[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* |
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| 5 | * ABSTRACT: computation with long rational numbers (Hubert Grassmann) |
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| 6 | */ |
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[d663f2] | 7 | |
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[22a09d] | 8 | #include "config.h" |
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| 9 | #include <misc/auxiliary.h> |
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| 10 | |
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| 11 | #ifdef HAVE_FACTORY |
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| 12 | #include <factory/factory.h> |
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| 13 | #endif |
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[35aab3] | 14 | |
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[ea11dc] | 15 | #include <coeffs/longrat.h> |
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[246d15] | 16 | |
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[9eb0f9] | 17 | |
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[246d15] | 18 | // 64 bit version: |
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[3feb05] | 19 | #if SIZE_OF_LONG == 8 |
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[246d15] | 20 | #define MAX_NUM_SIZE 60 |
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[3feb05] | 21 | #define POW_2_28 (1L<<60) |
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[246d15] | 22 | #define LONG long |
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| 23 | #else |
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| 24 | #define MAX_NUM_SIZE 28 |
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| 25 | #define POW_2_28 (1L<<28) |
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| 26 | #define LONG int |
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| 27 | #endif |
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| 28 | |
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| 29 | static inline number nlShort3(number x) // assume x->s==3 |
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| 30 | { |
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| 31 | assume(x->s==3); |
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[cc3240c] | 32 | if (mpz_cmp_ui(x->z,(long)0)==0) |
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| 33 | { |
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| 34 | mpz_clear(x->z); |
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| 35 | FREE_RNUMBER(x); |
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| 36 | return INT_TO_SR(0); |
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| 37 | } |
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| 38 | if (mpz_size1(x->z)<=MP_SMALL) |
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[246d15] | 39 | { |
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| 40 | LONG ui=mpz_get_si(x->z); |
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| 41 | if ((((ui<<3)>>3)==ui) |
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| 42 | && (mpz_cmp_si(x->z,(long)ui)==0)) |
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| 43 | { |
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| 44 | mpz_clear(x->z); |
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[896561] | 45 | FREE_RNUMBER(x); |
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[246d15] | 46 | return INT_TO_SR(ui); |
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| 47 | } |
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| 48 | } |
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| 49 | return x; |
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| 50 | } |
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| 51 | |
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[35aab3] | 52 | #ifndef LONGRAT_CC |
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| 53 | #define LONGRAT_CC |
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| 54 | |
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| 55 | #include <string.h> |
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| 56 | #include <float.h> |
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[9eb0f9] | 57 | |
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[2d805a] | 58 | #include <coeffs/coeffs.h> |
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[31213a4] | 59 | #include <reporter/reporter.h> |
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| 60 | #include <omalloc/omalloc.h> |
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[9eb0f9] | 61 | |
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[2d805a] | 62 | #include <coeffs/numbers.h> |
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| 63 | #include <coeffs/modulop.h> |
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| 64 | #include <coeffs/shortfl.h> |
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| 65 | #include <coeffs/mpr_complex.h> |
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[35aab3] | 66 | |
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| 67 | #ifndef BYTES_PER_MP_LIMB |
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| 68 | #define BYTES_PER_MP_LIMB sizeof(mp_limb_t) |
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| 69 | #endif |
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| 70 | |
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[8181f5] | 71 | //#define SR_HDL(A) ((long)(A)) |
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[46f6af6] | 72 | /*#define SR_INT 1L*/ |
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[35aab3] | 73 | /*#define INT_TO_SR(INT) ((number) (((long)INT << 2) + SR_INT))*/ |
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| 74 | // #define SR_TO_INT(SR) (((long)SR) >> 2) |
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| 75 | |
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| 76 | #define MP_SMALL 1 |
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| 77 | //#define mpz_isNeg(A) (mpz_cmp_si(A,(long)0)<0) |
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| 78 | #define mpz_isNeg(A) ((A)->_mp_size<0) |
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| 79 | #define mpz_limb_size(A) ((A)->_mp_size) |
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| 80 | #define mpz_limb_d(A) ((A)->_mp_d) |
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| 81 | #define MPZ_DIV(A,B,C) mpz_tdiv_q((A),(B),(C)) |
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| 82 | #define MPZ_EXACTDIV(A,B,C) mpz_divexact((A),(B),(C)) |
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| 83 | |
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[73a9ffb] | 84 | /// Our Type! |
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| 85 | static const n_coeffType ID = n_Q; |
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[35aab3] | 86 | |
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[73a9ffb] | 87 | void _nlDelete_NoImm(number *a); |
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[fa31d2] | 88 | |
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[35aab3] | 89 | /*************************************************************** |
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| 90 | * |
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| 91 | * Routines which are never inlined by p_Numbers.h |
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| 92 | * |
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| 93 | *******************************************************************/ |
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| 94 | #ifndef P_NUMBERS_H |
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| 95 | |
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[246d15] | 96 | number nlShort3_noinline(number x) // assume x->s==3 |
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| 97 | { |
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| 98 | return nlShort3(x); |
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| 99 | } |
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| 100 | |
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[35aab3] | 101 | |
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[eb059c5] | 102 | number nlOne=INT_TO_SR(1); |
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[35aab3] | 103 | |
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| 104 | #if (__GNU_MP_VERSION*10+__GNU_MP_VERSION_MINOR < 31) |
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| 105 | void mpz_mul_si (mpz_ptr r, mpz_srcptr s, long int si) |
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| 106 | { |
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| 107 | if (si>=0) |
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| 108 | mpz_mul_ui(r,s,si); |
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| 109 | else |
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| 110 | { |
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| 111 | mpz_mul_ui(r,s,-si); |
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| 112 | mpz_neg(r,r); |
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| 113 | } |
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| 114 | } |
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| 115 | #endif |
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| 116 | |
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[fa31d2] | 117 | static number nlMapP(number from, const coeffs src, const coeffs dst) |
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[35aab3] | 118 | { |
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[fa31d2] | 119 | assume( getCoeffType(dst) == ID ); |
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| 120 | assume( getCoeffType(src) == n_Zp ); |
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[9bb5457] | 121 | |
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[35aab3] | 122 | number to; |
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[fa31d2] | 123 | to = nlInit(npInt(from,src), dst); |
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[35aab3] | 124 | return to; |
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| 125 | } |
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| 126 | |
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[fa31d2] | 127 | static number nlMapLongR(number from, const coeffs src, const coeffs dst); |
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| 128 | static number nlMapR(number from, const coeffs src, const coeffs dst); |
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[35aab3] | 129 | |
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[d663f2] | 130 | |
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[894f5b1] | 131 | #ifdef HAVE_RINGS |
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| 132 | /*2 |
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| 133 | * convert from a GMP integer |
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| 134 | */ |
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[9bb5457] | 135 | number nlMapGMP(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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[894f5b1] | 136 | { |
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[896561] | 137 | number z=ALLOC_RNUMBER(); |
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[894f5b1] | 138 | #if defined(LDEBUG) |
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| 139 | z->debug=123456; |
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| 140 | #endif |
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[a604c3] | 141 | mpz_init_set(z->z,(mpz_ptr) from); |
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[20704f] | 142 | //mpz_init_set_ui(&z->n,1); |
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[894f5b1] | 143 | z->s = 3; |
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[246d15] | 144 | z=nlShort3(z); |
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[894f5b1] | 145 | return z; |
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| 146 | } |
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| 147 | |
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| 148 | /*2 |
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| 149 | * convert from an machine long |
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| 150 | */ |
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[9bb5457] | 151 | number nlMapMachineInt(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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[894f5b1] | 152 | { |
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[896561] | 153 | number z=ALLOC_RNUMBER(); |
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[894f5b1] | 154 | #if defined(LDEBUG) |
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| 155 | z->debug=123456; |
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| 156 | #endif |
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[a604c3] | 157 | mpz_init_set_ui(z->z,(unsigned long) from); |
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[894f5b1] | 158 | z->s = 3; |
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[246d15] | 159 | z=nlShort3(z); |
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[894f5b1] | 160 | return z; |
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| 161 | } |
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| 162 | #endif |
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| 163 | |
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[35aab3] | 164 | |
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| 165 | #ifdef LDEBUG |
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[9bb5457] | 166 | BOOLEAN nlDBTest(number a, const char *f,const int l, const coeffs /*r*/) |
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[35aab3] | 167 | { |
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| 168 | if (a==NULL) |
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| 169 | { |
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| 170 | Print("!!longrat: NULL in %s:%d\n",f,l); |
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| 171 | return FALSE; |
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| 172 | } |
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| 173 | //if ((int)a==1) Print("!! 0x1 as number ? %s %d\n",f,l); |
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[7447d8] | 174 | if ((((long)a)&3L)==3L) |
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[35aab3] | 175 | { |
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| 176 | Print(" !!longrat:ptr(3) in %s:%d\n",f,l); |
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| 177 | return FALSE; |
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| 178 | } |
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[7447d8] | 179 | if ((((long)a)&3L)==1L) |
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[35aab3] | 180 | { |
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[246d15] | 181 | if (((((LONG)(long)a)<<1)>>1)!=((LONG)(long)a)) |
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[35aab3] | 182 | { |
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[2132395] | 183 | Print(" !!longrat:arith:%lx in %s:%d\n",(long)a, f,l); |
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[35aab3] | 184 | return FALSE; |
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| 185 | } |
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| 186 | return TRUE; |
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| 187 | } |
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[4a2260e] | 188 | /* TODO: If next line is active, then computations in algebraic field |
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| 189 | extensions over Q will throw a lot of assume violations although |
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| 190 | everything is computed correctly and no seg fault appears. |
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| 191 | Maybe the test is not appropriate in this case. */ |
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[d12f186] | 192 | omCheckIf(omCheckAddrSize(a,sizeof(*a)), return FALSE); |
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[35aab3] | 193 | if (a->debug!=123456) |
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| 194 | { |
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| 195 | Print("!!longrat:debug:%d in %s:%d\n",a->debug,f,l); |
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| 196 | a->debug=123456; |
