Primorial numbers: Difference between revisions
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Multiplying the vector elements in pairs is much faster for essentially the same reason that merge sort is faster than insertion sort.<br> |
Multiplying the vector elements in pairs is much faster for essentially the same reason that merge sort is faster than insertion sort.<br> |
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You could probably optimise the number of mpz_init() this invokes a fair bit, if you really wanted to. |
You could probably optimise the number of mpz_init() this invokes a fair bit, if you really wanted to. |
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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: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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function vecprod(sequence s) |
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if s={} then |
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<span style="color: #008080;">function</span> <span style="color: #000000;">vecprod</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> |
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s = {mpz_init(1)} |
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<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> |
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else |
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_init</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(s) do |
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<span style="color: #008080;">else</span> |
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s[i] = mpz_init(s[i]) |
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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;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #000000;">s</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: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
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while length(s)>1 do |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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for i=1 to floor(length(s)/2) do |
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<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</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: #008080;">do</span> |
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mpz_mul(s[i],s[i],s[-i]) |
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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;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
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s = s[1..ceil(length(s)/2)] |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end while |
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<span style="color: #000000;">s</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: #7060A8;">ceil</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)]</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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return s[1] |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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constant t0 = time(), |
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tests = tagset(9,0)&sq_power(10,tagset(6)), |
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<span style="color: #008080;">constant</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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primes = get_primes(1_000_000) |
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<span style="color: #000000;">max10</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;">4</span><span style="color: #0000FF;">:</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span> |
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<span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)&</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">max10</span><span style="color: #0000FF;">)),</span> |
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for i=1 to length(tests) do |
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<span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1_000_000</span><span style="color: #0000FF;">)</span> |
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integer ti = tests[i] |
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mpz primorial = vecprod(primes[1..ti]) |
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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;">tests</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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string ps = iff(ti<10?sprintf("= %s",{mpz_get_str(primorial,comma_fill:=true)}) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">ti</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> |
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:sprintf("has %,d digits",mpz_sizeinbase(primorial,10))) |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">primorial</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vecprod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">])</span> |
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printf(1,"Primorial(%,d) %s\n", {ti, ps}) |
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<span style="color: #004080;">string</span> <span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ti</span><span style="color: #0000FF;"><</span><span style="color: #000000;">10</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"= %s"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primorial</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)})</span> |
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end for |
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<span style="color: #0000FF;">:</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"has %,d digits"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_sizeinbase</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primorial</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)))</span> |
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?elapsed(time()-t0)</lang> |
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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;">"Primorial(%,d) %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ps</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</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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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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"6.2s" |
"6.2s" |
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</pre> |
</pre> |
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Under pwa/p2js Primorial(10,000) is obtained in 2s but 10^5 appears to be well beyond reach. |
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=={{header|PicoLisp}}== |
=={{header|PicoLisp}}== |
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