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Bernoulli numbers: Difference between revisions
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→{{header|REXX}}: elided a dead variable, added a note about calculation time.
(Added Quackery.) |
m (→{{header|REXX}}: elided a dead variable, added a note about calculation time.) |
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Line 3,483:
<br>
:::::::::::: where <big><big> <math> \binom kr</math> </big></big> is a binomial coefficient. <br>
<lang rexx>/*REXX program calculates
parse arg N .; if N=='' | N=="," then N= 60 /*Not specified? Then use the default.*/
numeric digits max(9, n*2) /*increase the decimal digits if needed*/
w= max(length(N), 4); Nw= N + w + N % 4 /*used for aligning (output) fractions.*/
say 'B(n)' center("Bernoulli
say copies('─',w) copies("─", max(78-w,Nw+2*w)) /*display 2nd line of title, separators*/
!.=
b= bern(#); if b==0 then iterate /*calculate Bernoulli number, skip if 0*/
indent= max(0, nW - pos('/', b) ) /*calculate the alignment (indentation)*/
say right(#, w) left('', indent) b /*display the indented Bernoulli number*/
end /*#*/ /* [↑] align the Bernoulli fractions. */
exit
/*──────────────────────────────────────────────────────────────────────────────────────*/
bern: parse arg x; if x==0 then return '1/1' /*handle the special case of zero. */
Line 3,507:
$lcm= LCM(sd, ad) /*use Least Common Denominator function*/
sn= $lcm % sd * sn; sd= $lcm /*calculate the current numerator. */
an= $lcm % ad * an
sn= sn + an /* " " current " */
end /*k*/ /* [↑] calculate the SN/SD sequence.*/
Line 3,520:
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure expose !.; parse arg x,y; if x==y then return 1
if !.
if x-y < y then y= x-y /*x-y < y? Then use a new Y.*/
z= perm(x, y); do j=2 for y-1; z= z % j
end /*j*/
!.
/*──────────────────────────────────────────────────────────────────────────────────────*/
GCD: procedure; parse arg x,y; x= abs(x)
do until y==0; parse value x//y y with y x; end; return x
/*──────────────────────────────────────────────────────────────────────────────────────*/
LCM: procedure; parse arg x,y
$= x * y
end /*until*/
return $ % x
/*──────────────────────────────────────────────────────────────────────────────────────*/
perm: procedure expose !.; parse arg x,y; if !.
z= 1; do j=x-y+1 to x; z= z*j; end; !.
{{out|output|text= when using the default input:}}
<pre>
B(n)
──── ───────────────────────────────────────────────────────────────────────────────────────
0 1/1
Line 3,576 ⟶ 3,575:
60 -1215233140483755572040304994079820246041491/56786730
</pre>
Output notes: This version of REXX can compute and display all values up to '''B<sub>110</sub>''' in sub─second.
<br><br>
=={{header|Ruby}}==
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