Anonymous user
Bernoulli numbers: Difference between revisions
→{{header|factor}}
Line 832:
</pre>
=={{header|factor}}==
One could use the "bernoulli" word from the math.extras vocabulary
<lang>
IN: scratchpad
:: bernoulli-numbers ( n -- )▼
n 1 + 0 <array> :> tab▼
0 1 1 "%2d : %d / %d\n" printf▼
▲ 1 :> s!
1 -1 2 "%2d : %d / %d\n" printf▼
1 1 tab set-nth▼
30 iota [ 1 + 2 * dup bernoulli [ numerator ] [ denominator ] bi▼
2 n [a,b] [| k |▼
tab nth * ▼
k tab set-nth ▼
] each▼
2 n [a,b] [| k | ▼
k n [a,b] [| j | ▼
j tab nth ▼
j k - 2 + * ▼
j 1 - tab nth ▼
j k - * + ▼
j tab set-nth▼
▲ ] each
] each▼
1 n [a,b] [| k |▼
k 2 * dup ▼
2 swap ^ ▼
dup 1 - * ▼
k tab nth ▼
s * k tab set-nth ▼
s -1 * s!▼
] each▼
▲ 0 1 1 "%2d : %d / %d\n" printf
▲ 1 -1 2 "%2d : %d / %d\n" printf
1 n [a,b] [| k |▼
k 2 * k tab nth▼
▲ [ numerator ] [ denominator ] bi
"%2d : %d / %d\n" printf▼
] each▼
;▼
IN: scratchpad 30 bernoulli-numbers▼
0 : 1 / 1
1 : -1 / 2
Line 904 ⟶ 873:
58 : 84483613348880041862046775994036021 / 354
60 : -1215233140483755572040304994079820246041491 / 56786730
Running time: 0.00489444 seconds
</lang>
Alternatively a method described by Brent and Harvey (2011) in "Fast computation of Bernoulli, Tangent and Secant numbers" https://arxiv.org/pdf/1108.0286.pdf is shown.
<lang>
▲:: bernoulli-numbers ( n -- )
▲ n 1 + 0 <array> :> tab
▲ 1 1 tab set-nth
▲ 2 n [a,b] [| k |
k 1 - dup
▲ tab nth *
▲ k tab set-nth
▲ ] each
▲ 2 n [a,b] [| k |
▲ k n [a,b] [| j |
▲ j tab nth
▲ j k - 2 + *
▲ j 1 - tab nth
▲ j k - * +
▲ j tab set-nth
] each
▲ ] each
1 :> s!
▲ 1 n [a,b] [| k |
▲ k 2 * dup
▲ k tab nth
▲ s * k tab set-nth
▲ s -1 * s!
▲ ] each
0 1 1 "%2d : %d / %d\n" printf
1 -1 2 "%2d : %d / %d\n" printf
▲ 1 n [a,b] [| k |
▲ k 2 * k tab nth
[ numerator ] [ denominator ] bi
▲ "%2d : %d / %d\n" printf
▲ ] each
▲;
</lang>
It gives the same result as the native implementation, but is slightly faster.
<lang>
...
Running time: 0.004331652 seconds
</lang>
| |||