factor/basis/math/primes/factors/factors.factor

! Copyright (C) 2007-2009 Samuel Tardieu.
! See http://factorcode.org/license.txt for BSD license.
USING: arrays combinators kernel make math math.functions
math.primes math.ranges sequences sequences.product sorting ;
IN: math.primes.factors

<PRIVATE

: count-factor ( n d -- n' c )
    [ 1 ] 2dip [ /i ] keep
    [ dupd /mod zero? ] curry [ nip [ 1 + ] dip ] while drop
    swap ;

: write-factor ( n d -- n' d' )
    2dup divisor? [
        [ [ count-factor ] keep swap 2array , ] keep
        ! If the remainder is a prime number, increase d so that
        ! the caller stops looking for factors.
        over prime? [ drop dup ] when
    ] when ;

: (group-factors) ( n -- seq )
    [
        2
        [ 2dup sq < ] [ write-factor next-prime ] until
        drop dup 2 < [ drop ] [ 1 2array , ] if
    ] { } make ;

PRIVATE>

: group-factors ( n -- seq )
    dup prime? [ 1 2array 1array ] [ (group-factors) ] if ; flushable

: unique-factors ( n -- seq ) group-factors [ first ] map ; flushable

: factors ( n -- seq )
    group-factors [ first2 swap <array> ] map concat ; flushable

: totient ( n -- t )
    {
        { [ dup 2 < ] [ drop 0 ] }
        [ dup unique-factors [ 1 [ 1 - * ] reduce ] [ product ] bi / * ]
    } cond ; foldable

: divisors ( n -- seq )
    group-factors [ first2 [0,b] [ ^ ] with map ] map
    [ product ] product-map natural-sort ;