-USING: kernel math math.constants math.functions math.intervals
-math.vectors namespaces sequences ;
+! Copyright (C) 2008 Doug Coleman, Slava Pestov, Aaron Schaefer.
+! See http://factorcode.org/license.txt for BSD license.
+USING: combinators.short-circuit kernel math math.constants
+math.functions math.vectors sequences ;
IN: math.analysis
<PRIVATE
! http://www.rskey.org/gamma.htm "Lanczos Approximation"
! n=6: error ~ 3 x 10^-11
-: gamma-g6 5.15 ; inline
+CONSTANT: gamma-g6 5.15
-: gamma-p6
+CONSTANT: gamma-p6
{
2.50662827563479526904 225.525584619175212544 -268.295973841304927459
- 80.9030806934622512966 -5.00757863970517583837 0.0114684895434781459556
- } ; inline
+ 80.9030806934622512966 -5.00757863970517583837 0.0114684895434781459556
+ }
: gamma-z ( x n -- seq )
[ + recip ] with map 1.0 0 pick set-nth ;
: (gamma-lanczos6) ( x -- log[gamma[x+1]] )
#! log(gamma(x+1)
- dup 0.5 + dup gamma-g6 + dup >r log * r> -
- swap 6 gamma-z gamma-p6 v. log + ;
+ [ 0.5 + dup gamma-g6 + [ log * ] keep - ]
+ [ 6 gamma-z gamma-p6 v. log ] bi + ;
: gamma-lanczos6 ( x -- gamma[x] )
#! gamma(x) = gamma(x+1) / x
- dup (gamma-lanczos6) exp swap / ;
+ [ (gamma-lanczos6) exp ] keep / ;
: gammaln-lanczos6 ( x -- gammaln[x] )
#! log(gamma(x)) = log(gamma(x+1)) - log(x)
- dup (gamma-lanczos6) swap log - ;
+ [ (gamma-lanczos6) ] keep log - ;
: gamma-neg ( gamma[abs[x]] x -- gamma[x] )
dup pi * sin * * pi neg swap / ; inline
: gamma ( x -- y )
#! gamma(x) = integral 0..inf [ t^(x-1) exp(-t) ] dt
#! gamma(n+1) = n! for n > 0
- dup 0.0 <= over 1.0 mod zero? and [
- drop 1./0.
- ] [
- dup abs gamma-lanczos6 swap dup 0 > [ drop ] [ gamma-neg ] if
+ dup { [ 0.0 <= ] [ 1.0 mod zero? ] } 1&& [
+ drop 1/0.
+ ] [
+ [ abs gamma-lanczos6 ] keep dup 0 > [ drop ] [ gamma-neg ] if
] if ;
: gammaln ( x -- gamma[x] )
#! gammaln(x) is an alternative when gamma(x)'s range
#! varies too widely
dup 0 < [
- drop 1./0.
- ] [
- dup abs gammaln-lanczos6 swap dup 0 > [ drop ] [ gamma-neg ] if
+ drop 1/0.
+ ] [
+ [ abs gammaln-lanczos6 ] keep dup 0 > [ drop ] [ gamma-neg ] if
] if ;
: nth-root ( n x -- y )
- over 0 = [ "0th root is undefined" throw ] when >r recip r> swap ^ ;
+ swap recip ^ ;
! Forth Scientific Library Algorithm #1
!
: stirling-fact ( n -- fact )
[ pi 2 * * sqrt ]
- [ dup e / swap ^ ]
- [ 12 * recip 1 + ]
- tri * * ;
+ [ [ e / ] keep ^ ]
+ [ 12 * recip 1 + ] tri * * ;
+