/** @file utils.h
*
- * Interface to several small and furry utilities.
- *
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * Interface to several small and furry utilities needed within GiNaC but not
+ * of any interest to the user of the library. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 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
#include <strstream>
#include <string>
#include "config.h"
+#include "assertion.h"
+
+#ifndef NO_NAMESPACE_GINAC
+namespace GiNaC {
+#endif // ndef NO_NAMESPACE_GINAC
template<class T>
-string ToString(T const & t)
+string ToString(const T & t)
{
char buf[256];
ostrstream(buf,sizeof(buf)) << t << ends;
return buf;
}
+/** Exception thrown by classes which provide their own series expansion to
+ * signal that ordinary Taylor expansion is safe. */
+class do_taylor {};
+
unsigned log2(unsigned n);
-int compare_pointers(void const * a, void const * b);
+int compare_pointers(const void * a, const void * b);
-#define DYNCONSTCAST(FINALTYPE,BASICTYPE,EXPRESSION) \
- dynamic_cast<FINALTYPE>(const_cast<BASICTYPE>(EXPRESSION))
+/** Rotate lower 31 bits of unsigned value by one bit to the left
+ * (upper bits get cleared). */
+inline unsigned rotate_left_31(unsigned n)
+{
+ // clear highest bit and shift 1 bit to the left
+ n=(n & 0x7FFFFFFFU) << 1;
+
+ // overflow? clear highest bit and set lowest bit
+ if (n & 0x80000000U) {
+ n=(n & 0x7FFFFFFFU) | 0x00000001U;
+ }
+ GINAC_ASSERT(n<0x80000000U);
+
+ return n;
+}
+
+/** Golden ratio hash function. */
+inline unsigned golden_ratio_hash(unsigned n)
+{
+ // This function requires arithmetic with at least 64 significant bits
+#if SIZEOF_LONG_DOUBLE > 8
+ // If "long double" is bigger than 64 bits, we assume that the mantissa
+ // has at least 64 bits. This is not guaranteed but it's a good guess.
+ const static long double golden_ratio = .618033988749894848204586834370;
+ long double m = golden_ratio * n;
+ return unsigned((m - int(m)) * 0x80000000);
+#elif SIZEOF_LONG >= 8
+ // "long" has 64 bits, so we prefer it because it might be more efficient
+ // than "long long"
+ unsigned long l = n * 0x4f1bbcddL;
+ return (l & 0x7fffffffU) ^ (l >> 32);
+#elif SIZEOF_LONG_LONG >= 8
+ // This requires ´long long´ (or an equivalent 64 bit type)---which is,
+ // unfortunately, not ANSI-compliant:
+ unsigned long long l = n * 0x4f1bbcddLL;
+ return (l & 0x7fffffffU) ^ (l >> 32);
+#else
+#error "No 64 bit data type. You lose."
+#endif
+}
// modified from stl_algo.h: always do com(*first1,*first2) instead of comp(*first2,*first1)
template <class InputIterator1, class InputIterator2, class OutputIterator,
OutputIterator mymerge(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp) {
- while (first1 != last1 && first2 != last2) {
- if (comp(*first1, *first2)) {
- *result = *first1;
- ++first1;
- }
- else {
- *result = *first2;
- ++first2;
+ while (first1 != last1 && first2 != last2) {
+ if (comp(*first1, *first2)) {
+ *result = *first1;
+ ++first1;
+ }
+ else {
+ *result = *first2;
+ ++first2;
+ }
+ ++result;
}
- ++result;
- }
- return copy(first2, last2, copy(first1, last1, result));
+ return copy(first2, last2, copy(first1, last1, result));
}
// like merge(), but three lists with *last2<*first3
InputIterator2 first2, InputIterator2 last2,
InputIterator3 first3, InputIterator3 last3,
OutputIterator result, Compare comp) {
- while (first1 != last1 && first2 != last2) {
- if (comp(*first1, *first2)) {
- *result = *first1;
- ++first1;
+ while (first1 != last1 && first2 != last2) {
+ if (comp(*first1, *first2)) {
+ *result = *first1;
+ ++first1;
+ }
+ else {
+ *result = *first2;
+ ++first2;
+ }
+ ++result;
+ }
+
+ if (first1==last1) {
+ // list1 empty, copy rest of list2, then list3
+ return copy(first3, last3, copy(first2, last2, result));
+ } else {
+ // list2 empty, merge rest of list1 with list3
+ return mymerge(first1,last1,first3,last3,result,comp);
}
- else {
- *result = *first2;
- ++first2;
+}
+
+// Compute the sign of a permutation of a vector of things.