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| 197 | return FALSE; |
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| 198 | } |
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| 199 | if ((a->s<0)||(a->s>4)) |
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| 200 | { |
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| 201 | Print("!!longrat:s=%d in %s:%d\n",a->s,f,l); |
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| 202 | return FALSE; |
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| 203 | } |
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[c28ecf] | 204 | /* TODO: If next line is active, then computations in algebraic field |
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| 205 | extensions over Q will throw a lot of assume violations although |
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| 206 | everything is computed correctly and no seg fault appears. |
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| 207 | Maybe the test is not appropriate in this case. */ |
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[896561] | 208 | //omCheckAddrSize(a->z[0]._mp_d,a->z[0]._mp_alloc*BYTES_PER_MP_LIMB); |
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[a604c3] | 209 | if (a->z[0]._mp_alloc==0) |
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[2132395] | 210 | Print("!!longrat:z->alloc=0 in %s:%d\n",f,l); |
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[35aab3] | 211 | |
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| 212 | if (a->s<2) |
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| 213 | { |
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[c28ecf] | 214 | /* TODO: If next line is active, then computations in algebraic field |
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| 215 | extensions over Q will throw a lot of assume violations although |
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| 216 | everything is computed correctly and no seg fault appears. |
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| 217 | Maybe the test is not appropriate in this case. */ |
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[896561] | 218 | //omCheckIf(omCheckAddrSize(a->n[0]._mp_d,a->n[0]._mp_alloc*BYTES_PER_MP_LIMB), return FALSE); |
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[a604c3] | 219 | if (a->z[0]._mp_alloc==0) |
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[2132395] | 220 | Print("!!longrat:n->alloc=0 in %s:%d\n",f,l); |
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[a604c3] | 221 | if ((mpz_size1(a->n) ==1) && (mpz_cmp_si(a->n,(long)1)==0)) |
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[35aab3] | 222 | { |
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| 223 | Print("!!longrat:integer as rational in %s:%d\n",f,l); |
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[8fd3bd5] | 224 | mpz_clear(a->n); a->s=3; |
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[35aab3] | 225 | return FALSE; |
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| 226 | } |
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[a604c3] | 227 | else if (mpz_isNeg(a->n)) |
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[35aab3] | 228 | { |
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| 229 | Print("!!longrat:div. by negative in %s:%d\n",f,l); |
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[a604c3] | 230 | mpz_neg(a->z,a->z); |
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| 231 | mpz_neg(a->n,a->n); |
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[35aab3] | 232 | return FALSE; |
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| 233 | } |
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| 234 | return TRUE; |
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| 235 | } |
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[9257fe] | 236 | //if (a->s==2) |
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| 237 | //{ |
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| 238 | // Print("!!longrat:s=2 in %s:%d\n",f,l); |
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| 239 | // return FALSE; |
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| 240 | //} |
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[a604c3] | 241 | if (mpz_size1(a->z)>MP_SMALL) return TRUE; |
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[246d15] | 242 | LONG ui=(int)mpz_get_si(a->z); |
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[35aab3] | 243 | if ((((ui<<3)>>3)==ui) |
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[a604c3] | 244 | && (mpz_cmp_si(a->z,(long)ui)==0)) |
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[35aab3] | 245 | { |
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| 246 | Print("!!longrat:im int %d in %s:%d\n",ui,f,l); |
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| 247 | f=NULL; |
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| 248 | return FALSE; |
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| 249 | } |
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| 250 | return TRUE; |
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| 251 | } |
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| 252 | #endif |
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| 253 | |
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[a934fc8] | 254 | #ifdef HAVE_FACTORY |
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[9bb5457] | 255 | CanonicalForm nlConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs /*r*/ ) |
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[a934fc8] | 256 | { |
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[abb4787] | 257 | if (setChar) setCharacteristic( 0 ); |
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| 258 | |
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[a934fc8] | 259 | CanonicalForm term; |
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| 260 | if ( SR_HDL(n) & SR_INT ) |
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| 261 | { |
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| 262 | term = SR_TO_INT(n); |
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| 263 | } |
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| 264 | else |
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| 265 | { |
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| 266 | if ( n->s == 3 ) |
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| 267 | { |
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[8b46459] | 268 | mpz_t dummy; |
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[8710ff0] | 269 | long lz=mpz_get_si(n->z); |
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| 270 | if (mpz_cmp_si(n->z,lz)==0) term=lz; |
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| 271 | else |
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| 272 | { |
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| 273 | mpz_init_set( dummy,n->z ); |
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| 274 | term = make_cf( dummy ); |
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| 275 | } |
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[a934fc8] | 276 | } |
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| 277 | else |
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| 278 | { |
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| 279 | // assume s==0 or s==1 |
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[8b46459] | 280 | mpz_t num, den; |
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[a934fc8] | 281 | On(SW_RATIONAL); |
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[8b46459] | 282 | mpz_init_set( num, n->z ); |
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| 283 | mpz_init_set( den, n->n ); |
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[a934fc8] | 284 | term = make_cf( num, den, ( n->s != 1 )); |
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| 285 | } |
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| 286 | } |
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| 287 | return term; |
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| 288 | } |
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| 289 | |
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| 290 | number nlConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
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| 291 | { |
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| 292 | if (n.isImm()) |
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| 293 | { |
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[8710ff0] | 294 | long lz=n.intval(); |
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| 295 | int iz=(int)lz; |
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| 296 | if ((long)iz==lz) |
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| 297 | { |
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| 298 | return nlInit(n.intval(),r); |
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| 299 | } |
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| 300 | else return nlRInit(lz); |
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[a934fc8] | 301 | return nlInit(n.intval(),r); |
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| 302 | } |
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| 303 | else |
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| 304 | { |
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[d663f2] | 305 | number z = ALLOC_RNUMBER(); //Q!? // (number)omAllocBin(rnumber_bin); |
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[a934fc8] | 306 | #if defined(LDEBUG) |
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| 307 | z->debug=123456; |
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| 308 | #endif |
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| 309 | gmp_numerator( n, z->z ); |
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| 310 | if ( n.den().isOne() ) |
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| 311 | z->s = 3; |
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| 312 | else |
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| 313 | { |
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| 314 | gmp_denominator( n, z->n ); |
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| 315 | z->s = 0; |
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| 316 | } |
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| 317 | nlNormalize(z,r); |
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| 318 | return z; |
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| 319 | } |
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| 320 | } |
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| 321 | #endif |
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[246d15] | 322 | number nlRInit (long i); |
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[35aab3] | 323 | |
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[371bc5f] | 324 | static number nlMapR(number from, const coeffs src, const coeffs dst) |
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[35aab3] | 325 | { |
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[fa31d2] | 326 | assume( getCoeffType(dst) == ID ); |
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| 327 | assume( getCoeffType(src) == n_R ); |
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[9bb5457] | 328 | |
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[35aab3] | 329 | double f=nrFloat(from); |
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[eb059c5] | 330 | if (f==0.0) return INT_TO_SR(0); |
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[35aab3] | 331 | int f_sign=1; |
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| 332 | if (f<0.0) |
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| 333 | { |
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| 334 | f_sign=-1; |
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| 335 | f=-f; |
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| 336 | } |
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| 337 | int i=0; |
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| 338 | mpz_t h1; |
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| 339 | mpz_init_set_ui(h1,1); |
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| 340 | while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG) |
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| 341 | { |
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| 342 | f*=FLT_RADIX; |
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| 343 | mpz_mul_ui(h1,h1,FLT_RADIX); |
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| 344 | i++; |
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| 345 | } |
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[a642c64] | 346 | number re=nlRInit(1); |
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[bbf7a8] | 347 | mpz_set_d(re->z,f); |
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[a642c64] | 348 | memcpy(&(re->n),&h1,sizeof(h1)); |
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| 349 | re->s=0; /* not normalized */ |
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[371bc5f] | 350 | if(f_sign==-1) re=nlNeg(re,dst); |
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| 351 | nlNormalize(re,dst); |
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[a642c64] | 352 | return re; |
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[35aab3] | 353 | } |
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| 354 | |
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[9bb5457] | 355 | static number nlMapLongR(number from, const coeffs src, const coeffs dst) |
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[35aab3] | 356 | { |
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[fa31d2] | 357 | assume( getCoeffType(dst) == ID ); |
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| 358 | assume( getCoeffType(src) == n_long_R ); |
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[9bb5457] | 359 | |
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[35aab3] | 360 | gmp_float *ff=(gmp_float*)from; |
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| 361 | mpf_t *f=ff->_mpfp(); |
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| 362 | number res; |
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[a604c3] | 363 | mpz_ptr dest,ndest; |
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[35aab3] | 364 | int size, i,negative; |
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| 365 | int e,al,bl; |
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| 366 | mp_ptr qp,dd,nn; |
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| 367 | |
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| 368 | size = (*f)[0]._mp_size; |
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| 369 | if (size == 0) |
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[eb059c5] | 370 | return INT_TO_SR(0); |
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[35aab3] | 371 | if(size<0) |
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| 372 | { |
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| 373 | negative = 1; |
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| 374 | size = -size; |
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| 375 | } |
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| 376 | else |
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| 377 | negative = 0; |
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| 378 | |
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| 379 | qp = (*f)[0]._mp_d; |
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| 380 | while(qp[0]==0) |
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| 381 | { |
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| 382 | qp++; |
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| 383 | size--; |
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| 384 | } |
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| 385 | |
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| 386 | e=(*f)[0]._mp_exp-size; |
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[896561] | 387 | res = ALLOC_RNUMBER(); |
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[35aab3] | 388 | #if defined(LDEBUG) |
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| 389 | res->debug=123456; |
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| 390 | #endif |
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[a604c3] | 391 | dest = res->z; |
