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* Copyright (C) 1999-2001 William J Turner,
* 2001 Bradford Hovinen
2015 reorg bds
*
* Written by William J Turner <wjturner@math.ncsu.edu>,
* Bradford Hovinen <hovinen@cis.udel.edu>
*
* -----------------------------------------------------------
* 2002-09-26 Bradford Hovinen <bghovinen@math.uwaterloo.ca>
*
* Refactoring: The switch object now only contains the information necessary
* for a single 2x2 block. The butterfly black box maintains a vector of switch
* objects that it keeps in parallel with its vector of indices. There is a new
* lightweight class, called a SwitchFactory, that constructs switches on the
* fly. It is defined individually for each switch type, and a instance thereof
* is passed to the butterfly, which then uses it to construct its vector.
*
* This eliminates two problems: first, because switch objects are constructed
* by the butterfly itself, there is no need to know a priori the length of the
* vector of indices. Second, the switch object itself becomes simpler, as it
* need only be responsible for a single 2x2 block.
*
* -----------------------------------------------------------
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*
*/
#ifndef __LINBOX_butterfly_INL
#define __LINBOX_butterfly_INL
#include <vector>
#include "linbox/blackbox/blackbox-interface.h"
#include "linbox/vector/vector-domain.h"
#include "linbox/field/hom.h"
/** @file blackbox/butterfly.inl
*
* First linbox block: butterfly method implementations
* Second LinBox block: butterfly switch and switch factory impls.
*
*/
namespace LinBox
{
// Implementation of Butterfly methods
template <class Field, class Switch>
inline Butterfly<Field, Switch>::Butterfly (const Field &F, size_t n, typename Switch::Factory &factory) :
_field (&F), _VD (F), _n (n)
{
buildIndices ();
for (unsigned int i = 0; i < _indices.size (); ++i)
_switches.push_back (factory.makeSwitch ());
}
template <class Field, class Switch>
template<class OutVector, class InVector>
inline OutVector& Butterfly<Field, Switch>::apply (OutVector& y, const InVector& x) const
{
std::vector< std::pair<size_t, size_t> >::const_iterator idx_iter = _indices.begin ();
typename std::vector<Switch>::const_iterator switch_iter = _switches.begin ();
_VD.copy (y, x);
for (; idx_iter != _indices.end (); ++idx_iter, ++switch_iter)
switch_iter->apply (field(), y[idx_iter->first], y[idx_iter->second]);
return y;
}
template <class Field, class Switch>
template <class OutVector, class InVector>
inline OutVector& Butterfly<Field, Switch>::applyTranspose (OutVector& y, const InVector& x) const
{
std::vector< std::pair<size_t, size_t> >::const_reverse_iterator idx_iter = _indices.rbegin ();
typename std::vector<Switch>::const_reverse_iterator switch_iter = _switches.rbegin ();
_VD.copy (y, x);
for (; idx_iter != _indices.rend (); ++idx_iter, ++switch_iter)
switch_iter->applyTranspose (field(), y[idx_iter->first], y[idx_iter->second]);
return y;
}
template <class Field, class Switch>
void Butterfly<Field, Switch>::buildIndices ()
{
for (size_t value (_n), l_p (0), n_p (1);
n_p != 0;
value >>= 1, ++l_p, n_p <<= 1)
{
if (value & 1) {
_l_vec.push_back (l_p);
_n_vec.push_back (n_p);
}
}
// Create vector of indices to switch
size_t n_p ; // size of group and number of levels in group
size_t level (0), difference (1); // track levels done for powers of 2
// Vector containing indices for last level of last power of 2.
std::vector< std::pair< size_t, size_t > > p_ind;
// Vector and iterator used for computing p_ind.
