utils.h

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/*
 *  GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany
 *
 *  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, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#ifndef GINAC_UTILS_H
#define GINAC_UTILS_H
 
#include "assertion.h"
 
#include <functional>
#include <cstdint> // for uintptr_t
#include <string>
 
namespace GiNaC {
 
class dunno {};
 
// some compilers (e.g. cygwin) define a macro log2, causing confusion
#ifdef log2
#undef log2
#endif
 
unsigned log2(unsigned n);
 
inline unsigned rotate_left(unsigned n)
{
    return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
}
 
template <class T>
inline int compare_pointers(const T * a, const T * b)
{
    // '<' is not defined for pointers that don't point to the same array,
    // but std::less is.
    if (std::less<const T *>()(a, b))
        return -1;
    else if (std::less<const T *>()(b, a))
        return 1;
    return 0;
}
 
inline unsigned golden_ratio_hash(uintptr_t n)
{
    return n * UINT64_C(0x4f1bbcdd);
}
 
/* Compute the sign of a permutation of a container, with and without an
   explicitly supplied comparison function. If the sign returned is 1 or -1,
   the container is sorted after the operation. */
template <class It>
int permutation_sign(It first, It last)
{
    using std::swap;
    if (first == last)
        return 0;
    --last;
    if (first == last)
        return 0;
    It flag = first;
    int sign = 1;
 
    do {
        It i = last, other = last;
        --other;
        bool swapped = false;
        while (i != first) {
            if (*i < *other) {
                swap(*other, *i);
                flag = other;
                swapped = true;
                sign = -sign;
            } else if (!(*other < *i))
                return 0;
            --i;
            if (i != first)
                --other;
        }
        if (!swapped)
            return sign;
        ++flag;
        if (flag == last)
            return sign;
        first = flag;
        i = first; other = first;
        ++other;
        swapped = false;
        while (i != last) {
            if (*other < *i) {
                swap(*i, *other);
                flag = other;
                swapped = true;
                sign = -sign;
            } else if (!(*i < *other))
                return 0;
            ++i;
            if (i != last)
                ++other;
        }
        if (!swapped)
            return sign;
        last = flag;
        --last;
    } while (first != last);
 
    return sign;
}
 
template <class It, class Cmp, class Swap>
int permutation_sign(It first, It last, Cmp comp, Swap swapit)
{
    if (first == last)
        return 0;
    --last;
    if (first == last)
        return 0;
    It flag = first;
    int sign = 1;
 
    do {
        It i = last, other = last;
        --other;
        bool swapped = false;
        while (i != first) {
            if (comp(*i, *other)) {
                swapit(*other, *i);
                flag = other;
                swapped = true;
                sign = -sign;
            } else if (!comp(*other, *i))
                return 0;
            --i;
            if (i != first)
                --other;
        }
        if (!swapped)
            return sign;
        ++flag;
        if (flag == last)
            return sign;
        first = flag;
        i = first; other = first;
        ++other;
        swapped = false;
        while (i != last) {
            if (comp(*other, *i)) {
                swapit(*i, *other);
                flag = other;
                swapped = true;
                sign = -sign;
            } else if (!comp(*i, *other))
                return 0;
            ++i; 
            if (i != last)
                ++other;
        }
        if (!swapped)
            return sign;
        last = flag;
        --last;
    } while (first != last);
 
    return sign;
}
 
/* Implementation of shaker sort, only compares adjacent elements. */
template <class It, class Cmp, class Swap>
void shaker_sort(It first, It last, Cmp comp, Swap swapit)
{
    if (first == last)
        return;
    --last;
    if (first == last)
        return;
    It flag = first;
 
    do {
        It i = last, other = last;
        --other;
        bool swapped = false;
        while (i != first) {
            if (comp(*i, *other)) {
                swapit(*other, *i);
                flag = other;
                swapped = true;
            }
            --i;
            if (i != first)
                --other;
        }
        if (!swapped)
            return;
        ++flag;
        if (flag == last)
            return;
        first = flag;
        i = first; other = first;
        ++other;
        swapped = false;
        while (i != last) {
            if (comp(*other, *i)) {
                swapit(*i, *other);
                flag = other;
                swapped = true;
            }
            ++i;
            if (i != last)
                ++other;
        }
        if (!swapped)
            return;
        last = flag;
        --last;
    } while (first != last);
}
 