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[35aab3] | 392 | |
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| 393 | if (e<0) |
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| 394 | { |
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| 395 | al = dest->_mp_size = size; |
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| 396 | if (al<2) al = 2; |
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| 397 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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| 398 | for (i=0;i<size;i++) dd[i] = qp[i]; |
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| 399 | bl = 1-e; |
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| 400 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
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| 401 | nn[bl-1] = 1; |
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| 402 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
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[a604c3] | 403 | ndest = res->n; |
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[35aab3] | 404 | ndest->_mp_d = nn; |
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| 405 | ndest->_mp_alloc = ndest->_mp_size = bl; |
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| 406 | res->s = 0; |
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| 407 | } |
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| 408 | else |
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| 409 | { |
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| 410 | al = dest->_mp_size = size+e; |
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| 411 | if (al<2) al = 2; |
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| 412 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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| 413 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
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| 414 | for (i=0;i<e;i++) dd[i] = 0; |
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| 415 | res->s = 3; |
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| 416 | } |
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| 417 | |
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| 418 | dest->_mp_d = dd; |
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| 419 | dest->_mp_alloc = al; |
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| 420 | if (negative) dest->_mp_size = -dest->_mp_size; |
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| 421 | |
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| 422 | if (res->s==0) |
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[371bc5f] | 423 | nlNormalize(res,dst); |
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[bbf7a8] | 424 | else if (mpz_size1(res->z)<=MP_SMALL) |
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[35aab3] | 425 | { |
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| 426 | // res is new, res->ref is 1 |
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[246d15] | 427 | res=nlShort3(res); |
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[35aab3] | 428 | } |
---|
[2b957a] | 429 | nlTest(res, dst); |
---|
[35aab3] | 430 | return res; |
---|
| 431 | } |
---|
| 432 | |
---|
| 433 | //static number nlMapLongR(number from) |
---|
| 434 | //{ |
---|
| 435 | // gmp_float *ff=(gmp_float*)from; |
---|
| 436 | // const mpf_t *f=ff->mpfp(); |
---|
| 437 | // int f_size=ABS((*f)[0]._mp_size); |
---|
| 438 | // if (f_size==0) |
---|
| 439 | // return nlInit(0); |
---|
| 440 | // int f_sign=1; |
---|
| 441 | // number work=ngcCopy(from); |
---|
| 442 | // if (!ngcGreaterZero(work)) |
---|
| 443 | // { |
---|
| 444 | // f_sign=-1; |
---|
| 445 | // work=ngcNeg(work); |
---|
| 446 | // } |
---|
| 447 | // int i=0; |
---|
| 448 | // mpz_t h1; |
---|
| 449 | // mpz_init_set_ui(h1,1); |
---|
| 450 | // while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG) |
---|
| 451 | // { |
---|
| 452 | // f*=FLT_RADIX; |
---|
| 453 | // mpz_mul_ui(h1,h1,FLT_RADIX); |
---|
| 454 | // i++; |
---|
| 455 | // } |
---|
| 456 | // number r=nlRInit(1); |
---|
| 457 | // mpz_set_d(&(r->z),f); |
---|
[611871] | 458 | // memcpy(&(r->n),&h1,sizeof(h1)); |
---|
[35aab3] | 459 | // r->s=0; /* not normalized */ |
---|
| 460 | // nlNormalize(r); |
---|
| 461 | // return r; |
---|
| 462 | // |
---|
| 463 | // |
---|
| 464 | // number r=nlRInit(1); |
---|
| 465 | // int f_shift=f_size+(*f)[0]._mp_exp; |
---|
| 466 | // if ( f_shift > 0) |
---|
| 467 | // { |
---|
| 468 | // r->s=0; |
---|
| 469 | // mpz_init(&r->n); |
---|
| 470 | // mpz_setbit(&r->n,f_shift*BYTES_PER_MP_LIMB*8); |
---|
| 471 | // mpz_setbit(&r->z,f_size*BYTES_PER_MP_LIMB*8-1); |
---|
| 472 | // // now r->z has enough space |
---|
[611871] | 473 | // memcpy(mpz_limb_d(&r->z),((*f)[0]._mp_d),f_size*BYTES_PER_MP_LIMB); |
---|
[35aab3] | 474 | // nlNormalize(r); |
---|
| 475 | // } |
---|
| 476 | // else |
---|
| 477 | // { |
---|
| 478 | // r->s=3; |
---|
| 479 | // if (f_shift==0) |
---|
| 480 | // { |
---|
| 481 | // mpz_setbit(&r->z,f_size*BYTES_PER_MP_LIMB*8-1); |
---|
| 482 | // // now r->z has enough space |
---|
[611871] | 483 | // memcpy(mpz_limb_d(&r->z),((*f)[0]._mp_d),f_size*BYTES_PER_MP_LIMB); |
---|
[35aab3] | 484 | // } |
---|
| 485 | // else /* f_shift < 0 */ |
---|
| 486 | // { |
---|
| 487 | // mpz_setbit(&r->z,(f_size-f_shift)*BYTES_PER_MP_LIMB*8-1); |
---|
| 488 | // // now r->z has enough space |
---|
[611871] | 489 | // memcpy(mpz_limb_d(&r->z)-f_shift,((*f)[0]._mp_d), |
---|
[35aab3] | 490 | // f_size*BYTES_PER_MP_LIMB); |
---|
| 491 | // } |
---|
| 492 | // } |
---|
| 493 | // if ((*f)[0]._mp_size<0); |
---|
| 494 | // r=nlNeg(r); |
---|
| 495 | // return r; |
---|
| 496 | //} |
---|
| 497 | |
---|
[121fd9] | 498 | int nlSize(number a, const coeffs) |
---|
[35aab3] | 499 | { |
---|
| 500 | if (a==INT_TO_SR(0)) |
---|
| 501 | return 0; /* rational 0*/ |
---|
| 502 | if (SR_HDL(a) & SR_INT) |
---|
| 503 | return 1; /* immidiate int */ |
---|
[a604c3] | 504 | int s=a->z[0]._mp_alloc; |
---|
[9bb5457] | 505 | // while ((s>0) &&(a->z._mp_d[s]==0L)) s--; |
---|
[e08bce] | 506 | //#if SIZEOF_LONG == 8 |
---|
| 507 | // if (a->z._mp_d[s] < (unsigned long)0x100000000L) s=s*2-1; |
---|
| 508 | // else s *=2; |
---|
| 509 | //#endif |
---|
[790096] | 510 | // s++; |
---|
[35aab3] | 511 | if (a->s<2) |
---|
| 512 | { |
---|
[a604c3] | 513 | int d=a->n[0]._mp_alloc; |
---|
[9bb5457] | 514 | // while ((d>0) && (a->n._mp_d[d]==0L)) d--; |
---|
[e08bce] | 515 | //#if SIZEOF_LONG == 8 |
---|
| 516 | // if (a->n._mp_d[d] < (unsigned long)0x100000000L) d=d*2-1; |
---|
| 517 | // else d *=2; |
---|
| 518 | //#endif |
---|
[1da0b5] | 519 | s+=d; |
---|
[35aab3] | 520 | } |
---|
| 521 | return s; |
---|
| 522 | } |
---|
| 523 | |
---|
| 524 | /*2 |
---|
| 525 | * convert number to int |
---|
| 526 | */ |
---|
[a642c64] | 527 | int nlInt(number &i, const coeffs r) |
---|
[35aab3] | 528 | { |
---|
[2b957a] | 529 | nlTest(i, r); |
---|
[a642c64] | 530 | nlNormalize(i,r); |
---|
[35aab3] | 531 | if (SR_HDL(i) &SR_INT) return SR_TO_INT(i); |
---|
| 532 | if (i->s==3) |
---|
| 533 | { |
---|
[a604c3] | 534 | if(mpz_size1(i->z)>MP_SMALL) return 0; |
---|
| 535 | int ul=(int)mpz_get_si(i->z); |
---|
| 536 | if (mpz_cmp_si(i->z,(long)ul)!=0) return 0; |
---|
[35aab3] | 537 | return ul; |
---|
| 538 | } |
---|
[a604c3] | 539 | mpz_t tmp; |
---|
[35aab3] | 540 | int ul; |
---|
[a604c3] | 541 | mpz_init(tmp); |
---|
| 542 | MPZ_DIV(tmp,i->z,i->n); |
---|
| 543 | if(mpz_size1(tmp)>MP_SMALL) ul=0; |
---|
[35aab3] | 544 | else |
---|
| 545 | { |
---|
[a604c3] | 546 | ul=(int)mpz_get_si(tmp); |
---|
| 547 | if (mpz_cmp_si(tmp,(long)ul)!=0) ul=0; |
---|
[35aab3] | 548 | } |
---|
[a604c3] | 549 | mpz_clear(tmp); |
---|
[35aab3] | 550 | return ul; |
---|
| 551 | } |
---|
| 552 | |
---|
[7f7573] | 553 | /*2 |
---|
| 554 | * convert number to bigint |
---|
| 555 | */ |
---|
[a642c64] | 556 | number nlBigInt(number &i, const coeffs r) |
---|
[7f7573] | 557 | { |
---|
[2b957a] | 558 | nlTest(i, r); |
---|
[a642c64] | 559 | nlNormalize(i,r); |
---|
[7f7573] | 560 | if (SR_HDL(i) &SR_INT) return (i); |
---|
| 561 | if (i->s==3) |
---|
| 562 | { |
---|
[a642c64] | 563 | return nlCopy(i,r); |
---|
[7f7573] | 564 | } |
---|
| 565 | number tmp=nlRInit(1); |
---|
[a604c3] | 566 | MPZ_DIV(tmp->z,i->z,i->n); |
---|
[246d15] | 567 | tmp=nlShort3(tmp); |
---|
[7f7573] | 568 | return tmp; |
---|
| 569 | } |
---|
| 570 | |
---|
[35aab3] | 571 | /* |
---|
| 572 | * 1/a |
---|
| 573 | */ |
---|
[a642c64] | 574 | number nlInvers(number a, const coeffs r) |
---|
[35aab3] | 575 | { |
---|
[2b957a] | 576 | nlTest(a, r); |
---|
[35aab3] | 577 | number n; |
---|
| 578 | if (SR_HDL(a) & SR_INT) |
---|
| 579 | { |
---|
[246d15] | 580 | if ((a==INT_TO_SR(1L)) || (a==INT_TO_SR(-1L))) |
---|
[35aab3] | 581 | { |
---|
| 582 | return a; |
---|
| 583 | } |
---|
[a642c64] | 584 | if (nlIsZero(a,r)) |
---|
[35aab3] | 585 | { |
---|
[b7e838] | 586 | WerrorS(nDivBy0); |
---|
[35aab3] | 587 | return INT_TO_SR(0); |
---|
| 588 | } |
---|
[896561] | 589 | n=ALLOC_RNUMBER(); |
---|
[35aab3] | 590 | #if defined(LDEBUG) |
---|
| 591 | n->debug=123456; |
---|
| 592 | #endif |
---|
| 593 | n->s=1; |
---|
[7447d8] | 594 | if ((long)a>0L) |
---|
[35aab3] | 595 | { |
---|
[a604c3] | 596 | mpz_init_set_si(n->z,(long)1); |
---|
| 597 | mpz_init_set_si(n->n,(long)SR_TO_INT(a)); |
---|
[35aab3] | 598 | } |
---|
| 599 | else |
---|
| 600 | { |
---|
[a604c3] | 601 | mpz_init_set_si(n->z,(long)-1); |
---|
| 602 | mpz_init_set_si(n->n,(long)-SR_TO_INT(a)); |
---|
[35aab3] | 603 | } |
---|
[2b957a] | 604 | nlTest(n, r); |
---|
[35aab3] | 605 | return n; |
---|
| 606 | } |
---|
[896561] | 607 | n=ALLOC_RNUMBER(); |
---|
[35aab3] | 608 | #if defined(LDEBUG) |
---|
| 609 | n->debug=123456; |
---|
| 610 | #endif |
---|
| 611 | { |
---|
| 612 | n->s=a->s; |
---|
[a604c3] | 613 | mpz_init_set(n->n,a->z); |
---|
[35aab3] | 614 | switch (a->s) |
---|
| 615 | { |
---|
| 616 | case 0: |
---|
| 617 | case 1: |
---|
[a604c3] | 618 | mpz_init_set(n->z,a->n); |
---|
| 619 | if (mpz_isNeg(n->n)) /* && n->s<2*/ |
---|
[35aab3] | 620 | { |
---|
[a604c3] | 621 | mpz_neg(n->z,n->z); |
---|
| 622 | mpz_neg(n->n,n->n); |
---|
[35aab3] | 623 | } |
---|
[a604c3] | 624 | if (mpz_cmp_si(n->n,(long)1)==0) |
---|
[35aab3] | 625 | { |
---|
[a604c3] | 626 | mpz_clear(n->n); |
---|
[35aab3] | 627 | n->s=3; |
---|
[246d15] | 628 | n=nlShort3(n); |
---|
[35aab3] | 629 | } |
---|
| 630 | break; |
---|
| 631 | case 3: |
---|
| 632 | n->s=1; |
---|
[a604c3] | 633 | if (mpz_isNeg(n->n)) /* && n->s<2*/ |
---|
[35aab3] | 634 | { |
---|
[a604c3] | 635 | mpz_neg(n->n,n->n); |
---|
| 636 | mpz_init_set_si(n->z,(long)-1); |
---|
[35aab3] | 637 | } |
---|
| 638 | else |
---|
| 639 | { |
---|
[a604c3] | 640 | mpz_init_set_si(n->z,(long)1); |
---|
[35aab3] | 641 | } |
---|
| 642 | break; |
---|
| 643 | } |
---|
| 644 | } |
---|
[2b957a] | 645 | nlTest(n, r); |
---|
[35aab3] | 646 | return n; |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | |
---|
| 650 | /*2 |
---|
| 651 | * u := a / b in Z, if b | a (else undefined) |
---|
| 652 | */ |
---|
[2b957a] | 653 | number nlExactDiv(number a, number b, const coeffs r) |
---|
[35aab3] | 654 | { |
---|
| 655 | if (b==INT_TO_SR(0)) |
---|
| 656 | { |
---|
[b7e838] | 657 | WerrorS(nDivBy0); |
---|
[35aab3] | 658 | return INT_TO_SR(0); |
---|
| 659 | } |
---|
| 660 | if (a==INT_TO_SR(0)) |
---|
| 661 | return INT_TO_SR(0); |
---|
| 662 | number u; |
---|
| 663 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 664 | { |
---|
| 665 | /* the small int -(1<<28) divided by -1 is the large int (1<<28) */ |
---|
[246d15] | 666 | if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L))) |
---|
[35aab3] | 667 | { |
---|
[246d15] | 668 | return nlRInit(POW_2_28); |
---|
[35aab3] | 669 | } |
---|
[246d15] | 670 | long aa=SR_TO_INT(a); |
---|
| 671 | long bb=SR_TO_INT(b); |
---|
[35aab3] | 672 | return INT_TO_SR(aa/bb); |
---|
| 673 | } |
---|
| 674 | number bb=NULL; |
---|
| 675 | if (SR_HDL(b) & SR_INT) |
---|
| 676 | { |
---|
| 677 | bb=nlRInit(SR_TO_INT(b)); |
---|
| 678 | b=bb; |
---|
| 679 | } |
---|
[896561] | 680 | u=ALLOC_RNUMBER(); |
---|
[35aab3] | 681 | #if defined(LDEBUG) |
---|
| 682 | u->debug=123456; |
---|
| 683 | #endif |
---|
[a604c3] | 684 | mpz_init(u->z); |
---|
[35aab3] | 685 | /* u=a/b */ |
---|
| 686 | u->s = 3; |
---|
[a604c3] | 687 | MPZ_EXACTDIV(u->z,a->z,b->z); |
---|
[35aab3] | 688 | if (bb!=NULL) |
---|
| 689 | { |
---|
[a604c3] | 690 | mpz_clear(bb->z); |
---|
[35aab3] | 691 | #if defined(LDEBUG) |
---|
| 692 | bb->debug=654324; |
---|
| 693 | #endif |
---|
[d663f2] | 694 | FREE_RNUMBER(bb); // omFreeBin((void *)bb, rnumber_bin); |
---|
[35aab3] | 695 | } |
---|
[246d15] | 696 | u=nlShort3(u); |
---|
[2b957a] | 697 | nlTest(u, r); |
---|
[35aab3] | 698 | return u; |
---|
| 699 | } |
---|
| 700 | |
---|
| 701 | /*2 |
---|
| 702 | * u := a / b in Z |
---|
| 703 | */ |
---|
[2b957a] | 704 | number nlIntDiv (number a, number b, const coeffs r) |
---|
[35aab3] | 705 | { |
---|
| 706 | if (b==INT_TO_SR(0)) |
---|
| 707 | { |
---|
[b7e838] | 708 | WerrorS(nDivBy0); |
---|
[35aab3] | 709 | return INT_TO_SR(0); |
---|
| 710 | } |
---|
| 711 | if (a==INT_TO_SR(0)) |
---|
| 712 | return INT_TO_SR(0); |
---|
| 713 | number u; |
---|
| 714 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 715 | { |
---|
| 716 | /* the small int -(1<<28) divided by -1 is the large int (1<<28) */ |
---|
[246d15] | 717 | if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L))) |
---|
[35aab3] | 718 | { |
---|
[246d15] | 719 | return nlRInit(POW_2_28); |
---|
[35aab3] | 720 | } |
---|
[246d15] | 721 | long aa=SR_TO_INT(a); |
---|
| 722 | long bb=SR_TO_INT(b); |
---|
[7326063] | 723 | //return INT_TO_SR((aa-(aa%bb))/bb); |
---|
| 724 | return INT_TO_SR(aa/bb); |
---|
[35aab3] | 725 | } |
---|
| 726 | if (SR_HDL(a) & SR_INT) |
---|
| 727 | { |
---|
| 728 | /* the small int -(1<<28) divided by 2^28 is 1 */ |
---|
[246d15] | 729 | if (a==INT_TO_SR(-(POW_2_28))) |
---|
[35aab3] | 730 | { |
---|
[246d15] | 731 | if(mpz_cmp_si(b->z,(POW_2_28))==0) |
---|
[35aab3] | 732 | { |
---|
| 733 | return INT_TO_SR(-1); |
---|
| 734 | } |
---|
| 735 | } |
---|
| 736 | /* a is a small and b is a large int: -> 0 */ |
---|
| 737 | return INT_TO_SR(0); |
---|
| 738 | } |
---|
| 739 | number bb=NULL; |
---|
| 740 | if (SR_HDL(b) & SR_INT) |
---|
| 741 | { |
---|
| 742 | bb=nlRInit(SR_TO_INT(b)); |
---|
| 743 | b=bb; |
---|
| 744 | } |
---|
[896561] | 745 | u=ALLOC_RNUMBER(); |
---|
[35aab3] | 746 | #if defined(LDEBUG) |
---|
| 747 | u->debug=123456; |
---|
| 748 | #endif |
---|
[98bda9] | 749 | assume(a->s==3); |
---|
| 750 | assume(b->s==3); |
---|
[a604c3] | 751 | mpz_init_set(u->z,a->z); |
---|
[35aab3] | 752 | /* u=u/b */ |
---|
| 753 | u->s = 3; |
---|
[a604c3] | 754 | MPZ_DIV(u->z,u->z,b->z); |
---|
[35aab3] | 755 | if (bb!=NULL) |
---|
| 756 | { |
---|
[a604c3] | 757 | mpz_clear(bb->z); |
---|
[35aab3] | 758 | #if defined(LDEBUG) |
---|
| 759 | bb->debug=654324; |
---|
| 760 | #endif |
---|
[d663f2] | 761 | FREE_RNUMBER(bb); // omFreeBin((void *)bb, rnumber_bin); |
---|
[35aab3] | 762 | } |
---|
[246d15] | 763 | u=nlShort3(u); |
---|
[2b957a] | 764 | nlTest(u, r); |
---|
[35aab3] | 765 | return u; |
---|
| 766 | } |
---|
| 767 | |
---|
| 768 | /*2 |
---|
| 769 | * u := a mod b in Z, u>=0 |
---|
| 770 | */ |
---|
[a642c64] | 771 | number nlIntMod (number a, number b, const coeffs r) |
---|
[35aab3] | 772 | { |
---|
| 773 | if (b==INT_TO_SR(0)) |
---|
| 774 | { |
---|
[b7e838] | 775 | WerrorS(nDivBy0); |
---|
[35aab3] | 776 | return INT_TO_SR(0); |
---|
| 777 | } |
---|
| 778 | if (a==INT_TO_SR(0)) |
---|
| 779 | return INT_TO_SR(0); |
---|
| 780 | number u; |
---|
| 781 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 782 | { |
---|
[7326063] | 783 | //return INT_TO_SR(SR_TO_INT(a)%SR_TO_INT(b)); |
---|
| 784 | if ((long)a>0L) |
---|
| 785 | { |
---|
| 786 | if ((long)b>0L) |
---|
| 787 | return INT_TO_SR(SR_TO_INT(a)%SR_TO_INT(b)); |
---|
| 788 | else |
---|
| 789 | return INT_TO_SR(SR_TO_INT(a)%(-SR_TO_INT(b))); |
---|
| 790 | } |
---|
| 791 | else |
---|
| 792 | { |
---|
| 793 | if ((long)b>0L) |
---|
| 794 | { |
---|
| 795 | long i=(-SR_TO_INT(a))%SR_TO_INT(b); |
---|
| 796 | if ( i != 0L ) i = (SR_TO_INT(b))-i; |
---|
| 797 | return INT_TO_SR(i); |
---|
| 798 | } |
---|
| 799 | else |
---|
| 800 | { |
---|
| 801 | long i=(-SR_TO_INT(a))%(-SR_TO_INT(b)); |
---|
| 802 | if ( i != 0L ) i = (-SR_TO_INT(b))-i; |
---|