std::vector< std::pair< size_t, size_t > > temp_ind;
std::vector< std::pair< size_t, size_t > >::iterator iter;
// Loop over sub-groups of powers of two
for (size_t p (0), start_index (0);
p < _n_vec.size ();
++p, start_index += n_p)
{
// update size
n_p = _n_vec[p];
size_t l_p = _l_vec[p];
// loop over levels of sub-group network
for ( ; level < l_p; ++level, difference <<= 1) {
// Create
temp_ind = p_ind;
// the second sub group is a shift of the first
for (iter = temp_ind.begin (); iter != temp_ind.end (); ++iter) {
iter->first += difference;
iter->second += difference;
}
// add the second group to the first
p_ind.insert (p_ind.end (), temp_ind.begin (), temp_ind.end ());
// add switches to mix the two sub groups
temp_ind = std::vector< std::pair<size_t, size_t> >
(difference, std::pair<size_t, size_t> (0, 0));
size_t i = 0;
for (iter = temp_ind.begin (); iter != temp_ind.end (); ++i, ++iter) {
iter->first += i;
iter->second += i + difference;
}
// add the combining group to the first and second
p_ind.insert (p_ind.end (), temp_ind.begin (), temp_ind.end ());
}
// Add this level to total list of indices and correct starting point
temp_ind = p_ind;
for (iter = temp_ind.begin (); iter != temp_ind.end (); ++iter) {
iter->first += start_index;
iter->second += start_index;
}
_indices.insert (_indices.end (), temp_ind.begin (), temp_ind.end ());
// Combine everything so far
temp_ind = std::vector< std::pair<size_t, size_t> > (start_index, std::pair<size_t, size_t> (0, 0));
iter = temp_ind.begin ();
for (size_t index = 0; index < start_index; ++index, ++iter) {
iter->first = index;
iter->second += index + n_p;
}
_indices.insert (_indices.end (), temp_ind.begin (), temp_ind.end ());
}
}
inline std::vector<bool> setButterfly (const std::vector<bool>& x,
size_t j)
{
size_t n = x.size ();
commentator().start ("Setting butterfly switches", "setButterfly");
std::ostream &report = commentator().report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION);
report << "Called set switches with vector of size " << n
<< " and offset " << j << std::endl;
// return empty vector if zero or one elements in x because
// no switching will be done.
if (x.size () <= 1) {
commentator().indent (report);
report << "No switches needed. Returning with empty vector." << std::endl;
commentator().stop ("done");
return std::vector<bool> ();
}
commentator().indent (report);
report << "Counting the number of switches that exist." << std::endl;
// break inputs into groups of size powers of 2.
// calculate size of groups, and powers of 2 that give sizes
// store these values in vectors n and l, respectively
std::vector<size_t> l_vec, n_vec;
for (size_t value (n), l_p (0), n_p (1);
n_p != 0;
value >>= 1, ++l_p, n_p <<= 1)
{
commentator().indent (report);
report << " looping at value = " << value
<< ", l_p = " << l_p
<< ", n_p = " << n_p << std::endl;
if (value & 1) {
l_vec.push_back (l_p);
n_vec.push_back (n_p);
commentator().indent (report);
report << " inserted value = " << value
<< ", l_p = " << l_p
<< ", n_p = " << n_p << std::endl;
}
}
// Calculate total number of switches required
size_t s (0);
for (size_t ii = 0; ii < n_vec.size (); ++ii)
s += n_vec[ii] * l_vec[ii] / 2;
for (size_t ii = 0; ii < n_vec.size () - 1; ++ii)
for (size_t jj = 0; jj <= ii; ++jj)
s += n_vec[jj];
commentator().indent (report);
report << "There are a total of " << s << " switches" << std::endl;
// Set largest power of 2 in decomposition of n = x.size ()
size_t n_p (*n_vec.rbegin ());
commentator().indent (report);
report << "Found largest power of 2 in decomposition of " << n
<< " as n_p = " << n_p << std::endl;
if ( (n != n_p) && (j != 0) ) {
commentator().indent (report);
report << "Non-zero offset " << j
<< " used with non-power size."