/* In-place cyclic permutation of a container (no copying, only swapping). */
template <class It, class Swap>
void cyclic_permutation(It first, It last, It new_first, Swap swapit)
{
    unsigned num = last - first;
again:
    if (first == new_first || num < 2)
        return;
 
    unsigned num1 = new_first - first, num2 = last - new_first;
    if (num1 >= num2) {
        It a = first, b = new_first;
        while (b != last) {
            swapit(*a, *b);
            ++a; ++b;
        }
        if (num1 > num2) {
            first += num2;
            num = num1;
            goto again;
        }
    } else {
        It a = new_first, b = last;
        do {
            --a; --b;
            swapit(*a, *b);
        } while (a != first);
        last -= num1;
        num = num2;
        goto again;
    }
}
 
class basic_partition_generator {
protected:
    // Partitions n into m parts, not including zero parts.
    // (Cf. OEIS sequence A008284; implementation adapted from Jörg Arndt's
    // FXT library)
    struct mpartition2
    {
        // partition: x[1] + x[2] + ... + x[m] = n and sentinel x[0] == 0
        std::vector<unsigned> x;
        unsigned n;   // n>0
        unsigned m;   // 0<m<=n
        mpartition2(unsigned n_, unsigned m_)
          : x(m_+1), n(n_), m(m_)
        {
            for (unsigned k=1; k<m; ++k)
                x[k] = 1;
            x[m] = n - m + 1;
        }
        bool next_partition()
        {
            unsigned u = x[m];  // last element
            unsigned k = m;
            unsigned s = u;
            while (--k) {
                s += x[k];
                if (x[k] + 2 <= u)
                    break;
            }
            if (k==0)
                return false;  // current is last
            unsigned f = x[k] + 1;
            while (k < m) {
                x[k] = f;
                s -= f;
                ++k;
            }
            x[m] = s;
            return true;
        }
    };
    mpartition2 mpgen;
    basic_partition_generator(unsigned n_, unsigned m_)
      : mpgen(n_, m_)
    { }
};
 
class partition_with_zero_parts_generator : public basic_partition_generator {
private:
    unsigned m;  // number of parts 0<m
    mutable std::vector<unsigned> partition;  // current partition
    mutable bool current_updated;  // whether partition vector has been updated
public:
    partition_with_zero_parts_generator(unsigned n_, unsigned m_)
      : basic_partition_generator(n_, 1), m(m_), partition(m_), current_updated(false)
    { }
    // returns current partition in non-decreasing order, padded with zeros
    const std::vector<unsigned>& get() const
    {
        if (!current_updated) {
            for (unsigned i = 0; i < m - mpgen.m; ++i)
                partition[i] = 0;  // pad with zeros
 
            for (unsigned i = m - mpgen.m; i < m; ++i)
                partition[i] = mpgen.x[i - m + mpgen.m + 1];
 
            current_updated = true;
        }
        return partition;
    }
    bool next()
    {
        current_updated = false;
        if (!mpgen.next_partition()) {
            if (mpgen.m == m || mpgen.m == mpgen.n)
                return false;  // current is last
            // increment number of parts
            mpgen = mpartition2(mpgen.n, mpgen.m + 1);
        }
        return true;
    }
};
 
