110 lines
30 KiB
Plaintext
110 lines
30 KiB
Plaintext
-->
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<span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span> <span style="color: #000080;font-style:italic;">-- (no mpfr_exp(), mpfr_gamma() in pwa/p2js)</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">dp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">30</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"%5s: %33s, %33s, %32s\n"</span>
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<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;">-- (mpfr_get_fixed(maxlen), mpfr_gamma)</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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<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">87</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 87 decimal places. </span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">mc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">40</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mc</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;">if</span> <span style="color: #7060A8;">mpfr_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #000080;font-style:italic;">-- mc[1] := sqrt(2*PI)</span>
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<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- k1_factrl = (k - 1)!*(-1)^k with 0!==1</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">tmk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #000080;font-style:italic;">-- mc[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl</span>
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<span style="color: #7060A8;">mpfr_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- k1_factrl *= -(k-1)</span>
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<span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,-(</span><span style="color: #000000;">k</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;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #000080;font-style:italic;">-- accm += mc[k]/(z+k-1)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">ck</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]),</span>
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<span style="color: #000000;">zk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</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: #000080;font-style:italic;">-- atom zc = z+length(mc)
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-- accm *= exp(-zc)*power(zc,z+0.5) -- Gamma(z+1)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">ez</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">zh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">))</span>
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<span style="color: #7060A8;">mpfr_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- return accm/z</span>
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<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">accm</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">mPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">mqPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
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<span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">pistr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">makempfr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">res</span>
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<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'/'</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
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<span style="color: #7060A8;">mpfr_div_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">to_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]))</span>
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<span style="color: #008080;">elsif</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #0000FF;">{</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">else</span>
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<span style="color: #7060A8;">mpfr_div_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">else</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">mq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">zm</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: #000000;">dp</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">makempfr</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
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<span style="color: #7060A8;">mpfr_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mul</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">zs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">es</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
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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: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">zs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</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;">procedure</span>
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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;">" z %s %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" spouge "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" expected "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #000000;">pistr</span><span style="color: #0000FF;">})</span>
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<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.75</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">2.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"4/3"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">3.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"8/15"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}},</span><span style="color: #000000;">mq</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/1000"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"999.4237724845954661149822012996"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/100"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"99.43258511915060371353298887051"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">29</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/10"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.513507698668731836292487177265"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">25</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.332621544394415268169923885627e155"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">150</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"3.80892263763056972698595524350735e260"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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