3 * Interface to several small and furry utilities needed within GiNaC but not
4 * of any interest to the user of the library. */
7 * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 #ifndef __GINAC_UTILS_H__
25 #define __GINAC_UTILS_H__
30 #include "assertion.h"
32 #ifndef NO_NAMESPACE_GINAC
34 #endif // ndef NO_NAMESPACE_GINAC
37 string ToString(const T & t)
40 ostrstream(buf,sizeof(buf)) << t << ends;
44 /** Exception thrown by classes which provide their own series expansion to
45 * signal that ordinary Taylor expansion is safe. */
48 // cygwin defines a macro log2, causing confusion
50 unsigned log2(unsigned n);
53 int compare_pointers(const void * a, const void * b);
55 /** Rotate lower 31 bits of unsigned value by one bit to the left
56 * (upper bits get cleared). */
57 inline unsigned rotate_left_31(unsigned n)
59 // clear highest bit and shift 1 bit to the left
60 n=(n & 0x7FFFFFFFU) << 1;
62 // overflow? clear highest bit and set lowest bit
63 if (n & 0x80000000U) {
64 n=(n & 0x7FFFFFFFU) | 0x00000001U;
66 GINAC_ASSERT(n<0x80000000U);
71 /** Golden ratio hash function. */
72 inline unsigned golden_ratio_hash(unsigned n)
74 // This function requires arithmetic with at least 64 significant bits
75 #if SIZEOF_LONG_DOUBLE > 8
76 // If "long double" is bigger than 64 bits, we assume that the mantissa
77 // has at least 64 bits. This is not guaranteed but it's a good guess.
78 const static long double golden_ratio = .618033988749894848204586834370;
79 long double m = golden_ratio * n;
80 return unsigned((m - int(m)) * 0x80000000);
81 #elif SIZEOF_LONG >= 8
82 // "long" has 64 bits, so we prefer it because it might be more efficient
84 unsigned long l = n * 0x4f1bbcddL;
85 return (l & 0x7fffffffU) ^ (l >> 32);
86 #elif SIZEOF_LONG_LONG >= 8
87 // This requires ´long long´ (or an equivalent 64 bit type)---which is,
88 // unfortunately, not ANSI-compliant:
89 unsigned long long l = n * 0x4f1bbcddLL;
90 return (l & 0x7fffffffU) ^ (l >> 32);
92 #error "No 64 bit data type. You lose."
96 // modified from stl_algo.h: always do com(*first1,*first2) instead of comp(*first2,*first1)
97 template <class InputIterator1, class InputIterator2, class OutputIterator,
99 OutputIterator mymerge(InputIterator1 first1, InputIterator1 last1,
100 InputIterator2 first2, InputIterator2 last2,
101 OutputIterator result, Compare comp) {
102 while (first1 != last1 && first2 != last2) {
103 if (comp(*first1, *first2)) {
113 return copy(first2, last2, copy(first1, last1, result));
116 // like merge(), but three lists with *last2<*first3
117 template <class InputIterator1, class InputIterator2, class InputIterator3,
118 class OutputIterator, class Compare>
119 OutputIterator mymerge3(InputIterator1 first1, InputIterator1 last1,
120 InputIterator2 first2, InputIterator2 last2,
121 InputIterator3 first3, InputIterator3 last3,
122 OutputIterator result, Compare comp) {
123 while (first1 != last1 && first2 != last2) {
124 if (comp(*first1, *first2)) {
136 // list1 empty, copy rest of list2, then list3
137 return copy(first3, last3, copy(first2, last2, result));
139 // list2 empty, merge rest of list1 with list3
140 return mymerge(first1,last1,first3,last3,result,comp);
144 // Compute the sign of a permutation of a vector of things.
145 template <typename T>
146 int permutation_sign(vector<T> s)
151 for (typename vector<T>::iterator i=s.begin(); i!=s.end()-1; ++i) {
152 for (typename vector<T>::iterator j=i+1; j!=s.end(); ++j) {
164 // Collection of `construct on first use' wrappers for safely avoiding
165 // internal object replication without running into the `static
166 // initialization order fiasco'. This chest of numbers helps speed up
167 // the library but should not be used outside it since it is
168 // potentially confusing.