<< "Offset reset to zero." << std::endl;
j = 0;
}
else
j %= n;
if (n == n_p) {
n_p /= 2; // >> is not portable!
commentator().indent (report);
report << "n = " << n << " is a power of two. "
<< "Resetting n_p to be half of n: n_p = " << n_p << std::endl;
}
// count true elements not in largest power of 2 block
size_t r_1(0);
for (std::vector<bool>::const_iterator iter = x.begin ();
iter != x.begin () + (ptrdiff_t)(n - n_p);
++iter)
if (*iter) ++r_1;
// count total number of true elements in x.
size_t r (r_1);
for (std::vector<bool>::const_iterator iter = x.begin () + (ptrdiff_t)(n - n_p);
iter != x.end ();
++iter)
if (*iter) ++r;
commentator().indent (report);
report << "The vector x will be broken into two sub-vectors,"
<< "x_1 = x[0,...," << n - n_p - 1 << "] and x_2 = x["
<< n - n_p << ",...," << n - 1 << "]."
<< "There are a total of " << r << " true Elements in x, "
<< r_1 << " of which occured in the first sub-vector."
<< "The output vector will have " << s << " entries and will"
<< "switch the true Elements of x into a contiguous block"
<< "[" << j << "," << j + r
<< ") = [" << j << "," << j + r - 1<< "]." << std::endl;
if (r == 0) {
commentator().indent (report);
report << "There are no true Elements in x, so the recursion is"
<< "being broken and a vector of false flags returned." << std::endl;
commentator().stop ("done");
return std::vector<bool> (s, false);
}
else if (r == n) {
commentator().indent (report);
report << "There are no false Elements in x, so the recursion is"
<< "being broken and a vector of false flags returned." << std::endl;
commentator().stop ("done");
return std::vector<bool> (s, false);
}
// Calculate where the true elements are supposed to end up
// Here, they will be in a contiguous block starting after the
// offset. s_1 are the true elements after the offset and in the first
// sub-group, s_2 are the ones in the second sub group, and s_3 are the
// elements that wrap around to the beginning. s_1 and s_3 cannot both
// be non-zero unless s_2 == n_p. (I.e., the second group is full.)
// Also, because for n != 2 n_p the offset is zero, in that case
// s_3 must be zero. Any of them may be zero if the corrsponding block
// is empty.
// s_2 is only used for tracing the program, so it is not always computed.
size_t s_1;
if (j < n - n_p) {
if (j + r < n - n_p)
s_1 = r;
else
s_1 = n - n_p - j;
}
else
s_1 = 0;
size_t s_2 = 0;
if (commentator().isPrinted (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION)) {
if (j + r < n - n_p)
s_2 = 0;
else {
if (j + r < n)
s_2 = j + r;
else
s_2 = n;
if (j < n - n_p)
s_2 -= (n - n_p);
else
s_2 -= j;
}
}
size_t s_3 = ((j + r) > n) ? j + r - n : 0;
commentator().indent (report);
report << "The number of Elements in each of the three blocks of "
<< "true Elements in the end result are"
<< "s_1 = " << s_1
<< ", s_2 = " << s_2
<< ", and s_3 = " << s_3 << "." << std::endl;
// Create empty vector for output. y_temp is used to retrieve output
// from recursion before inserting into output.
std::vector<bool> y_1, y_2, y_3 = std::vector<bool> (n - n_p, false);
if ((s_1 + s_3) == r_1) {
commentator().indent (report);
report << "Case I: s_1 + s_3 == r_1 and s_2 == r - r_1."
<< "No Elements are moved between the two sub-vectors." << std::endl;
if (j < (n - n_p)) {
commentator().indent (report);
report << " A: j < (n - n_p). j_1 = j = " << j << ", j_2 = 0";
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () + (ptrdiff_t)(n - n_p)), j);
y_2 = setButterfly (std::vector<bool>(x.begin () + (ptrdiff_t)(n - n_p), x.end ()), 0);
}
else {
commentator().indent (report);
report << " A: j >= (n - n_p). j_1 = 0, j_2 = j - (n - n_p) = "
<< j - (n - n_p) << std::endl;
// This case cannot occur for n != 2*n_p because j != 0
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () + (ptrdiff_t)(n - n_p)), 0);
y_2 = setButterfly (std::vector<bool>(x.begin () + (ptrdiff_t)(n - n_p), x.end ()), j - (n - n_p));
}
}
else if ((s_1 + s_3) > r_1) {
commentator().indent (report);
report << "Case II: s_1 + s_3 > r_1 and s_2 < r - r_1."
