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+/*
+ Copyright (C) 2018 David Robillard <d@drobilla.net>
+ Copyright (C) 2006-2007 Chris Hamilton <chamilton@cs.dal.ca>
+
+ 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, see <https://www.gnu.org/licenses/>.
+*/
+
+#ifndef CHILBERT_ALGORITHM_HPP
+#define CHILBERT_ALGORITHM_HPP
+
+#include "chilbert/BoundedBitVec.hpp"
+#include "chilbert/DynamicBitVec.hpp"
+#include "chilbert/SmallBitVec.hpp"
+#include "chilbert/StaticBitVec.hpp"
+#include "chilbert/chilbert.hpp"
+#include "chilbert/detail/gray_code_rank.hpp"
+
+#include <cassert>
+#include <climits>
+#include <numeric>
+#include <type_traits>
+
+namespace chilbert {
+namespace detail {
+
+/** The dimension across which the Hilbert curve travels principally.
+ *
+ * D0 is d + 1, where d is the actual dimension you want to walk across.
+ * MUST HAVE 0 <= D0 < n.
+ */
+static constexpr size_t D0 = 1;
+
+template <class T>
+size_t
+num_bits(const T&, std::enable_if_t<std::is_integral<T>::value>* = nullptr)
+{
+ return sizeof(T) * CHAR_BIT;
+}
+
+template <class T>
+size_t
+num_bits(const T& vec,
+ std::enable_if_t<std::is_same<T, SmallBitVec>::value ||
+ std::is_same<T, DynamicBitVec>::value>* = nullptr)
+{
+ return vec.size();
+}
+
+template <size_t N>
+size_t
+num_bits(const StaticBitVec<N>&, void* = nullptr)
+{
+ return N;
+}
+
+template <size_t MaxN>
+size_t
+num_bits(const BoundedBitVec<MaxN>& vec, void* = nullptr)
+{
+ return vec.size();
+}
+
+/** Copy a range of bits from one field to the start of another.
+ *
+ * @param h Source bit field
+ * @param n Number of bits
+ * @param i Start bit index in source
+ * @param[out] w Destination bit field
+ */
+template <class H, class I>
+inline void
+get_bits(const H& h, const size_t n, const size_t i, I& w)
+{
+ for (size_t j = 0; j < n; j++) {
+ set_bit(w, j, test_bit(h, i + j));
+ }
+}
+
+/** Set a range of bits in one field from the start of another.
+ *
+ * @param[out] h Destination bit field
+ * @param n Number of bits
+ * @param i Start bit index in destination
+ * @param w Source bit field
+ */
+template <class H, class I>
+inline void
+set_bits(H& h, const size_t n, const size_t i, const I& w)
+{
+ for (size_t j = 0; j < n; j++) {
+ set_bit(h, i + j, test_bit(w, j));
+ }
+}
+
+/** Set the leading bits in `l` to bit `i` from the corresponding value in `p`.
+ *
+ * @param p Point.
+ * @param n Number of bits to set.
+ * @param i Bit position to copy from values in `p`.
+ * @param[out] l Output bits.
+ */
+template <class P, class I>
+inline void
+get_location(const P* const p, const size_t n, const size_t i, I& l)
+{
+ for (size_t j = 0; j < n; ++j) {
+ set_bit(l, j, test_bit(p[j], i));
+ }
+}
+
+/** Set bit `i` in values in `p` to the corresponding leadings bits in `l`.
+ *
+ * @param[out] p Point.
+ * @param n Number of bits to set.
+ * @param i Bit position to set in values in `p`.
+ * @param l Input bits.
+ */
+template <class P, class I>
+inline void
+set_location(P* const p, const size_t n, const size_t i, const I& l)
+{
+ for (size_t j = 0; j < n; j++) {
+ set_bit(p[j], i, test_bit(l, j));
+ }
+}
+
+// 'Transforms' a point.
+template <class I>
+inline void
+transform(const I& e, const size_t d, const size_t n, I& a)
+{
+ assert(a.size() == n);
+ a ^= e;
+ a.rotr(d);
+}
+
+// Inverse 'transforms' a point.
