View source for Ramanujan's constant

=={{header|Phix}}==
{{trans|Go}}
{{libheader|Phix/mpfr}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span> <span style="color: #000080;font-style:italic;">-- no mpfr_exp() under p2js (yet), sorry</span>
 <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_set_default_prec[ision] has been renamed)</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: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">120</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (18 before, 100 after, plus 2 for kicks.)</span>
  
 <span style="color: #008080;">function</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">pi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
     <span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
     <span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">t</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</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;">"Ramanujan's constant to 100 decimal places is:\n"</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;">"%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">163</span><span style="color: #0000FF;">),</span><span style="color: #000000;">100</span><span style="color: #0000FF;">))</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">heegners</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">96</span><span style="color: #0000FF;">},</span>
                      <span style="color: #0000FF;">{</span><span style="color: #000000;">43</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">960</span><span style="color: #0000FF;">},</span>
                      <span style="color: #0000FF;">{</span><span style="color: #000000;">67</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5280</span><span style="color: #0000FF;">},</span>
                      <span style="color: #0000FF;">{</span><span style="color: #000000;">163</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">640320</span><span style="color: #0000FF;">},</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;">"\nHeegner numbers yielding 'almost' integers:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">mpfr</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">qh</span>
 <span style="color: #004080;">mpz</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</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;">heegners</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;">h0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h1</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">heegners</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">qh</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h0</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">744</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpfr_set_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpfr_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qh</span><span style="color: #0000FF;">)</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">qhs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">),</span>
            <span style="color: #000000;">cs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">),</span>
            <span style="color: #000000;">ts</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</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;">"%3d: %51s ~= %18s (diff: %s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">h0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">qhs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ts</span><span style="color: #0000FF;">})</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
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<pre>
Ramanujan's constant to 100 decimal places is:
262537412640768743.9999999999992500725971981856888793538563373369908627075374103782106479101186073129511813461860645042

Heegner numbers yielding 'almost' integers:
 19:             885479.77768015431949753789348171962682 ~=             885480 (diff: 0.22231984568050246210651828037318)
 43:          884736743.99977746603490666193746207858538 ~=          884736744 (diff: 0.00022253396509333806253792141462)
 67:       147197952743.99999866245422450682926131257863 ~=       147197952744 (diff: 0.00000133754577549317073868742137)
163: 262537412640768743.99999999999925007259719818568888 ~= 262537412640768744 (diff: 0.00000000000074992740280181431112)
</pre>