\ newtonian equations & functions
\
\ hp_util
\ functions used as part of the collection of software componenets:
\ "henri poincare."
\
\ based on ideas presented by Joel Ryan.
\
\ Code: Han-earl Park
\ Copyright	2000 Buster & Friends C-ALTO Labs
\ (Den haag, December 1997 -
\ (Valencia, October 1998 -
\
\ MOD: HeP 10/15/98	Change name of the collective software components
\					to "forces in motion".
\ MOD: HeP 11/19/98	Chage name of file to fim_util
\ MOD: HeP 11/29/98	Can't find my copy of the fixed point SQRT so build one
\					from scratch.
\ MOD: HeP 11/30/98	Use the sqrt implemetation by Wil Baden found in
\					Julian V. Noble's "forth primer".
\ MOD: HeP 12/13/98	Get rid of the aliases of vec->abs.
\ MOD: HeP 07/27/99	Change name of components to "henri poincare"


anew task-hp_util


variable nfunc-dimensions

: #DIMENSIONS!	( n --  , set current number of dimensions )
	nfunc-dimensions !
;
: #DIMENSIONS@	(  -- n , retrieve number of dimensions )
	nfunc-dimensions @
;



\ square and square root

: SQUARE	( n -- n*n , square value )
	dup *
;

\ the word SQRT is taken from Julian V. Noble's "forth primer"
\ and is based on an routine by Wil Baden.

: SQRT		( n -- rt , calculate square root of n )
	0
	swap 0			\ set n as tthe limit			
	DO
		1+
		dup 2* 1+	\ 2n+1
	+LOOP			\ add 2n+1 to sum and loop if less than n
;



\ newton's second "law":  dv = f / m

: FM->DV	( force mass -- dvelocity , calculate acceleration )
	/
;



\ calculate vector components





\ convert vectored values to absolute form

\
\	|n| = sqrt( x*x + y*y + z*z + ... )
\

: VEC->ABS*ABS	( x y z... -- |n*n| , vector components to squared magnitude )
	0
	#dimensions@ 0
	DO
		swap		( x y z 0 -- x y 0 z )
		square		( x y 0 z -- x y 0 z*z )
		+			( x y 0 z*z -- x y z*z )
	LOOP
;

: VEC->ABS	( x y z... -- |n| , convert from vectored to absolute values )
	vec->abs*abs
	sqrt
;