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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
161 lines
4.6 KiB
Plaintext
161 lines
4.6 KiB
Plaintext
NAME
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mod - compute the remainder for an integer quotient
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SYNOPSIS
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mod(x, y, rnd)
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x % y
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TYPES
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If x is a matrix or list, the returned value is a matrix or list v of
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the same structure for which each element v[[i]] = mod(x[[i]], y, rnd).
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If x is an xx-object or x is not an object and y is an xx-object,
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this function calls the user-defined function xx_mod(x, y, rnd);
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the types of arguments and returned value are as required by the
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definition of xx_mod().
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If neither x nor y is an object, or x is not a matrix or list:
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x number (real or complex)
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y real
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rnd integer, defaults to config("mod")
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return number
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DESCRIPTION
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The expression:
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x % y
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is equivalent to call:
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mod(x, y)
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The function:
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mod(x, y, rnd)
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is equivalent to:
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config("mod", rnd), x % y
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except that the global config("mod") value does not change.
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If x is real or complex and y is zero, mod(x, y, rnd) returns x.
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If x is complex, mod(x, y, rnd) returns
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mod(re(x), y, rnd) + mod(im(x), y, rnd) * 1i.
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In the following it is assumed x is real and y is nonzero.
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If x/y is an integer mod(x, y, rnd) returns zero.
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If x/y is not an integer, mod(x, y, rnd) returns one of the two
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values of r for which for some integer q exists such that x = q * y + r
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and abs(r) < abs(y). Which of the two values or r that is returned is
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controlled by rnd.
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If bit 4 of rnd is set (e.g. if 16 <= rnd < 32) abs(r) <= abs(y)/2;
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this uniquely determines r if abs(r) < abs(y)/2. If bit 4 of rnd is
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set and abs(r) = abs(y)/2, or if bit 4 of r is not set, the result for
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r depends on rnd as in the following table:
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rnd & 15 sign of r parity of q
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0 sgn(y)
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1 -sgn(y)
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2 sgn(x)
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3 -sgn(x)
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4 +
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5 -
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6 sgn(x/y)
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7 -sgn(x/y)
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8 even
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9 odd
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10 even if x/y > 0, otherwise odd
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11 odd if x/y > 0, otherwise even
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12 even if y > 0, otherwise odd
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13 odd if y > 0, otherwise even
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14 even if x > 0, otherwise odd
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15 odd if x > 0, otherwise even
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NOTE: Blank entries in the table above indicate that the
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description would be complicated and probably not of
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much interest.
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The C language method of modulus and integer division is:
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config("quomod", 2)
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config("quo", 2)
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config("mod", 2)
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This dependence on rnd is consistent with quo(x, y, rnd) and
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appr(x, y, rnd) in that for any real x and y and any integer rnd,
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x = y * quo(x, y, rnd) + mod(x, y, rnd).
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mod(x, y, rnd) = x - appr(x, y, rnd)
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If y and rnd are fixed and mod(x, y, rnd) is to be considered as
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a canonical residue of x % y, bits 1 and 3 of rnd should be
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zero: if 0 <= rnd < 32, it is only for rnd = 0, 1, 4, 5, 16, 17,
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20, or 21, that the set of possible values for mod(x, y, rnd)
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form an interval of length y, and for any x1, x2,
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mod(x1, y, rnd) = mod(x2, y, rnd)
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is equivalent to:
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x1 is congruent to x2 modulo y.
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This is particularly relevant when working with the ring of
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integers modulo an integer y.
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EXAMPLE
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; print mod(11,5,0), mod(11,5,1), mod(-11,5,2), mod(-11,-5,3)
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1 -4 -1 4
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; print mod(12.5,5,16), mod(12.5,5,17), mod(12.5,5,24), mod(-7.5,-5,24)
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2.5 -2.5 2.5 2.5
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; A = list(11,13,17,23,29)
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; print mod(A,10,0)
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list (5 elements, 5 nonzero):
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[[0]] = 1
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[[1]] = 3
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[[2]] = 7
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[[3]] = 3
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[[4]] = 9
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LIMITS
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none
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LINK LIBRARY
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void modvalue(VALUE *x, VALUE *y, VALUE *rnd, VALUE *result)
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NUMBER *qmod(NUMBER *y, NUMBER *y, long rnd)
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SEE ALSO
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quo, quomod, //, %
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## Copyright (C) 1999-2006 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 1995/09/18 02:09:31
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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