| 803 | return INT_TO_SR(i); |
---|
| 804 | } |
---|
| 805 | } |
---|
[35aab3] | 806 | } |
---|
| 807 | if (SR_HDL(a) & SR_INT) |
---|
| 808 | { |
---|
[7326063] | 809 | /* a is a small and b is a large int: -> a or (a+b) or (a-b) */ |
---|
| 810 | if ((long)a<0L) |
---|
| 811 | { |
---|
| 812 | if (mpz_isNeg(b->z)) |
---|
| 813 | return nlSub(a,b,r); |
---|
| 814 | /*else*/ |
---|
| 815 | return nlAdd(a,b,r); |
---|
| 816 | } |
---|
| 817 | /*else*/ |
---|
| 818 | return a; |
---|
| 819 | |
---|
[824c47] | 820 | /* a is a small and b is a large int: -> a */ |
---|
[7326063] | 821 | //return a; |
---|
[35aab3] | 822 | } |
---|
| 823 | number bb=NULL; |
---|
| 824 | if (SR_HDL(b) & SR_INT) |
---|
| 825 | { |
---|
| 826 | bb=nlRInit(SR_TO_INT(b)); |
---|
| 827 | b=bb; |
---|
| 828 | } |
---|
[896561] | 829 | u=ALLOC_RNUMBER(); |
---|
[35aab3] | 830 | #if defined(LDEBUG) |
---|
| 831 | u->debug=123456; |
---|
| 832 | #endif |
---|
[a604c3] | 833 | mpz_init(u->z); |
---|
[35aab3] | 834 | u->s = 3; |
---|
[a604c3] | 835 | mpz_mod(u->z,a->z,b->z); |
---|
[35aab3] | 836 | if (bb!=NULL) |
---|
| 837 | { |
---|
[a604c3] | 838 | mpz_clear(bb->z); |
---|
[35aab3] | 839 | #if defined(LDEBUG) |
---|
| 840 | bb->debug=654324; |
---|
| 841 | #endif |
---|
[d663f2] | 842 | FREE_RNUMBER(bb); // omFreeBin((void *)bb, rnumber_bin); |
---|
[35aab3] | 843 | } |
---|
[a604c3] | 844 | if (mpz_isNeg(u->z)) |
---|
[35aab3] | 845 | { |
---|
[a604c3] | 846 | if (mpz_isNeg(b->z)) |
---|
| 847 | mpz_sub(u->z,u->z,b->z); |
---|
[35aab3] | 848 | else |
---|
[a604c3] | 849 | mpz_add(u->z,u->z,b->z); |
---|
[35aab3] | 850 | } |
---|
[246d15] | 851 | u=nlShort3(u); |
---|
[2b957a] | 852 | nlTest(u, r); |
---|
[35aab3] | 853 | return u; |
---|
| 854 | } |
---|
| 855 | |
---|
| 856 | /*2 |
---|
| 857 | * u := a / b |
---|
| 858 | */ |
---|
[a642c64] | 859 | number nlDiv (number a, number b, const coeffs r) |
---|
[35aab3] | 860 | { |
---|
| 861 | number u; |
---|
[a642c64] | 862 | if (nlIsZero(b,r)) |
---|
[35aab3] | 863 | { |
---|
[b7e838] | 864 | WerrorS(nDivBy0); |
---|
[35aab3] | 865 | return INT_TO_SR(0); |
---|
| 866 | } |
---|
[896561] | 867 | u=ALLOC_RNUMBER(); |
---|
[35aab3] | 868 | u->s=0; |
---|
| 869 | #if defined(LDEBUG) |
---|
| 870 | u->debug=123456; |
---|
| 871 | #endif |
---|
| 872 | // ---------- short / short ------------------------------------ |
---|
| 873 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 874 | { |
---|
[246d15] | 875 | long i=SR_TO_INT(a); |
---|
| 876 | long j=SR_TO_INT(b); |
---|
[1a97da] | 877 | if ((i==-POW_2_28) && (j== -1L)) |
---|
[e11ed0] | 878 | { |
---|
[896561] | 879 | FREE_RNUMBER(u); |
---|
[1a97da] | 880 | return nlRInit(POW_2_28); |
---|
| 881 | } |
---|
[246d15] | 882 | long r=i%j; |
---|
[35aab3] | 883 | if (r==0) |
---|
| 884 | { |
---|
[d663f2] | 885 | FREE_RNUMBER(u); // omFreeBin((void *)u, rnumber_bin); |
---|
[35aab3] | 886 | return INT_TO_SR(i/j); |
---|
| 887 | } |
---|
[a604c3] | 888 | mpz_init_set_si(u->z,(long)i); |
---|
| 889 | mpz_init_set_si(u->n,(long)j); |
---|
[35aab3] | 890 | } |
---|
| 891 | else |
---|
| 892 | { |
---|
[a604c3] | 893 | mpz_init(u->z); |
---|
[35aab3] | 894 | // ---------- short / long ------------------------------------ |
---|
| 895 | if (SR_HDL(a) & SR_INT) |
---|
| 896 | { |
---|
| 897 | // short a / (z/n) -> (a*n)/z |
---|
| 898 | if (b->s<2) |
---|
| 899 | { |
---|
[a604c3] | 900 | mpz_mul_si(u->z,b->n,SR_TO_INT(a)); |
---|
[35aab3] | 901 | } |
---|
| 902 | else |
---|
| 903 | // short a / long z -> a/z |
---|
| 904 | { |
---|
[a604c3] | 905 | mpz_set_si(u->z,SR_TO_INT(a)); |
---|
[35aab3] | 906 | } |
---|
[a604c3] | 907 | if (mpz_cmp(u->z,b->z)==0) |
---|
[35aab3] | 908 | { |
---|
[a604c3] | 909 | mpz_clear(u->z); |
---|
[896561] | 910 | FREE_RNUMBER(u); |
---|
[35aab3] | 911 | return INT_TO_SR(1); |
---|
| 912 | } |
---|
[a604c3] | 913 | mpz_init_set(u->n,b->z); |
---|
[35aab3] | 914 | } |
---|
| 915 | // ---------- long / short ------------------------------------ |
---|
| 916 | else if (SR_HDL(b) & SR_INT) |
---|
| 917 | { |
---|
[a604c3] | 918 | mpz_set(u->z,a->z); |
---|
[35aab3] | 919 | // (z/n) / b -> z/(n*b) |
---|
| 920 | if (a->s<2) |
---|
| 921 | { |
---|
[a604c3] | 922 | mpz_init_set(u->n,a->n); |
---|
[7447d8] | 923 | if ((long)b>0L) |
---|
[a604c3] | 924 | mpz_mul_ui(u->n,u->n,SR_TO_INT(b)); |
---|
[35aab3] | 925 | else |
---|
| 926 | { |
---|
[a604c3] | 927 | mpz_mul_ui(u->n,u->n,-SR_TO_INT(b)); |
---|
| 928 | mpz_neg(u->z,u->z); |
---|
[35aab3] | 929 | } |
---|
| 930 | } |
---|
| 931 | else |
---|
| 932 | // long z / short b -> z/b |
---|
| 933 | { |
---|
[a604c3] | 934 | //mpz_set(u->z,a->z); |
---|
| 935 | mpz_init_set_si(u->n,SR_TO_INT(b)); |
---|
[35aab3] | 936 | } |
---|
| 937 | } |
---|
| 938 | // ---------- long / long ------------------------------------ |
---|
| 939 | else |
---|
| 940 | { |
---|
[a604c3] | 941 | mpz_set(u->z,a->z); |
---|
| 942 | mpz_init_set(u->n,b->z); |
---|
| 943 | if (a->s<2) mpz_mul(u->n,u->n,a->n); |
---|
| 944 | if (b->s<2) mpz_mul(u->z,u->z,b->n); |
---|
[35aab3] | 945 | } |
---|
| 946 | } |
---|
[a604c3] | 947 | if (mpz_isNeg(u->n)) |
---|
[35aab3] | 948 | { |
---|
[a604c3] | 949 | mpz_neg(u->z,u->z); |
---|
| 950 | mpz_neg(u->n,u->n); |
---|
[35aab3] | 951 | } |
---|
[a604c3] | 952 | if (mpz_cmp_si(u->n,(long)1)==0) |
---|
[35aab3] | 953 | { |
---|
[a604c3] | 954 | mpz_clear(u->n); |
---|
[35aab3] | 955 | u->s=3; |
---|
[246d15] | 956 | u=nlShort3(u); |
---|
[35aab3] | 957 | } |
---|
[2b957a] | 958 | nlTest(u, r); |
---|
[35aab3] | 959 | return u; |
---|
| 960 | } |
---|
| 961 | |
---|
| 962 | /*2 |
---|
| 963 | * u:= x ^ exp |
---|
| 964 | */ |
---|
[a642c64] | 965 | void nlPower (number x,int exp,number * u, const coeffs r) |
---|
[35aab3] | 966 | { |
---|
[6242bb3] | 967 | *u = INT_TO_SR(0); // 0^e, e!=0 |
---|
[a642c64] | 968 | if (!nlIsZero(x,r)) |
---|
[35aab3] | 969 | { |
---|
[2b957a] | 970 | nlTest(x, r); |
---|
[35aab3] | 971 | number aa=NULL; |
---|
| 972 | if (SR_HDL(x) & SR_INT) |
---|
| 973 | { |
---|
| 974 | aa=nlRInit(SR_TO_INT(x)); |
---|
| 975 | x=aa; |
---|
| 976 | } |
---|
[ee7dcf] | 977 | else if (x->s==0) |
---|
[a642c64] | 978 | nlNormalize(x,r); |
---|
[896561] | 979 | *u=ALLOC_RNUMBER(); |
---|
[35aab3] | 980 | #if defined(LDEBUG) |
---|
| 981 | (*u)->debug=123456; |
---|
| 982 | #endif |
---|
[a604c3] | 983 | mpz_init((*u)->z); |
---|
| 984 | mpz_pow_ui((*u)->z,x->z,(unsigned long)exp); |
---|
[35aab3] | 985 | if (x->s<2) |
---|
| 986 | { |
---|
[a604c3] | 987 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
[35aab3] | 988 | { |
---|
| 989 | x->s=3; |
---|
[a604c3] | 990 | mpz_clear(x->n); |
---|
[35aab3] | 991 | } |
---|
| 992 | else |
---|
| 993 | { |
---|
[a604c3] | 994 | mpz_init((*u)->n); |
---|
| 995 | mpz_pow_ui((*u)->n,x->n,(unsigned long)exp); |
---|
[35aab3] | 996 | } |
---|
| 997 | } |
---|
| 998 | (*u)->s = x->s; |
---|
[246d15] | 999 | if ((*u)->s==3) *u=nlShort3(*u); |
---|
[35aab3] | 1000 | if (aa!=NULL) |
---|
| 1001 | { |
---|
[a604c3] | 1002 | mpz_clear(aa->z); |
---|
[896561] | 1003 | FREE_RNUMBER(aa); |
---|
[35aab3] | 1004 | } |
---|
| 1005 | } |
---|
[6242bb3] | 1006 | else if (exp==0) |
---|
| 1007 | *u = INT_TO_SR(1); // 0^0 |
---|
[35aab3] | 1008 | #ifdef LDEBUG |
---|
[deca7f6] | 1009 | if (exp<0) Print("nlPower: neg. exp. %d\n",exp); |
---|
[2b957a] | 1010 | nlTest(*u, r); |
---|
[35aab3] | 1011 | #endif |
---|
| 1012 | } |
---|
| 1013 | |
---|
| 1014 | |
---|
| 1015 | /*2 |
---|
| 1016 | * za >= 0 ? |
---|
| 1017 | */ |
---|
[2b957a] | 1018 | BOOLEAN nlGreaterZero (number a, const coeffs r) |
---|
[35aab3] | 1019 | { |
---|
[2b957a] | 1020 | nlTest(a, r); |
---|
[246d15] | 1021 | if (SR_HDL(a) & SR_INT) return SR_HDL(a)>1L /* represents number(0) */; |
---|
[a604c3] | 1022 | return (!mpz_isNeg(a->z)); |
---|
[35aab3] | 1023 | } |
---|
| 1024 | |
---|
| 1025 | /*2 |
---|
| 1026 | * a > b ? |
---|
| 1027 | */ |
---|
[a642c64] | 1028 | BOOLEAN nlGreater (number a, number b, const coeffs r) |
---|
[35aab3] | 1029 | { |
---|
[2b957a] | 1030 | nlTest(a, r); |
---|
| 1031 | nlTest(b, r); |
---|
[a642c64] | 1032 | number re; |
---|
[35aab3] | 1033 | BOOLEAN rr; |
---|
[a642c64] | 1034 | re=nlSub(a,b,r); |
---|
| 1035 | rr=(!nlIsZero(re,r)) && (nlGreaterZero(re,r)); |
---|
| 1036 | nlDelete(&re,r); |
---|
[35aab3] | 1037 | return rr; |
---|
| 1038 | } |
---|
| 1039 | |
---|
| 1040 | /*2 |
---|
| 1041 | * a == -1 ? |
---|
| 1042 | */ |
---|
[2b957a] | 1043 | BOOLEAN nlIsMOne (number a, const coeffs r) |
---|
[35aab3] | 1044 | { |
---|
| 1045 | #ifdef LDEBUG |
---|
| 1046 | if (a==NULL) return FALSE; |
---|
[2b957a] | 1047 | nlTest(a, r); |
---|
[35aab3] | 1048 | #endif |
---|
[246d15] | 1049 | //if (SR_HDL(a) & SR_INT) return (a==INT_TO_SR(-1L)); |
---|
[5f4ae4] | 1050 | //return FALSE; |
---|
[246d15] | 1051 | return (a==INT_TO_SR(-1L)); |
---|
[35aab3] | 1052 | } |
---|
| 1053 | |
---|
| 1054 | /*2 |
---|
| 1055 | * result =gcd(a,b) |
---|
| 1056 | */ |
---|
[a642c64] | 1057 | number nlGcd(number a, number b, const coeffs r) |
---|
[35aab3] | 1058 | { |
---|
| 1059 | number result; |
---|
[2b957a] | 1060 | nlTest(a, r); |
---|
| 1061 | nlTest(b, r); |
---|
[35aab3] | 1062 | //nlNormalize(a); |
---|
| 1063 | //nlNormalize(b); |
---|
[246d15] | 1064 | if ((a==INT_TO_SR(1L))||(a==INT_TO_SR(-1L)) |
---|
| 1065 | || (b==INT_TO_SR(1L))||(b==INT_TO_SR(-1L))) |
---|
| 1066 | return INT_TO_SR(1L); |
---|
[f553f3] | 1067 | if (a==INT_TO_SR(0)) /* gcd(0,b) ->b */ |
---|
[a642c64] | 1068 | return nlCopy(b,r); |
---|
[f553f3] | 1069 | if (b==INT_TO_SR(0)) /* gcd(a,0) -> a */ |
---|
[a642c64] | 1070 | return nlCopy(a,r); |
---|
[35aab3] | 1071 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 1072 | { |
---|
[246d15] | 1073 | long i=SR_TO_INT(a); |
---|
| 1074 | long j=SR_TO_INT(b); |
---|
| 1075 | if((i==0L)||(j==0L)) |
---|
[35aab3] | 1076 | return INT_TO_SR(1); |
---|
[246d15] | 1077 | long l; |
---|
[35aab3] | 1078 | i=ABS(i); |
---|
| 1079 | j=ABS(j); |
---|
| 1080 | do |
---|
| 1081 | { |
---|
| 1082 | l=i%j; |
---|
| 1083 | i=j; |
---|
| 1084 | j=l; |
---|
[246d15] | 1085 | } while (l!=0L); |
---|
[794463] | 1086 | if (i==POW_2_28) |
---|
| 1087 | result=nlRInit(POW_2_28); |
---|
| 1088 | else |
---|
| 1089 | result=INT_TO_SR(i); |
---|
[2b957a] | 1090 | nlTest(result,r); |
---|
[794463] | 1091 | return result; |
---|
[35aab3] | 1092 | } |
---|
| 1093 | if (((!(SR_HDL(a) & SR_INT))&&(a->s<2)) |
---|
| 1094 | || ((!(SR_HDL(b) & SR_INT))&&(b->s<2))) return INT_TO_SR(1); |
---|
| 1095 | if (SR_HDL(a) & SR_INT) |
---|
| 1096 | { |
---|
[794463] | 1097 | LONG aa=ABS(SR_TO_INT(a)); |
---|
| 1098 | unsigned long t=mpz_gcd_ui(NULL,b->z,(long)aa); |
---|
| 1099 | if (t==POW_2_28) |
---|
| 1100 | result=nlRInit(POW_2_28); |
---|
| 1101 | else |
---|
| 1102 | result=INT_TO_SR(t); |
---|
[35aab3] | 1103 | } |
---|
| 1104 | else |
---|
| 1105 | if (SR_HDL(b) & SR_INT) |
---|
| 1106 | { |
---|
[794463] | 1107 | LONG bb=ABS(SR_TO_INT(b)); |
---|
| 1108 | unsigned long t=mpz_gcd_ui(NULL,a->z,(long)bb); |
---|
| 1109 | if (t==POW_2_28) |
---|
| 1110 | result=nlRInit(POW_2_28); |
---|
| 1111 | else |
---|
| 1112 | result=INT_TO_SR(t); |
---|
[35aab3] | 1113 | } |
---|
| 1114 | else |
---|
| 1115 | { |
---|
[896561] | 1116 | result=ALLOC_RNUMBER(); |
---|
[a604c3] | 1117 | mpz_init(result->z); |
---|
| 1118 | mpz_gcd(result->z,a->z,b->z); |
---|
[ea66a97] | 1119 | result->s = 3; |
---|
| 1120 | #ifdef LDEBUG |
---|
| 1121 | result->debug=123456; |
---|
| 1122 | #endif |
---|
[246d15] | 1123 | result=nlShort3(result); |
---|
[35aab3] | 1124 | } |
---|
[2b957a] | 1125 | nlTest(result, r); |
---|
[35aab3] | 1126 | return result; |
---|
| 1127 | } |
---|
| 1128 | |
---|
[18057e] | 1129 | number nlShort1(number x) // assume x->s==0/1 |
---|
[e8a0aa] | 1130 | { |
---|
[18057e] | 1131 | assume(x->s<2); |
---|
[a604c3] | 1132 | if (mpz_cmp_ui(x->z,(long)0)==0) |
---|
[e8a0aa] | 1133 | { |
---|
[106406] | 1134 | _nlDelete_NoImm(&x); |
---|
[e8a0aa] | 1135 | return INT_TO_SR(0); |
---|
| 1136 | } |
---|
[18057e] | 1137 | if (x->s<2) |
---|
| 1138 | { |
---|
[a604c3] | 1139 | if (mpz_cmp(x->z,x->n)==0) |
---|
[18057e] | 1140 | { |
---|
[106406] | 1141 | _nlDelete_NoImm(&x); |
---|
[18057e] | 1142 | return INT_TO_SR(1); |
---|
| 1143 | } |
---|
| 1144 | } |
---|
| 1145 | return x; |
---|
| 1146 | } |
---|
[35aab3] | 1147 | /*2 |
---|
| 1148 | * simplify x |
---|
| 1149 | */ |
---|
[a642c64] | 1150 | void nlNormalize (number &x, const coeffs r) |
---|
[35aab3] | 1151 | { |
---|
| 1152 | if ((SR_HDL(x) & SR_INT) ||(x==NULL)) |
---|
| 1153 | return; |
---|
| 1154 | if (x->s==3) |
---|
| 1155 | { |
---|
[246d15] | 1156 | x=nlShort3_noinline(x); |
---|
[2b957a] | 1157 | nlTest(x,r); |
---|
[18057e] | 1158 | return; |
---|
[35aab3] | 1159 | } |
---|
[3ccafbf] | 1160 | else if (x->s==0) |
---|
[35aab3] | 1161 | { |
---|
[a604c3] | 1162 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
[35aab3] | 1163 | { |
---|
[a604c3] | 1164 | mpz_clear(x->n); |
---|
[3ccafbf] | 1165 | x->s=3; |
---|
[246d15] | 1166 | x=nlShort3(x); |
---|
[eb059c5] | 1167 | } |
---|
[3ccafbf] | 1168 | else |
---|
[eb059c5] | 1169 | { |
---|
[a604c3] | 1170 | mpz_t gcd; |
---|
| 1171 | mpz_init(gcd); |
---|
| 1172 | mpz_gcd(gcd,x->z,x->n); |
---|
[3ccafbf] | 1173 | x->s=1; |
---|
[a604c3] | 1174 | if (mpz_cmp_si(gcd,(long)1)!=0) |
---|
[eb059c5] | 1175 | { |
---|
[a604c3] | 1176 | mpz_t r; |
---|
| 1177 | mpz_init(r); |
---|
| 1178 | MPZ_EXACTDIV(r,x->z,gcd); |
---|
| 1179 | mpz_set(x->z,r); |
---|
| 1180 | MPZ_EXACTDIV(r,x->n,gcd); |
---|
| 1181 | mpz_set(x->n,r); |
---|
| 1182 | mpz_clear(r); |
---|
| 1183 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
[3ccafbf] | 1184 | { |
---|
[a604c3] | 1185 | mpz_clear(x->n); |
---|
[3ccafbf] | 1186 | x->s=3; |
---|
[246d15] | 1187 | x=nlShort3_noinline(x); |
---|
[3ccafbf] | 1188 | } |
---|
[eb059c5] | 1189 | } |
---|
[a604c3] | 1190 | mpz_clear(gcd); |
---|
[35aab3] | 1191 | } |
---|
| 1192 | } |
---|
[2b957a] | 1193 | nlTest(x, r); |
---|
[35aab3] | 1194 | } |
---|
| 1195 | |
---|
| 1196 | /*2 |
---|
| 1197 | * returns in result->z the lcm(a->z,b->n) |
---|
| 1198 | */ |
---|
[a642c64] | 1199 | number nlLcm(number a, number b, const coeffs r) |
---|
[35aab3] | 1200 | { |
---|
| 1201 | number result; |
---|
[2b957a] | 1202 | nlTest(a, r); |
---|
| 1203 | nlTest(b, r); |
---|
[35aab3] | 1204 | if ((SR_HDL(b) & SR_INT) |
---|
| 1205 | || (b->s==3)) |
---|
| 1206 | { |
---|
| 1207 | // b is 1/(b->n) => b->n is 1 => result is a |
---|
[a642c64] | 1208 | return nlCopy(a,r); |
---|
[35aab3] | 1209 | } |
---|
[896561] | 1210 | result=ALLOC_RNUMBER(); |
---|
[35aab3] | 1211 | #if defined(LDEBUG) |
---|
| 1212 | result->debug=123456; |
---|
| 1213 | #endif |
---|
| 1214 | result->s=3; |
---|
[a604c3] | 1215 | mpz_t gcd; |
---|
| 1216 | mpz_init(gcd); |
---|
| 1217 | mpz_init(result->z); |
---|
[35aab3] | 1218 | if (SR_HDL(a) & SR_INT) |
---|
[a604c3] | 1219 | mpz_gcd_ui(gcd,b->n,ABS(SR_TO_INT(a))); |
---|
[35aab3] | 1220 | else |
---|
[a604c3] | 1221 | mpz_gcd(gcd,a->z,b->n); |
---|
| 1222 | if (mpz_cmp_si(gcd,(long)1)!=0) |
---|
[35aab3] | 1223 | { |
---|
[a604c3] | 1224 | mpz_t bt; |
---|
| 1225 | mpz_init_set(bt,b->n); |
---|
| 1226 | MPZ_EXACTDIV(bt,bt,gcd); |
---|
[35aab3] | 1227 | if (SR_HDL(a) & SR_INT) |
---|
[a604c3] | 1228 | mpz_mul_si(result->z,bt,SR_TO_INT(a)); |
---|
[35aab3] | 1229 | else |
---|
[a604c3] | 1230 | mpz_mul(result->z,bt,a->z); |
---|
| 1231 | mpz_clear(bt); |
---|
[35aab3] | 1232 | } |
---|
| 1233 | else |
---|
| 1234 | if (SR_HDL(a) & SR_INT) |
---|
[a604c3] | 1235 | mpz_mul_si(result->z,b->n,SR_TO_INT(a)); |
---|
[35aab3] | 1236 | else |
---|
[a604c3] | 1237 | mpz_mul(result->z,b->n,a->z); |
---|
| 1238 | mpz_clear(gcd); |
---|
[246d15] | 1239 | result=nlShort3(result); |
---|
[2b957a] | 1240 | nlTest(result, r); |
---|
[35aab3] | 1241 | return result; |
---|
| 1242 | } |
---|
| 1243 | |
---|
[79020f] | 1244 | // Map q \in QQ \to Zp |
---|
| 1245 | // src = Q, dst = Zp (or an extension of Zp?) |
---|
| 1246 | number nlModP(number q, const coeffs Q, const coeffs Zp) |
---|
[35aab3] | 1247 | { |
---|
[79020f] | 1248 | assume( getCoeffType(Q) == ID ); |
---|
| 1249 | |
---|
| 1250 | const int p = n_GetChar(Zp); |
---|
| 1251 | assume( p > 0 ); |
---|
| 1252 | |
---|
| 1253 | const long P = p; |
---|
| 1254 | assume( P > 0 ); |
---|
| 1255 | |
---|
| 1256 | // embedded long within q => only long numerator has to be converted |
---|
| 1257 | // to int (modulo char.) |
---|
| 1258 | if (SR_HDL(q) & SR_INT) |
---|
[35aab3] | 1259 | { |
---|
[79020f] | 1260 | long i = SR_TO_INT(q); |
