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This commit is contained in:
Landon Curt Noll
92
help/mod
92
help/mod
@@ -16,35 +16,35 @@ TYPES
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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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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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return number
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DESCRIPTION
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The expression:
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x % y
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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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mod(x, y)
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The function:
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mod(x, y, rnd)
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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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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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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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@@ -60,40 +60,40 @@ DESCRIPTION
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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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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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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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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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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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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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@@ -101,11 +101,11 @@ DESCRIPTION
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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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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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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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@@ -121,11 +121,11 @@ EXAMPLE
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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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[[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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@@ -145,7 +145,7 @@ SEE ALSO
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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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## 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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@@ -153,8 +153,8 @@ SEE ALSO
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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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## 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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## 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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