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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, 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. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include "maths/perm.h"
namespace regina {
template <int n>
void Perm<n>::precompute() {
std::scoped_lock lock(precomputeMutex);
if (invLower_)
return;
if constexpr (sizeof(size_t) <= 2 /* we always have n >= 8 here */) {
// We are on a 16-bit machine.
throw FailedPrecondition("This appears to be a 16-bit machine, and so "
"cannot build tables for Perm<n>::precompute() for any n ≥ 8.");
} else if constexpr (sizeof(size_t) == 3 && n >= 9) {
// We are on a 24-bit machine.
throw FailedPrecondition("This appears to be a 24-bit machine, and so "
"cannot build tables for Perm<n>::precompute() for any n ≥ 9.");
} else if constexpr (sizeof(size_t) < 8 && n >= 13) {
// This is smaller than 64 bits; make the conservative (but very
// reasonable) assumption that we are on a 32-bit machine.
throw FailedPrecondition("This appears to be a 32-bit machine, and so "
"cannot build tables for Perm<n>::precompute() for any n ≥ 13.");
} else {
try {
invLower_ = new ImagePack[lowerCount];
invUpper_ = new ImagePack[upperCount];
} catch (const std::bad_alloc&) {
throw FailedPrecondition("Not enough memory available to "
"dynamically allocate tables for Perm<n>::precompute().");
}
LowerSlice lower;
do {
ImagePack d = 0;
for (int i = 0; i < LowerSlice::length; ++i)
d |= (static_cast<ImagePack>(i) << (imageBits * lower.image[i]));
invLower_[lower.pack()] = d;
} while (lower.lexInc());
UpperSlice upper;
do {
ImagePack d = 0;
for (int i = 0; i < UpperSlice::length; ++i)
d |= (static_cast<ImagePack>(i + LowerSlice::length)
<< (imageBits * upper.image[i]));
invUpper_[upper.pack()] = d;
} while (upper.lexInc());
}
}
template <int n>
void Perm<n>::lexInc() {
// The algorithm for lexicographical "next permutation": find the *last*
// point in the sequence of images where successive images increase:
// ..... p < q > r > s > ... > z
// We then change p to whichever of z,...,s,r,q first exceeds it,
// and then place the remaining images (along with p) in increasing order.
int q = (*this)[n - 1];
int p = (*this)[n - 2];
if (p < q) {
// The next permutation just swaps the last two images.
swapImages(n - 2, n - 1);
return;
}
int pIdx = n - 2;
while (p > q && pIdx > 0) {
q = p;
--pIdx;
p = (*this)[pIdx];
}
if (p > q) {
// The sequence was entirely decreasing.
// We have reached the end of our iteration.
code_ = idCode_;
return;
}
// Reverse the sequence from pIdx onwards.
for (int i = 1; pIdx + i < n - i; ++i)
swapImages(pIdx + i, n - i);
// Now identify which element needs to be swapped with p.
for (int i = pIdx + 1; i < n; ++i)
if ((*this)[i] > p) {
swapImages(pIdx, i);
return;
}
}
template <int n>
Perm<n>& Perm<n>::operator ++() {
// We implement a lexicographic "next permutation" algorithm as above;
// however, we want to increment according to Sn index, not orderedSn index.
// Thus some mod 2 fiddling around signs is required.
if (sign() > 0) {
// Going from even to odd, we always just swap the last two elements.
swapImages(n - 2, n - 1);
return *this;
}
bool needSignChange = true;
// The algorithm for lexicographical "next permutation": find the *last*
// point in the sequence of images where successive images increase:
// ..... p < q > r > s > ... > z
// We then change p to whichever of z,...,s,r,q first exceeds it,
// and then place the remaining images (along with p) in increasing order.
// The sign changes iff the length of the sequence q > r > ... > z
// is 0 or 1 (mod 4).
int q = (*this)[n - 1];
int p = (*this)[n - 2];
int pIdx = n - 2;
if (p < q) {
// The next permutation just swaps the last two images.
// However, since we started with an odd permutation, this will be
// going *backwards* in the Sn ordering.
// Swap them now, and carry on to get the *following* permutation.
swapImages(n - 2, n - 1);
std::swap(p, q);
needSignChange = false;
}
while (p > q && pIdx > 0) {
q = p;
--pIdx;
p = (*this)[pIdx];
}
if (p > q) {
// The sequence was entirely decreasing.
// We have reached the end of our iteration.
code_ = idCode_;
return *this;
}
// Reverse the sequence from pIdx onwards.
for (int i = 1; pIdx + i < n - i; ++i)
swapImages(pIdx + i, n - i);
// Now identify which element needs to be swapped with p.
for (int i = pIdx + 1; i < n; ++i)
if ((*this)[i] > p) {
swapImages(pIdx, i);
break;
}
// Did the sign change?
int seqRem = (n - 1 - pIdx) % 4;
if (seqRem == 0 || seqRem == 1) {
// The sign changed.
if (! needSignChange)
swapImages(n - 2, n - 1);
} else {
// The sign did not change.
if (needSignChange)
swapImages(n - 2, n - 1);
}
// Woof.
return *this;
}
// Explicitly instantiate all of the higher-order permutation classes,
// so that their static data members are defined in one and only one place.
//
// See the notes alongside the matching extern declarations in the header
// for why we are doing this. (Short answer: Windows is a terrible platform
// to try to port software to.)
//
template class Perm<8>;
template class Perm<9>;
template class Perm<10>;
template class Perm<11>;
template class Perm<12>;
template class Perm<13>;
template class Perm<14>;
template class Perm<15>;
template class Perm<16>;
} // namespace regina
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