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Bernoulli numbers: Difference between revisions

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Bernoulli numbers (view source)

Revision as of 13:41, 5 June 2021

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→‎{{header|Phix}}: added syntax colouring the hard way
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m (→‎{{header|Phix}}: added syntax colouring the hard way)
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{{libheader|Phix/mpfr}}
{{trans|C}}
<!--<lang Phix>include builtins/mpfr.e(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
procedure bernoulli(mpq rop, integer n)
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">/</span><span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
sequence a = mpq_init(n+1)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpq</span> <span style="color: #000000;">rop</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
for m=1 to n+1 do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
mpq_set_si(a[m], 1, m)
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
for j=m-1 to 1 by -1 do
<span style="color: #7060A8;">mpq_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
mpq_sub(a[j], a[j+1], a[j])
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">m</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
mpq_set_si(rop, j, 1)
<span style="color: #7060A8;">mpq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
mpq_mul(a[j], a[j], rop)
<span style="color: #7060A8;">mpq_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #7060A8;">mpq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">rop</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
mpq_set(rop, a[1])
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
a = mpq_free(a)
<span style="color: #7060A8;">mpq_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
end procedure
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
mpq rop = mpq_init()
mpz n = mpz_init(),
<span style="color: #004080;">mpq</span> <span style="color: #000000;">rop</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_init</span><span style="color: #0000FF;">()</span>
d = mpz_init()
<span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
for i=0 to 60 do
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
bernoulli(rop, i)
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">60</span> <span style="color: #008080;">do</span>
if mpq_cmp_si(rop, 0, 1) then
<span style="color: #000000;">bernoulli</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpq_get_num(n, rop)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpq_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
mpq_get_den(d, rop)
<span style="color: #7060A8;">mpq_get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rop</span><span style="color: #0000FF;">)</span>
string ns = mpfr_sprintf("%44Zd",n),
<span style="color: #7060A8;">mpq_get_den</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rop</span><span style="color: #0000FF;">)</span>
ds = mpfr_sprintf("%Zd",d)
<span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span>
printf(1,"B(%2d) = %s / %s\n", {i,ns,ds})
<span style="color: #000000;">ds</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
end if
<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;">"B(%2d) = %44s / %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ds</span><span style="color: #0000FF;">})</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
{n,d} = mpz_free({n,d})
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
rop = mpq_free(rop)</lang>
<span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">rop</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpq_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rop</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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