---|
| 1261 | if (i<0L) |
---|
| 1262 | return n_Init( static_cast<int>( P - ((-i)%P) ), Zp); |
---|
| 1263 | else |
---|
| 1264 | return n_Init( static_cast<int>( i % P ), Zp ); |
---|
[35aab3] | 1265 | } |
---|
[79020f] | 1266 | |
---|
| 1267 | const unsigned long PP = p; |
---|
| 1268 | |
---|
| 1269 | // numerator modulo char. should fit into int |
---|
[e11ed0] | 1270 | number z = n_Init( static_cast<int>(mpz_fdiv_ui(q->z, PP)), Zp ); |
---|
[79020f] | 1271 | |
---|
| 1272 | // denominator != 1? |
---|
| 1273 | if (q->s!=3) |
---|
[35aab3] | 1274 | { |
---|
[79020f] | 1275 | // denominator modulo char. should fit into int |
---|
| 1276 | number n = n_Init( static_cast<int>(mpz_fdiv_ui(q->n, PP)), Zp ); |
---|
| 1277 | |
---|
| 1278 | number res = n_Div( z, n, Zp ); |
---|
| 1279 | |
---|
| 1280 | n_Delete(&z, Zp); |
---|
| 1281 | n_Delete(&n, Zp); |
---|
| 1282 | |
---|
| 1283 | return res; |
---|
[35aab3] | 1284 | } |
---|
[79020f] | 1285 | |
---|
| 1286 | return z; |
---|
[35aab3] | 1287 | } |
---|
| 1288 | |
---|
[894f5b1] | 1289 | #ifdef HAVE_RINGS |
---|
| 1290 | /*2 |
---|
[1919112] | 1291 | * convert number i (from Q) to GMP and warn if denom != 1 |
---|
[894f5b1] | 1292 | */ |
---|
[2518db] | 1293 | void nlGMP(number &i, number n, const coeffs r) |
---|
[894f5b1] | 1294 | { |
---|
| 1295 | // Hier brauche ich einfach die GMP Zahl |
---|
[2b957a] | 1296 | nlTest(i, r); |
---|
[2518db] | 1297 | nlNormalize(i, r); |
---|
[894f5b1] | 1298 | if (SR_HDL(i) & SR_INT) |
---|
| 1299 | { |
---|
[246d15] | 1300 | mpz_set_si((mpz_ptr) n, SR_TO_INT(i)); |
---|
[0959dc] | 1301 | return; |
---|
[894f5b1] | 1302 | } |
---|
| 1303 | if (i->s!=3) |
---|
| 1304 | { |
---|
| 1305 | WarnS("Omitted denominator during coefficient mapping !"); |
---|
| 1306 | } |
---|
[a604c3] | 1307 | mpz_set((mpz_ptr) n, i->z); |
---|
[894f5b1] | 1308 | } |
---|
| 1309 | #endif |
---|
| 1310 | |
---|
[35aab3] | 1311 | /*2 |
---|
| 1312 | * acces to denominator, other 1 for integers |
---|
| 1313 | */ |
---|
[a642c64] | 1314 | number nlGetDenom(number &n, const coeffs r) |
---|
[35aab3] | 1315 | { |
---|
| 1316 | if (!(SR_HDL(n) & SR_INT)) |
---|
| 1317 | { |
---|
| 1318 | if (n->s==0) |
---|
| 1319 | { |
---|
[a642c64] | 1320 | nlNormalize(n,r); |
---|
[35aab3] | 1321 | } |
---|
| 1322 | if (!(SR_HDL(n) & SR_INT)) |
---|
| 1323 | { |
---|
| 1324 | if (n->s!=3) |
---|
| 1325 | { |
---|
[896561] | 1326 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 1327 | u->s=3; |
---|
| 1328 | #if defined(LDEBUG) |
---|
| 1329 | u->debug=123456; |
---|
| 1330 | #endif |
---|
[a604c3] | 1331 | mpz_init_set(u->z,n->n); |
---|
[246d15] | 1332 | u=nlShort3_noinline(u); |
---|
[35aab3] | 1333 | return u; |
---|
| 1334 | } |
---|
| 1335 | } |
---|
| 1336 | } |
---|
| 1337 | return INT_TO_SR(1); |
---|
| 1338 | } |
---|
| 1339 | |
---|
| 1340 | /*2 |
---|
| 1341 | * acces to Nominator, nlCopy(n) for integers |
---|
| 1342 | */ |
---|
[a642c64] | 1343 | number nlGetNumerator(number &n, const coeffs r) |
---|
[35aab3] | 1344 | { |
---|
| 1345 | if (!(SR_HDL(n) & SR_INT)) |
---|
| 1346 | { |
---|
| 1347 | if (n->s==0) |
---|
| 1348 | { |
---|
[a642c64] | 1349 | nlNormalize(n,r); |
---|
[35aab3] | 1350 | } |
---|
| 1351 | if (!(SR_HDL(n) & SR_INT)) |
---|
| 1352 | { |
---|
[896561] | 1353 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 1354 | #if defined(LDEBUG) |
---|
| 1355 | u->debug=123456; |
---|
| 1356 | #endif |
---|
| 1357 | u->s=3; |
---|
[a604c3] | 1358 | mpz_init_set(u->z,n->z); |
---|
[35aab3] | 1359 | if (n->s!=3) |
---|
| 1360 | { |
---|
[246d15] | 1361 | u=nlShort3_noinline(u); |
---|
[35aab3] | 1362 | } |
---|
| 1363 | return u; |
---|
| 1364 | } |
---|
| 1365 | } |
---|
| 1366 | return n; // imm. int |
---|
| 1367 | } |
---|
| 1368 | |
---|
| 1369 | /*************************************************************** |
---|
| 1370 | * |
---|
| 1371 | * routines which are needed by Inline(d) routines |
---|
| 1372 | * |
---|
| 1373 | *******************************************************************/ |
---|
| 1374 | BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b) |
---|
| 1375 | { |
---|
| 1376 | assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT)); |
---|
| 1377 | // long - short |
---|
| 1378 | BOOLEAN bo; |
---|
| 1379 | if (SR_HDL(b) & SR_INT) |
---|
| 1380 | { |
---|
| 1381 | if (a->s!=0) return FALSE; |
---|
| 1382 | number n=b; b=a; a=n; |
---|
| 1383 | } |
---|
| 1384 | // short - long |
---|
| 1385 | if (SR_HDL(a) & SR_INT) |
---|
| 1386 | { |
---|
| 1387 | if (b->s!=0) |
---|
| 1388 | return FALSE; |
---|
[a604c3] | 1389 | if (((long)a > 0L) && (mpz_isNeg(b->z))) |
---|
[35aab3] | 1390 | return FALSE; |
---|
[a604c3] | 1391 | if (((long)a < 0L) && (!mpz_isNeg(b->z))) |
---|
[35aab3] | 1392 | return FALSE; |
---|
[a604c3] | 1393 | mpz_t bb; |
---|
| 1394 | mpz_init_set(bb,b->n); |
---|
| 1395 | mpz_mul_si(bb,bb,(long)SR_TO_INT(a)); |
---|
| 1396 | bo=(mpz_cmp(bb,b->z)==0); |
---|
| 1397 | mpz_clear(bb); |
---|
[35aab3] | 1398 | return bo; |
---|
| 1399 | } |
---|
| 1400 | // long - long |
---|
| 1401 | if (((a->s==1) && (b->s==3)) |
---|
| 1402 | || ((b->s==1) && (a->s==3))) |
---|
| 1403 | return FALSE; |
---|
[a604c3] | 1404 | if (mpz_isNeg(a->z)&&(!mpz_isNeg(b->z))) |
---|
[35aab3] | 1405 | return FALSE; |
---|
[a604c3] | 1406 | if (mpz_isNeg(b->z)&&(!mpz_isNeg(a->z))) |
---|
[35aab3] | 1407 | return FALSE; |
---|
[a604c3] | 1408 | mpz_t aa; |
---|
| 1409 | mpz_t bb; |
---|
| 1410 | mpz_init_set(aa,a->z); |
---|
| 1411 | mpz_init_set(bb,b->z); |
---|
| 1412 | if (a->s<2) mpz_mul(bb,bb,a->n); |
---|
| 1413 | if (b->s<2) mpz_mul(aa,aa,b->n); |
---|
| 1414 | bo=(mpz_cmp(aa,bb)==0); |
---|
| 1415 | mpz_clear(aa); |
---|
| 1416 | mpz_clear(bb); |
---|
[35aab3] | 1417 | return bo; |
---|
| 1418 | } |
---|
| 1419 | |
---|
| 1420 | // copy not immediate number a |
---|
[e69b7c] | 1421 | number _nlCopy_NoImm(number a) |
---|
[35aab3] | 1422 | { |
---|
| 1423 | assume(!((SR_HDL(a) & SR_INT)||(a==NULL))); |
---|
[e69b7c] | 1424 | //nlTest(a, r); |
---|
[896561] | 1425 | number b=ALLOC_RNUMBER(); |
---|
[35aab3] | 1426 | #if defined(LDEBUG) |
---|
| 1427 | b->debug=123456; |
---|
| 1428 | #endif |
---|
| 1429 | switch (a->s) |
---|
| 1430 | { |
---|
| 1431 | case 0: |
---|
| 1432 | case 1: |
---|
[a604c3] | 1433 | mpz_init_set(b->n,a->n); |
---|
[35aab3] | 1434 | case 3: |
---|
[a604c3] | 1435 | mpz_init_set(b->z,a->z); |
---|
[35aab3] | 1436 | break; |
---|
| 1437 | } |
---|
| 1438 | b->s = a->s; |
---|
| 1439 | return b; |
---|
| 1440 | } |
---|
| 1441 | |
---|
[fee4c2] | 1442 | void _nlDelete_NoImm(number *a) |
---|
[35aab3] | 1443 | { |
---|
| 1444 | { |
---|
| 1445 | switch ((*a)->s) |
---|
| 1446 | { |
---|
| 1447 | case 0: |
---|
| 1448 | case 1: |
---|
[a604c3] | 1449 | mpz_clear((*a)->n); |
---|
[35aab3] | 1450 | case 3: |
---|
[a604c3] | 1451 | mpz_clear((*a)->z); |
---|
[35aab3] | 1452 | #ifdef LDEBUG |
---|
| 1453 | (*a)->s=2; |
---|
| 1454 | #endif |
---|
| 1455 | } |
---|
[d663f2] | 1456 | FREE_RNUMBER(*a); // omFreeBin((void *) *a, rnumber_bin); |
---|
[35aab3] | 1457 | } |
---|
| 1458 | } |
---|
| 1459 | |
---|
[e69b7c] | 1460 | number _nlNeg_NoImm(number a) |
---|
[35aab3] | 1461 | { |
---|
| 1462 | { |
---|
[a604c3] | 1463 | mpz_neg(a->z,a->z); |
---|
[246d15] | 1464 | if (a->s==3) |
---|
[35aab3] | 1465 | { |
---|
[246d15] | 1466 | a=nlShort3(a); |
---|
[35aab3] | 1467 | } |
---|
| 1468 | } |
---|
| 1469 | return a; |
---|
| 1470 | } |
---|
| 1471 | |
---|
[e69b7c] | 1472 | number _nlAdd_aNoImm_OR_bNoImm(number a, number b) |
---|
[35aab3] | 1473 | { |
---|
[896561] | 1474 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 1475 | #if defined(LDEBUG) |
---|
| 1476 | u->debug=123456; |
---|
| 1477 | #endif |
---|
[a604c3] | 1478 | mpz_init(u->z); |
---|
[35aab3] | 1479 | if (SR_HDL(b) & SR_INT) |
---|
| 1480 | { |
---|
| 1481 | number x=a; |
---|
| 1482 | a=b; |
---|
| 1483 | b=x; |
---|
| 1484 | } |
---|
| 1485 | if (SR_HDL(a) & SR_INT) |
---|
| 1486 | { |
---|
| 1487 | switch (b->s) |
---|
| 1488 | { |
---|
| 1489 | case 0: |
---|
| 1490 | case 1:/* a:short, b:1 */ |
---|
| 1491 | { |
---|
[a604c3] | 1492 | mpz_t x; |
---|
| 1493 | mpz_init(x); |
---|
| 1494 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
| 1495 | mpz_add(u->z,b->z,x); |
---|
| 1496 | mpz_clear(x); |
---|
| 1497 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1498 | { |
---|
[a604c3] | 1499 | mpz_clear(u->z); |
---|
[896561] | 1500 | FREE_RNUMBER(u); |
---|
[35aab3] | 1501 | return INT_TO_SR(0); |
---|
| 1502 | } |
---|
[a604c3] | 1503 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 1504 | { |
---|
[a604c3] | 1505 | mpz_clear(u->z); |
---|
[896561] | 1506 | FREE_RNUMBER(u); |
---|
[35aab3] | 1507 | return INT_TO_SR(1); |
---|
| 1508 | } |
---|
[a604c3] | 1509 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 1510 | u->s = 0; |
---|
| 1511 | break; |
---|
| 1512 | } |
---|
| 1513 | case 3: |
---|
| 1514 | { |
---|
[7447d8] | 1515 | if ((long)a>0L) |
---|
[a604c3] | 1516 | mpz_add_ui(u->z,b->z,SR_TO_INT(a)); |
---|
[35aab3] | 1517 | else |
---|
[a604c3] | 1518 | mpz_sub_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
| 1519 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1520 | { |
---|
[a604c3] | 1521 | mpz_clear(u->z); |
---|
[896561] | 1522 | FREE_RNUMBER(u); |
---|
[35aab3] | 1523 | return INT_TO_SR(0); |
---|
| 1524 | } |
---|
| 1525 | u->s = 3; |
---|
[246d15] | 1526 | u=nlShort3(u); |
---|
[35aab3] | 1527 | break; |
---|
| 1528 | } |
---|
| 1529 | } |
---|
| 1530 | } |
---|
| 1531 | else |
---|
| 1532 | { |
---|
| 1533 | switch (a->s) |
---|
| 1534 | { |
---|
| 1535 | case 0: |
---|
| 1536 | case 1: |
---|
| 1537 | { |
---|
| 1538 | switch(b->s) |
---|
| 1539 | { |
---|
| 1540 | case 0: |
---|
| 1541 | case 1: |
---|
| 1542 | { |
---|
[a604c3] | 1543 | mpz_t x; |
---|
| 1544 | mpz_init(x); |
---|
[e8a0aa] | 1545 | |
---|
[a604c3] | 1546 | mpz_mul(x,b->z,a->n); |
---|
| 1547 | mpz_mul(u->z,a->z,b->n); |
---|
| 1548 | mpz_add(u->z,u->z,x); |
---|
| 1549 | mpz_clear(x); |
---|
[e8a0aa] | 1550 | |
---|
[a604c3] | 1551 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1552 | { |
---|
[a604c3] | 1553 | mpz_clear(u->z); |
---|
[896561] | 1554 | FREE_RNUMBER(u); |
---|
[35aab3] | 1555 | return INT_TO_SR(0); |
---|
| 1556 | } |
---|
[a604c3] | 1557 | mpz_init(u->n); |
---|
| 1558 | mpz_mul(u->n,a->n,b->n); |
---|
| 1559 | if (mpz_cmp(u->z,u->n)==0) |
---|
[35aab3] | 1560 | { |
---|
[a604c3] | 1561 | mpz_clear(u->z); |
---|
| 1562 | mpz_clear(u->n); |
---|
[896561] | 1563 | FREE_RNUMBER(u); |
---|
[35aab3] | 1564 | return INT_TO_SR(1); |
---|
| 1565 | } |
---|
| 1566 | u->s = 0; |
---|
| 1567 | break; |
---|
| 1568 | } |
---|
| 1569 | case 3: /* a:1 b:3 */ |
---|
| 1570 | { |
---|
[a604c3] | 1571 | mpz_mul(u->z,b->z,a->n); |
---|
| 1572 | mpz_add(u->z,u->z,a->z); |
---|
| 1573 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1574 | { |
---|
[a604c3] | 1575 | mpz_clear(u->z); |
---|
[896561] | 1576 | FREE_RNUMBER(u); |
---|
[35aab3] | 1577 | return INT_TO_SR(0); |
---|
| 1578 | } |
---|
[a604c3] | 1579 | if (mpz_cmp(u->z,a->n)==0) |
---|
[35aab3] | 1580 | { |
---|
[a604c3] | 1581 | mpz_clear(u->z); |
---|
[896561] | 1582 | FREE_RNUMBER(u); |
---|
[35aab3] | 1583 | return INT_TO_SR(1); |
---|
| 1584 | } |
---|
[a604c3] | 1585 | mpz_init_set(u->n,a->n); |
---|
[35aab3] | 1586 | u->s = 0; |
---|
| 1587 | break; |
---|
| 1588 | } |
---|
| 1589 | } /*switch (b->s) */ |
---|
| 1590 | break; |
---|
| 1591 | } |
---|
| 1592 | case 3: |
---|
| 1593 | { |
---|
| 1594 | switch(b->s) |
---|
| 1595 | { |
---|
| 1596 | case 0: |
---|
| 1597 | case 1:/* a:3, b:1 */ |
---|
| 1598 | { |
---|
[a604c3] | 1599 | mpz_mul(u->z,a->z,b->n); |
---|
| 1600 | mpz_add(u->z,u->z,b->z); |
---|
| 1601 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1602 | { |
---|
[a604c3] | 1603 | mpz_clear(u->z); |
---|
[896561] | 1604 | FREE_RNUMBER(u); |
---|
[35aab3] | 1605 | return INT_TO_SR(0); |
---|
| 1606 | } |
---|
[a604c3] | 1607 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 1608 | { |
---|
[a604c3] | 1609 | mpz_clear(u->z); |
---|
[896561] | 1610 | FREE_RNUMBER(u); |
---|
[35aab3] | 1611 | return INT_TO_SR(1); |
---|
| 1612 | } |
---|
[a604c3] | 1613 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 1614 | u->s = 0; |
---|
| 1615 | break; |
---|
| 1616 | } |
---|
| 1617 | case 3: |
---|
| 1618 | { |
---|
[a604c3] | 1619 | mpz_add(u->z,a->z,b->z); |
---|
| 1620 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1621 | { |
---|
[a604c3] | 1622 | mpz_clear(u->z); |
---|
[896561] | 1623 | FREE_RNUMBER(u); |
---|
[35aab3] | 1624 | return INT_TO_SR(0); |
---|
| 1625 | } |
---|
| 1626 | u->s = 3; |
---|
[246d15] | 1627 | u=nlShort3(u); |
---|
[35aab3] | 1628 | break; |
---|
| 1629 | } |
---|
| 1630 | } |
---|
| 1631 | break; |
---|
| 1632 | } |
---|
| 1633 | } |
---|
| 1634 | } |
---|
| 1635 | return u; |
---|
| 1636 | } |
---|
| 1637 | |
---|
[65c5f5] | 1638 | void _nlInpAdd_aNoImm_OR_bNoImm(number &a, number b) |
---|
| 1639 | { |
---|
| 1640 | if (SR_HDL(b) & SR_INT) |
---|
| 1641 | { |
---|
| 1642 | switch (a->s) |
---|
| 1643 | { |
---|
| 1644 | case 0: |
---|
| 1645 | case 1:/* b:short, a:1 */ |
---|
| 1646 | { |
---|
| 1647 | mpz_t x; |
---|
| 1648 | mpz_init(x); |
---|
| 1649 | mpz_mul_si(x,a->n,SR_TO_INT(b)); |
---|
| 1650 | mpz_add(a->z,a->z,x); |
---|
| 1651 | mpz_clear(x); |
---|
| 1652 | a->s = 0; |
---|
| 1653 | a=nlShort1(a); |
---|
| 1654 | break; |
---|
| 1655 | } |
---|
| 1656 | case 3: |
---|
| 1657 | { |
---|
| 1658 | if ((long)b>0L) |
---|
| 1659 | mpz_add_ui(a->z,a->z,SR_TO_INT(b)); |
---|
| 1660 | else |
---|
| 1661 | mpz_sub_ui(a->z,a->z,-SR_TO_INT(b)); |
---|
| 1662 | a->s = 3; |
---|
| 1663 | a=nlShort3_noinline(a); |
---|
| 1664 | break; |
---|
| 1665 | } |
---|
| 1666 | } |
---|
| 1667 | return; |
---|
| 1668 | } |
---|
| 1669 | else if (SR_HDL(a) & SR_INT) |
---|
| 1670 | { |
---|
| 1671 | number u=ALLOC_RNUMBER(); |
---|
| 1672 | #if defined(LDEBUG) |
---|
| 1673 | u->debug=123456; |
---|
| 1674 | #endif |
---|
| 1675 | mpz_init(u->z); |
---|
| 1676 | switch (b->s) |
---|
| 1677 | { |
---|
| 1678 | case 0: |
---|
| 1679 | case 1:/* a:short, b:1 */ |
---|
| 1680 | { |
---|
| 1681 | mpz_t x; |
---|
| 1682 | mpz_init(x); |
---|
| 1683 | |
---|
| 1684 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
| 1685 | mpz_add(u->z,b->z,x); |
---|
| 1686 | mpz_clear(x); |
---|
| 1687 | // result cannot be 0, if coeffs are normalized |
---|
| 1688 | mpz_init_set(u->n,b->n); |
---|
| 1689 | u->s = 0; |
---|
| 1690 | u=nlShort1(u); |
---|
| 1691 | break; |
---|
| 1692 | } |
---|
| 1693 | case 3: |
---|
| 1694 | { |
---|
| 1695 | if ((long)a>0L) |
---|
| 1696 | mpz_add_ui(u->z,b->z,SR_TO_INT(a)); |
---|
| 1697 | else |
---|
| 1698 | mpz_sub_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
| 1699 | // result cannot be 0, if coeffs are normalized |
---|
| 1700 | u->s = 3; |
---|
| 1701 | u=nlShort3_noinline(u); |
---|
| 1702 | break; |
---|
| 1703 | } |
---|
| 1704 | } |
---|
| 1705 | a=u; |
---|
| 1706 | } |
---|
| 1707 | else |
---|
| 1708 | { |
---|
| 1709 | switch (a->s) |
---|
| 1710 | { |
---|
| 1711 | case 0: |
---|
| 1712 | case 1: |
---|
| 1713 | { |
---|
| 1714 | switch(b->s) |
---|
| 1715 | { |
---|
| 1716 | case 0: |
---|
| 1717 | case 1: /* a:1 b:1 */ |
---|
| 1718 | { |
---|
| 1719 | mpz_t x; |
---|
| 1720 | mpz_t y; |
---|
| 1721 | mpz_init(x); |
---|
| 1722 | mpz_init(y); |
---|
| 1723 | mpz_mul(x,b->z,a->n); |
---|
| 1724 | mpz_mul(y,a->z,b->n); |
---|
| 1725 | mpz_add(a->z,x,y); |
---|
| 1726 | mpz_clear(x); |
---|
| 1727 | mpz_clear(y); |
---|
| 1728 | mpz_mul(a->n,a->n,b->n); |
---|
| 1729 | a->s = 0; |
---|
| 1730 | break; |
---|
| 1731 | } |
---|
| 1732 | case 3: /* a:1 b:3 */ |
---|
| 1733 | { |
---|
| 1734 | mpz_t x; |
---|
| 1735 | mpz_init(x); |
---|
| 1736 | mpz_mul(x,b->z,a->n); |
---|
| 1737 | mpz_add(a->z,a->z,x); |
---|
| 1738 | mpz_clear(x); |
---|
| 1739 | a->s = 0; |
---|
| 1740 | break; |
---|
| 1741 | } |
---|
| 1742 | } /*switch (b->s) */ |
---|
| 1743 | a=nlShort1(a); |
---|
| 1744 | break; |
---|
| 1745 | } |
---|
| 1746 | case 3: |
---|
| 1747 | { |
---|
| 1748 | switch(b->s) |
---|
| 1749 | { |
---|
| 1750 | case 0: |
---|
| 1751 | case 1:/* a:3, b:1 */ |
---|
| 1752 | { |
---|
| 1753 | mpz_t x; |
---|
| 1754 | mpz_init(x); |
---|
| 1755 | mpz_mul(x,a->z,b->n); |
---|
| 1756 | mpz_add(a->z,b->z,x); |
---|
| 1757 | mpz_clear(x); |
---|
| 1758 | mpz_init_set(a->n,b->n); |
---|
| 1759 | a->s = 0; |
---|
| 1760 | a=nlShort1(a); |
---|
| 1761 | break; |
---|
| 1762 | } |
---|
| 1763 | case 3: |
