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NAME
mod - compute the remainder for an integer quotient
SYNOPSIS
mod(x, y [,rnd])
x % y
TYPES
If x is a matrix or list, the returned value is a matrix or list v of
the same structure for which each element v[[i]] = mod(x[[i]], y, rnd).
If x is an xx-object or x is not an object and y is an xx-object,
this function calls the user-defined function xx_mod(x, y, rnd);
the types of arguments and returned value are as required by the
definition of xx_mod().
If neither x nor y is an object, or x is not a matrix or list:
x number (real or complex)
y real
rnd integer, defaults to config("mod")
return number
DESCRIPTION
The expression:
x % y
is equivalent to call:
mod(x, y)
The function:
mod(x, y, rnd)
is equivalent to:
config("mod", rnd), x % y
except that the global config("mod") value does not change.
If x is real or complex and y is zero, mod(x, y, rnd) returns x.
If x is complex, mod(x, y, rnd) returns
mod(re(x), y, rnd) + mod(im(x), y, rnd) * 1i.
In the following it is assumed x is real and y is nonzero.
If x/y is an integer mod(x, y, rnd) returns zero.
If x/y is not an integer, mod(x, y, rnd) returns one of the two
values of r for which for some integer q exists such that x = q * y + r
and abs(r) < abs(y). Which of the two values or r that is returned is
controlled by rnd.
If bit 4 of rnd is set (e.g. if 16 <= rnd < 32) abs(r) <= abs(y)/2;
this uniquely determines r if abs(r) < abs(y)/2. If bit 4 of rnd is
set and abs(r) = abs(y)/2, or if bit 4 of r is not set, the result for
r depends on rnd as in the following table:
rnd & 15 sign of r parity of q
0 sgn(y)
1 -sgn(y)
2 sgn(x)
3 -sgn(x)
4 +
5 -
6 sgn(x/y)
7 -sgn(x/y)
8 even
9 odd
10 even if x/y > 0, otherwise odd
11 odd if x/y > 0, otherwise even
12 even if y > 0, otherwise odd
13 odd if y > 0, otherwise even
14 even if x > 0, otherwise odd
15 odd if x > 0, otherwise even
NOTE: Blank entries in the table above indicate that the
description would be complicated and probably not of
much interest.
The C language method of modulus and integer division is:
config("quomod", 2)
config("quo", 2)
config("mod", 2)
This dependence on rnd is consistent with quo(x, y, rnd) and
appr(x, y, rnd) in that for any real x and y and any integer rnd,
x = y * quo(x, y, rnd) + mod(x, y, rnd).
mod(x, y, rnd) = x - appr(x, y, rnd)
If y and rnd are fixed and mod(x, y, rnd) is to be considered as
a canonical residue of x % y, bits 1 and 3 of rnd should be
zero: if 0 <= rnd < 32, it is only for rnd = 0, 1, 4, 5, 16, 17,
20, or 21, that the set of possible values for mod(x, y, rnd)
form an interval of length y, and for any x1, x2,
mod(x1, y, rnd) = mod(x2, y, rnd)
is equivalent to:
x1 is congruent to x2 modulo y.
This is particularly relevant when working with the ring of
integers modulo an integer y.
EXAMPLE
; print mod(11,5,0), mod(11,5,1), mod(-11,5,2), mod(-11,-5,3)
1 -4 -1 4
; print mod(12.5,5,16), mod(12.5,5,17), mod(12.5,5,24), mod(-7.5,-5,24)
2.5 -2.5 2.5 2.5
; A = list(11,13,17,23,29)
; print mod(A,10,0)
list (5 elements, 5 nonzero):
[[0]] = 1
[[1]] = 3
[[2]] = 7
[[3]] = 3
[[4]] = 9
LIMITS
none
LINK LIBRARY
void modvalue(VALUE *x, VALUE *y, VALUE *rnd, VALUE *result)
NUMBER *qmod(NUMBER *y, NUMBER *y, long rnd)
SEE ALSO
quo, quomod, //, %
## Copyright (C) 1999-2006,2021 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
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 1995/09/18 02:09:31
## 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/
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