/usr/share/calc/help/rcsq is in apcalc-common 2.12.5.0-1build1.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | NAME
rcsq - REDC squaring
SYNOPSIS
rcsq(x, m)
TYPES
x integer
m odd positive integer
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 rcsq(x,m) returns the value of B^-N * x^2 % m,
where the inverse implicit in B^-N is modulo m
and the modulus operator % gives the least non-negative residue.
The normal use of rcsq() may be said to be that of squaring modulo m a
value encoded by rcin() and REDC functions, as in:
rcin(x^2, m) = rcsq(rcin(x,m), m)
from which we get:
x^2 % m = rcout(rcsq(rcin(x,m), m), m)
Alternatively, x^2 % m may be evaluated usually more quickly by:
x^2 % m = rcin(rcsq(x,m), m).
RUNTIME
If the value of m in rcsq(x,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 two times that
required for multiplying two N-word integers.
Two algorithms are available for evaluating rcsq(x, m), the one
which is usually faster for small N is used when N <
config("redc2"); the other is usually faster for larger N. If
config("redc2") is set at about 90 and 0 <= x < m, the runtime
required for rcsq(x, m)i is at most about f times the runtime
required for an N-word by N-word multiplication, where f increases
from about 1.1 for N = 1 to near 2.8 for N > 90. More runtime may
be required if x has to be reduced modulo m.
EXAMPLE
Using a 64-bit machine with B = 2^32:
; for (i = 0; i < 9; i++) print rcsq(i,9),:; print;
0 7 1 0 4 4 0 1 7
; for (i = 0; i < 9; i++) print rcin((rcsq(i,9),:; print;
0 1 4 0 7 7 0 4 1
LIMITS
none
LINK LIBRARY
void zredcsquare(REDC *rp, ZVALUE z1, ZVALUE *res)
SEE ALSO
rcin, rcout, rcmul, rcpow
## Copyright (C) 1999 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## 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
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: rcsq,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/rcsq,v $
##
## 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/
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