---|
| 1764 | { |
---|
| 1765 | mpz_add(a->z,a->z,b->z); |
---|
| 1766 | a->s = 3; |
---|
| 1767 | a=nlShort3_noinline(a); |
---|
| 1768 | break; |
---|
| 1769 | } |
---|
| 1770 | } |
---|
| 1771 | break; |
---|
| 1772 | } |
---|
| 1773 | } |
---|
| 1774 | } |
---|
| 1775 | } |
---|
| 1776 | |
---|
[e69b7c] | 1777 | number _nlSub_aNoImm_OR_bNoImm(number a, number b) |
---|
[35aab3] | 1778 | { |
---|
[896561] | 1779 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 1780 | #if defined(LDEBUG) |
---|
| 1781 | u->debug=123456; |
---|
| 1782 | #endif |
---|
[a604c3] | 1783 | mpz_init(u->z); |
---|
[35aab3] | 1784 | if (SR_HDL(a) & SR_INT) |
---|
| 1785 | { |
---|
| 1786 | switch (b->s) |
---|
| 1787 | { |
---|
| 1788 | case 0: |
---|
| 1789 | case 1:/* a:short, b:1 */ |
---|
| 1790 | { |
---|
[a604c3] | 1791 | mpz_t x; |
---|
| 1792 | mpz_init(x); |
---|
| 1793 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
| 1794 | mpz_sub(u->z,x,b->z); |
---|
| 1795 | mpz_clear(x); |
---|
| 1796 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1797 | { |
---|
[a604c3] | 1798 | mpz_clear(u->z); |
---|
[896561] | 1799 | FREE_RNUMBER(u); |
---|
[35aab3] | 1800 | return INT_TO_SR(0); |
---|
| 1801 | } |
---|
[a604c3] | 1802 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 1803 | { |
---|
[a604c3] | 1804 | mpz_clear(u->z); |
---|
[896561] | 1805 | FREE_RNUMBER(u); |
---|
[35aab3] | 1806 | return INT_TO_SR(1); |
---|
| 1807 | } |
---|
[a604c3] | 1808 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 1809 | u->s = 0; |
---|
| 1810 | break; |
---|
| 1811 | } |
---|
| 1812 | case 3: |
---|
| 1813 | { |
---|
[7447d8] | 1814 | if ((long)a>0L) |
---|
[35aab3] | 1815 | { |
---|
[a604c3] | 1816 | mpz_sub_ui(u->z,b->z,SR_TO_INT(a)); |
---|
| 1817 | mpz_neg(u->z,u->z); |
---|
[35aab3] | 1818 | } |
---|
| 1819 | else |
---|
| 1820 | { |
---|
[a604c3] | 1821 | mpz_add_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
| 1822 | mpz_neg(u->z,u->z); |
---|
[35aab3] | 1823 | } |
---|
[a604c3] | 1824 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1825 | { |
---|
[a604c3] | 1826 | mpz_clear(u->z); |
---|
[896561] | 1827 | FREE_RNUMBER(u); |
---|
[35aab3] | 1828 | return INT_TO_SR(0); |
---|
| 1829 | } |
---|
| 1830 | u->s = 3; |
---|
[246d15] | 1831 | u=nlShort3(u); |
---|
[35aab3] | 1832 | break; |
---|
| 1833 | } |
---|
| 1834 | } |
---|
| 1835 | } |
---|
| 1836 | else if (SR_HDL(b) & SR_INT) |
---|
| 1837 | { |
---|
| 1838 | switch (a->s) |
---|
| 1839 | { |
---|
| 1840 | case 0: |
---|
| 1841 | case 1:/* b:short, a:1 */ |
---|
| 1842 | { |
---|
[a604c3] | 1843 | mpz_t x; |
---|
| 1844 | mpz_init(x); |
---|
| 1845 | mpz_mul_si(x,a->n,SR_TO_INT(b)); |
---|
| 1846 | mpz_sub(u->z,a->z,x); |
---|
| 1847 | mpz_clear(x); |
---|
| 1848 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1849 | { |
---|
[a604c3] | 1850 | mpz_clear(u->z); |
---|
[896561] | 1851 | FREE_RNUMBER(u); |
---|
[35aab3] | 1852 | return INT_TO_SR(0); |
---|
| 1853 | } |
---|
[a604c3] | 1854 | if (mpz_cmp(u->z,a->n)==0) |
---|
[35aab3] | 1855 | { |
---|
[a604c3] | 1856 | mpz_clear(u->z); |
---|
[896561] | 1857 | FREE_RNUMBER(u); |
---|
[35aab3] | 1858 | return INT_TO_SR(1); |
---|
| 1859 | } |
---|
[a604c3] | 1860 | mpz_init_set(u->n,a->n); |
---|
[35aab3] | 1861 | u->s = 0; |
---|
| 1862 | break; |
---|
| 1863 | } |
---|
| 1864 | case 3: |
---|
| 1865 | { |
---|
[7447d8] | 1866 | if ((long)b>0L) |
---|
[35aab3] | 1867 | { |
---|
[a604c3] | 1868 | mpz_sub_ui(u->z,a->z,SR_TO_INT(b)); |
---|
[35aab3] | 1869 | } |
---|
| 1870 | else |
---|
| 1871 | { |
---|
[a604c3] | 1872 | mpz_add_ui(u->z,a->z,-SR_TO_INT(b)); |
---|
[35aab3] | 1873 | } |
---|
[a604c3] | 1874 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1875 | { |
---|
[a604c3] | 1876 | mpz_clear(u->z); |
---|
[896561] | 1877 | FREE_RNUMBER(u); |
---|
[35aab3] | 1878 | return INT_TO_SR(0); |
---|
| 1879 | } |
---|
| 1880 | u->s = 3; |
---|
[246d15] | 1881 | u=nlShort3(u); |
---|
[35aab3] | 1882 | break; |
---|
| 1883 | } |
---|
| 1884 | } |
---|
| 1885 | } |
---|
| 1886 | else |
---|
| 1887 | { |
---|
| 1888 | switch (a->s) |
---|
| 1889 | { |
---|
| 1890 | case 0: |
---|
| 1891 | case 1: |
---|
| 1892 | { |
---|
| 1893 | switch(b->s) |
---|
| 1894 | { |
---|
| 1895 | case 0: |
---|
| 1896 | case 1: |
---|
| 1897 | { |
---|
[a604c3] | 1898 | mpz_t x; |
---|
| 1899 | mpz_t y; |
---|
| 1900 | mpz_init(x); |
---|
| 1901 | mpz_init(y); |
---|
| 1902 | mpz_mul(x,b->z,a->n); |
---|
| 1903 | mpz_mul(y,a->z,b->n); |
---|
| 1904 | mpz_sub(u->z,y,x); |
---|
| 1905 | mpz_clear(x); |
---|
| 1906 | mpz_clear(y); |
---|
| 1907 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1908 | { |
---|
[a604c3] | 1909 | mpz_clear(u->z); |
---|
[896561] | 1910 | FREE_RNUMBER(u); |
---|
[35aab3] | 1911 | return INT_TO_SR(0); |
---|
| 1912 | } |
---|
[a604c3] | 1913 | mpz_init(u->n); |
---|
| 1914 | mpz_mul(u->n,a->n,b->n); |
---|
| 1915 | if (mpz_cmp(u->z,u->n)==0) |
---|
[35aab3] | 1916 | { |
---|
[a604c3] | 1917 | mpz_clear(u->z); |
---|
| 1918 | mpz_clear(u->n); |
---|
[896561] | 1919 | FREE_RNUMBER(u); |
---|
[35aab3] | 1920 | return INT_TO_SR(1); |
---|
| 1921 | } |
---|
| 1922 | u->s = 0; |
---|
| 1923 | break; |
---|
| 1924 | } |
---|
| 1925 | case 3: /* a:1, b:3 */ |
---|
| 1926 | { |
---|
[a604c3] | 1927 | mpz_t x; |
---|
| 1928 | mpz_init(x); |
---|
| 1929 | mpz_mul(x,b->z,a->n); |
---|
| 1930 | mpz_sub(u->z,a->z,x); |
---|
| 1931 | mpz_clear(x); |
---|
| 1932 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1933 | { |
---|
[a604c3] | 1934 | mpz_clear(u->z); |
---|
[896561] | 1935 | FREE_RNUMBER(u); |
---|
[35aab3] | 1936 | return INT_TO_SR(0); |
---|
| 1937 | } |
---|
[a604c3] | 1938 | if (mpz_cmp(u->z,a->n)==0) |
---|
[35aab3] | 1939 | { |
---|
[a604c3] | 1940 | mpz_clear(u->z); |
---|
[896561] | 1941 | FREE_RNUMBER(u); |
---|
[35aab3] | 1942 | return INT_TO_SR(1); |
---|
| 1943 | } |
---|
[a604c3] | 1944 | mpz_init_set(u->n,a->n); |
---|
[35aab3] | 1945 | u->s = 0; |
---|
| 1946 | break; |
---|
| 1947 | } |
---|
| 1948 | } |
---|
| 1949 | break; |
---|
| 1950 | } |
---|
| 1951 | case 3: |
---|
| 1952 | { |
---|
| 1953 | switch(b->s) |
---|
| 1954 | { |
---|
| 1955 | case 0: |
---|
| 1956 | case 1: /* a:3, b:1 */ |
---|
| 1957 | { |
---|
[a604c3] | 1958 | mpz_t x; |
---|
| 1959 | mpz_init(x); |
---|
| 1960 | mpz_mul(x,a->z,b->n); |
---|
| 1961 | mpz_sub(u->z,x,b->z); |
---|
| 1962 | mpz_clear(x); |
---|
| 1963 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1964 | { |
---|
[a604c3] | 1965 | mpz_clear(u->z); |
---|
[896561] | 1966 | FREE_RNUMBER(u); |
---|
[35aab3] | 1967 | return INT_TO_SR(0); |
---|
| 1968 | } |
---|
[a604c3] | 1969 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 1970 | { |
---|
[a604c3] | 1971 | mpz_clear(u->z); |
---|
[896561] | 1972 | FREE_RNUMBER(u); |
---|
[35aab3] | 1973 | return INT_TO_SR(1); |
---|
| 1974 | } |
---|
[a604c3] | 1975 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 1976 | u->s = 0; |
---|
| 1977 | break; |
---|
| 1978 | } |
---|
| 1979 | case 3: /* a:3 , b:3 */ |
---|
| 1980 | { |
---|
[a604c3] | 1981 | mpz_sub(u->z,a->z,b->z); |
---|
| 1982 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
[35aab3] | 1983 | { |
---|
[a604c3] | 1984 | mpz_clear(u->z); |
---|
[896561] | 1985 | FREE_RNUMBER(u); |
---|
[35aab3] | 1986 | return INT_TO_SR(0); |
---|
| 1987 | } |
---|
| 1988 | u->s = 3; |
---|
[246d15] | 1989 | u=nlShort3(u); |
---|
[35aab3] | 1990 | break; |
---|
| 1991 | } |
---|
| 1992 | } |
---|
| 1993 | break; |
---|
| 1994 | } |
---|
| 1995 | } |
---|
| 1996 | } |
---|
| 1997 | return u; |
---|
| 1998 | } |
---|
| 1999 | |
---|
| 2000 | // a and b are intermediate, but a*b not |
---|
[e69b7c] | 2001 | number _nlMult_aImm_bImm_rNoImm(number a, number b) |
---|
[35aab3] | 2002 | { |
---|
[896561] | 2003 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 2004 | #if defined(LDEBUG) |
---|
| 2005 | u->debug=123456; |
---|
| 2006 | #endif |
---|
| 2007 | u->s=3; |
---|
[246d15] | 2008 | mpz_init_set_si(u->z,SR_TO_INT(a)); |
---|
| 2009 | mpz_mul_si(u->z,u->z,SR_TO_INT(b)); |
---|
[35aab3] | 2010 | return u; |
---|
| 2011 | } |
---|
| 2012 | |
---|
| 2013 | // a or b are not immediate |
---|
[e69b7c] | 2014 | number _nlMult_aNoImm_OR_bNoImm(number a, number b) |
---|
[35aab3] | 2015 | { |
---|
| 2016 | assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT)); |
---|
[896561] | 2017 | number u=ALLOC_RNUMBER(); |
---|
[35aab3] | 2018 | #if defined(LDEBUG) |
---|
| 2019 | u->debug=123456; |
---|
| 2020 | #endif |
---|
[a604c3] | 2021 | mpz_init(u->z); |
---|
[35aab3] | 2022 | if (SR_HDL(b) & SR_INT) |
---|
| 2023 | { |
---|
| 2024 | number x=a; |
---|
| 2025 | a=b; |
---|
| 2026 | b=x; |
---|
| 2027 | } |
---|
| 2028 | if (SR_HDL(a) & SR_INT) |
---|
| 2029 | { |
---|
| 2030 | u->s=b->s; |
---|
| 2031 | if (u->s==1) u->s=0; |
---|
[7447d8] | 2032 | if ((long)a>0L) |
---|
[35aab3] | 2033 | { |
---|
[a604c3] | 2034 | mpz_mul_ui(u->z,b->z,(unsigned long)SR_TO_INT(a)); |
---|
[35aab3] | 2035 | } |
---|
| 2036 | else |
---|
| 2037 | { |
---|
| 2038 | if (a==INT_TO_SR(-1)) |
---|
| 2039 | { |
---|
[a604c3] | 2040 | mpz_set(u->z,b->z); |
---|
| 2041 | mpz_neg(u->z,u->z); |
---|
[35aab3] | 2042 | u->s=b->s; |
---|
| 2043 | } |
---|
| 2044 | else |
---|
| 2045 | { |
---|
[a604c3] | 2046 | mpz_mul_ui(u->z,b->z,(unsigned long)-SR_TO_INT(a)); |
---|
| 2047 | mpz_neg(u->z,u->z); |
---|
[35aab3] | 2048 | } |
---|
| 2049 | } |
---|
| 2050 | if (u->s<2) |
---|
| 2051 | { |
---|
[a604c3] | 2052 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 2053 | { |
---|
[a604c3] | 2054 | mpz_clear(u->z); |
---|
[896561] | 2055 | FREE_RNUMBER(u); |
---|
[35aab3] | 2056 | return INT_TO_SR(1); |
---|
| 2057 | } |
---|
[a604c3] | 2058 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 2059 | } |
---|
| 2060 | else //u->s==3 |
---|
| 2061 | { |
---|
[246d15] | 2062 | u=nlShort3(u); |
---|
[35aab3] | 2063 | } |
---|
| 2064 | } |
---|
| 2065 | else |
---|
| 2066 | { |
---|
[a604c3] | 2067 | mpz_mul(u->z,a->z,b->z); |
---|
[35aab3] | 2068 | u->s = 0; |
---|
| 2069 | if(a->s==3) |
---|
| 2070 | { |
---|
| 2071 | if(b->s==3) |
---|
| 2072 | { |
---|
| 2073 | u->s = 3; |
---|
| 2074 | } |
---|
| 2075 | else |
---|
| 2076 | { |
---|
[a604c3] | 2077 | if (mpz_cmp(u->z,b->n)==0) |
---|
[35aab3] | 2078 | { |
---|
[a604c3] | 2079 | mpz_clear(u->z); |
---|
[896561] | 2080 | FREE_RNUMBER(u); |
---|
[35aab3] | 2081 | return INT_TO_SR(1); |
---|
| 2082 | } |
---|
[a604c3] | 2083 | mpz_init_set(u->n,b->n); |
---|
[35aab3] | 2084 | } |
---|
| 2085 | } |
---|
| 2086 | else |
---|
| 2087 | { |
---|
| 2088 | if(b->s==3) |
---|
| 2089 | { |
---|
[a604c3] | 2090 | if (mpz_cmp(u->z,a->n)==0) |
---|
[35aab3] | 2091 | { |
---|
[a604c3] | 2092 | mpz_clear(u->z); |
---|
[896561] | 2093 | FREE_RNUMBER(u); |
---|
[35aab3] | 2094 | return INT_TO_SR(1); |
---|
| 2095 | } |
---|
[a604c3] | 2096 | mpz_init_set(u->n,a->n); |
---|
[35aab3] | 2097 | } |
---|
| 2098 | else |
---|
| 2099 | { |
---|
[a604c3] | 2100 | mpz_init(u->n); |
---|
| 2101 | mpz_mul(u->n,a->n,b->n); |
---|
| 2102 | if (mpz_cmp(u->z,u->n)==0) |
---|
[35aab3] | 2103 | { |
---|
[a604c3] | 2104 | mpz_clear(u->z); |
---|
| 2105 | mpz_clear(u->n); |
---|
[896561] | 2106 | FREE_RNUMBER(u); |
---|
[35aab3] | 2107 | return INT_TO_SR(1); |
---|
| 2108 | } |
---|
| 2109 | } |
---|
| 2110 | } |
---|
| 2111 | } |
---|
| 2112 | return u; |
---|
| 2113 | } |
---|
| 2114 | |
---|
[371bc5f] | 2115 | /*2 |
---|
[fa31d2] | 2116 | * copy a to b for mapping |
---|
[371bc5f] | 2117 | */ |
---|
[fa31d2] | 2118 | number nlCopyMap(number a, const coeffs src, const coeffs dst) |
---|
[371bc5f] | 2119 | { |
---|
[fa31d2] | 2120 | assume( getCoeffType(dst) == ID ); |
---|
| 2121 | assume( getCoeffType(src) == ID ); |
---|
[9bb5457] | 2122 | |
---|
[371bc5f] | 2123 | if ((SR_HDL(a) & SR_INT)||(a==NULL)) |
---|
| 2124 | { |
---|
| 2125 | return a; |
---|
| 2126 | } |
---|
[e69b7c] | 2127 | return _nlCopy_NoImm(a); |
---|
[371bc5f] | 2128 | } |
---|
[2b957a] | 2129 | |
---|
[371bc5f] | 2130 | nMapFunc nlSetMap(const coeffs src, const coeffs dst) |
---|
| 2131 | { |
---|
[fa31d2] | 2132 | assume( getCoeffType(dst) == ID ); |
---|
[2b957a] | 2133 | // assume( getCoeffType(src) == ID ); |
---|
[9bb5457] | 2134 | |
---|
[1cce47] | 2135 | if (nCoeff_is_Q(src)) |
---|
[371bc5f] | 2136 | { |
---|
[c14846c] | 2137 | return ndCopyMap; |
---|
[371bc5f] | 2138 | } |
---|
[1cce47] | 2139 | if (nCoeff_is_Zp(src)) |
---|
[371bc5f] | 2140 | { |
---|
| 2141 | return nlMapP; |
---|
| 2142 | } |
---|
[1cce47] | 2143 | if (nCoeff_is_R(src)) |
---|
[371bc5f] | 2144 | { |
---|
| 2145 | return nlMapR; |
---|
| 2146 | } |
---|
[1cce47] | 2147 | if (nCoeff_is_long_R(src)) |
---|
[371bc5f] | 2148 | { |
---|
| 2149 | return nlMapLongR; /* long R -> Q */ |
---|
| 2150 | } |
---|
| 2151 | #ifdef HAVE_RINGS |
---|
[1cce47] | 2152 | if (nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src)) |
---|
[371bc5f] | 2153 | { |
---|
| 2154 | return nlMapGMP; |
---|
| 2155 | } |
---|
[1cce47] | 2156 | if (nCoeff_is_Ring_2toM(src)) |
---|
[371bc5f] | 2157 | { |
---|
| 2158 | return nlMapMachineInt; |
---|
| 2159 | } |
---|
| 2160 | #endif |
---|
| 2161 | return NULL; |
---|
| 2162 | } |
---|
[35aab3] | 2163 | /*2 |
---|
| 2164 | * z := i |
---|
| 2165 | */ |
---|
[246d15] | 2166 | number nlRInit (long i) |
---|
[35aab3] | 2167 | { |
---|
[896561] | 2168 | number z=ALLOC_RNUMBER(); |
---|
[35aab3] | 2169 | #if defined(LDEBUG) |
---|
| 2170 | z->debug=123456; |
---|
| 2171 | #endif |
---|
[246d15] | 2172 | mpz_init_set_si(z->z,i); |
---|
[35aab3] | 2173 | z->s = 3; |
---|
| 2174 | return z; |
---|
| 2175 | } |
---|
| 2176 | |
---|
| 2177 | /*2 |
---|
| 2178 | * z := i/j |
---|
| 2179 | */ |
---|
[a642c64] | 2180 | number nlInit2 (int i, int j, const coeffs r) |
---|
[35aab3] | 2181 | { |
---|
[896561] | 2182 | number z=ALLOC_RNUMBER(); |
---|
[35aab3] | 2183 | #if defined(LDEBUG) |
---|
| 2184 | z->debug=123456; |
---|
| 2185 | #endif |
---|
[a604c3] | 2186 | mpz_init_set_si(z->z,(long)i); |
---|
| 2187 | mpz_init_set_si(z->n,(long)j); |
---|
[35aab3] | 2188 | z->s = 0; |
---|
[a642c64] | 2189 | nlNormalize(z,r); |
---|
[35aab3] | 2190 | return z; |
---|
| 2191 | } |
---|
| 2192 | |
---|
[a642c64] | 2193 | number nlInit2gmp (mpz_t i, mpz_t j, const coeffs r) |
---|
[a1ab2a] | 2194 | { |
---|
[896561] | 2195 | number z=ALLOC_RNUMBER(); |
---|
[a1ab2a] | 2196 | #if defined(LDEBUG) |
---|
| 2197 | z->debug=123456; |
---|
| 2198 | #endif |
---|
[a604c3] | 2199 | mpz_init_set(z->z,i); |
---|
| 2200 | mpz_init_set(z->n,j); |
---|
[a1ab2a] | 2201 | z->s = 0; |
---|
[a642c64] | 2202 | nlNormalize(z,r); |
---|
[a1ab2a] | 2203 | return z; |
---|
| 2204 | } |
---|
| 2205 | |
---|
[35aab3] | 2206 | #else // DO_LINLINE |
---|
| 2207 | |
---|
| 2208 | // declare immedate routines |
---|
[2f3764] | 2209 | number nlRInit (long i); |
---|
[35aab3] | 2210 | BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b); |
---|
| 2211 | number _nlCopy_NoImm(number a); |
---|
| 2212 | number _nlNeg_NoImm(number a); |
---|
| 2213 | number _nlAdd_aNoImm_OR_bNoImm(number a, number b); |
---|
[65c5f5] | 2214 | void _nlInpAdd_aNoImm_OR_bNoImm(number &a, number b); |
---|
[35aab3] | 2215 | number _nlSub_aNoImm_OR_bNoImm(number a, number b); |
---|
| 2216 | number _nlMult_aNoImm_OR_bNoImm(number a, number b); |
---|
| 2217 | number _nlMult_aImm_bImm_rNoImm(number a, number b); |
---|
| 2218 | |
---|
| 2219 | #endif |
---|
| 2220 | |
---|
| 2221 | /*************************************************************** |
---|
| 2222 | * |
---|
| 2223 | * Routines which might be inlined by p_Numbers.h |
---|
| 2224 | * |
---|
| 2225 | *******************************************************************/ |
---|
| 2226 | #if defined(DO_LINLINE) || !defined(P_NUMBERS_H) |
---|
| 2227 | |
---|
| 2228 | // routines which are always inlined/static |
---|
| 2229 | |
---|
| 2230 | /*2 |
---|
| 2231 | * a = b ? |
---|
| 2232 | */ |
---|
[2b957a] | 2233 | LINLINE BOOLEAN nlEqual (number a, number b, const coeffs r) |
---|
[35aab3] | 2234 | { |
---|
[2b957a] | 2235 | nlTest(a, r); |
---|
| 2236 | nlTest(b, r); |
---|
[35aab3] | 2237 | // short - short |
---|
| 2238 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) return a==b; |
---|
| 2239 | return _nlEqual_aNoImm_OR_bNoImm(a, b); |
---|
| 2240 | } |
---|
| 2241 | |
---|
[2f3764] | 2242 | LINLINE number nlInit (long i, const coeffs r) |
---|
[35aab3] | 2243 | { |
---|
| 2244 | number n; |
---|
[246d15] | 2245 | LONG ii=(LONG)i; |
---|
| 2246 | if ( ((ii << 3) >> 3) == ii ) n=INT_TO_SR(ii); |
---|
| 2247 | else n=nlRInit(ii); |
---|
