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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
109 lines
3.9 KiB
Plaintext
109 lines
3.9 KiB
Plaintext
NAME
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prevcand - previous candidate for primeness
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SYNOPSIS
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prevcand(n [,count [, skip [, residue [, modulus]]]])
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TYPES
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n integer
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count integer with absolute value less than 2^24, defaults to 1
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skip integer, defaults to 1
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residue integer, defaults to 0
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modulus integer, defaults to 1
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return integer
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DESCRIPTION
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The sign of n is ignored; in the following it is assumed that n >= 0.
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prevcand(n, count, skip, residue, modulus) returns the greatest
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positive integer i less than abs(n) expressible as
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residue + k * modulus, where k is an integer, for which
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ptest(i,count,skip) == 1, or if there is no such integer i, zero.
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If n < 2^32, count >= 0, and the returned value i is not zero, i is
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definitely prime. If n > 2^32, count != 0, and i is not zero,
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i is probably prime, particularly if abs(count) is greater than 1.
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With the default argument values, if n > 2, prevcand(n) returns the a
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probably prime integer i less than n such that every integer
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between i and n is composite.
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If skip == 0, the bases used in the probabilistic test are random
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and then the probability that the returned value is composite is
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less than 1/4^abs(count).
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If skip == 1 (the default value) the bases used in the probabilistic
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test are the first abs(count) primes 2, 3, 5, ...
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For other values of skip, the bases used are the abs(count) consecutive
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integer skip, skip + 1, ...
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If modulus = 0, the only values that may be returned are zero and the
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value of residue. The latter is returned if it is positive, less
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than n, and is such that ptest(residue, count, skip) = 1.
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RUNTIME
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The runtime for v = prevcand(n, ...) will depend strongly on the
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number and nature of the integers between n and v. If this number
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is reasonably large the size of count is largely irrelevant as the
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compositeness of the numbers between n and v will usually be
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determined by the test for small prime factors or one pseudoprime
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test with some base b. If N > 1, count should be positive so that
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candidates divisible by small primes will be passed over quickly.
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On the average for random n with large word-count N, the runtime
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seems to be between roughly K/N^3 some constant K.
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EXAMPLE
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; print prevcand(50), prevcand(2), prevcand(125,-1), prevcand(125,-2)
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47 1 113 113
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; print prevcand(100,1,1,1,6), prevcand(100,1,1,-1,6)
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97 89
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; print prevcand(100,1,1,2,6), prevcand(100,1,1,4,6),
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2 0
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; print prevcand(100,1,1,53,0), prevcand(100,1,1,53,106)
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53 53
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; print prevcand(125,1,3), prevcand(125,-1,3), prevcand(125,-2,3)
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113 121 113
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; print prevcand(2e60, 1, 1, 31, 1e30)
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1999999999999999999999999999914000000000000000000000000000031
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LIMITS
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none
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LINK LIBRARY
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int zprevcand(ZVALUE n, long count, long skip, ZVALUE res, ZVALUE mod,
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ZVALUE *cand)
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SEE ALSO
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factor, isprime, lfactor, nextcand, nextprime, prevprime,
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pfact, pix, ptest
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## Copyright (C) 1999-2006 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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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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## 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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## distributed with calc under the filename COPYING-LGPL. You should have
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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 00:27:43
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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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