pmacs3/code_examples/fib.fs

\ compute the nth fibonacci number, starting at 0
: fib ( n -- n2 )
    dup ( n n )
    2 < if
        drop 1 ( 1 )
    else
        dup 2 - recurse  ( n fib[n-2] )
        swap             ( fib[n-2] n )
        1 - recurse      ( fib[n-2] fib[n-1] )
        +                ( n2 )
    endif ;

create memo 100 cells allot

\ initialize it
: init ( n -- )
    dup ( n n )
    if  ( n )
        dup 0 swap ( n 0 n )
        1 - ( n 0 n-1 )
        cells memo + ( n n-1+memo )
        1 - ( n 0 n-1+memo)
        !   ( n )
        1 - ( n-1 )
        recurse
    else
        drop
    endif ;

: fib2x ( n -- n2 )
    dup ( n n )
    2 < if ( n )
        drop 1 ( 1 )
    else
        dup cells memo + ( n n+memo )
        @  ( n ${n+memo} )
        dup 0 > if    ( n ${n+memo} )
            swap drop ( ${n+memo} )
        else
            drop            ( n )
            dup dup         ( n n n )
            2 - recurse     ( n n fib2[n-2] )
            swap            ( n fib2[n-2] n )
            1 - recurse ( n fib2[n-2] fib2[n-1] )
            +               ( n fib2[n] )
            dup rot         ( fib2[n] fib2[n] n )
            cells memo + !        ( fib2[n] )
        endif
    endif ;

: fib2
    \ allocate a lookup table and run fib2x
    100 init fib2x ;

: expx ( total n n2 -- total*n^n2 )
    ?dup if         ( total n n2 )
        swap rot    ( n2 n total )
        over *      ( n2 n total*n )
        swap rot 1- ( n*total n n2-1 )
        recurse
    else            ( total n )
        drop        ( total )
    endif ;

: exp ( n n2 -- n^n2 )
    1 rot rot ( 1 n n2 )
    expx ;    ( 1*n^n2 )