mirror of
https://github.com/VCMP-SqMod/SqMod.git
synced 2025-01-19 03:57:14 +01:00
85 lines
3.3 KiB
C++
85 lines
3.3 KiB
C++
|
/**
|
||
|
|
* \file LeadingZeros.hpp
|
||
|
|
* \brief Header for LeadingZeros
|
||
|
|
*
|
||
|
|
* Count the leading zeros in a real number.
|
||
|
|
*
|
||
|
|
* Copyright (c) Charles Karney (2006-2011) <charles@karney.com> and licensed
|
||
|
|
* under the MIT/X11 License. For more information, see
|
||
|
|
* http://randomlib.sourceforge.net/
|
||
|
|
**********************************************************************/
|
||
|
|
|
||
|
|
#if !defined(RANDOMLIB_LEADINGZEROS_HPP)
|
||
|
|
#define RANDOMLIB_LEADINGZEROS_HPP 1
|
||
|
|
|
||
|
|
namespace RandomLib {
|
||
|
|
/**
|
||
|
|
* \brief Count of leading zeros.
|
||
|
|
*
|
||
|
|
* Count of leading zero bits after the binary point in a real number
|
||
|
|
* uniformly distributed in (0,1). (This is equivalent to the geometric
|
||
|
|
* distribution with probability 1/2.) For example
|
||
|
|
* \code
|
||
|
|
#include <RandomLib/LeadingZeros.hpp>
|
||
|
|
|
||
|
|
RandomLib::Random r; // A RandomGenerator works here too
|
||
|
|
std::cout << "Seed set to " << r.SeedString() << "\n";
|
||
|
|
LeadingZeros zeros;
|
||
|
|
std::cout << "Count of leading zeros:";
|
||
|
|
for (size_t i = 0; i < 20; ++i)
|
||
|
|
std::cout << " " << zeros(r);
|
||
|
|
std::cout << "\n";
|
||
|
|
\endcode
|
||
|
|
**********************************************************************/
|
||
|
|
class LeadingZeros {
|
||
|
|
public:
|
||
|
|
/**
|
||
|
|
* Return the number of zero bits after the binary point in a real number
|
||
|
|
* uniformly distributed in (0,1). Thus \e k is returned with probability
|
||
|
|
* 1/2<sup><i>k</i>+1</sup>. Because MT19937 is \e not a perfect random
|
||
|
|
* number generator, this always returns a result in [0, 19937).
|
||
|
|
*
|
||
|
|
* @tparam Random the type of the random generator.
|
||
|
|
* @param[in,out] r a random generator.
|
||
|
|
* @return the random sample.
|
||
|
|
**********************************************************************/
|
||
|
|
template<class Random> unsigned operator()(Random& r) const throw();
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class Random>
|
||
|
|
unsigned LeadingZeros::operator()(Random& r) const throw() {
|
||
|
|
// It's simpler to count the number of trailing ones in each w-bit block
|
||
|
|
// stopping when we get to a zero bit.
|
||
|
|
//
|
||
|
|
// Process a word in chunks of size m. The algorithm here can deal with
|
||
|
|
// any m assuming that z is modified accordingly. m = 4 is an approximate
|
||
|
|
// optimum.
|
||
|
|
//
|
||
|
|
// Can also adapt this routine to use RandomNumber::highest_bit_idx
|
||
|
|
// instead. However the result is considerably slower.
|
||
|
|
const int m = 4;
|
||
|
|
STATIC_ASSERT(m <= Random::width, "LeadingZeros: m too large");
|
||
|
|
// mask with m low bits set
|
||
|
|
const typename Random::result_type mask = ~(Random::max << m);
|
||
|
|
// Number of trailing 1 bits in [0, 1<<m). However, correct results are
|
||
|
|
// also obtained with any permutation of this array. This particular
|
||
|
|
// permutation is useful since the initial 1/2, 1/4, etc. can be used for
|
||
|
|
// m-1, m-2, etc. To generate the array for the next higher m, append a
|
||
|
|
// duplicate of the array and increment the last entry by one.
|
||
|
|
const unsigned z[1 << m] =
|
||
|
|
{ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, };
|
||
|
|
typename Random::result_type x = r();
|
||
|
|
for (unsigned b = m, n = 0; b < Random::width; b += m) {
|
||
|
|
n += z[x & mask]; // count trailing 1s in chunk
|
||
|
|
if (n < b) // chunk contains a 0
|
||
|
|
return n;
|
||
|
|
x >>= m; // shift out the chunk we've processed
|
||
|
|
}
|
||
|
|
// x is all ones (prob 1/2^w); process the next word.
|
||
|
|
return Random::width + operator()(r);
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace RandomLib
|
||
|
|
|
||
|
|
#endif // RANDOMLIB_LEADINGZEROS_HPP
|