+template <typename T>
+int permutation_sign(vector<T> s)
+{
+ if (s.size() < 2)
+ return 0;
+ int sigma = 1;
+ for (typename vector<T>::iterator i=s.begin(); i!=s.end()-1; ++i) {
+ for (typename vector<T>::iterator j=i+1; j!=s.end(); ++j) {
+ if (*i == *j)
+ return 0;
+ if (*i > *j) {
+ iter_swap(i,j);
+ sigma = -sigma;
+ }
+ }
}
- ++result;
- }
-
- if (first1==last1) {
- // list1 empty, copy rest of list2, then list3
- return copy(first3, last3, copy(first2, last2, result));
- } else {
- // list2 empty, merge rest of list1 with list3
- return mymerge(first1,last1,first3,last3,result,comp);
- }
+ return sigma;
}
+// 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 numeric;
+class ex;
+
+const numeric & _num_120(void); // -120
+const ex & _ex_120(void);
+const numeric & _num_60(void); // -60
+const ex & _ex_60(void);
+const numeric & _num_30(void); // -30
+const ex & _ex_30(void);
+const numeric & _num_25(void); // -25
+const ex & _ex_25(void);
+const numeric & _num_24(void); // -24
+const ex & _ex_24(void);
+const numeric & _num_20(void); // -20
+const ex & _ex_20(void);
+const numeric & _num_18(void); // -18
+const ex & _ex_18(void);
+const numeric & _num_15(void); // -15
+const ex & _ex_15(void);
+const numeric & _num_12(void); // -12
+const ex & _ex_12(void);
+const numeric & _num_11(void); // -11
+const ex & _ex_11(void);
+const numeric & _num_10(void); // -10
+const ex & _ex_10(void);
+const numeric & _num_9(void); // -9
+const ex & _ex_9(void);
+const numeric & _num_8(void); // -8
+const ex & _ex_8(void);
+const numeric & _num_7(void); // -7
+const ex & _ex_7(void);
+const numeric & _num_6(void); // -6
+const ex & _ex_6(void);
+const numeric & _num_5(void); // -5
+const ex & _ex_5(void);
+const numeric & _num_4(void); // -4
+const ex & _ex_4(void);
+const numeric & _num_3(void); // -3
+const ex & _ex_3(void);
+const numeric & _num_2(void); // -2
+const ex & _ex_2(void);
+const numeric & _num_1(void); // -1
+const ex & _ex_1(void);
+const numeric & _num_1_2(void); // -1/2
+const ex & _ex_1_2(void);
+const numeric & _num_1_3(void); // -1/3
+const ex & _ex_1_3(void);
+const numeric & _num_1_4(void); // -1/4
+const ex & _ex_1_4(void);
+const numeric & _num0(void); // 0
+const ex & _ex0(void);
+const numeric & _num1_4(void); // 1/4
+const ex & _ex1_4(void);
+const numeric & _num1_3(void); // 1/3
+const ex & _ex1_3(void);
+const numeric & _num1_2(void); // 1/2
+const ex & _ex1_2(void);
+const numeric & _num1(void); // 1
+const ex & _ex1(void);
+const numeric & _num2(void); // 2
+const ex & _ex2(void);
+const numeric & _num3(void); // 3
+const ex & _ex3(void);
+const numeric & _num4(void); // 4
+const ex & _ex4(void);
+const numeric & _num5(void); // 5
+const ex & _ex5(void);
+const numeric & _num6(void); // 6
+const ex & _ex6(void);
+const numeric & _num7(void); // 7
+const ex & _ex7(void);
+const numeric & _num8(void); // 8
+const ex & _ex8(void);
+const numeric & _num9(void); // 9
+const ex & _ex9(void);
+const numeric & _num10(void); // 10
+const ex & _ex10(void);
+const numeric & _num11(void); // 11
+const ex & _ex11(void);
+const numeric & _num12(void); // 12
+const ex & _ex12(void);
+const numeric & _num15(void); // 15
+const ex & _ex15(void);
+const numeric & _num18(void); // 18
+const ex & _ex18(void);
+const numeric & _num20(void); // 20
+const ex & _ex20(void);
+const numeric & _num24(void); // 24
+const ex & _ex24(void);
+const numeric & _num25(void); // 25
+const ex & _ex25(void);
+const numeric & _num30(void); // 30
+const ex & _ex30(void);
+const numeric & _num60(void); // 60
+const ex & _ex60(void);
+const numeric & _num120(void); // 120
+const ex & _ex120(void);
+
+#ifndef NO_NAMESPACE_GINAC
+} // namespace GiNaC
+#endif // ndef NO_NAMESPACE_GINAC
+
#endif // ndef __GINAC_UTILS_H__