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Landon Curt Noll
2024-07-11 22:03:52 -07:00
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96
help/cmp
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@@ -12,79 +12,79 @@ TYPES
For non-object x and y:
x any
y any
x any
y any
return if x and y are both real: -1, 0, or 1
if x and y are both numbers but not both real:
-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
if x and y are both strings: -1, 0, or 1
all other cases: the null value
return if x and y are both real: -1, 0, or 1
if x and y are both numbers but not both real:
-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
if x and y are both strings: -1, 0, or 1
all other cases: the null value
DESCRIPTION
x and y both real: cmp(x, y) = sgn(x - y), i.e. -1, 0, or 1
according as x < y, x == y, or x > y
according as x < y, x == y, or x > y
x and y both numbers, at least one being complex:
cmp(x,y) = sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i
cmp(x,y) = sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i
x and y both strings: successive characters are compared until either
different characters are encountered or at least one string is
completed. If the comparison ends because of different characters,
cmp(x,y) = 1 or -1 according as the greater character is in x or y.
If all characters compared in both strings are equal, then
cmp(x,y) = -1, 0 or 1 according as the length of x is less than,
equal to, or greater than the length of y. (This comparison
is performed via the strcmp() libc function.)
different characters are encountered or at least one string is
completed. If the comparison ends because of different characters,
cmp(x,y) = 1 or -1 according as the greater character is in x or y.
If all characters compared in both strings are equal, then
cmp(x,y) = -1, 0 or 1 according as the length of x is less than,
equal to, or greater than the length of y. (This comparison
is performed via the strcmp() libc function.)
objects: comparisons of objects are usually intended for some total or
partial ordering and appropriate definitions of cmp(a,b) may
make use of comparison of numerical or string components.
definitions using comparison of numbers or strings are usually
appropriate. For example, after
partial ordering and appropriate definitions of cmp(a,b) may
make use of comparison of numerical or string components.
definitions using comparison of numbers or strings are usually
appropriate. For example, after
obj point {x,y};
obj point {x,y};
if points with real components are to be partially ordered by their
Euclidean distance from the origin, an appropriate point_rel
function may be that given by
if points with real components are to be partially ordered by their
Euclidean distance from the origin, an appropriate point_rel
function may be that given by
define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);
define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);
A total "lexicographic" ordering is that given by:
A total "lexicographic" ordering is that given by:
define point_rel(a,b) {
if (a.y != b.y)
return sgn(a.y - b.y);
return (a.x - b.x);
}
define point_rel(a,b) {
if (a.y != b.y)
return sgn(a.y - b.y);
return (a.x - b.x);
}
A comparison function that compares points analogously to
cmp(a,b) for real and complex numbers is that given by
A comparison function that compares points analogously to
cmp(a,b) for real and complex numbers is that given by
define point_rel(P1, P2) {
return obj point = {sgn(P1.x-P2.x), sgn(P1.y-P2.y)};
}
define point_rel(P1, P2) {
return obj point = {sgn(P1.x-P2.x), sgn(P1.y-P2.y)};
}
The range of this function is the set of nine points with zero
or unit components.
The range of this function is the set of nine points with zero
or unit components.
Some properties of cmp(a,b) for real or complex a and b are:
cmp(a + c, b + c) = cmp(a, b)
cmp(a + c, b + c) = cmp(a, b)
cmp(a, b) == 0 if and only if a == b
cmp(a, b) == 0 if and only if a == b
cmp(b, a) = -cmp(a, b)
cmp(b, a) = -cmp(a, b)
if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)
if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)
Then a function that defines "b is between a and c" in an often useful
sense is
define between(a,b,c) = (cmp(a,b) == cmp(b,c)).
define between(a,b,c) = (cmp(a,b) == cmp(b,c)).
For example, in this sense, 3 + 4i is between 1 + 5i and 4 + 2i.
@@ -122,7 +122,7 @@ SEE ALSO
##
## 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
## 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
@@ -130,8 +130,8 @@ SEE ALSO
## 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: 1994/10/20 02:52:30
## File existed as early as: 1994
## Under source code control: 1994/10/20 02:52:30
## File existed as early as: 1994
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/