+template <class I>
+inline void
+transform_inv(const I& e, const size_t d, const size_t n, I& a)
+{
+ assert(a.size() == n);
+ a.rotl(d);
+ a ^= e;
+}
+
+// Update for method 1 (GrayCodeInv in the loop)
+template <class I>
+inline void
+update1(const I& l, const I& t, const I& w, const size_t n, I& e, size_t& d)
+{
+ assert(0 <= d && d < n);
+ e = l;
+ e.flip(d); //#D d == n-1 ? 0 : d+1 );
+
+ // Update direction
+ d += 1 + t.find_first();
+ if (d >= n) {
+ d -= n;
+ }
+ if (d >= n) {
+ d -= n;
+ }
+ assert(0 <= d && d < n);
+
+ if (!w.test(0)) {
+ e.flip(d == 0 ? n - 1 : d - 1); //#D d );
+ }
+}
+
+// Update for method 2 (GrayCodeInv out of loop)
+template <class I>
+inline void
+update2(const I& l, const I& t, const size_t n, I& e, size_t& d)
+{
+ assert(0 <= d && d < n);
+ e = l;
+ e.flip(d); //#D d == n-1 ? 0 : d+1 );
+
+ // Update direction
+ d += 1 + t.find_first();
+ if (d >= n) {
+ d -= n;
+ }
+ if (d >= n) {
+ d -= n;
+ }
+ assert(0 <= d && d < n);
+}
+
+template <class P, class H, class I>
+inline void
+coords_to_index(const P* const p,
+ const size_t m,
+ const size_t n,
+ H& h,
+ I&& scratch,
+ size_t* const ds = nullptr)
+{
+ I e{std::move(scratch)};
+ I l{e};
+ I t{e};
+ I w{e};
+
+ // Initialize
+ e.reset();
+ l.reset();
+ reset_bits(h);
+
+ // Work from MSB to LSB
+ size_t d = D0;
+ size_t ho = m * n;
+ for (intptr_t i = static_cast<intptr_t>(m - 1); i >= 0; i--) {
+ if (ds) {
+ ds[i] = d;
+ }
+
+ // Get corner of sub-hypercube where point lies.
+ get_location<P, I>(p, n, static_cast<size_t>(i), l);
+
+ // Mirror and reflect the location.
+ // t = T_{(e,d)}(l)
+ t = l;
+ transform<I>(e, d, n, t);
+
+ w = t;
+ if (static_cast<size_t>(i) < m - 1) {
+ w.flip(n - 1);
+ }
+
+ // Concatenate to the index.
+ ho -= n;
+ set_bits<H, I>(h, n, ho, w);
+
+ // Update the entry point and direction.
+ update2<I>(l, t, n, e, d);
+ }
+
+ gray_code_inv(h);
+}
+
+template <class P, class H, class I>
+inline void
+index_to_coords(P* p, const size_t m, const size_t n, const H& h, I&& scratch)
+{
+ I e{std::move(scratch)};
+ I l{e};
+ I t{e};
+ I w{e};
+
+ // Initialize
+ e.reset();
+ l.reset();
+ for (size_t j = 0; j < n; j++) {
+ reset_bits(p[j]);
+ }
+
+ // Work from MSB to LSB
+ size_t d = D0;
+ size_t ho = m * n;
+ for (intptr_t i = static_cast<intptr_t>(m - 1); i >= 0; i--) {
+ // Get the Hilbert index bits
+ ho -= n;
+ get_bits<H, I>(h, n, ho, w);
+
+ // t = GrayCode(w)
+ t = w;
+ gray_code(t);
+
+ // Reverse the transform
+ // l = T^{-1}_{(e,d)}(t)
+ l = t;
+ transform_inv<I>(e, d, n, l);
+
+ // Distribute these bits
+ // to the coordinates.
+ set_location<P, I>(p, n, static_cast<size_t>(i), l);
+
+ // Update the entry point and direction.
+ update1<I>(l, t, w, n, e, d);
+ }
+}
+
+template <class P, class HC, class I>
+inline void
+coords_to_compact_index(const P* const p,
+ const size_t* const ms,
+ const size_t n,
+ HC& hc,
+ I&& scratch,
+ size_t M = 0,
+ size_t m = 0)
+{
+ // Get total precision and max precision if not supplied
+ if (M == 0 || m == 0) {
+ M = m = 0;
+ for (size_t i = 0; i < n; i++) {
+ assert(num_bits(p[i]) >= ms[i]);
+ if (ms[i] > m) {
+ m = ms[i];
+ }
+ M += ms[i];
+ }
+ }
+
+ const size_t mn = m * n;
+
+ assert(num_bits(hc) >= M);
+
+ // If we could avoid allocation altogether (ie: have a
+ // fixed buffer allocated on the stack) then this increases
+ // speed by a bit (4% when n=4, m=20)
+ size_t* const ds = new size_t[m];
+
+ if (mn > SmallBitVec::bits_per_rack) {
+ DynamicBitVec h(mn);
+ detail::coords_to_index<P, DynamicBitVec, I>(
+ p, m, n, h, std::move(scratch), ds);
+ compact_index<DynamicBitVec, HC>(ms, ds, n, m, h, hc);
+ } else {
+ SmallBitVec h(mn);
+ detail::coords_to_index<P, SmallBitVec, I>(
+ p, m, n, h, std::move(scratch), ds);
+ compact_index<SmallBitVec, HC>(ms, ds, n, m, h, hc);
+ }
+
+ delete[] ds;
+}
+