<< "Elements are moved from the right sub-vector to the left." << std::endl;
// This means that s_2 < n_p, so either s_1 = 0 or s_3 = 0 (or both).
if (j < (n - n_p)) {
commentator().indent (report);
report << " A: j < (n - n_p). j_1 = j, j_2 = 2*n_p + j + r_1 - n = "
<< 2*n_p + j + r_1 - n << std::endl;
// In this case, s_1 > 0, so s_3 = 0, and wrap-around cannot occur.
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () + (ptrdiff_t)(n - n_p)), j);
y_2 = setButterfly (std::vector<bool>(x.begin () + (ptrdiff_t)(n - n_p), x.end ()), 2*n_p + j + r_1 - n);
for (std::vector<bool>::iterator iter = (y_3.begin () + (ptrdiff_t)(j + r_1));
iter != (y_3.begin () + (ptrdiff_t)(n - n_p));
++iter)
*iter = true;
}
else {
commentator().indent (report);
report << " A: j >= (n - n_p). j_1 = j + r - n - r_1 = "
<< j + r - n - r_1 << ", j_2 = j - (n - n_p) = "
<< j - (n - n_p) << std::endl;
// In this case, s_1 = 0, so s_3 >= 0, and wrap-around may occur.
// This case cannot occur for n != 2*n_p because j != 0.
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () + (ptrdiff_t)(n - n_p)), j + r - n - r_1);
y_2 = setButterfly (std::vector<bool>(x.begin () + (ptrdiff_t)(n - n_p), x.end ()), j - (n - n_p));
for (std::vector<bool>::iterator iter = y_3.begin ();
iter != (y_3.begin () + (ptrdiff_t)(j + r - n - r_1));
++iter)
*iter = true;
}
}
else if ((s_1 + s_3) < r_1) {
commentator().indent (report);
report << "Case III: s_1 + s_3 < r_1 and s_2 > r - r_1."
<< "Elements are moved from the left sub-vector to the right." << std::endl;
// This case also means that s_1 + s_3 < n - n_p, or the contiguous
// block cannot encompass the entire first sub-vector. For this
// reason, this case is not considered when n != 2*n_p (when j = 0).
if (j < (n - n_p)) {
commentator().indent (report);
report << " A: j < (n - n_p). j_1 = j = " << j
<< ", j_2 = j + r_1 - n + n_p = " << j + r_1 - n + n_p << std::endl;
// In this case, s_1 > 0, so s_3 = 0, and wrap-around cannot occur.
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () +(ptrdiff_t) (n - n_p)), j);
y_2 = setButterfly (std::vector<bool>(x.begin () +(ptrdiff_t) (n - n_p), x.end ()), j + r_1 - n + n_p);
for (std::vector<bool>::iterator iter = (y_3.begin () +(ptrdiff_t) s_3);
iter != (y_3.begin () + (ptrdiff_t)(j + r_1 - n + n_p));
++iter)
*iter = true;
}
else {
commentator().indent (report);
report << " A: j >= (n - n_p). j_1 = j + r - n_p - r_1 = "
<< j + r - n_p - r_1 << ", j_2 = j - (n - n_p) = "
<< j - (n - n_p) << std::endl;
// In this case, s_1 = 0, so s_3 >= 0, and wrap-around may occur.
// This case cannot occur for n != 2*n_p because j != 0.
y_1 = setButterfly (std::vector<bool>(x.begin (), x.begin () + (ptrdiff_t)(n - n_p)), j + r - n_p - r_1);
y_2 = setButterfly (std::vector<bool>(x.begin () + (ptrdiff_t)(n - n_p), x.end ()), j - (n - n_p));
for (std::vector<bool>::iterator iter (y_3.begin () + (ptrdiff_t)(j + r - n_p - r_1));
iter != (y_3.begin () + (ptrdiff_t)(n - n_p));
++iter)
*iter = true;
}
}
// Create output vector.
std::vector<bool> y (y_1);
y.insert (y.end (), y_2.begin (), y_2.end ());
y.insert (y.end (), y_3.begin (), y_3.end ());
commentator().indent (report);
report << "The output vector for n = " << n << " has " << y.size ()
<< " entries."
