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math.extras: fix spelling of stirling, add ramanujan approximation of factorial.

db4
John Benediktsson 2012-09-25 10:48:09 -07:00
parent b5d0ccf200
commit b601d154c1
2 changed files with 11 additions and 8 deletions
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2
extra/math/extras/extras-docs.factor
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@ -9,7 +9,7 @@ HELP: bernoulli
{ $values { "p" integer } { "n" rational } } { $values { "p" integer } { "n" rational } }
{ $description "Return the Bernoulli number " { $snippet "p" } "." } ; { $description "Return the Bernoulli number " { $snippet "p" } "." } ;
HELP: sterling HELP: stirling
{ $values { "n" integer } { "k" integer } { "x" integer } } { $values { "n" integer } { "k" integer } { "x" integer } }
{ $description "Return the Stirling number of the second kind for a set with " { $snippet "n" } " elements partitioned into " { $snippet "k" } " disjoint non-empty sets." } ; { $description "Return the Stirling number of the second kind for a set with " { $snippet "n" } " elements partitioned into " { $snippet "k" } " disjoint non-empty sets." } ;

17
extra/math/extras/extras.factor
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@ -1,7 +1,7 @@
! Copyright (C) 2012 John Benediktsson ! Copyright (C) 2012 John Benediktsson
! See http://factorcode.org/license.txt for BSD license ! See http://factorcode.org/license.txt for BSD license
USING: combinators.short-circuit grouping kernel math USING: combinators.short-circuit grouping kernel locals math
math.combinatorics math.constants math.functions math.order math.combinatorics math.constants math.functions math.order
math.primes math.ranges math.statistics math.vectors memoize math.primes math.ranges math.statistics math.vectors memoize
sequences ; sequences ;
@ -10,18 +10,21 @@ IN: math.extras
<PRIVATE <PRIVATE
DEFER: sterling DEFER: stirling
: (sterling) ( n k -- x ) : (stirling) ( n k -- x )
[ [ 1 - ] bi@ sterling ] [ [ 1 - ] bi@ stirling ]
[ [ 1 - ] dip sterling ] [ [ 1 - ] dip stirling ]
[ nip * + ] 2tri ; [ nip * + ] 2tri ;
PRIVATE> PRIVATE>
MEMO: sterling ( n k -- x ) MEMO: stirling ( n k -- x )
2dup { [ = ] [ nip 1 = ] } 2|| 2dup { [ = ] [ nip 1 = ] } 2||
[ 2drop 1 ] [ (sterling) ] if ; [ 2drop 1 ] [ (stirling) ] if ;
:: ramanujan ( x -- y )
pi sqrt x e / x ^ * x 8 * 4 + x * 1 + x * 1/30 + 1/6 ^ * ;
<PRIVATE <PRIVATE