+template <class P, class HC, class I>
+inline void
+compact_index_to_coords(P* const p,
+ const size_t* ms,
+ const size_t n,
+ const HC& hc,
+ I&& scratch,
+ size_t M,
+ size_t m)
+{
+ I e{std::move(scratch)};
+ I l{e};
+ I t{e};
+ I w{e};
+ I r{e};
+ I mask{e};
+ I ptrn{e};
+
+ // Get total precision and max precision
+ // if not supplied
+ if (M == 0 || m == 0) {
+ M = m = 0;
+ for (size_t i = 0; i < n; i++) {
+ if (ms[i] > m) {
+ m = ms[i];
+ }
+ M += ms[i];
+ }
+ }
+
+ assert(num_bits(hc) >= M);
+ assert(num_bits(p[0]) >= m);
+
+ // Initialize
+ e.reset();
+ l.reset();
+ for (size_t j = 0; j < n; j++) {
+ reset_bits(p[j]);
+ }
+
+ // Work from MSB to LSB
+ size_t d = D0;
+
+ for (intptr_t i = static_cast<intptr_t>(m - 1); i >= 0; i--) {
+ // Get the mask and ptrn
+ size_t b = 0;
+ extract_mask<I>(ms, n, d, static_cast<size_t>(i), mask, b);
+ ptrn = e;
+ assert(ptrn.size() == n);
+ ptrn.rotr(d);
+
+ // Get the Hilbert index bits
+ M -= b;
+ r.reset(); // GetBits doesn't do this
+ get_bits<HC, I>(hc, b, M, r);
+
+ // w = GrayCodeRankInv(r)
+ // t = GrayCode(w)
+ gray_code_rank_inv<I>(mask, ptrn, r, n, b, t, w);
+
+ // Reverse the transform
+ // l = T^{-1}_{(e,d)}(t)
+ l = t;
+ transform_inv<I>(e, d, n, l);
+
+ // Distribute these bits
+ // to the coordinates.
+ set_location<P, I>(p, n, static_cast<size_t>(i), l);
+
+ // Update the entry point and direction.
+ update1<I>(l, t, w, n, e, d);
+ }
+}
+
+} // namespace detail
+
+template <class P, class H>
+inline void
+coords_to_index(const P* const p, const size_t m, const size_t n, H& h)
+{
+ assert(detail::num_bits(h) >= n * m);
+ assert(detail::num_bits(p[0]) >= m);
+
+ if (n <= SmallBitVec::bits_per_rack) {
+ // Intermediate variables will fit in fixed width
+ detail::coords_to_index<P, H, SmallBitVec>(p, m, n, h, SmallBitVec(n));
+ } else {
+ // Otherwise, they must be DynamicBitVecs
+ detail::coords_to_index<P, H, DynamicBitVec>(
+ p, m, n, h, DynamicBitVec(n));
+ }
+}
+
+template <class P, class H>
+inline void
+index_to_coords(P* const p, const size_t m, const size_t n, const H& h)
+{
+ assert(m > 0);
+ assert(n > 0);
+ assert(detail::num_bits(h) >= n * m);
+ assert(detail::num_bits(p[0]) >= m);
+
+ if (n <= SmallBitVec::bits_per_rack) {
+ // Intermediate variables will fit in fixed width
+ detail::index_to_coords<P, H, SmallBitVec>(p, m, n, h, SmallBitVec(n));
+ } else {
+ // Otherwise, they must be DynamicBitVecs
+ detail::index_to_coords<P, H, DynamicBitVec>(
+ p, m, n, h, DynamicBitVec(n));
+ }
+}
+
+template <class P, class HC>
+inline void
+coords_to_compact_index(const P* const p,
+ const size_t* const ms,
+ size_t n,
+ HC& hc,
+ const size_t M,
+ const size_t m)
+{
+ assert(hc.size() >= std::accumulate(ms, ms + n, size_t(0)));
+
+ if (n <= SmallBitVec::bits_per_rack) {
+ // Intermediate variables will fit in fixed width
+ detail::coords_to_compact_index<P, HC, SmallBitVec>(
+ p, ms, n, hc, SmallBitVec(n), M, m);
+ } else {
+ // Otherwise, they must be DynamicBitVecs
+ detail::coords_to_compact_index<P, HC, DynamicBitVec>(
+ p, ms, n, hc, DynamicBitVec(n), M, m);
+ }
+}
+
+template <class P, class HC>
+inline void
+compact_index_to_coords(P* const p,
+ const size_t* ms,
+ const size_t n,
+ const HC& hc,
+ const size_t M,
+ const size_t m)
+{
+ assert(hc.size() >= std::accumulate(ms, ms + n, size_t(0)));
+
+ if (n <= SmallBitVec::bits_per_rack) {
+ // Intermediate variables will fit in fixed width
+ SmallBitVec scratch(n);
+ detail::compact_index_to_coords<P, HC, SmallBitVec>(
+ p, ms, n, hc, std::move(scratch), M, m);
+ } else {
+ // Otherwise, they must be DynamicBitVecs
+ DynamicBitVec scratch(n);
+ detail::compact_index_to_coords<P, HC, DynamicBitVec>(
+ p, ms, n, hc, std::move(scratch), M, m);
+ }
+}
+
+} // namespace chilbert
+
+#endif
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