Catalan numbers: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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See also [[Catalan_numbers/Pascal%27s_triangle#Phix]] which may be faster. |
See also [[Catalan_numbers/Pascal%27s_triangle#Phix]] which may be faster. |
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<!--<lang Phix>--> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #000080;font-style:italic;">-- returns inf/-nan for n>85, and needs the rounding for n>=14, accurate to n=29</span> |
<span style="color: #000080;font-style:italic;">-- returns inf/-nan for n>85, and needs the rounding for n>=14, accurate to n=29</span> |
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<span style="color: #008080;">function</span> <span style="color: #000000;">catalan1</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: #008080;">function</span> <span style="color: #000000;">catalan1</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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=== memoized recursive gmp version === |
=== memoized recursive gmp version === |
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{{libheader|Phix/mpfr}} |
{{libheader|Phix/mpfr}} |
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<!--<lang Phix>--> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;"> |
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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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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<span style="color: #004080;">sequence</span> <span style="color: #000000;">c2cache</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c2cache</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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<span style="color: # |
<span style="color: #004080;">mpz</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> |
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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;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">catalan2m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #000000;">catalan2m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">))</span> |
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">catalan2m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #000000;">catalan2m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">))</span> |