173 const numeric & _num_120(void); // -120
174 const ex & _ex_120(void);
175 const numeric & _num_60(void); // -60
176 const ex & _ex_60(void);
177 const numeric & _num_48(void); // -48
178 const ex & _ex_48(void);
179 const numeric & _num_30(void); // -30
180 const ex & _ex_30(void);
181 const numeric & _num_25(void); // -25
182 const ex & _ex_25(void);
183 const numeric & _num_24(void); // -24
184 const ex & _ex_24(void);
185 const numeric & _num_20(void); // -20
186 const ex & _ex_20(void);
187 const numeric & _num_18(void); // -18
188 const ex & _ex_18(void);
189 const numeric & _num_15(void); // -15
190 const ex & _ex_15(void);
191 const numeric & _num_12(void); // -12
192 const ex & _ex_12(void);
193 const numeric & _num_11(void); // -11
194 const ex & _ex_11(void);
195 const numeric & _num_10(void); // -10
196 const ex & _ex_10(void);
197 const numeric & _num_9(void); // -9
198 const ex & _ex_9(void);
199 const numeric & _num_8(void); // -8
200 const ex & _ex_8(void);
201 const numeric & _num_7(void); // -7
202 const ex & _ex_7(void);
203 const numeric & _num_6(void); // -6
204 const ex & _ex_6(void);
205 const numeric & _num_5(void); // -5
206 const ex & _ex_5(void);
207 const numeric & _num_4(void); // -4
208 const ex & _ex_4(void);
209 const numeric & _num_3(void); // -3
210 const ex & _ex_3(void);
211 const numeric & _num_2(void); // -2
212 const ex & _ex_2(void);
213 const numeric & _num_1(void); // -1
214 const ex & _ex_1(void);
215 const numeric & _num_1_2(void); // -1/2
216 const ex & _ex_1_2(void);
217 const numeric & _num_1_3(void); // -1/3
218 const ex & _ex_1_3(void);
219 const numeric & _num_1_4(void); // -1/4
220 const ex & _ex_1_4(void);
221 const numeric & _num0(void); // 0
222 const ex & _ex0(void);
223 const numeric & _num1_4(void); // 1/4
224 const ex & _ex1_4(void);
225 const numeric & _num1_3(void); // 1/3
226 const ex & _ex1_3(void);
227 const numeric & _num1_2(void); // 1/2
228 const ex & _ex1_2(void);
229 const numeric & _num1(void); // 1
230 const ex & _ex1(void);
231 const numeric & _num2(void); // 2
232 const ex & _ex2(void);
233 const numeric & _num3(void); // 3
234 const ex & _ex3(void);
235 const numeric & _num4(void); // 4
236 const ex & _ex4(void);
237 const numeric & _num5(void); // 5
238 const ex & _ex5(void);
239 const numeric & _num6(void); // 6
240 const ex & _ex6(void);
241 const numeric & _num7(void); // 7
242 const ex & _ex7(void);
243 const numeric & _num8(void); // 8
244 const ex & _ex8(void);
245 const numeric & _num9(void); // 9
246 const ex & _ex9(void);
247 const numeric & _num10(void); // 10
248 const ex & _ex10(void);
249 const numeric & _num11(void); // 11
250 const ex & _ex11(void);
251 const numeric & _num12(void); // 12
252 const ex & _ex12(void);
253 const numeric & _num15(void); // 15
254 const ex & _ex15(void);
255 const numeric & _num18(void); // 18
256 const ex & _ex18(void);
257 const numeric & _num20(void); // 20
258 const ex & _ex20(void);
259 const numeric & _num24(void); // 24
260 const ex & _ex24(void);
261 const numeric & _num25(void); // 25
262 const ex & _ex25(void);
263 const numeric & _num30(void); // 30
264 const ex & _ex30(void);
265 const numeric & _num48(void); // 48
266 const ex & _ex48(void);
267 const numeric & _num60(void); // 60
268 const ex & _ex60(void);
269 const numeric & _num120(void); // 120
270 const ex & _ex120(void);
272 #ifndef NO_NAMESPACE_GINAC
274 #endif // ndef NO_NAMESPACE_GINAC
276 #endif // ndef __GINAC_UTILS_H__