class partition_generator : public basic_partition_generator {
private:
    mutable std::vector<unsigned> partition;  // current partition
    mutable bool current_updated;  // whether partition vector has been updated
public:
    partition_generator(unsigned n_, unsigned m_)
      : basic_partition_generator(n_, m_), partition(m_), current_updated(false)
    { }
    // returns current partition in non-decreasing order, padded with zeros
    const std::vector<unsigned>& get() const
    {
        if (!current_updated) {
            for (unsigned i = 0; i < mpgen.m; ++i)
                partition[i] = mpgen.x[i + 1];
 
            current_updated = true;
        }
        return partition;
    }
    bool next()
    {
        current_updated = false;
        return mpgen.next_partition();
    }
};
 
class composition_generator {
private:
    // Generates all distinct permutations of a multiset.
    // (Based on Aaron Williams' algorithm 1 from "Loopless Generation of
    // Multiset Permutations using a Constant Number of Variables by Prefix
    // Shifts." <https://dl.acm.org/doi/pdf/10.5555/1496770.1496877>)
    struct coolmulti {
        // element of singly linked list
        struct element {
            unsigned value;
            element* next;
            element(unsigned val, element* n)
              : value(val), next(n) {}
            ~element()
            {   // recurses down to the end of the singly linked list
                delete next;
            }
        };
        element *head, *i, *after_i;
        // NB: Partition must be sorted in non-decreasing order.
        explicit coolmulti(const std::vector<unsigned>& partition)
          : head(nullptr), i(nullptr), after_i(nullptr)
        {
            for (unsigned n = 0; n < partition.size(); ++n) {
                head = new element(partition[n], head);
                if (n <= 1)
                    i = head;
            }
            after_i = i->next;
        }
        ~coolmulti()
        {   // deletes singly linked list
            delete head;
        }
        void next_permutation()
        {
            element *before_k;
            if (after_i->next != nullptr && i->value >= after_i->next->value)
                before_k = after_i;
            else
                before_k = i;
            element *k = before_k->next;
            before_k->next = k->next;
            k->next = head;
            if (k->value < head->value)
                i = k;
            after_i = i->next;
            head = k;
        }
        bool finished() const
        {
            return after_i->next == nullptr && after_i->value >= head->value;
        }
    } cmgen;
    bool atend;  // needed for simplifying iteration over permutations
    bool trivial;  // likewise, true if all elements are equal
    mutable std::vector<unsigned> composition;  // current compositions
    mutable bool current_updated;  // whether composition vector has been updated
public:
    explicit composition_generator(const std::vector<unsigned>& partition)
      : cmgen(partition), atend(false), trivial(true), composition(partition.size()), current_updated(false)
    {
        for (unsigned i=1; i<partition.size(); ++i)
            trivial = trivial && (partition[0] == partition[i]);
    }
    const std::vector<unsigned>& get() const
    {
        if (!current_updated) {
            coolmulti::element* it = cmgen.head;
            size_t i = 0;
            while (it != nullptr) {
                composition[i] = it->value;
                it = it->next;
                ++i;
            }
            current_updated = true;
        }
        return composition;
    }
    bool next()
    {
        // This ugly contortion is needed because the original coolmulti
        // algorithm requires code duplication of the payload procedure,
        // one before the loop and one inside it.
        if (trivial || atend)
            return false;
        cmgen.next_permutation();
        current_updated = false;
        atend = cmgen.finished();
        return true;
    }
};
 
const numeric
multinomial_coefficient(const std::vector<unsigned> & p);
 
 
// Collection of `construct on first use' wrappers for safely avoiding
// internal object replication without running into the `static
// initialization order fiasco'.  This chest of numbers helps speed up
// the library but should not be used outside it since it is
// potentially confusing.
 
