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Ramanujan's constant: Difference between revisions

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Ramanujan's constant (view source)

Revision as of 18:53, 23 June 2021

8,367 bytes added ,  2 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|Phix}}: mpfr_set_default_precision renamed)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
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{{trans|Go}}
{{libheader|Phix/mpfr}}
<!--<lang Phix>(phixonline)-->
<lang Phix>requires("1.0.0") -- (mpfr_set_default_prec[ision] has been renamed)
<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>
include mpfr.e
<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>
mpfr_set_default_precision(-120) -- (18 before, 100 after, plus 2 for kicks.)
<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>
function q(integer d)
mpfr pi = mpfr_init()
<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>
mpfr_const_pi(pi)
<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>
mpfr t = mpfr_init(d)
<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
mpfr_sqrt(t,t)
<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>
mpfr_mul(t,pi,t)
<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>
mpfr_exp(t,t)
<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>
return t
<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>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">t</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
printf(1,"Ramanujan's constant to 100 decimal places is:\n")
mpfr_printf(1, "%.100Rf\n", q(163))
<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>
sequence heegners = {{19, 96},
<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>
{43, 960},
<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>
{67, 5280},
<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>
{163, 640320},
<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>
printf(1,"\nHeegner numbers yielding 'almost' integers:\n")
<span style="color: #0000FF;">}</span>
mpfr t = mpfr_init(), qh
<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>
mpz c = mpz_init()
<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>
for i=1 to length(heegners) do
<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>
integer {h0,h1} = heegners[i]
<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>
qh = q(h0)
<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>
mpz_ui_pow_ui(c,h1,3)
<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>
mpz_add_ui(c,c,744)
<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>
mpfr_set_z(t,c)
<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>
mpfr_sub(t,t,qh)
<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>
string qhs = mpfr_sprintf("%51.32Rf",qh),
<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>
cs = mpz_get_str(c),
<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>
ts = mpfr_sprintf("%.32Rf",t)
<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>
printf(1,"%3d: %s ~= %18s (diff: %s)\n", {h0, qhs, cs, ts})
<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>
end for</lang>▼
<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>
▲end for<!--</lang>-->
{{out}}
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