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 unsigned log2(unsigned n);
50 int compare_pointers(const void * a, const void * b);
52 /** Rotate lower 31 bits of unsigned value by one bit to the left
53 * (upper bits get cleared). */
54 inline unsigned rotate_left_31(unsigned n)
56 // clear highest bit and shift 1 bit to the left
57 n=(n & 0x7FFFFFFFU) << 1;
59 // overflow? clear highest bit and set lowest bit
60 if (n & 0x80000000U) {
61 n=(n & 0x7FFFFFFFU) | 0x00000001U;
63 GINAC_ASSERT(n<0x80000000U);
68 /** Golden ratio hash function. */
69 inline unsigned golden_ratio_hash(unsigned n)
71 // This function requires arithmetic with at least 64 significant bits
72 #if SIZEOF_LONG_DOUBLE > 8
73 // If "long double" is bigger than 64 bits, we assume that the mantissa
74 // has at least 64 bits. This is not guaranteed but it's a good guess.
75 const static long double golden_ratio = .618033988749894848204586834370;
76 long double m = golden_ratio * n;
77 return unsigned((m - int(m)) * 0x80000000);
78 #elif SIZEOF_LONG >= 8
79 // "long" has 64 bits, so we prefer it because it might be more efficient
81 unsigned long l = n * 0x4f1bbcddL;
82 return (l & 0x7fffffffU) ^ (l >> 32);
83 #elif SIZEOF_LONG_LONG >= 8
84 // This requires ´long long´ (or an equivalent 64 bit type)---which is,
85 // unfortunately, not ANSI-compliant:
86 unsigned long long l = n * 0x4f1bbcddLL;
87 return (l & 0x7fffffffU) ^ (l >> 32);
89 #error "No 64 bit data type. You lose."
93 // modified from stl_algo.h: always do com(*first1,*first2) instead of comp(*first2,*first1)
94 template <class InputIterator1, class InputIterator2, class OutputIterator,
96 OutputIterator mymerge(InputIterator1 first1, InputIterator1 last1,
97 InputIterator2 first2, InputIterator2 last2,
98 OutputIterator result, Compare comp) {
99 while (first1 != last1 && first2 != last2) {
100 if (comp(*first1, *first2)) {
110 return copy(first2, last2, copy(first1, last1, result));
113 // like merge(), but three lists with *last2<*first3
114 template <class InputIterator1, class InputIterator2, class InputIterator3,
115 class OutputIterator, class Compare>
116 OutputIterator mymerge3(InputIterator1 first1, InputIterator1 last1,
117 InputIterator2 first2, InputIterator2 last2,
118 InputIterator3 first3, InputIterator3 last3,
119 OutputIterator result, Compare comp) {
120 while (first1 != last1 && first2 != last2) {
121 if (comp(*first1, *first2)) {
133 // list1 empty, copy rest of list2, then list3
134 return copy(first3, last3, copy(first2, last2, result));
136 // list2 empty, merge rest of list1 with list3
137 return mymerge(first1,last1,first3,last3,result,comp);
141 // Compute the sign of a permutation of a vector of things.
142 template <typename T>
143 int permutation_sign(vector<T> s)
148 for (typename vector<T>::iterator i=s.begin(); i!=s.end()-1; ++i) {
149 for (typename vector<T>::iterator j=i+1; j!=s.end(); ++j) {
161 // Collection of `construct on first use' wrappers for safely avoiding
162 // internal object replication without running into the `static
163 // initialization order fiasco'. This chest of numbers helps speed up
164 // the library but should not be used outside it since it is
165 // potentially confusing.
170 const numeric & _num_120(void); // -120
171 const ex & _ex_120(void);
172 const numeric & _num_60(void); // -60
173 const ex & _ex_60(void);
174 const numeric & _num_30(void); // -30
175 const ex & _ex_30(void);
176 const numeric & _num_25(void); // -25
177 const ex & _ex_25(void);
178 const numeric & _num_24(void); // -24
179 const ex & _ex_24(void);
180 const numeric & _num_20(void); // -20
181 const ex & _ex_20(void);
182 const numeric & _num_18(void); // -18
183 const ex & _ex_18(void);
184 const numeric & _num_15(void); // -15
185 const ex & _ex_15(void);
186 const numeric & _num_12(void); // -12
187 const ex & _ex_12(void);
188 const numeric & _num_11(void); // -11
189 const ex & _ex_11(void);
190 const numeric & _num_10(void); // -10
191 const ex & _ex_10(void);
192 const numeric & _num_9(void); // -9
193 const ex & _ex_9(void);
194 const numeric & _num_8(void); // -8
195 const ex & _ex_8(void);
196 const numeric & _num_7(void); // -7
197 const ex & _ex_7(void);
198 const numeric & _num_6(void); // -6
199 const ex & _ex_6(void);
200 const numeric & _num_5(void); // -5
201 const ex & _ex_5(void);
202 const numeric & _num_4(void); // -4
203 const ex & _ex_4(void);
204 const numeric & _num_3(void); // -3
205 const ex & _ex_3(void);
206 const numeric & _num_2(void); // -2
207 const ex & _ex_2(void);
208 const numeric & _num_1(void); // -1
209 const ex & _ex_1(void);
210 const numeric & _num_1_2(void); // -1/2
211 const ex & _ex_1_2(void);
212 const numeric & _num_1_3(void); // -1/3
213 const ex & _ex_1_3(void);
214 const numeric & _num_1_4(void); // -1/4
215 const ex & _ex_1_4(void);
216 const numeric & _num0(void); // 0
217 const ex & _ex0(void);
218 const numeric & _num1_4(void); // 1/4
219 const ex & _ex1_4(void);
220 const numeric & _num1_3(void); // 1/3
221 const ex & _ex1_3(void);
222 const numeric & _num1_2(void); // 1/2
223 const ex & _ex1_2(void);
224 const numeric & _num1(void); // 1
225 const ex & _ex1(void);
226 const numeric & _num2(void); // 2
227 const ex & _ex2(void);
228 const numeric & _num3(void); // 3
229 const ex & _ex3(void);
230 const numeric & _num4(void); // 4
231 const ex & _ex4(void);
232 const numeric & _num5(void); // 5
233 const ex & _ex5(void);
234 const numeric & _num6(void); // 6
235 const ex & _ex6(void);
236 const numeric & _num7(void); // 7
237 const ex & _ex7(void);
238 const numeric & _num8(void); // 8
239 const ex & _ex8(void);
240 const numeric & _num9(void); // 9
241 const ex & _ex9(void);
242 const numeric & _num10(void); // 10
243 const ex & _ex10(void);
244 const numeric & _num11(void); // 11
245 const ex & _ex11(void);
246 const numeric & _num12(void); // 12
247 const ex & _ex12(void);
248 const numeric & _num15(void); // 15
249 const ex & _ex15(void);
250 const numeric & _num18(void); // 18
251 const ex & _ex18(void);
252 const numeric & _num20(void); // 20
253 const ex & _ex20(void);
254 const numeric & _num24(void); // 24
255 const ex & _ex24(void);
256 const numeric & _num25(void); // 25
257 const ex & _ex25(void);
258 const numeric & _num30(void); // 30
259 const ex & _ex30(void);
260 const numeric & _num60(void); // 60
261 const ex & _ex60(void);
262 const numeric & _num120(void); // 120
263 const ex & _ex120(void);
265 #ifndef NO_NAMESPACE_GINAC
267 #endif // ndef NO_NAMESPACE_GINAC
269 #endif // ndef __GINAC_UTILS_H__