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 integer, 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 integer, 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                opposite 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
    commonly 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
    protection, 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) 1999-2006,2021,2026  Landon Curt Noll
##
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## Under source code control:   1995/05/07 03:17:03
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