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28
help/rcout
28
help/rcout
@@ -5,30 +5,30 @@ SYNOPSIS
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rcout(x, m)
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TYPES
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x integer
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m odd positive integer
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x integer
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m odd positive integer
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return integer v, 0 <= v < m.
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return integer v, 0 <= v < m.
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DESCRIPTION
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Let B be the base calc uses for representing integers internally
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(B = 2^16 for 32-bit machines, 2^32 for 64-bit machines) and N the
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number of words (base-B digits) in the representation of m. Then
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number of words (base-B digits) in the representation of m. Then
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rcout(x,m) returns the value of B^-N * x % m, where the inverse
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implicit in B^-N is modulo m and the modulus operator % gives the
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least non-negative residue. The functions rcin() and rcout() are
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least non-negative residue. The functions rcin() and rcout() are
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inverses of each other for all x:
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rcout(rcin(x,m), m) = rcin(rcout(x,m),m) = x % m.
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rcout(rcin(x,m), m) = rcin(rcout(x,m),m) = x % m.
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The normal use of rcout() may be said to be that of decoding
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values encoded by rcin() and REDC functions, as in:
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x * y % m = rcout(rcmul(rcin(x,m),rcin(y,m),m),m),
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x * y % m = rcout(rcmul(rcin(x,m),rcin(y,m),m),m),
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x^2 % m = rcout(rcsq(rcin(x,m),m),m),
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x^2 % m = rcout(rcsq(rcin(x,m),m),m),
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x ^ k % m = rcout(rcpow(rcin(x,m),k,m),m).
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x ^ k % m = rcout(rcpow(rcin(x,m),k,m),m).
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RUNTIME
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If the value of m in rcout(x,m) is being used for the first time in
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@@ -71,7 +71,7 @@ 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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@@ -79,8 +79,8 @@ 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: 1996/02/25 02:22:21
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## File existed as early as: 1996
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## Under source code control: 1996/02/25 02:22:21
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## File existed as early as: 1996
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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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