<< " " << y_1.size () << " from the first sub-vector"
<< " " << y_2.size () << " from the second sub-vector"
<< " " << y_3.size () << " from recombining the two"
<< "And the output vector y is:"
<< "-------------------------- " << std::endl;
for (size_t i = 0; i < y.size (); ++i) {
commentator().indent (report);
report << " " << i << ": " << y[i] << std::endl;
}
commentator().indent (report);
report << "-------------------------- " << std::endl;
commentator().stop ("done");
return y;
} // std::vector<bool> setButterfly (const std::vector<bool>& x, size_t j)
//@}
// Begin cekstv switch
template <class Field> class CekstvSwitchFactory;
template <class Field>
class CekstvSwitch {
public:
/// Typedef
typedef typename Field::Element Element;
typedef CekstvSwitch<Field> Self_t;
typedef CekstvSwitchFactory<Field> Factory;
CekstvSwitch () {}
/** Constructor from a field and a field element.
* @param a vector of switches
*/
CekstvSwitch (const typename Field::Element &a) :
_a (a)
{}
/** Destructor.
*/
~CekstvSwitch () {}
/** Apply switch function.
* Switches the elements in references according to the
* exchange matrix introduced in "Efficient Matrix
* Preconditioners for Black Box Linear Algebra" by Chen, Eberly,
* Kaltofen, Saunders, Turner, and Villard and the current field element
* specified in the switch object.
* @return bool true if swapped, false otherwise
* @param F
* @param x reference to first element to be switched
* @param y reference to second element to be switched
*/
bool apply (const Field &F, Element &x, Element &y) const;
/** Apply switch transpose function.
* Switches the elements in references according to the
* transpose of the exchange matrix introduced in "Efficient Matrix
* Preconditioners for Black Box Linear Algebra" by Chen, Eberly,
* Kaltofen, Saunders, Turner, and Villard and the current field element
* specified in the switch object.
* @return bool true if swapped, false otherwise
* @param F
* @param x reference to first element to be switched
* @param y reference to second element to be switched
*/
bool applyTranspose (const Field &F, Element &x, Element &y) const;
template<typename _Tp1>
struct rebind
{
typedef CekstvSwitch<_Tp1> other;
// special rebind operator() with two fields,
// indeed local field is not stored in the switch
void operator() (other & Ap, const Self_t& A, const _Tp1& T, const Field& F) {
Hom<Field, _Tp1>(F,T).image(Ap.getData(), A.getData());
}
};
typename Field::Element& getData() { return _a; }
const typename Field::Element& getData() const { return _a; }
private:
// Parameter of this 2x2 block
typename Field::Element _a;
};
template <class Field>
class CekstvSwitchFactory {
public:
/** Constructor from an STL vector of bools
*/
CekstvSwitchFactory (typename Field::RandIter r) :
_r (r)
{}
/** Construct and return a boolean switch object
*/
CekstvSwitch<Field> makeSwitch ()
{ typename Field::Element a; return CekstvSwitch<Field> (_r.random (a)); }
private:
typename Field::RandIter _r;
};
template <class Field>
inline bool CekstvSwitch<Field>::apply (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const
{
F.axpyin (x, _a, y);
F.addin (y, x);
return true;
}
template <class Field>
inline bool CekstvSwitch<Field>::applyTranspose (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const
{
F.addin (x, y);
F.axpyin (y, _a, x);
return true;
}
// End cekstv switch
#if 0
// Begin specialization of cekstv switch object
template <>
class CekstvSwitch<GF2>
{
public:
typedef GF2 Field;
/// Typedef
typedef Field::Element Element;
typedef CekstvSwitch<Field> Self_t;
typedef CekstvSwitchFactory<Field> Factory;
/** Constructor from a field and a field element.
