/** @file utils.h
*
* Interface to several small and furry utilities needed within GiNaC but not
* of any interest to the user of the library. */
/*
* GiNaC Copyright (C) 1999-2007 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 "config.h"
#include <string>
#include <functional>
#include "assertion.h"
namespace GiNaC {
/** Exception class thrown by functions to signal unimplemented functionality
* so the expression may just be .hold() */
class dunno {};
// some compilers (e.g. cygwin) define a macro log2, causing confusion
#ifdef log2
#undef log2
#endif
unsigned log2(unsigned n);
/** Compare two pointers (just to establish some sort of canonical order).
* @return -1, 0, or 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;
}
/** Rotate bits of unsigned value by one bit to the left. */
inline unsigned rotate_left(unsigned n)
{
return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
}
/** Truncated multiplication with golden ratio, for computing hash values. */
inline unsigned golden_ratio_hash(unsigned n)
{
// This function works much better when fast arithmetic with at
// least 64 significant bits is available.
#if SIZEOF_LONG >= 8
// So 'long' has 64 bits. Excellent! We prefer it because it might be
// more efficient than 'long long'.
unsigned long l = n * 0x4f1bbcddUL;
return (unsigned)l;
#elif SIZEOF_LONG_LONG >= 8
// This requires 'long long' (or an equivalent 64 bit type)---which is,
// unfortunately, not ANSI-C++-compliant.
// (Yet C99 demands it, which is reason for hope.)
unsigned long long l = n * 0x4f1bbcddULL;
return (unsigned)l;
#else
// Without a type with 64 significant bits do the multiplication manually
// by splitting n up into the lower and upper two bytes.
const unsigned n0 = (n & 0x0000ffffU);
const unsigned n1 = (n & 0xffff0000U) >> 16;
return (n0 * 0x0000bcddU) + ((n1 * 0x0000bcddU + n0 * 0x00004f1bU) << 16);
#endif
}
/* 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)
{
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) {
std::iter_swap(other, i);
flag = other;
swapped = true;
sign = -sign;
} else if (!(*other < *i))
return 0;
--i; --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) {
std::iter_swap(i, other);
flag = other;
swapped = true;
sign = -sign;
} else if (!(*i < *other))
return 0;
++i; ++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; --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; ++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; --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; ++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;
}
}
// 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() : inherited(TINFO_##classname) { setflag(status_flags::evaluated | status_flags::expanded); }
#define DEFAULT_UNARCHIVE(classname) \
ex classname::unarchive(const archive_node &n, lst &sym_lst) \
{ \
return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
}
#define DEFAULT_ARCHIVING(classname) \
classname::classname(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) {} \
DEFAULT_UNARCHIVE(classname) \
void classname::archive(archive_node &n) const \
{ \
inherited::archive(n); \
}
#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__
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