NAME
    quomod - assign quotient and remainder to two lvalues

SYNOPSIS
    quomod(x, y, Q, R [, rnd])

TYPES
    x		real
    y		real
    Q		null-or-real-valued lvalue with assign-to permission
    R		null-or-real-valued lvalue with assign-to permission
    rnd		nonnegative integer, defaults to config("quomod")

    return	0 or 1

DESCRIPTION
    If y is nonzero and x/y is an integer q, this function assigns
    q to Q and zero to R, and returns zero.

    If y is zero, zero is assigned to Q, x to R and 0 or 1 returned
    according as x is zero or nonzero.

    In the remaining case, y nonzero and x/y not an intger, there
    are two pairs (q,r) for which x = q * y + r, q is an integer, and
    abs(r) < abs(y).  Depending on the low 5 bits of rnd, the q and r
    of one of these pairs will be assigned to Q and R respectively,
    and the number 1 returned. The effects of rnd can be described in
    terms of the way q is related to x/y, e.g. by rounding down,
    rounding towards zero, rounding to a nearest integeri, etc. or
    by properties of the remainder r, e.g. positive, negative,
    smallest, etc. The effects of the most commonly used values of
    rnd are described in the following table:

       rnd	        q			      r

	0   round down. q = floor(x/y)	   same sign as y
	1   round up, q = ceil(x/y)	   opposite sign to y
	2   round to zero, q = int(x/y)	   same sign as x, r = y * frac(x/y)
	3   round from zero		   oppsite sign to x
	4				   positive
	5				   negative
	6				   same sign as x/y
	7				   opposite sigh to x/y

	8   to nearest even
	9   to nearest odd

    For 16 <= rnd < 32, the rounding is to the nearest integer and r
    is the smallest (in absolute value) remainder except when x/y is
    halfway between consecutive integers, in which case the rounding
    is as given by the 4 low bits of rnd. Using rnd = 24 gives the
    cpmmonly used principle of rounding: round to the nearest integer,
    but take the even integer when there are two equally close integers.

    For more detail on the effects of rnd for values other than those
    listed above, see "help quo" and "help mod".

    In all cases, the values assigned to Q and R by quomod(x, y, Q, R, rnd)
    are the same as those given by Q = quo(x,y,rnd), R = mod(x,y,rnd).
    If config("quo") == rnd, Q is also given by quo(x,y) or x // y.
    If config("mod") == rnd, R is also given by mod(x,y) or x % y.

    The rounding used by the C language for x / y  and x % y corresponds
    to rnd = 2.

    An error values is returned and the values of Q and R are not changed
    if Q and R are not both lvalues, or if the current value of any
    argument is not as specified above, or if Q or R has no-assign-to
    prptection, e.g. after protect(Q,1).


EXAMPLE
    ; global u, v;
    ; global mat M[2];
    ; print quomod(13,5,u,v), u, v, quomod(15.6,5.2,M[0],M[1]), M[0], M[1];
    1 2 3 0 3 0

    ; A = assoc();
    ; print quomod(13, 5, A[1], A[2]), A[1], A[2]
    ; 1 2 3

    ; print quomod(10, -3, u, v), u, v;
    1 -4 -2
    ; print quomod(10, -3, u, v, 0), u, v;
    1 -4 -2
    ; print quomod(10, -3, u, v, 1), u, v;
    1 -3 1
    ; print quomod(10, -3, u, v, 2), u, v;
    1 -3 1
    ; print quomod(-10, -3, u, v, 2), u, v;
    1 3 -1

LIMITS
    rnd < 2^31

LINK LIBRARY
    BOOL qquomod(NUMBER *q1, NUMBER *q2, NUMBER **quo, NUMBER **mod)

SEE ALSO
    //,	 %, quo, mod, floor. ceil, int. frac

## Copyright (C) 1999-2006  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
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## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: quomod,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/quomod,v $
##
## Under source code control:	1995/05/07 03:17:03
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