[2b957a] | 2248 | nlTest(n, r); |
---|
[35aab3] | 2249 | return n; |
---|
| 2250 | } |
---|
| 2251 | |
---|
| 2252 | /*2 |
---|
| 2253 | * a == 1 ? |
---|
| 2254 | */ |
---|
[2b957a] | 2255 | LINLINE BOOLEAN nlIsOne (number a, const coeffs r) |
---|
[35aab3] | 2256 | { |
---|
| 2257 | #ifdef LDEBUG |
---|
| 2258 | if (a==NULL) return FALSE; |
---|
[2b957a] | 2259 | nlTest(a, r); |
---|
[35aab3] | 2260 | #endif |
---|
[89ca47] | 2261 | return (a==INT_TO_SR(1)); |
---|
[35aab3] | 2262 | } |
---|
| 2263 | |
---|
[121fd9] | 2264 | LINLINE BOOLEAN nlIsZero (number a, const coeffs) |
---|
[35aab3] | 2265 | { |
---|
[cc3240c] | 2266 | #if 0 |
---|
| 2267 | if (a==INT_TO_SR(0)) return TRUE; |
---|
| 2268 | if ((SR_HDL(a) & SR_INT)||(a==NULL)) return FALSE; |
---|
| 2269 | if (mpz_cmp_si(a->z,(long)0)==0) |
---|
| 2270 | { |
---|
| 2271 | printf("gmp-0 in nlIsZero\n"); |
---|
| 2272 | dErrorBreak(); |
---|
| 2273 | return TRUE; |
---|
| 2274 | } |
---|
| 2275 | return FALSE; |
---|
| 2276 | #else |
---|
[35aab3] | 2277 | return (a==INT_TO_SR(0)); |
---|
[cc3240c] | 2278 | #endif |
---|
[35aab3] | 2279 | } |
---|
| 2280 | |
---|
| 2281 | /*2 |
---|
| 2282 | * copy a to b |
---|
| 2283 | */ |
---|
[121fd9] | 2284 | LINLINE number nlCopy(number a, const coeffs) |
---|
[35aab3] | 2285 | { |
---|
| 2286 | if ((SR_HDL(a) & SR_INT)||(a==NULL)) |
---|
| 2287 | { |
---|
| 2288 | return a; |
---|
| 2289 | } |
---|
[e69b7c] | 2290 | return _nlCopy_NoImm(a); |
---|
[35aab3] | 2291 | } |
---|
| 2292 | |
---|
| 2293 | |
---|
| 2294 | /*2 |
---|
| 2295 | * delete a |
---|
| 2296 | */ |
---|
[a642c64] | 2297 | LINLINE void nlDelete (number * a, const coeffs r) |
---|
[35aab3] | 2298 | { |
---|
| 2299 | if (*a!=NULL) |
---|
| 2300 | { |
---|
[2b957a] | 2301 | nlTest(*a, r); |
---|
[35aab3] | 2302 | if ((SR_HDL(*a) & SR_INT)==0) |
---|
| 2303 | { |
---|
[fee4c2] | 2304 | _nlDelete_NoImm(a); |
---|
[35aab3] | 2305 | } |
---|
| 2306 | *a=NULL; |
---|
| 2307 | } |
---|
| 2308 | } |
---|
| 2309 | |
---|
| 2310 | /*2 |
---|
| 2311 | * za:= - za |
---|
| 2312 | */ |
---|
[e69b7c] | 2313 | LINLINE number nlNeg (number a, const coeffs R) |
---|
[35aab3] | 2314 | { |
---|
[e69b7c] | 2315 | nlTest(a, R); |
---|
[35aab3] | 2316 | if(SR_HDL(a) &SR_INT) |
---|
| 2317 | { |
---|
| 2318 | int r=SR_TO_INT(a); |
---|
[246d15] | 2319 | if (r==(-(POW_2_28))) a=nlRInit(POW_2_28); |
---|
[35aab3] | 2320 | else a=INT_TO_SR(-r); |
---|
| 2321 | return a; |
---|
| 2322 | } |
---|
[630ca9] | 2323 | a = _nlNeg_NoImm(a); |
---|
| 2324 | nlTest(a, R); |
---|
| 2325 | return a; |
---|
| 2326 | |
---|
[35aab3] | 2327 | } |
---|
| 2328 | |
---|
| 2329 | /*2 |
---|
| 2330 | * u:= a + b |
---|
| 2331 | */ |
---|
[e69b7c] | 2332 | LINLINE number nlAdd (number a, number b, const coeffs R) |
---|
[35aab3] | 2333 | { |
---|
| 2334 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 2335 | { |
---|
[246d15] | 2336 | LONG r=SR_HDL(a)+SR_HDL(b)-1L; |
---|
[35aab3] | 2337 | if ( ((r << 1) >> 1) == r ) |
---|
[37a003] | 2338 | return (number)(long)r; |
---|
[35aab3] | 2339 | else |
---|
| 2340 | return nlRInit(SR_TO_INT(r)); |
---|
| 2341 | } |
---|
[630ca9] | 2342 | number u = _nlAdd_aNoImm_OR_bNoImm(a, b); |
---|
| 2343 | nlTest(u, R); |
---|
| 2344 | return u; |
---|
[35aab3] | 2345 | } |
---|
| 2346 | |
---|
[18057e] | 2347 | number nlShort1(number a); |
---|
[246d15] | 2348 | number nlShort3_noinline(number x); |
---|
[e8a0aa] | 2349 | |
---|
[cc3240c] | 2350 | LINLINE void nlInpAdd(number &a, number b, const coeffs r) |
---|
[e8a0aa] | 2351 | { |
---|
[65c5f5] | 2352 | // a=a+b |
---|
[e8a0aa] | 2353 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 2354 | { |
---|
[246d15] | 2355 | LONG r=SR_HDL(a)+SR_HDL(b)-1L; |
---|
[e8a0aa] | 2356 | if ( ((r << 1) >> 1) == r ) |
---|
[cc3240c] | 2357 | a=(number)(long)r; |
---|
[e8a0aa] | 2358 | else |
---|
[cc3240c] | 2359 | a=nlRInit(SR_TO_INT(r)); |
---|
[e8a0aa] | 2360 | } |
---|
| 2361 | else |
---|
| 2362 | { |
---|
[65c5f5] | 2363 | _nlInpAdd_aNoImm_OR_bNoImm(a,b); |
---|
| 2364 | nlTest(a,r); |
---|
[e8a0aa] | 2365 | } |
---|
| 2366 | } |
---|
| 2367 | |
---|
[7dc3e1c] | 2368 | LINLINE number nlMult (number a, number b, const coeffs R) |
---|
[35aab3] | 2369 | { |
---|
[2b957a] | 2370 | nlTest(a, R); |
---|
| 2371 | nlTest(b, R); |
---|
[35aab3] | 2372 | if (a==INT_TO_SR(0)) return INT_TO_SR(0); |
---|
| 2373 | if (b==INT_TO_SR(0)) return INT_TO_SR(0); |
---|
| 2374 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 2375 | { |
---|
[12777c] | 2376 | LONG r=(LONG)((unsigned LONG)(SR_HDL(a)-1L))*((unsigned LONG)(SR_HDL(b)>>1)); |
---|
[246d15] | 2377 | if ((r/(SR_HDL(b)>>1))==(SR_HDL(a)-1L)) |
---|
[35aab3] | 2378 | { |
---|
| 2379 | number u=((number) ((r>>1)+SR_INT)); |
---|
[246d15] | 2380 | if (((((LONG)SR_HDL(u))<<1)>>1)==SR_HDL(u)) return (u); |
---|
[35aab3] | 2381 | return nlRInit(SR_HDL(u)>>2); |
---|
| 2382 | } |
---|
[630ca9] | 2383 | number u = _nlMult_aImm_bImm_rNoImm(a, b); |
---|
| 2384 | nlTest(u, R); |
---|
| 2385 | return u; |
---|
[9bb5457] | 2386 | |
---|
[35aab3] | 2387 | } |
---|
[630ca9] | 2388 | number u = _nlMult_aNoImm_OR_bNoImm(a, b); |
---|
| 2389 | nlTest(u, R); |
---|
| 2390 | return u; |
---|
[9bb5457] | 2391 | |
---|
[35aab3] | 2392 | } |
---|
| 2393 | |
---|
| 2394 | |
---|
| 2395 | /*2 |
---|
| 2396 | * u:= a - b |
---|
| 2397 | */ |
---|
[a642c64] | 2398 | LINLINE number nlSub (number a, number b, const coeffs r) |
---|
[35aab3] | 2399 | { |
---|
| 2400 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
| 2401 | { |
---|
[246d15] | 2402 | LONG r=SR_HDL(a)-SR_HDL(b)+1; |
---|
[35aab3] | 2403 | if ( ((r << 1) >> 1) == r ) |
---|
| 2404 | { |
---|
[246d15] | 2405 | return (number)(long)r; |
---|
[35aab3] | 2406 | } |
---|
| 2407 | else |
---|
| 2408 | return nlRInit(SR_TO_INT(r)); |
---|
| 2409 | } |
---|
[630ca9] | 2410 | number u = _nlSub_aNoImm_OR_bNoImm(a, b); |
---|
| 2411 | nlTest(u, r); |
---|
| 2412 | return u; |
---|
[9bb5457] | 2413 | |
---|
[35aab3] | 2414 | } |
---|
| 2415 | |
---|
[a642c64] | 2416 | LINLINE void nlInpMult(number &a, number b, const coeffs r) |
---|
[4e35a89] | 2417 | { |
---|
[896561] | 2418 | number aa=a; |
---|
| 2419 | if (((SR_HDL(b)|SR_HDL(aa))&SR_INT)) |
---|
[4e35a89] | 2420 | { |
---|
[a642c64] | 2421 | number n=nlMult(aa,b,r); |
---|
[4e35a89] | 2422 | nlDelete(&a,r); |
---|
| 2423 | a=n; |
---|
| 2424 | } |
---|
| 2425 | else |
---|
| 2426 | { |
---|
[896561] | 2427 | mpz_mul(aa->z,a->z,b->z); |
---|
| 2428 | if (aa->s==3) |
---|
[4e35a89] | 2429 | { |
---|
| 2430 | if(b->s!=3) |
---|
| 2431 | { |
---|
| 2432 | mpz_init_set(a->n,b->n); |
---|
| 2433 | a->s=0; |
---|
| 2434 | } |
---|
| 2435 | } |
---|
| 2436 | else |
---|
| 2437 | { |
---|
| 2438 | if(b->s!=3) |
---|
| 2439 | { |
---|
| 2440 | mpz_mul(a->n,a->n,b->n); |
---|
| 2441 | } |
---|
| 2442 | a->s=0; |
---|
| 2443 | } |
---|
| 2444 | } |
---|
| 2445 | } |
---|
[35aab3] | 2446 | #endif // DO_LINLINE |
---|
| 2447 | |
---|
| 2448 | #ifndef P_NUMBERS_H |
---|
| 2449 | |
---|
[d663f2] | 2450 | static void nlMPZ(mpz_t m, number &n, const coeffs r) |
---|
| 2451 | { |
---|
| 2452 | assume( getCoeffType(r) == ID ); |
---|
[e11ed0] | 2453 | |
---|
[d663f2] | 2454 | nlTest(n, r); |
---|
| 2455 | nlNormalize(n, r); |
---|
| 2456 | if (SR_HDL(n) & SR_INT) mpz_init_set_si(m, SR_TO_INT(n)); /* n fits in an int */ |
---|
| 2457 | else mpz_init_set(m, (mpz_ptr)n->z); |
---|
| 2458 | } |
---|
| 2459 | |
---|
| 2460 | |
---|
[2d2e40] | 2461 | static number nlInitMPZ(mpz_t m, const coeffs) |
---|
[d663f2] | 2462 | { |
---|
| 2463 | number z = ALLOC_RNUMBER(); |
---|
| 2464 | mpz_init_set(z->z, m); |
---|
| 2465 | mpz_init_set_ui(z->n, 1); |
---|
| 2466 | z->s = 3; |
---|
[e11ed0] | 2467 | return z; |
---|
[d663f2] | 2468 | } |
---|
| 2469 | |
---|
| 2470 | |
---|
[a642c64] | 2471 | void nlInpGcd(number &a, number b, const coeffs r) |
---|
[35aab3] | 2472 | { |
---|
| 2473 | if ((SR_HDL(b)|SR_HDL(a))&SR_INT) |
---|
| 2474 | { |
---|
| 2475 | number n=nlGcd(a,b,r); |
---|
| 2476 | nlDelete(&a,r); |
---|
| 2477 | a=n; |
---|
| 2478 | } |
---|
| 2479 | else |
---|
| 2480 | { |
---|
[a604c3] | 2481 | mpz_gcd(a->z,a->z,b->z); |
---|
[246d15] | 2482 | a=nlShort3_noinline(a); |
---|
[35aab3] | 2483 | } |
---|
| 2484 | } |
---|
[f59722] | 2485 | |
---|
[a642c64] | 2486 | void nlInpIntDiv(number &a, number b, const coeffs r) |
---|
[35aab3] | 2487 | { |
---|
| 2488 | if ((SR_HDL(b)|SR_HDL(a))&SR_INT) |
---|
| 2489 | { |
---|
[2b957a] | 2490 | number n=nlIntDiv(a,b, r); |
---|
[35aab3] | 2491 | nlDelete(&a,r); |
---|
| 2492 | a=n; |
---|
| 2493 | } |
---|
| 2494 | else |
---|
| 2495 | { |
---|
[a604c3] | 2496 | if (mpz_isNeg(a->z)) |
---|
[35aab3] | 2497 | { |
---|
[a604c3] | 2498 | if (mpz_isNeg(b->z)) |
---|
[35aab3] | 2499 | { |
---|
[a604c3] | 2500 | mpz_add(a->z,a->z,b->z); |
---|
[35aab3] | 2501 | } |
---|
| 2502 | else |
---|
| 2503 | { |
---|
[a604c3] | 2504 | mpz_sub(a->z,a->z,b->z); |
---|
[35aab3] | 2505 | } |
---|
[a604c3] | 2506 | mpz_add_ui(a->z,a->z,1); |
---|
[35aab3] | 2507 | } |
---|
| 2508 | else |
---|
| 2509 | { |
---|
[a604c3] | 2510 | if (mpz_isNeg(b->z)) |
---|
[35aab3] | 2511 | { |
---|
[a604c3] | 2512 | mpz_sub(a->z,a->z,b->z); |
---|
[35aab3] | 2513 | } |
---|
| 2514 | else |
---|
| 2515 | { |
---|
[a604c3] | 2516 | mpz_add(a->z,a->z,b->z); |
---|
[35aab3] | 2517 | } |
---|
[a604c3] | 2518 | mpz_sub_ui(a->z,a->z,1); |
---|
[35aab3] | 2519 | } |
---|
[a604c3] | 2520 | MPZ_DIV(a->z,a->z,b->z); |
---|
[246d15] | 2521 | a=nlShort3_noinline(a); |
---|
[35aab3] | 2522 | } |
---|
| 2523 | } |
---|
| 2524 | |
---|
[a642c64] | 2525 | number nlFarey(number nN, number nP, const coeffs r) |
---|
[3149a5] | 2526 | { |
---|
[a604c3] | 2527 | mpz_t tmp; mpz_init(tmp); |
---|
| 2528 | mpz_t A,B,C,D,E,N,P; |
---|
| 2529 | if (SR_HDL(nN) & SR_INT) mpz_init_set_si(N,SR_TO_INT(nN)); |
---|
| 2530 | else mpz_init_set(N,nN->z); |
---|
| 2531 | if (SR_HDL(nP) & SR_INT) mpz_init_set_si(P,SR_TO_INT(nP)); |
---|
| 2532 | else mpz_init_set(P,nP->z); |
---|
| 2533 | assume(!mpz_isNeg(P)); |
---|
| 2534 | if (mpz_isNeg(N)) mpz_add(N,N,P); |
---|
| 2535 | mpz_init_set_si(A,(long)0); |
---|
| 2536 | mpz_init_set_ui(B,(unsigned long)1); |
---|
| 2537 | mpz_init_set_si(C,(long)0); |
---|
| 2538 | mpz_init(D); |
---|
| 2539 | mpz_init_set(E,P); |
---|
[3149a5] | 2540 | number z=INT_TO_SR(0); |
---|
[a604c3] | 2541 | while(mpz_cmp_si(N,(long)0)!=0) |
---|
[3149a5] | 2542 | { |
---|
[a604c3] | 2543 | mpz_mul(tmp,N,N); |
---|
| 2544 | mpz_add(tmp,tmp,tmp); |
---|
| 2545 | if (mpz_cmp(tmp,P)<0) |
---|
[3149a5] | 2546 | { |
---|
| 2547 | // return N/B |
---|
[896561] | 2548 | z=ALLOC_RNUMBER(); |
---|
[64cce0] | 2549 | #ifdef LDEBUG |
---|
| 2550 | z->debug=123456; |
---|
| 2551 | #endif |
---|
[a604c3] | 2552 | if (mpz_isNeg(B)) |
---|
[26300d] | 2553 | { |
---|
[a604c3] | 2554 | mpz_neg(B,B); |
---|
| 2555 | mpz_neg(N,N); |
---|
[26300d] | 2556 | } |
---|
[a604c3] | 2557 | mpz_init_set(z->z,N); |
---|
| 2558 | mpz_init_set(z->n,B); |
---|
[3149a5] | 2559 | z->s = 0; |
---|
[a642c64] | 2560 | nlNormalize(z,r); |
---|
[3149a5] | 2561 | break; |
---|
| 2562 | } |
---|
[7453b4] | 2563 | //mpz_mod(D,E,N); |
---|
| 2564 | //mpz_div(tmp,E,N); |
---|
| 2565 | mpz_divmod(tmp,D,E,N); |
---|
[a604c3] | 2566 | mpz_mul(tmp,tmp,B); |
---|
| 2567 | mpz_sub(C,A,tmp); |
---|
| 2568 | mpz_set(E,N); |
---|
| 2569 | mpz_set(N,D); |
---|
| 2570 | mpz_set(A,B); |
---|
| 2571 | mpz_set(B,C); |
---|
| 2572 | } |
---|
| 2573 | mpz_clear(tmp); |
---|
| 2574 | mpz_clear(A); |
---|
| 2575 | mpz_clear(B); |
---|
| 2576 | mpz_clear(C); |
---|
| 2577 | mpz_clear(D); |
---|
| 2578 | mpz_clear(E); |
---|
| 2579 | mpz_clear(N); |
---|
| 2580 | mpz_clear(P); |
---|
[3149a5] | 2581 | return z; |
---|
| 2582 | } |
---|
[bbf7a8] | 2583 | |
---|
[3216ec] | 2584 | number nlExtGcd(number a, number b, number *s, number *t, const coeffs) |
---|
| 2585 | { |
---|
| 2586 | mpz_t aa,bb; |
---|
| 2587 | *s=ALLOC_RNUMBER(); |
---|
| 2588 | mpz_init((*s)->z); (*s)->s=3; |
---|
| 2589 | (*t)=ALLOC_RNUMBER(); |
---|
| 2590 | mpz_init((*t)->z); (*t)->s=3; |
---|
| 2591 | number g=ALLOC_RNUMBER(); |
---|
| 2592 | mpz_init(g->z); g->s=3; |
---|
| 2593 | if (SR_HDL(a) & SR_INT) |
---|
| 2594 | { |
---|
| 2595 | mpz_init_set_si(aa,SR_TO_INT(a)); |
---|
| 2596 | } |
---|
| 2597 | else |
---|
| 2598 | { |
---|
| 2599 | mpz_init_set(aa,a->z); |
---|
| 2600 | } |
---|
| 2601 | if (SR_HDL(b) & SR_INT) |
---|
| 2602 | { |
---|
| 2603 | mpz_init_set_si(bb,SR_TO_INT(b)); |
---|
| 2604 | } |
---|
| 2605 | else |
---|
| 2606 | { |
---|
| 2607 | mpz_init_set(bb,b->z); |
---|
| 2608 | } |
---|
| 2609 | mpz_gcdext(g->z,(*s)->z,(*t)->z,aa,bb); |
---|
| 2610 | mpz_clear(aa); |
---|
| 2611 | mpz_clear(bb); |
---|
| 2612 | (*s)=nlShort3((*s)); |
---|
| 2613 | (*t)=nlShort3((*t)); |
---|
| 2614 | g=nlShort3(g); |
---|
| 2615 | return g; |
---|
| 2616 | } |
---|
| 2617 | |
---|
[03f7b5] | 2618 | void nlCoeffWrite (const coeffs, BOOLEAN /*details*/) |
---|
[8167af] | 2619 | { |
---|
| 2620 | PrintS("// characteristic : 0\n"); |
---|
| 2621 | } |
---|
| 2622 | |
---|
[e8c8d5] | 2623 | number nlChineseRemainder(number *x, number *q,int rl, const coeffs C) |
---|
| 2624 | // elemenst in the array are x[0..(rl-1)], q[0..(rl-1)] |
---|
| 2625 | { |
---|
| 2626 | #ifdef HAVE_FACTORY |
---|
| 2627 | setCharacteristic( 0 ); // only in char 0 |
---|
| 2628 | CFArray X(rl), Q(rl); |
---|
| 2629 | int i; |
---|
| 2630 | for(i=rl-1;i>=0;i--) |
---|
| 2631 | { |
---|
| 2632 | X[i]=C->convSingNFactoryN(x[i],FALSE,C); // may be larger MAX_INT |
---|
| 2633 | Q[i]=C->convSingNFactoryN(q[i],FALSE,C); // may be larger MAX_INT |
---|
| 2634 | } |
---|
| 2635 | CanonicalForm xnew,qnew; |
---|
| 2636 | chineseRemainder(X,Q,xnew,qnew); |
---|
| 2637 | number n=C->convFactoryNSingN(xnew,C); |
---|
| 2638 | number p=C->convFactoryNSingN(qnew,C); |
---|
| 2639 | number p2=nlIntDiv(p,nlInit(2, C),C); |
---|
| 2640 | if (nlGreater(n,p2,C)) |
---|
| 2641 | { |
---|
| 2642 | number n2=nlSub(n,p,C); |
---|
| 2643 | nlDelete(&n,C); |
---|
| 2644 | n=n2; |
---|
| 2645 | } |
---|
| 2646 | nlDelete(&p,C); |
---|
| 2647 | nlDelete(&p2,C); |
---|
| 2648 | return n; |
---|
| 2649 | #else |
---|
| 2650 | WerrorS("not implemented"); |
---|
[fea2af] | 2651 | return nlInit(0, C); |
---|
[e8c8d5] | 2652 | #endif |
---|
| 2653 | } |
---|
| 2654 | |
---|
[dc79bd] | 2655 | void nlClearContent(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
[de88371] | 2656 | { |
---|
| 2657 | assume(cf != NULL); |
---|
| 2658 | assume(getCoeffType(cf) == ID); |
---|
[9952bd] | 2659 | |
---|
| 2660 | numberCollectionEnumerator.Reset(); |
---|
| 2661 | |
---|
| 2662 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 2663 | { |
---|
| 2664 | c = n_Init(1, cf); |
---|
| 2665 | return; |
---|
| 2666 | } |
---|
| 2667 | |
---|
[de88371] | 2668 | // all coeffs are given by integers!!! |
---|
| 2669 | |
---|
[4f9652] | 2670 | // part 1, find a small candidate for gcd |
---|
| 2671 | number cand1,cand; |
---|
| 2672 | int s1,s; |
---|
| 2673 | s=2147483647; // max. int |
---|
[9952bd] | 2674 | |
---|
[dc79bd] | 2675 | const BOOLEAN lc_is_pos=nlGreaterZero(numberCollectionEnumerator.Current(),cf); |
---|
[9952bd] | 2676 | |
---|
| 2677 | int normalcount = 0; |
---|
[4f9652] | 2678 | do |
---|
| 2679 | { |
---|
[9952bd] | 2680 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2681 | nlNormalize(n, cf); ++normalcount; |
---|
| 2682 | cand1 = n; |
---|
| 2683 | |
---|
| 2684 | if (SR_HDL(cand1)&SR_INT) { cand=cand1; break; } |
---|
| 2685 | assume(cand1->s==3); // all coeffs should be integers // ==0?!! after printing |
---|
[4f9652] | 2686 | s1=mpz_size1(cand1->z); |
---|
| 2687 | if (s>s1) |
---|
| 2688 | { |
---|
| 2689 | cand=cand1; |
---|
| 2690 | s=s1; |
---|
| 2691 | } |
---|
[e11ed0] | 2692 | } while (numberCollectionEnumerator.MoveNext() ); |
---|
| 2693 | |
---|
[9952bd] | 2694 | // assume( nlGreaterZero(cand,cf) ); // cand may be a negative integer! |
---|
| 2695 | |
---|
[d1d27f1] | 2696 | cand=nlCopy(cand,cf); |
---|
[4f9652] | 2697 | // part 2: compute gcd(cand,all coeffs) |
---|
[9952bd] | 2698 | |
---|
[4f9652] | 2699 | numberCollectionEnumerator.Reset(); |
---|
[9952bd] | 2700 | |
---|
| 2701 | while (numberCollectionEnumerator.MoveNext() ) |
---|
[4f9652] | 2702 | { |
---|
[9952bd] | 2703 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2704 | |
---|
| 2705 | if( (--normalcount) <= 0) |
---|
| 2706 | nlNormalize(n, cf); |
---|
| 2707 | |
---|
| 2708 | nlInpGcd(cand, n, cf); |
---|
| 2709 | |
---|
| 2710 | assume( nlGreaterZero(cand,cf) ); |
---|
| 2711 | |
---|