* @param F field in which arithmetic is done
* @param switches vector of switches
*/
CekstvSwitch (const Field::Element &a) :
_a (a)
{}
~CekstvSwitch () {}
bool apply (const Field &F, Element &x, Element &y) const
{
F.axpyin (x, _a, y);
F.addin (y, x);
return true;
}
bool applyTranspose (const Field &F, Element &x, Element &y) const
{
F.addin (x, y);
F.axpyin (y, _a, x);
return true;
}
bool apply (const Field &F, stdBitReference x, stdBitReference y) const
{
F.axpyin (x, _a, y);
F.addin (y, x);
return true;
}
bool applyTranspose (const Field &F, stdBitReference x, stdBitReference y) const
{
F.addin (x, y);
F.axpyin (y, _a, x);
return true;
}
template<typename _Tp1>
struct rebind
{
typedef CekstvSwitch<_Tp1> other;
// special rebind operator() with two fields,
// indeed local field is not stored in the switch
void operator() (other *& Ap, const Self_t& A, const _Tp1& T, const Field& F) {
typename _Tp1::Element u;
Hom<Field, _Tp1>(F,T).image(u, A._a);
Ap = new other(u);
}
};
private:
// Parameter of this 2x2 block
Field::Element _a;
};
// End, specialization of cekstv switch object
#endif
// Begin boolean switch
class BooleanSwitchFactory;
/** Boolean switch object.
* This is a switch predicate object that is applied
* to two references to elements to switch them as needed
* by the \ref Butterfly\ Switching\ Network\ BlackBox\ Matrix\ Object.
*/
class BooleanSwitch {
public:
typedef BooleanSwitch Self_t;
typedef BooleanSwitchFactory Factory;
/** Constructor from an STL vector of booleans.
* The switch is applied using the vector of booleans.
* A true value means to swap the two elements, and a false
* value means not to.
* The apply function starts at the beginning of the vector moving
* forward through it, and applyTranspose function starts at the end
* moving backwards. Both repeat the vector after they pass through it.
* @param s vector of switches
*/
BooleanSwitch (const bool s) :
_s (s)
{}
/** Destructor.
*/
~BooleanSwitch () {}
/** Apply switch function.
* Switches the elements in references according to current boolean
* value. Swaps the elements if boolean is true, otherwise does nothing.
* It is templatized by the element type to be swapped.
* @return bool \c true if swapped, \c false otherwise
* @param F
* @param x reference to first element to be switched
* @param y reference to second element to be switched
*/
template <class Field>
bool apply (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const;
/** Apply switch transpose function.
* Switches the elements in references according to current boolean
* value. Swaps the elements if boolean is true, otherwise does nothing.
* It is templatized by the element type to be swapped.
* @return bool \c true if swapped, \c false otherwise
* @param F
* @param x reference to first element to be switched
* @param y reference to second element to be switched
*/
template <class Field>
bool applyTranspose (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const;
template<typename _Tp1>
struct rebind {
typedef BooleanSwitch other;
};
protected:
bool _s;
}; // class boolean_switch
/** Boolean switch factory
*
* This class facilitates construction of boolean switch objects by the
* butterfly matrix.
*/
}// linbox
namespace LinBox {
class BooleanSwitchFactory {
public:
/** Constructor from an STL vector of bools
*/
BooleanSwitchFactory (const std::vector<bool> &switches) :
_switches (switches), _iter (switches.begin ())
{}
/** Construct and return a boolean switch object
*
* This function walks through the switches object given in the
* constructor, advancing on each invocation. It wraps around to the
* beginning of the vector when it reaches the end.
*/
BooleanSwitch makeSwitch ()
{
if (_iter == _switches.end ())
_iter = _switches.begin ();
return BooleanSwitch (*_iter++);
}
private:
const std::vector<bool> &_switches;
std::vector<bool>::const_iterator _iter;
};
template <class Field>
inline bool BooleanSwitch::apply (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const
{
if (_s)
std::swap (x, y);
return _s;
}
template <class Field>
inline bool BooleanSwitch::applyTranspose (const Field &F,
typename Field::Element &x,
typename Field::Element &y) const
{
if (_s)
std::swap (x, y);
return _s;
}
// End boolean switch
}// namespace LinBox
#endif // __LINBOX_butterfly_INL
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// mode: C++
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