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Evaluate binomial coefficients: Difference between revisions

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Evaluate binomial coefficients (view source)

Revision as of 00:57, 10 June 2021

1,553 bytes added ,  3 years ago
m
→‎{{header|Phix}}: mpz_binom() renamed as mpz_bin_uiui() to match gmp proper (erm, ish)
(Added Arturo implementation)
m (→‎{{header|Phix}}: mpz_binom() renamed as mpz_bin_uiui() to match gmp proper (erm, ish))
Line 1,909:
<!--</lang>-->
Example:
<!--<lang Phix>?choose(5,3phixonline)</lang-->
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">choose</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>
<!--</lang>-->
{{out}}
<pre>
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However errors will creep in should any result or interim value exceed 9,007,199,254,740,992 (on 32-bit), so:
{{libheader|Phix/mpfr}}
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">includewith</span> <span style="color: #000000008080;">builtinsjavascript_semantics</span><span style="color: #0000FF;">\</span><span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #0000FF008080;">?include</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF000000;">(</span><span style="color: #7060A8;">mpz_binombuiltins</span><span style="color: #0000FF;">(\</span><span style="color: #000000004080;">5mpfr</span><span style="color: #0000FF;">,.</span><span style="color: #000000;">3e</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">?=</span> <span style="color: #7060A80000FF;">mpz_get_str{{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">(,</span><span style="color: #7060A8000000;">mpz_binom3</span><span style="color: #0000FF;">(},{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">))},{</span><span style="color: #000000;">60</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1200</span><span style="color: #0000FF;">,</span><span style="color: #000000;">120</span><span style="color: #0000FF;">}}</span>
<span style="color: #0000FF004080;">?mpz</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF000000;">(r</span><span style="color: #7060A8;">mpz_binom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">60</span><span style="color: #0000FF;">,</span><span style="color: #0000007060A8;">30mpz_init</span><span style="color: #0000FF;">)()</span>
<span style="color: #0000FF008080;">?for</span> <span style="color: #7060A8000000;">mpz_get_stri</span><span style="color: #0000FF;">(=</span><span style="color: #7060A8000000;">mpz_binom1</span> <span style="color: #0000FF008080;">(to</span> <span style="color: #0000007060A8;">1200length</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">120tests</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #7060A8;">mpz_bin_uiui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</lang>-->
{{out}}
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"1004576581793084916475353119318331966507299414258370667602185866686463289093457468590558508056798211449853806741873396451735444387513582540860551330127062642417424083600"
</pre>
Note that I have re-implemented mpz_bin_uiui() mainly for the benefit of pwa/p2js, and some tweaks may be in order (please ask if needed) to match gmp proper for -ve n.
 
=={{header|PHP}}==
Petelomax
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