Goldbach's comet: Difference between revisions

</pre>

=={{header|Phix}}==

{{libheader|Phix/pGUI}}

{{libheader|Phix/online}}

You can run this online [http://phix.x10.mx/p2js/goldbach.htm here].

<!--<lang Phix>(phixonline)-->

<span style="color: #000080;font-style:italic;">--

-- demo\rosetta\Goldbachs_comet.exw

-- ================================

--

-- Note: this plots n/2 vs G(n) for n=6 to 4000 by 2, matching wp and

-- Algol 68, Python, and Raku. However, while not wrong, Arturo

-- and Wren apparently plot n vs G(n) for n=6 to 2000 by 2, so

-- should you spot any (very) minor differences, that'd be why.

--</span>

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4000</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$],</span>

<span style="color: #000000;">goldbach</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reinstate</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">),{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>

<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;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes</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: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">></span><span style="color: #000000;">limit</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #000000;">goldbach</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">fhg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagstart</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>

<span style="color: #004080;">string</span> <span style="color: #000000;">fhgs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fhg</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d"</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">gm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e6</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">499999</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]),</span><span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">))</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;">"The first 100 G values:\n%s\n\nG(1,000,000) = %,d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">fhgs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gm</span><span style="color: #0000FF;">})</span>

<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>

<span style="color: #008080;">include</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">get_data</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">xR</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">yR</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xR</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">xB</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">yB</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xB</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">xG</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">yG</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">,</span><span style="color: #000000;">xG</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">return</span> <span style="color: #0000FF;">{{</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xR</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">yR</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_RED</span><span style="color: #0000FF;">},</span>

<span style="color: #0000FF;">{</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xB</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">yB</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_BLUE</span><span style="color: #0000FF;">},</span>

<span style="color: #0000FF;">{</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xG</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">yG</span><span style="color: #0000FF;">,</span><span style="color: #004600;">CD_DARK_GREEN</span><span style="color: #0000FF;">}}</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>

<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">graph</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">IupGraph</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_data</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"RASTERSIZE=640x440"</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"XTICK=%d,XMIN=0,XMAX=%d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})</span>

<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"YTICK=20,YMIN=0,YMAX=%d"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">goldbach</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">20</span><span style="color: #0000FF;">})</span>

<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"MODE=MARK, MARKSTYLE=PLUS"</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">graph</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`TITLE="Goldbach's comet"`</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">IupSetAttributes</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"MINSIZE=400x300"</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>

<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>

<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<!--</lang>-->

{{out}}

<pre>

The first 100 G values:

1 1 1 2 1 2 2 2 2 3

3 3 2 3 2 4 4 2 3 4

3 4 5 4 3 5 3 4 6 3

5 6 2 5 6 5 5 7 4 5

8 5 4 9 4 5 7 3 6 8

5 6 8 6 7 10 6 6 12 4

5 10 3 7 9 6 5 8 7 8

11 6 5 12 4 8 11 5 8 10

5 6 13 9 6 11 7 7 14 6

8 13 5 8 11 7 9 13 8 9

G(1,000,000) = 5,402