Factors of an integer: Difference between revisions
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→{{header|Phix}}: added some larger number examples
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{1,3,5,15,823,2469,4115,12345}
</pre>
You can find the implementation of factors()
and mpz_factors(), mpz_prime_factors(), and mpz_pollard_rho() in mpfr.e for larger numbers, for example:
<div style="font-size: 11px">
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- [p2js/integer() bugs]</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3491888400</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"factors"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {2,3,4,5,"...",698377680,872972100,1163962800.0,1745944200.0," (1,918 factors)"}</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3491888400</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"factors"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {2,3,4,5,"...",698377680,872972100,1163962800.0,1745944200.0," (1,918 factors)"}
-- If the include1 parameter is 1 or "BOTH", then you'll also get 1 and 3491888400</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3491888400</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {2,3,5,7,11,13,17,19}</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3491888400</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- <nowiki>{{</nowiki>2,4},{3,3},{5,2},{7,1},{11,1},{13,1},{17,1},{19,1<nowiki>}}</nowiki></span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"3491888400"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {2,3,5,7,11,13,17,19}</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"3491888400"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- <nowiki>{{</nowiki>2,4},{3,3},{5,2},{7,1},{11,1},{13,1},{17,1},{19,1<nowiki>}}</nowiki>
-- Note that mpz_prime_factors() only accepts string or mpz, and not a raw native atom/integer.</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">108233175859200</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- 666</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">108233175859200</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- 666</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"10677106534462215678539721403561279"</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">mpz_prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- <nowiki>{{</nowiki>29269,1},{32579,1},{98731,2},{104729,3<nowiki>}}</nowiki></span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_factors</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: #008000;">"factors"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- {1,29269,"...","364792324112959639158827476291","10677106534462215678539721403561279"," (48 factors)"}</span>
<!--</syntaxhighlight>-->
</div>
Note the value in (string) d exceeds the precision limit of an IEEE-754 float, and would trigger a suitable human readable run-time error if passed to any of the non-mpz routines. Sadly, 1200034005600070000008900000000000000000 exceeds the capabilities of my mpz_pollard_rho(), which I had hoped to showcase - perhaps you would like to improve it?
=={{header|Phixmonti}}==
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