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/* boost random/detail/const_mod.hpp header file
*
* Copyright Jens Maurer 2000-2001
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* See http://www.boost.org for most recent version including documentation.
*
* $Id$
*
* Revision history
* 2001-02-18 moved to individual header files
*/
#ifndef BOOST_RANDOM_CONST_MOD_HPP
#define BOOST_RANDOM_CONST_MOD_HPP
#include <boost/assert.hpp>
#include <boost/static_assert.hpp>
#include <boost/integer_traits.hpp>
#include <boost/type_traits/make_unsigned.hpp>
#include <boost/random/detail/large_arithmetic.hpp>
#include <boost/random/detail/disable_warnings.hpp>
namespace boost {
namespace random {
template<class IntType, IntType m>
class const_mod
{
public:
static IntType apply(IntType x)
{
if(((unsigned_m() - 1) & unsigned_m()) == 0)
return (unsigned_type(x)) & (unsigned_m() - 1);
else {
IntType supress_warnings = (m == 0);
BOOST_ASSERT(supress_warnings == 0);
return x % (m + supress_warnings);
}
}
static IntType add(IntType x, IntType c)
{
if(((unsigned_m() - 1) & unsigned_m()) == 0)
return (unsigned_type(x) + unsigned_type(c)) & (unsigned_m() - 1);
else if(c == 0)
return x;
else if(x < m - c)
return x + c;
else
return x - (m - c);
}
static IntType mult(IntType a, IntType x)
{
if(((unsigned_m() - 1) & unsigned_m()) == 0)
return unsigned_type(a) * unsigned_type(x) & (unsigned_m() - 1);
else if(a == 0)
return 0;
else if(a == 1)
return x;
else if(m <= traits::const_max/a) // i.e. a*m <= max
return mult_small(a, x);
else if(traits::is_signed && (m%a < m/a))
return mult_schrage(a, x);
else
return mult_general(a, x);
}
static IntType mult_add(IntType a, IntType x, IntType c)
{
if(((unsigned_m() - 1) & unsigned_m()) == 0)
return (unsigned_type(a) * unsigned_type(x) + unsigned_type(c)) & (unsigned_m() - 1);
else if(a == 0)
return c;
else if(m <= (traits::const_max-c)/a) { // i.e. a*m+c <= max
IntType supress_warnings = (m == 0);
BOOST_ASSERT(supress_warnings == 0);
return (a*x+c) % (m + supress_warnings);
} else
return add(mult(a, x), c);
}
static IntType pow(IntType a, boost::uintmax_t exponent)
{
IntType result = 1;
while(exponent != 0) {
if(exponent % 2 == 1) {
result = mult(result, a);
}
a = mult(a, a);
exponent /= 2;
}
return result;
}
static IntType invert(IntType x)
{ return x == 0 ? 0 : (m == 0? invert_euclidian0(x) : invert_euclidian(x)); }
private:
typedef integer_traits<IntType> traits;
typedef typename make_unsigned<IntType>::type unsigned_type;
const_mod(); // don't instantiate
static IntType mult_small(IntType a, IntType x)
{
IntType supress_warnings = (m == 0);
BOOST_ASSERT(supress_warnings == 0);
return a*x % (m + supress_warnings);
}
static IntType mult_schrage(IntType a, IntType value)
{
const IntType q = m / a;
const IntType r = m % a;
BOOST_ASSERT(r < q); // check that overflow cannot happen
return sub(a*(value%q), r*(value/q));
}
static IntType mult_general(IntType a, IntType b)
{
IntType suppress_warnings = (m == 0);
BOOST_ASSERT(suppress_warnings == 0);
IntType modulus = m + suppress_warnings;
BOOST_ASSERT(modulus == m);
if(::boost::uintmax_t(modulus) <=
(::std::numeric_limits< ::boost::uintmax_t>::max)() / modulus)
{
return static_cast<IntType>(boost::uintmax_t(a) * b % modulus);
} else {
return static_cast<IntType>(detail::mulmod(a, b, modulus));
}
}
static IntType sub(IntType a, IntType b)
{
if(a < b)
return m - (b - a);
else
return a - b;
}
static unsigned_type unsigned_m()
{
if(m == 0) {
return unsigned_type((std::numeric_limits<IntType>::max)()) + 1;
} else {
return unsigned_type(m);
}
}
// invert c in the finite field (mod m) (m must be prime)
static IntType invert_euclidian(IntType c)
{
// we are interested in the gcd factor for c, because this is our inverse
BOOST_ASSERT(c > 0);
IntType l1 = 0;
IntType l2 = 1;
IntType n = c;
IntType p = m;
for(;;) {
IntType q = p / n;
l1 += q * l2;
p -= q * n;
if(p == 0)
return l2;
IntType q2 = n / p;
l2 += q2 * l1;
n -= q2 * p;
if(n == 0)
return m - l1;
}
}
// invert c in the finite field (mod m) (c must be relatively prime to m)
static IntType invert_euclidian0(IntType c)
{
// we are interested in the gcd factor for c, because this is our inverse
BOOST_ASSERT(c > 0);
if(c == 1) return 1;
IntType l1 = 0;
IntType l2 = 1;
IntType n = c;
IntType p = m;
IntType max = (std::numeric_limits<IntType>::max)();
IntType q = max / n;
BOOST_ASSERT(max % n != n - 1 && "c must be relatively prime to m.");
l1 += q * l2;
p = max - q * n + 1;
for(;;) {
if(p == 0)
return l2;
IntType q2 = n / p;
l2 += q2 * l1;
n -= q2 * p;
if(n == 0)
return m - l1;
q = p / n;
l1 += q * l2;
p -= q * n;
}
}
};
} // namespace random
} // namespace boost
#include <boost/random/detail/enable_warnings.hpp>
#endif // BOOST_RANDOM_CONST_MOD_HPP
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