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Special factorials: Difference between revisions

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Special factorials (view source)

Revision as of 22:55, 30 March 2021

13,062 bytes added ,  3 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (→‎{{header|FreeBASIC}}: -rm stray thing)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 440:
which means sf/H/af/ef aren't usable independently as-is, but reconstitution should be easy enough
(along with somewhat saner and thread-safe routine-local vars).
<!--<lang Phix>include mpfr.e-->
<span style="color: #008080;">include</span> <span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
 
mpz {r,fn} = mpz_inits(2) -- res, scratch var
<span style="color: #7060A8;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- res, scratch var</span>
 
procedure sf(integer i)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">sf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_fac_ui(fn, i)
<span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_mul(r,r,fn)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
procedure H(integer i)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">H</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_ui_pow_ui(fn, i, i)
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_mul(r,r,fn)
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
integer sgn = 0
<span style="color: #004080;">integer</span> <span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
procedure af(integer i)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">af</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_fac_ui(fn, i)
<span style="color: #7060A8;">mpz_fac_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_mul_si(fn,fn,sgn)
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sgn</span><span style="color: #0000FF;">)</span>
sgn *= -1
<span style="color: #000000;">sgn</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
mpz_add(r,r,fn)
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
procedure ef(integer i)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">ef</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
integer e = mpz_get_integer(r)
<span style="color: #004080;">integer</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
mpz_set_si(r,i)
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
mpz_pow_ui(r, r, e)
<span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
procedure test(string fmt, integer fn, init=1, m=9)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">init</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><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
sequence res = {}
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
for n=0 to m do
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">m</span> <span style="color: #008080;">do</span>
mpz_set_si(r,init)
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">init</span><span style="color: #0000FF;">)</span>
sgn = iff(and_bits(n,1)?1:-1) -- (af only)
<span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">and_bits</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><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: #000080;font-style:italic;">-- (af only)</span>
for i=1 to n do
<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: #000000;">n</span> <span style="color: #008080;">do</span>
fn(i) -- or papply(tagset(n),fn)
<span style="color: #000000;">fn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- or papply(tagset(n),fn)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
res = append(res,mpz_get_str(r))
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">))</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,fmt,{join(res)})
<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: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)})</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
test("First 10 superfactorials: %s\n",sf)
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"First 10 superfactorials: %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sf</span><span style="color: #0000FF;">)</span>
test("First 10 hyperfactorials: %s\n",H)
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"First 10 hyperfactorials: %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">H</span><span style="color: #0000FF;">)</span>
test("First 10 alternating factorials: %s\n",af,0)
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"First 10 alternating factorials: %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">af</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
test("First 5 exponential factorials: %s\n",ef,1,4)
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"First 5 exponential factorials: %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ef</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
ef(5) -- (nb now only works because ef(4) was just called)
<span style="color: #000000;">ef</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (nb now only works because ef(4) was just called)</span>
printf(1,"Number of digits in 5$: %,d\n",mpz_sizeinbase(r,10))
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Number of digits in 5$: %,d\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_sizeinbase</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">))</span>
 
function rf(integer n)
<span style="color: #008080;">function</span> <span style="color: #000000;">rf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
if n=1 then return "0" end if
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">"0"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
integer fac = 1, i = 1
<span style="color: #004080;">integer</span> <span style="color: #000000;">fac</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
while fac<n do
<span style="color: #008080;">while</span> <span style="color: #000000;">fac</span><span style="color: #0000FF;"><</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
fac *= i
<span style="color: #000000;">fac</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
if fac=n then return sprint(i) end if
<span style="color: #008080;">if</span> <span style="color: #000000;">fac</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
i += 1
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return "undefined"
<span style="color: #008080;">return</span> <span style="color: #008000;">"undefined"</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
printf(1,"Reverse factorials: %s\n",{join(apply({1,2,6,24,120,720,5040,40320,362880,3628800,119},rf))})</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;">"Reverse factorials: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">({</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">24</span><span style="color: #0000FF;">,</span><span style="color: #000000;">120</span><span style="color: #0000FF;">,</span><span style="color: #000000;">720</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5040</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40320</span><span style="color: #0000FF;">,</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3628800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">119</span><span style="color: #0000FF;">},</span><span style="color: #000000;">rf</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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