[39d731] | 2712 | if(nlIsOne(cand,cf)) |
---|
| 2713 | { |
---|
[9952bd] | 2714 | c = cand; |
---|
| 2715 | |
---|
[39d731] | 2716 | if(!lc_is_pos) |
---|
| 2717 | { |
---|
| 2718 | // make the leading coeff positive |
---|
[9952bd] | 2719 | c = nlNeg(c, cf); |
---|
[39d731] | 2720 | numberCollectionEnumerator.Reset(); |
---|
[9952bd] | 2721 | |
---|
| 2722 | while (numberCollectionEnumerator.MoveNext() ) |
---|
[39d731] | 2723 | { |
---|
[9952bd] | 2724 | number& nn = numberCollectionEnumerator.Current(); |
---|
| 2725 | nn = nlNeg(nn, cf); |
---|
| 2726 | } |
---|
[39d731] | 2727 | } |
---|
| 2728 | return; |
---|
| 2729 | } |
---|
[9952bd] | 2730 | } |
---|
[e11ed0] | 2731 | |
---|
[4f9652] | 2732 | // part3: all coeffs = all coeffs / cand |
---|
[9952bd] | 2733 | if (!lc_is_pos) |
---|
| 2734 | cand = nlNeg(cand,cf); |
---|
| 2735 | |
---|
| 2736 | c = cand; |
---|
[4f9652] | 2737 | numberCollectionEnumerator.Reset(); |
---|
[e11ed0] | 2738 | |
---|
[9952bd] | 2739 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 2740 | { |
---|
| 2741 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2742 | number t=nlIntDiv(n, cand, cf); // simple integer exact division, no ratios to remain |
---|
| 2743 | nlDelete(&n, cf); |
---|
| 2744 | n = t; |
---|
| 2745 | } |
---|
[de88371] | 2746 | } |
---|
| 2747 | |
---|
[dc79bd] | 2748 | void nlClearContentNoPositiveLead(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
| 2749 | { |
---|
| 2750 | assume(cf != NULL); |
---|
| 2751 | assume(getCoeffType(cf) == ID); |
---|
| 2752 | |
---|
| 2753 | numberCollectionEnumerator.Reset(); |
---|
| 2754 | |
---|
| 2755 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 2756 | { |
---|
| 2757 | c = n_Init(1, cf); |
---|
| 2758 | return; |
---|
| 2759 | } |
---|
| 2760 | |
---|
| 2761 | // all coeffs are given by integers!!! |
---|
| 2762 | |
---|
| 2763 | // part 1, find a small candidate for gcd |
---|
| 2764 | number cand1,cand; |
---|
| 2765 | int s1,s; |
---|
| 2766 | s=2147483647; // max. int |
---|
| 2767 | |
---|
| 2768 | const BOOLEAN lc_is_pos = TRUE; // nlGreaterZero(numberCollectionEnumerator.Current(),cf); |
---|
| 2769 | |
---|
| 2770 | int normalcount = 0; |
---|
| 2771 | do |
---|
| 2772 | { |
---|
| 2773 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2774 | nlNormalize(n, cf); ++normalcount; |
---|
| 2775 | cand1 = n; |
---|
| 2776 | |
---|
| 2777 | if (SR_HDL(cand1)&SR_INT) { cand=cand1; break; } |
---|
| 2778 | assume(cand1->s==3); // all coeffs should be integers // ==0?!! after printing |
---|
| 2779 | s1=mpz_size1(cand1->z); |
---|
| 2780 | if (s>s1) |
---|
| 2781 | { |
---|
| 2782 | cand=cand1; |
---|
| 2783 | s=s1; |
---|
| 2784 | } |
---|
| 2785 | } while (numberCollectionEnumerator.MoveNext() ); |
---|
| 2786 | |
---|
| 2787 | // assume( nlGreaterZero(cand,cf) ); // cand may be a negative integer! |
---|
| 2788 | |
---|
| 2789 | cand=nlCopy(cand,cf); |
---|
| 2790 | // part 2: compute gcd(cand,all coeffs) |
---|
| 2791 | |
---|
| 2792 | numberCollectionEnumerator.Reset(); |
---|
| 2793 | |
---|
| 2794 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 2795 | { |
---|
| 2796 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2797 | |
---|
| 2798 | if( (--normalcount) <= 0) |
---|
| 2799 | nlNormalize(n, cf); |
---|
| 2800 | |
---|
| 2801 | nlInpGcd(cand, n, cf); |
---|
| 2802 | |
---|
| 2803 | assume( nlGreaterZero(cand,cf) ); |
---|
| 2804 | |
---|
| 2805 | if(nlIsOne(cand,cf)) |
---|
| 2806 | { |
---|
| 2807 | c = cand; |
---|
| 2808 | |
---|
| 2809 | if(!lc_is_pos) |
---|
| 2810 | { |
---|
| 2811 | // make the leading coeff positive |
---|
| 2812 | c = nlNeg(c, cf); |
---|
| 2813 | numberCollectionEnumerator.Reset(); |
---|
| 2814 | |
---|
| 2815 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 2816 | { |
---|
| 2817 | number& nn = numberCollectionEnumerator.Current(); |
---|
| 2818 | nn = nlNeg(nn, cf); |
---|
| 2819 | } |
---|
| 2820 | } |
---|
| 2821 | return; |
---|
| 2822 | } |
---|
| 2823 | } |
---|
| 2824 | |
---|
| 2825 | // part3: all coeffs = all coeffs / cand |
---|
| 2826 | if (!lc_is_pos) |
---|
| 2827 | cand = nlNeg(cand,cf); |
---|
| 2828 | |
---|
| 2829 | c = cand; |
---|
| 2830 | numberCollectionEnumerator.Reset(); |
---|
| 2831 | |
---|
| 2832 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 2833 | { |
---|
| 2834 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2835 | number t=nlIntDiv(n, cand, cf); // simple integer exact division, no ratios to remain |
---|
| 2836 | nlDelete(&n, cf); |
---|
| 2837 | n = t; |
---|
| 2838 | } |
---|
| 2839 | } |
---|
| 2840 | |
---|
| 2841 | void nlClearDenominators(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
[de88371] | 2842 | { |
---|
| 2843 | assume(cf != NULL); |
---|
| 2844 | assume(getCoeffType(cf) == ID); |
---|
[9952bd] | 2845 | |
---|
| 2846 | numberCollectionEnumerator.Reset(); |
---|
| 2847 | |
---|
| 2848 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 2849 | { |
---|
| 2850 | c = n_Init(1, cf); |
---|
[dc79bd] | 2851 | // assume( n_GreaterZero(c, cf) ); |
---|
[9952bd] | 2852 | return; |
---|
| 2853 | } |
---|
| 2854 | |
---|
[d1d27f1] | 2855 | // all coeffs are given by integers after returning from this routine |
---|
| 2856 | |
---|
| 2857 | // part 1, collect product of all denominators /gcds |
---|
[e11ed0] | 2858 | number cand; |
---|
[d1d27f1] | 2859 | cand=ALLOC_RNUMBER(); |
---|
[9952bd] | 2860 | #if defined(LDEBUG) |
---|
[d1d27f1] | 2861 | cand->debug=123456; |
---|
[9952bd] | 2862 | #endif |
---|
[d1d27f1] | 2863 | cand->s=3; |
---|
| 2864 | |
---|
| 2865 | int s=0; |
---|
[9952bd] | 2866 | |
---|
[dc79bd] | 2867 | const BOOLEAN lc_is_pos=nlGreaterZero(numberCollectionEnumerator.Current(),cf); |
---|
[9952bd] | 2868 | |
---|
[d1d27f1] | 2869 | do |
---|
| 2870 | { |
---|
[560a3d] | 2871 | number& cand1 = numberCollectionEnumerator.Current(); |
---|
[e11ed0] | 2872 | |
---|
[d1d27f1] | 2873 | if (!(SR_HDL(cand1)&SR_INT)) |
---|
| 2874 | { |
---|
[e11ed0] | 2875 | nlNormalize(cand1, cf); |
---|
[d1d27f1] | 2876 | if ((!(SR_HDL(cand1)&SR_INT)) // not a short int |
---|
[9952bd] | 2877 | && (cand1->s==1)) // and is a normalised rational |
---|
[d1d27f1] | 2878 | { |
---|
| 2879 | if (s==0) // first denom, we meet |
---|
| 2880 | { |
---|
[9952bd] | 2881 | mpz_init_set(cand->z, cand1->n); // cand->z = cand1->n |
---|
[e11ed0] | 2882 | s=1; |
---|
[d1d27f1] | 2883 | } |
---|
| 2884 | else // we have already something |
---|
| 2885 | { |
---|
[9952bd] | 2886 | mpz_lcm(cand->z, cand->z, cand1->n); |
---|
[d1d27f1] | 2887 | } |
---|
| 2888 | } |
---|
| 2889 | } |
---|
[9952bd] | 2890 | } |
---|
| 2891 | while (numberCollectionEnumerator.MoveNext() ); |
---|
| 2892 | |
---|
[de88371] | 2893 | |
---|
[d1d27f1] | 2894 | if (s==0) // nothing to do, all coeffs are already integers |
---|
| 2895 | { |
---|
[9952bd] | 2896 | // mpz_clear(tmp); |
---|
[e11ed0] | 2897 | FREE_RNUMBER(cand); |
---|
[39d731] | 2898 | if (lc_is_pos) |
---|
| 2899 | c=nlInit(1,cf); |
---|
| 2900 | else |
---|
| 2901 | { |
---|
| 2902 | // make the leading coeff positive |
---|
| 2903 | c=nlInit(-1,cf); |
---|
[9952bd] | 2904 | |
---|
| 2905 | // TODO: incorporate the following into the loop below? |
---|
[39d731] | 2906 | numberCollectionEnumerator.Reset(); |
---|
[9952bd] | 2907 | while (numberCollectionEnumerator.MoveNext() ) |
---|
[39d731] | 2908 | { |
---|
[9952bd] | 2909 | number& n = numberCollectionEnumerator.Current(); |
---|
| 2910 | n = nlNeg(n, cf); |
---|
| 2911 | } |
---|
[39d731] | 2912 | } |
---|
[dc79bd] | 2913 | // assume( n_GreaterZero(c, cf) ); |
---|
[d1d27f1] | 2914 | return; |
---|
| 2915 | } |
---|
[9952bd] | 2916 | |
---|
| 2917 | cand = nlShort3(cand); |
---|
[e11ed0] | 2918 | |
---|
[d1d27f1] | 2919 | // part2: all coeffs = all coeffs * cand |
---|
[e11ed0] | 2920 | // make the lead coeff positive |
---|
[d1d27f1] | 2921 | numberCollectionEnumerator.Reset(); |
---|
[9952bd] | 2922 | |
---|
| 2923 | if (!lc_is_pos) |
---|
| 2924 | cand = nlNeg(cand, cf); |
---|
| 2925 | |
---|
[e11ed0] | 2926 | c = cand; |
---|
[9952bd] | 2927 | |
---|
| 2928 | while (numberCollectionEnumerator.MoveNext() ) |
---|
[d1d27f1] | 2929 | { |
---|
[560a3d] | 2930 | number &n = numberCollectionEnumerator.Current(); |
---|
| 2931 | n_InpMult(n, cand, cf); |
---|
[9952bd] | 2932 | } |
---|
[e11ed0] | 2933 | |
---|
[de88371] | 2934 | } |
---|
| 2935 | |
---|
[dc79bd] | 2936 | |
---|
| 2937 | void nlClearDenominatorsNoPositiveLead(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
| 2938 | { |
---|
| 2939 | assume(cf != NULL); |
---|
| 2940 | assume(getCoeffType(cf) == ID); |
---|
| 2941 | |
---|
| 2942 | numberCollectionEnumerator.Reset(); |
---|
| 2943 | |
---|
| 2944 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 2945 | { |
---|
| 2946 | c = n_Init(1, cf); |
---|
| 2947 | return; |
---|
| 2948 | } |
---|
| 2949 | |
---|
| 2950 | // all coeffs are given by integers after returning from this routine |
---|
| 2951 | |
---|
| 2952 | // part 1, collect product of all denominators /gcds |
---|
| 2953 | number cand; |
---|
| 2954 | cand=ALLOC_RNUMBER(); |
---|
| 2955 | #if defined(LDEBUG) |
---|
| 2956 | cand->debug=123456; |
---|
| 2957 | #endif |
---|
| 2958 | cand->s=3; |
---|
| 2959 | |
---|
| 2960 | int s=0; |
---|
| 2961 | |
---|
| 2962 | const BOOLEAN lc_is_pos = TRUE; // nlGreaterZero(numberCollectionEnumerator.Current(),cf); |
---|
| 2963 | |
---|
| 2964 | do |
---|
| 2965 | { |
---|
| 2966 | number& cand1 = numberCollectionEnumerator.Current(); |
---|
| 2967 | |
---|
| 2968 | if (!(SR_HDL(cand1)&SR_INT)) |
---|
| 2969 | { |
---|
| 2970 | nlNormalize(cand1, cf); |
---|
| 2971 | if ((!(SR_HDL(cand1)&SR_INT)) // not a short int |
---|
| 2972 | && (cand1->s==1)) // and is a normalised rational |
---|
| 2973 | { |
---|
| 2974 | if (s==0) // first denom, we meet |
---|
| 2975 | { |
---|
| 2976 | mpz_init_set(cand->z, cand1->n); // cand->z = cand1->n |
---|
| 2977 | s=1; |
---|
| 2978 | } |
---|
| 2979 | else // we have already something |
---|
| 2980 | { |
---|
| 2981 | mpz_lcm(cand->z, cand->z, cand1->n); |
---|
| 2982 | } |
---|
| 2983 | } |
---|
| 2984 | } |
---|
| 2985 | } |
---|
| 2986 | while (numberCollectionEnumerator.MoveNext() ); |
---|
| 2987 | |
---|
| 2988 | |
---|
| 2989 | if (s==0) // nothing to do, all coeffs are already integers |
---|
| 2990 | { |
---|
| 2991 | // mpz_clear(tmp); |
---|
| 2992 | FREE_RNUMBER(cand); |
---|
| 2993 | if (lc_is_pos) |
---|
| 2994 | c=nlInit(1,cf); |
---|
| 2995 | else |
---|
| 2996 | { |
---|
| 2997 | // make the leading coeff positive |
---|
| 2998 | c=nlInit(-1,cf); |
---|
| 2999 | |
---|
| 3000 | // TODO: incorporate the following into the loop below? |
---|
| 3001 | numberCollectionEnumerator.Reset(); |
---|
| 3002 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 3003 | { |
---|
| 3004 | number& n = numberCollectionEnumerator.Current(); |
---|
| 3005 | n = nlNeg(n, cf); |
---|
| 3006 | } |
---|
| 3007 | } |
---|
| 3008 | return; |
---|
| 3009 | } |
---|
| 3010 | |
---|
| 3011 | cand = nlShort3(cand); |
---|
| 3012 | |
---|
| 3013 | // part2: all coeffs = all coeffs * cand |
---|
| 3014 | // make the lead coeff positive |
---|
| 3015 | numberCollectionEnumerator.Reset(); |
---|
| 3016 | |
---|
| 3017 | if (!lc_is_pos) |
---|
| 3018 | cand = nlNeg(cand, cf); |
---|
| 3019 | |
---|
| 3020 | c = cand; |
---|
| 3021 | |
---|
| 3022 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 3023 | { |
---|
| 3024 | number &n = numberCollectionEnumerator.Current(); |
---|
| 3025 | n_InpMult(n, cand, cf); |
---|
| 3026 | } |
---|
| 3027 | |
---|
| 3028 | } |
---|
| 3029 | |
---|
[9bb5457] | 3030 | BOOLEAN nlInitChar(coeffs r, void*) |
---|
[e3c02d2] | 3031 | { |
---|
[73a9ffb] | 3032 | assume( getCoeffType(r) == ID ); |
---|
| 3033 | //const int ch = (int)(long)(p); |
---|
[9bb5457] | 3034 | |
---|
[e3c02d2] | 3035 | r->cfKillChar=NULL; |
---|
[121fd9] | 3036 | r->nCoeffIsEqual=ndCoeffIsEqual; |
---|
[577888] | 3037 | r->cfKillChar = ndKillChar; /* dummy */ |
---|
[e3c02d2] | 3038 | |
---|
[d663f2] | 3039 | r->cfInitMPZ = nlInitMPZ; |
---|
| 3040 | r->cfMPZ = nlMPZ; |
---|
[e11ed0] | 3041 | |
---|
[7bbbef] | 3042 | r->cfMult = nlMult; |
---|
| 3043 | r->cfSub = nlSub; |
---|
| 3044 | r->cfAdd = nlAdd; |
---|
| 3045 | r->cfDiv = nlDiv; |
---|
| 3046 | r->cfIntDiv= nlIntDiv; |
---|
| 3047 | r->cfIntMod= nlIntMod; |
---|
| 3048 | r->cfExactDiv= nlExactDiv; |
---|
[bbf7a8] | 3049 | r->cfInit = nlInit; |
---|
[7bbbef] | 3050 | r->cfSize = nlSize; |
---|
| 3051 | r->cfInt = nlInt; |
---|
[e11ed0] | 3052 | |
---|
[e8c8d5] | 3053 | r->cfChineseRemainder=nlChineseRemainder; |
---|
| 3054 | r->cfFarey=nlFarey; |
---|
[bbf7a8] | 3055 | #ifdef HAVE_RINGS |
---|
[7bbbef] | 3056 | //r->cfDivComp = NULL; // only for ring stuff |
---|
| 3057 | //r->cfIsUnit = NULL; // only for ring stuff |
---|
| 3058 | //r->cfGetUnit = NULL; // only for ring stuff |
---|
| 3059 | //r->cfDivBy = NULL; // only for ring stuff |
---|
[bbf7a8] | 3060 | #endif |
---|
[7bbbef] | 3061 | r->cfNeg = nlNeg; |
---|
| 3062 | r->cfInvers= nlInvers; |
---|
[2b957a] | 3063 | r->cfCopy = nlCopy; |
---|
| 3064 | r->cfRePart = nlCopy; |
---|
[7bbbef] | 3065 | //r->cfImPart = ndReturn0; |
---|
[ce1f78] | 3066 | r->cfWriteLong = nlWrite; |
---|
[7bbbef] | 3067 | r->cfRead = nlRead; |
---|
| 3068 | r->cfNormalize=nlNormalize; |
---|
| 3069 | r->cfGreater = nlGreater; |
---|
| 3070 | r->cfEqual = nlEqual; |
---|
| 3071 | r->cfIsZero = nlIsZero; |
---|
| 3072 | r->cfIsOne = nlIsOne; |
---|
| 3073 | r->cfIsMOne = nlIsMOne; |
---|
| 3074 | r->cfGreaterZero = nlGreaterZero; |
---|
| 3075 | r->cfPower = nlPower; |
---|
[bbf7a8] | 3076 | r->cfGetDenom = nlGetDenom; |
---|
| 3077 | r->cfGetNumerator = nlGetNumerator; |
---|
[7bbbef] | 3078 | r->cfGcd = nlGcd; |
---|
[3216ec] | 3079 | r->cfExtGcd = nlExtGcd; // only for ring stuff and Z |
---|
[7bbbef] | 3080 | r->cfLcm = nlLcm; |
---|
[bbf7a8] | 3081 | r->cfDelete= nlDelete; |
---|
[e3c02d2] | 3082 | r->cfSetMap = nlSetMap; |
---|
[7bbbef] | 3083 | //r->cfName = ndName; |
---|
| 3084 | r->cfInpMult=nlInpMult; |
---|
| 3085 | r->cfInit_bigint=nlCopyMap; |
---|
[8167af] | 3086 | r->cfCoeffWrite=nlCoeffWrite; |
---|
[de88371] | 3087 | |
---|
| 3088 | r->cfClearContent = nlClearContent; |
---|
| 3089 | r->cfClearDenominators = nlClearDenominators; |
---|
[e11ed0] | 3090 | |
---|
[e3c02d2] | 3091 | #ifdef LDEBUG |
---|
[bbf7a8] | 3092 | // debug stuff |
---|
[7bbbef] | 3093 | r->cfDBTest=nlDBTest; |
---|
[e3c02d2] | 3094 | #endif |
---|
[e5d267] | 3095 | #ifdef HAVE_FACTORY |
---|
| 3096 | r->convSingNFactoryN=nlConvSingNFactoryN; |
---|
| 3097 | r->convFactoryNSingN=nlConvFactoryNSingN; |
---|
| 3098 | #endif |
---|
[039016] | 3099 | |
---|
[8835e2b] | 3100 | // the variables: general stuff (required) |
---|
[bbf7a8] | 3101 | r->nNULL = INT_TO_SR(0); |
---|
[aff5ae] | 3102 | //r->type = n_Q; |
---|
[bbf7a8] | 3103 | r->ch = 0; |
---|
| 3104 | r->has_simple_Alloc=FALSE; |
---|
| 3105 | r->has_simple_Inverse=FALSE; |
---|
[9bb5457] | 3106 | |
---|
[8835e2b] | 3107 | // variables for this type of coeffs: |
---|
| 3108 | // (none) |
---|
[5d594a9] | 3109 | return FALSE; |
---|
[e3c02d2] | 3110 | } |
---|
[35aab3] | 3111 | #if 0 |
---|
| 3112 | number nlMod(number a, number b) |
---|
| 3113 | { |
---|
| 3114 | if (((SR_HDL(b)&SR_HDL(a))&SR_INT) |
---|
| 3115 | { |
---|
| 3116 | int bi=SR_TO_INT(b); |
---|
| 3117 | int ai=SR_TO_INT(a); |
---|
| 3118 | int bb=ABS(bi); |
---|
| 3119 | int c=ai%bb; |
---|
| 3120 | if (c<0) c+=bb; |
---|
| 3121 | return (INT_TO_SR(c)); |
---|
| 3122 | } |
---|
| 3123 | number al; |
---|
| 3124 | number bl; |
---|
| 3125 | if (SR_HDL(a))&SR_INT) |
---|
| 3126 | al=nlRInit(SR_TO_INT(a)); |
---|
| 3127 | else |
---|
| 3128 | al=nlCopy(a); |
---|
| 3129 | if (SR_HDL(b))&SR_INT) |
---|
| 3130 | bl=nlRInit(SR_TO_INT(b)); |
---|
| 3131 | else |
---|
| 3132 | bl=nlCopy(b); |
---|
| 3133 | number r=nlRInit(0); |
---|
| 3134 | mpz_mod(r->z,al->z,bl->z); |
---|
| 3135 | nlDelete(&al); |
---|
| 3136 | nlDelete(&bl); |
---|
| 3137 | if (mpz_size1(&r->z)<=MP_SMALL) |
---|
| 3138 | { |
---|
[246d15] | 3139 | LONG ui=(int)mpz_get_si(&r->z); |
---|
[35aab3] | 3140 | if ((((ui<<3)>>3)==ui) |
---|
[a604c3] | 3141 | && (mpz_cmp_si(x->z,(long)ui)==0)) |
---|
[35aab3] | 3142 | { |
---|
| 3143 | mpz_clear(&r->z); |
---|
[d663f2] | 3144 | FREE_RNUMBER(r); // omFreeBin((void *)r, rnumber_bin); |
---|
[35aab3] | 3145 | r=INT_TO_SR(ui); |
---|
| 3146 | } |
---|
| 3147 | } |
---|
| 3148 | return r; |
---|
| 3149 | } |
---|
| 3150 | #endif |
---|
| 3151 | #endif // not P_NUMBERS_H |
---|
| 3152 | #endif // LONGRAT_CC |
---|