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longrat.h
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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)
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 
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 
All the auxiliary stuff.
static int ABS(int v)
Definition: auxiliary.h:112
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FORCE_INLINE
Definition: auxiliary.h:329
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
Variable x
Definition: cfModGcd.cc:4082
CanonicalForm b
Definition: cfModGcd.cc:4103
Coefficient rings, fields and other domains suitable for Singular polynomials.
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:712
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:806
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
int j
Definition: facHensel.cc:110
STATIC_VAR jList * Q
Definition: janet.cc:30
void nlGMP(number &i, mpz_t n, const coeffs r)
Definition: longrat.cc:1619
number nlInit2(int i, int j, const coeffs r)
create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode
Definition: longrat.cc:2544
number nlInit2gmp(mpz_t i, mpz_t j, const coeffs r)
create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode
Definition: longrat.cc:2557
#define SR_INT
Definition: longrat.h:67
static FORCE_INLINE BOOLEAN nlIsInteger(number q, const coeffs r)
Definition: longrat.h:94
static FORCE_INLINE int nlQlogSize(number n, const coeffs r)
only used by slimgb (tgb.cc)
Definition: longrat.h:76
void nlMPZ(mpz_t m, number &n, const coeffs r)
Definition: longrat.cc:2819
number nlModP(number q, const coeffs Q, const coeffs Zp)
Definition: longrat.cc:1577
number nlChineseRemainderSym(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs CF)
Definition: longrat.cc:3095
number nlGetDenom(number &n, const coeffs r)
Definition: longrat.cc:1640
BOOLEAN nlInitChar(coeffs, void *)
Definition: longrat.cc:3475
mpz_t n
Definition: longrat.h:51
#define SR_HDL(A)
Definition: longrat.h:65
void nlDelete(number *a, const coeffs r)
Definition: longrat.cc:2666
number nlGetNumerator(number &n, const coeffs r)
Definition: longrat.cc:1669
#define SR_TO_INT(SR)
Definition: longrat.h:69
int debug
Definition: longrat.h:53
mpz_t z
Definition: longrat.h:50
BOOLEAN s
parameter s in number: 0 (or FALSE): not normalised rational 1 (or TRUE): normalised rational 3 : int...
Definition: longrat.h:62
void nlNormalize(number &x, const coeffs r)
Definition: longrat.cc:1486
void nlInpGcd(number &a, number b, const coeffs r)
Definition: longrat.cc:2933
'SR_INT' is the type of those integers small enough to fit into 29 bits.
Definition: longrat.h:49
#define assume(x)
Definition: mod2.h:387
The main handler for Singular numbers which are suitable for Singular polynomials.
static int SI_LOG2_LONG(long v)
Definition: si_log2.h:22