1 #ifndef LONGRAT_H
2 #define LONGRAT_H
3 /****************************************
4 * Computer Algebra System SINGULAR *
5 ****************************************/
6 /*
7 * ABSTRACT: computation with long rational numbers
8 */
9 #include "misc/auxiliary.h"
10
11 #include "coeffs/si_gmp.h"
12 #include "coeffs/coeffs.h"
13 #include "factory/si_log2.h"
14
15 number nlGetDenom(number &n, const coeffs r); /*for SAGE,, better: n_GetDenom */
16 number nlGetNumerator(number &n, const coeffs r); /*for SAGE, better: n_GetNumerator*/
17
18 /*-----------------------------------------------------------------*/
19 /**
20 ** 'SR_INT' is the type of those integers small enough to fit into 29 bits.
21 ** Therefor the value range of this small integers is: $-2^{28}...2^{28}-1$.
22 **
23 ** Small integers are represented by an immediate integer handle, containing
24 ** the value instead of pointing to it, which has the following form:
25 **
26 ** +-------+-------+-------+-------+- - - -+-------+-------+-------+
27 ** | guard | sign | bit | bit | | bit | tag | tag |
28 ** | bit | bit | 27 | 26 | | 0 | 0 | 1 |
29 ** +-------+-------+-------+-------+- - - -+-------+-------+-------+
30 **
31 ** Immediate integers handles carry the tag 'SR_INT', i.e. the last bit is 1.
32 ** This distuingishes immediate integers from other handles which point to
33 ** structures aligned on 4 byte boundaries and therefor have last bit zero.
34 ** (The second bit is reserved as tag to allow extensions of this scheme.)
35 ** Using immediates as pointers and dereferencing them gives address errors.
36 **
37 ** To aid overflow check the most significant two bits must always be equal,
38 ** that is to say that the sign bit of immediate integers has a guard bit.
39 **
40 ** The macros 'INT_TO_SR' and 'SR_TO_INT' should be used to convert between
41 ** a small integer value and its representation as immediate integer handle.
42 **
43 ** Large integers and rationals are represented by z and n
44 ** where n may be undefined (if s==3)
45 ** NULL represents only deleted values
46 */
47
48 struct snumber
49 {
50 mpz_t z; //< Zaehler
51 mpz_t n; //< Nenner
52 #if defined(LDEBUG)
53 int debug;
54 #endif
55
56 /**
57 * parameter s in number:
58 * 0 (or FALSE): not normalised rational
59 * 1 (or TRUE): normalised rational
60 * 3 : integer with n==NULL
61 **/
62 BOOLEAN s; //< integer parameter
63 };
64
65 #define SR_HDL(A) ((long)(A))
66
67 #define SR_INT 1L
68 #define INT_TO_SR(INT) ((number) (((long)INT << 2) + SR_INT))
69 #define SR_TO_INT(SR) (((long)SR) >> 2)
70
71 #define MP_SMALL 1
72
73 BOOLEAN nlInitChar(coeffs, void*);
74
75 /// only used by slimgb (tgb.cc)
nlQlogSize(number n,const coeffs r)76 static FORCE_INLINE int nlQlogSize (number n, const coeffs r)
77 {
78 assume( nCoeff_is_Q (r) );
79
80 if(SR_HDL(n)&SR_INT)
81 {
82 if (SR_HDL(n)==SR_INT) return 0;
83 long i = SR_TO_INT (n);
84 unsigned long v;
85 v = ABS(i);
86 return SI_LOG2_LONG(v) + 1;
87 }
88 //assume denominator is 0
89 number nn=(number) n;
90 return mpz_sizeinbase (nn->z, 2);
91 }
92
93
nlIsInteger(number q,const coeffs r)94 static FORCE_INLINE BOOLEAN nlIsInteger(number q, const coeffs r)
95 {
96 assume( nCoeff_is_Q (r) );
97 n_Test(q, r);
98
99 if (SR_HDL(q) & SR_INT)
100 return TRUE; // immediate int
101
102 return ( q->s == 3 );
103 }
104
105 void nlMPZ(mpz_t m, number &n, const coeffs r);
106 number nlModP(number q, const coeffs Q, const coeffs Zp);
107 void nlNormalize(number &x, const coeffs r);
108 void nlInpGcd(number &a, number b, const coeffs r);
109 void nlDelete(number *a, const coeffs r); /*for SAGE,, better: n_Delete */
110
111
112
113 /// create a rational i/j (implicitly) over Q
114 /// NOTE: make sure to use correct Q in debug mode
115 number nlInit2 (int i, int j, const coeffs r);
116
117 /// create a rational i/j (implicitly) over Q
118 /// NOTE: make sure to use correct Q in debug mode
119 number nlInit2gmp (mpz_t i, mpz_t j, const coeffs r);
120
121 #if 0 // substituted by nlMPZ
122 void nlGMP(number &i, mpz_t n, const coeffs r);
123 #endif
124 // for ring similiar to Q/Z (char 0 required):
125 number nlChineseRemainderSym(number *x, number *q,int rl, BOOLEAN sym, CFArray &inv_cache,const coeffs CF);
126
127
128 #endif
129
130
131