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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program 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 *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include <algorithm>
#include <functional>
#include "maths/numbertheory.h"
#include "utilities/stlutils.h"
namespace regina {
long reducedMod(long k, long modBase) {
long ans = k % modBase;
if (ans < 0) {
if ((ans + modBase) <= (-ans))
return (ans + modBase);
} else if (-(ans - modBase) < ans)
return (ans - modBase);
return ans;
}
unsigned long gcd(unsigned long a, unsigned long b) {
long tmp;
while (a != b && b != 0) {
tmp = a;
a = b;
b = tmp % b;
}
return a;
}
namespace {
long gcdWithCoeffsInternal(long a, long b, long& u, long& v) {
// This routine assumes a and b to be non-negative.
long a_orig = a;
long b_orig = b;
u = 1;
v = 0;
long uu = 0;
long vv = 1;
long tmp1, tmp2, q;
while (a != b && b != 0) {
// At each stage:
// u*(a_orig) + v*(b_orig) = a_curr;
// uu*(a_orig) + vv*(b_orig) = b_curr.
tmp1 = u; tmp2 = v;
u = uu; v = vv;
q = a / b;
uu = tmp1 - (q * uu); vv = tmp2 - (q * vv);
tmp1 = a;
a = b;
b = tmp1 % b;
}
// a is now our gcd.
// Put u and v in the correct range.
if (b_orig == 0)
return a;
// We are allowed to add (b_orig/d, -a_orig/d) to (u,v).
a_orig = -(a_orig / a);
b_orig = b_orig / a;
// Now we are allowed to add (b_orig, a_orig), where b_orig >= 0.
// Add enough copies to put u between 1 and b_orig inclusive.
long k;
if (u > 0)
k = -((u-1) / b_orig);
else
k = (b_orig-u) / b_orig;
if (k) {
u += k * b_orig;
v += k * a_orig;
}
return a;
}
}
long gcdWithCoeffs(long a, long b, long& u, long& v) {
long signA = (a > 0 ? 1 : a == 0 ? 0 : -1);
long signB = (b > 0 ? 1 : b == 0 ? 0 : -1);
long ans = gcdWithCoeffsInternal(a >= 0 ? a : -a,
b >= 0 ? b : -b, u, v);
u *= signA;
v *= signB;
return ans;
}
unsigned long modularInverse(unsigned long n, unsigned long k) {
if (n == 1)
return 0;
long u, v;
gcdWithCoeffs(n, k % n, u, v);
// GCD should equal 1, so u*n + k*v = 1.
// Inverse is v; note that -n < v <= 0.
// Since n >= 2 now and (n,k) = 1, we know v != 0.
return v + n;
}
namespace {
/**
* Finds the smallest prime factor of the given odd integer.
* You may specify a known lower bound for this smallest prime factor.
* If the given integer is prime, 0 is returned.
*
* \pre \a n is odd.
* \pre The smallest prime factor of \a n is known to
* be at least as large as (and possibly equal to) \a lowerBound.
* \pre \a lowerBound is odd.
*
* @param n the integer whose smallest prime factor we wish to find.
* @param lowerBound a known lower bound for this smallest prime factor.
* @return the smallest prime factor of \a n, or 0 if \a n is prime.
*/
unsigned long smallestPrimeFactor(unsigned long n,
unsigned long lowerBound = 1) {
while (lowerBound * lowerBound <= n) {
if (n % lowerBound == 0)
return lowerBound;
lowerBound += 2;
}
return 0;
}
}
void factorise(unsigned long n, std::list<unsigned long>& factors) {
// n > 0 is a precondition, but the effects are too unpleasant if
// it's broken (infinite memory consumption).
if (n == 0)
return;
// First take out all factors of 2.
while (n % 2 == 0) {
n = n / 2;
factors.push_back(2);
}
// Run through finding smallest factors.
unsigned long factor = 3;
while ((factor = smallestPrimeFactor(n, factor))) {
factors.push_back(factor);
n = n / factor;
}
// Anything left is prime.
if (n > 1)
factors.push_back(n);
}
void primesUpTo(const NLargeInteger& roof, std::list<NLargeInteger>& primes) {
// First check 2.
if (roof < 2)
return;
primes.push_back(NLargeInteger(2));
// Run through the rest.
NLargeInteger current(3);
while (current <= roof) {
// Is current prime?
if (find_if(primes.begin(), primes.end(), regina::stl::compose1(
bind2nd(std::equal_to<NLargeInteger>(), NLargeInteger::zero),
bind1st(std::modulus<NLargeInteger>(), current))) ==
primes.end())
primes.push_back(current);
current += 2;
}
}
} // namespace regina
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