class ex;
 
extern const numeric *_num_120_p;
extern const ex _ex_120;
extern const numeric *_num_60_p;
extern const ex _ex_60;
extern const numeric *_num_48_p;
extern const ex _ex_48;
extern const numeric *_num_30_p;
extern const ex _ex_30;
extern const numeric *_num_25_p;
extern const ex _ex_25;
extern const numeric *_num_24_p;
extern const ex _ex_24;
extern const numeric *_num_20_p;
extern const ex _ex_20;
extern const numeric *_num_18_p;
extern const ex _ex_18;
extern const numeric *_num_15_p;
extern const ex _ex_15;
extern const numeric *_num_12_p;
extern const ex _ex_12;
extern const numeric *_num_11_p;
extern const ex _ex_11;
extern const numeric *_num_10_p;
extern const ex _ex_10;
extern const numeric *_num_9_p;
extern const ex _ex_9;
extern const numeric *_num_8_p;
extern const ex _ex_8;
extern const numeric *_num_7_p;
extern const ex _ex_7;
extern const numeric *_num_6_p;
extern const ex _ex_6;
extern const numeric *_num_5_p;
extern const ex _ex_5;
extern const numeric *_num_4_p;
extern const ex _ex_4;
extern const numeric *_num_3_p;
extern const ex _ex_3;
extern const numeric *_num_2_p;
extern const ex _ex_2;
extern const numeric *_num_1_p;
extern const ex _ex_1;
extern const numeric *_num_1_2_p;
extern const ex _ex_1_2;
extern const numeric *_num_1_3_p;
extern const ex _ex_1_3;
extern const numeric *_num_1_4_p;
extern const ex _ex_1_4;
extern const numeric *_num0_p;
extern const basic *_num0_bp;
extern const ex _ex0;
extern const numeric *_num1_4_p;
extern const ex _ex1_4;
extern const numeric *_num1_3_p;
extern const ex _ex1_3;
extern const numeric *_num1_2_p;
extern const ex _ex1_2;
extern const numeric *_num1_p;
extern const ex _ex1;
extern const numeric *_num2_p;
extern const ex _ex2;
extern const numeric *_num3_p;
extern const ex _ex3;
extern const numeric *_num4_p;
extern const ex _ex4;
extern const numeric *_num5_p;
extern const ex _ex5;
extern const numeric *_num6_p;
extern const ex _ex6;
extern const numeric *_num7_p;
extern const ex _ex7;
extern const numeric *_num8_p;
extern const ex _ex8;
extern const numeric *_num9_p;
extern const ex _ex9;
extern const numeric *_num10_p;
extern const ex _ex10;
extern const numeric *_num11_p;
extern const ex _ex11;
extern const numeric *_num12_p;
extern const ex _ex12;
extern const numeric *_num15_p;
extern const ex _ex15;
extern const numeric *_num18_p;
extern const ex _ex18;
extern const numeric *_num20_p;
extern const ex _ex20;
extern const numeric *_num24_p;
extern const ex _ex24;
extern const numeric *_num25_p;
extern const ex _ex25;
extern const numeric *_num30_p;
extern const ex _ex30;
extern const numeric *_num48_p;
extern const ex _ex48;
extern const numeric *_num60_p;
extern const ex _ex60;
extern const numeric *_num120_p;
extern const ex _ex120;
 
 
// Helper macros for class implementations (mostly useful for trivial classes)
 
#define DEFAULT_CTOR(classname) \
classname::classname() { setflag(status_flags::evaluated | status_flags::expanded); }
 
#define DEFAULT_COMPARE(classname) \
int classname::compare_same_type(const basic & other) const \
{ \
    /* by default, the objects are always identical */ \
    return 0; \
}
 
#define DEFAULT_PRINT(classname, text) \
void classname::do_print(const print_context & c, unsigned level) const \
{ \
    c.s << text; \
}
 
#define DEFAULT_PRINT_LATEX(classname, text, latex) \
DEFAULT_PRINT(classname, text) \
void classname::do_print_latex(const print_latex & c, unsigned level) const \
{ \
    c.s << latex; \
}
 
} // namespace GiNaC
 
#endif // ndef GINAC_UTILS_H