;">"perfect: %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> |
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end for |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
printf(1,"elapsed: %3.2f seconds\n",time()-t0) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
<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;">"elapsed: %3.2f seconds\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> |
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integer pn5 = power(2,12)*(power(2,13)-1) -- 5th perfect number |
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if is_perfect(pn5) then |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">pn5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)*(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 5th perfect number</span> |
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printf(1,"perfect: %d\n",pn5) |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">is_perfect</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn5</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
|||
end if |
|||
<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;">"perfect: %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pn5</span><span style="color: #0000FF;">)</span> |
|||
end procedure |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
|||
get_perfect_numbers()</lang> |
|||
<span style="color: #000000;">get_perfect_numbers</span><span style="color: #0000FF;">()</span> |
|||
<!--</lang>--> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 3,376: | Line 3,382: | ||
perfect: 33550336 |
perfect: 33550336 |
||
</pre> |
</pre> |
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<small>Note that power(2,19) took over 270s under mpfr.js, so reduced to power(2,13) on that platform, making it finish in 0.99s</small> |
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=={{header|PicoLisp}}== |
=={{header|PicoLisp}}== |