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Landon Curt Noll
2024-07-11 22:03:52 -07:00
parent fe9cefe6ef
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30
help/rcpow
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@@ -5,16 +5,16 @@ SYNOPSIS
rcpow(x, k, m)
TYPES
x integer
k nonnegative integer
m odd positive integer
x integer
k nonnegative integer
m odd positive integer
return integer v, 0 <= v < m.
return integer v, 0 <= v < m.
DESCRIPTION
Let B be the base calc uses for representing integers internally
(B = 2^16 for 32-bit machines, 2^32 for 64-bit machines) and N the
number of words (base-B digits) in the representation of m. Then
number of words (base-B digits) in the representation of m. Then
rcpow(x,k,m) returns the value of B^-N * (B^N * x)^k % m, w here
the inverse implicit in B^-N is modulo m and the modulus operator %
gives the least nonnegative residue. Note that rcpow(x,0,m) =
@@ -23,27 +23,27 @@ DESCRIPTION
The normal use of rcpow() may be said to be that of finding the
encoded value of the k-th power of an integer modulo m:
rcin(x^k, m) = rcpow(rcin(x,m), k, m),
rcin(x^k, m) = rcpow(rcin(x,m), k, m),
from which one gets:
x^k % m = rcout(rcpow(rcin(x,m), k, m), m).
x^k % m = rcout(rcpow(rcin(x,m), k, m), m).
If x^k % m is to be evaluated for the same k and m and several
values of x, it may be worth while to first evaluate:
a = minv(rcpow(1, k, m), m);
a = minv(rcpow(1, k, m), m);
and use:
x^k % m = a * rcpow(x, k, m) % m.
x^k % m = a * rcpow(x, k, m) % m.
RUNTIME
If the value of m in rcpow(x,k,m) is being used for the first time
in a REDC function, the information required for the REDC
algorithms is calculated and stored for future use, possibly
replacing an already stored valued, in a table covering up to 5
(i.e. MAXREDC) values of m. The runtime required for this is about
(i.e. MAXREDC) values of m. The runtime required for this is about
two times that required for multiplying two N-word integers.
Two algorithms are available for evaluating rcpow(x,k,m), the one
@@ -80,7 +80,7 @@ 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
@@ -88,8 +88,8 @@ 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: 1996/02/25 02:22:21
## File existed as early as: 1996
## Under source code control: 1996/02/25 02:22:21
## File existed as early as: 1996
##
## 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/