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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!
138 lines
4.4 KiB
Plaintext
138 lines
4.4 KiB
Plaintext
NAME
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cmp - compare two values of certain simple or object types
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SYNOPSIS
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cmp(x, y)
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TYPES
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If x is an object of type xx, or x is not an object and y is an object
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of type xx, the function xx_rel has to have been defined; any
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further conditions on x and y, and the type of the returned
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value depends on the definition of xx_rel.
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For non-object x and y:
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x any
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y any
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return if x and y are both real: -1, 0, or 1
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if x and y are both numbers but not both real:
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-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
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if x and y are both strings: -1, 0, or 1
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all other cases: the null value
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DESCRIPTION
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x and y both real: cmp(x, y) = sgn(x - y), i.e. -1, 0, or 1
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according as x < y, x == y, or x > y
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x and y both numbers, at least one being complex:
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cmp(x,y) = sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i
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x and y both strings: successive characters are compared until either
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different characters are encountered or at least one string is
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completed. If the comparison ends because of different characters,
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cmp(x,y) = 1 or -1 according as the greater character is in x or y.
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If all characters compared in both strings are equal, then
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cmp(x,y) = -1, 0 or 1 according as the length of x is less than,
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equal to, or greater than the length of y. (This comparison
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is performed via the strcmp() libc function.)
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objects: comparisons of objects are usually intended for some total or
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partial ordering and appropriate definitions of cmp(a,b) may
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make use of comparison of numerical or string components.
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definitions using comparison of numbers or strings are usually
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appropriate. For example, after
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obj point {x,y};
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if points with real components are to be partially ordered by their
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euclidean distance from the origin, an appropriate point_rel
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function may be that given by
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define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);
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A total "lexicographic" ordering is that given by:
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define point_rel(a,b) {
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if (a.y != b.y)
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return sgn(a.y - b.y);
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return (a.x - b.x);
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}
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A comparison function that compares points analogously to
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cmp(a,b) for real and complex numbers is that given by
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define point_rel(P1, P2) {
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return obj point = {sgn(P1.x-P2.x), sgn(P1.y-P2.y)};
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}
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The range of this function is the set of nine points with zero
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or unit components.
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Some properties of cmp(a,b) for real or complex a and b are:
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cmp(a + c, b + c) = cmp(a, b)
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cmp(a, b) == 0 if and only if a == b
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cmp(b, a) = -cmp(a, b)
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if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)
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Then a function that defines "b is between a and c" in an often useful
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sense is
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define between(a,b,c) = (cmp(a,b) == cmp(b,c)).
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For example, in this sense, 3 + 4i is between 1 + 5i and 4 + 2i.
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Note that using cmp to compare non-object values of different types,
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for example, cmp(2, "2"), returns the null value.
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EXAMPLE
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; print cmp(3,4), cmp(4,3), cmp(4,4), cmp("a","b"), cmp("abcd","abc")
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-1 1 0 -1 1
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; print cmp(3,4i), cmp(4,4i), cmp(5,4i), cmp(-5,4i), cmp(-4i,5), cmp(-4i,-5)
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1-1i 1-1i 1-1i -1-1i -1-1i 1-1i
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; print cmp(3i,4i), cmp(4i,4i), cmp(5i,4i), cmp(3+4i,5), cmp(3+4i,-5)
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-1i 0 1i -1+1i 1+1i
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; print cmp(3+4i,3+4i), cmp(3+4i,3-4i), cmp(3+4i,2+3i), cmp(3+4i,-4-5i)
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0 1i 1+1i 1+1i
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LIMITS
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none
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LINK LIBRARY
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FLAG qrel(NUMBER *q1, NUMBER *q2)
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FLAG zrel(ZVALUE z1, ZVALUE z2)
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SEE ALSO
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sgn, test, operator
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## Copyright (C) 1999 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: 1994/10/20 02:52:30
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## File existed as early as: 1994
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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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