1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT: computation with long rational numbers (Hubert Grassmann) |
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7 | */ |
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8 | |
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9 | #include <coeffs/longrat.h> |
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10 | |
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11 | // 64 bit version: |
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12 | #if 0 |
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13 | #define MAX_NUM_SIZE 60 |
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14 | #define POW_2_28 0x10000000000000L |
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15 | #define LONG long |
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16 | #else |
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17 | #define MAX_NUM_SIZE 28 |
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18 | #define POW_2_28 (1L<<28) |
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19 | #define LONG int |
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20 | #endif |
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21 | |
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22 | static inline number nlShort3(number x) // assume x->s==3 |
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23 | { |
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24 | assume(x->s==3); |
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25 | if ((mpz_cmp_ui(x->z,(long)0)==0) |
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26 | || (mpz_size1(x->z)<=MP_SMALL)) |
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27 | { |
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28 | LONG ui=mpz_get_si(x->z); |
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29 | if ((((ui<<3)>>3)==ui) |
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30 | && (mpz_cmp_si(x->z,(long)ui)==0)) |
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31 | { |
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32 | mpz_clear(x->z); |
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33 | FREE_RNUMBER(x); |
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34 | return INT_TO_SR(ui); |
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35 | } |
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36 | } |
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37 | return x; |
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38 | } |
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39 | |
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40 | #ifndef LONGRAT_CC |
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41 | #define LONGRAT_CC |
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42 | |
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43 | #include <string.h> |
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44 | #include <float.h> |
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45 | #include "config.h" |
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46 | #include <coeffs/coeffs.h> |
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47 | #include <reporter/reporter.h> |
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48 | #include <omalloc/omalloc.h> |
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49 | #include <coeffs/numbers.h> |
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50 | #include <coeffs/modulop.h> |
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51 | #include <coeffs/shortfl.h> |
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52 | #include <coeffs/mpr_complex.h> |
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53 | #include <coeffs/longrat.h> |
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54 | |
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55 | |
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56 | #ifndef BYTES_PER_MP_LIMB |
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57 | #define BYTES_PER_MP_LIMB sizeof(mp_limb_t) |
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58 | #endif |
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59 | |
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60 | /*-----------------------------------------------------------------*/ |
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61 | /*3 |
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62 | * parameter s in number: |
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63 | * 0 (or FALSE): not normalised rational |
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64 | * 1 (or TRUE): normalised rational |
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65 | * 3 : integer with n==NULL |
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66 | */ |
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67 | /*3 |
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68 | ** 'SR_INT' is the type of those integers small enough to fit into 29 bits. |
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69 | ** Therefor the value range of this small integers is: $-2^{28}...2^{28}-1$. |
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70 | ** |
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71 | ** Small integers are represented by an immediate integer handle, containing |
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72 | ** the value instead of pointing to it, which has the following form: |
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73 | ** |
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74 | ** +-------+-------+-------+-------+- - - -+-------+-------+-------+ |
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75 | ** | guard | sign | bit | bit | | bit | tag | tag | |
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76 | ** | bit | bit | 27 | 26 | | 0 | 0 | 1 | |
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77 | ** +-------+-------+-------+-------+- - - -+-------+-------+-------+ |
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78 | ** |
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79 | ** Immediate integers handles carry the tag 'SR_INT', i.e. the last bit is 1. |
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80 | ** This distuingishes immediate integers from other handles which point to |
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81 | ** structures aligned on 4 byte boundaries and therefor have last bit zero. |
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82 | ** (The second bit is reserved as tag to allow extensions of this scheme.) |
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83 | ** Using immediates as pointers and dereferencing them gives address errors. |
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84 | ** |
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85 | ** To aid overflow check the most significant two bits must always be equal, |
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86 | ** that is to say that the sign bit of immediate integers has a guard bit. |
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87 | ** |
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88 | ** The macros 'INT_TO_SR' and 'SR_TO_INT' should be used to convert between |
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89 | ** a small integer value and its representation as immediate integer handle. |
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90 | ** |
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91 | ** Large integers and rationals are represented by z and n |
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92 | ** where n may be undefined (if s==3) |
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93 | ** NULL represents only deleted values |
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94 | */ |
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95 | #define SR_HDL(A) ((long)(A)) |
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96 | /*#define SR_INT 1L*/ |
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97 | /*#define INT_TO_SR(INT) ((number) (((long)INT << 2) + SR_INT))*/ |
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98 | // #define SR_TO_INT(SR) (((long)SR) >> 2) |
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99 | |
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100 | #define MP_SMALL 1 |
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101 | //#define mpz_isNeg(A) (mpz_cmp_si(A,(long)0)<0) |
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102 | #define mpz_isNeg(A) ((A)->_mp_size<0) |
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103 | #define mpz_limb_size(A) ((A)->_mp_size) |
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104 | #define mpz_limb_d(A) ((A)->_mp_d) |
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105 | #define MPZ_DIV(A,B,C) mpz_tdiv_q((A),(B),(C)) |
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106 | #define MPZ_EXACTDIV(A,B,C) mpz_divexact((A),(B),(C)) |
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107 | |
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108 | void _nlDelete_NoImm(number *a); |
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109 | |
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110 | static const n_coeffType ID = n_long_R; |
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111 | |
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112 | /*************************************************************** |
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113 | * |
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114 | * Routines which are never inlined by p_Numbers.h |
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115 | * |
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116 | *******************************************************************/ |
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117 | #ifndef P_NUMBERS_H |
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118 | |
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119 | number nlShort3_noinline(number x) // assume x->s==3 |
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120 | { |
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121 | return nlShort3(x); |
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122 | } |
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123 | |
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124 | //#ifndef SI_THREADS |
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125 | omBin rnumber_bin = omGetSpecBin(sizeof(snumber)); |
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126 | //#endif |
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127 | |
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128 | number nlOne=INT_TO_SR(1); |
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129 | |
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130 | #if (__GNU_MP_VERSION*10+__GNU_MP_VERSION_MINOR < 31) |
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131 | void mpz_mul_si (mpz_ptr r, mpz_srcptr s, long int si) |
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132 | { |
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133 | if (si>=0) |
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134 | mpz_mul_ui(r,s,si); |
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135 | else |
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136 | { |
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137 | mpz_mul_ui(r,s,-si); |
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138 | mpz_neg(r,r); |
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139 | } |
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140 | } |
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141 | #endif |
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142 | |
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143 | static number nlMapP(number from, const coeffs src, const coeffs dst) |
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144 | { |
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145 | assume( getCoeffType(dst) == ID ); |
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146 | assume( getCoeffType(src) == n_Zp ); |
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147 | |
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148 | number to; |
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149 | to = nlInit(npInt(from,src), dst); |
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150 | return to; |
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151 | } |
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152 | |
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153 | static number nlMapLongR(number from, const coeffs src, const coeffs dst); |
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154 | static number nlMapR(number from, const coeffs src, const coeffs dst); |
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155 | |
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156 | #ifdef HAVE_RINGS |
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157 | /*2 |
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158 | * convert from a GMP integer |
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159 | */ |
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160 | number nlMapGMP(number from, const coeffs src, const coeffs dst) |
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161 | { |
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162 | number z=ALLOC_RNUMBER(); |
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163 | #if defined(LDEBUG) |
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164 | z->debug=123456; |
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165 | #endif |
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166 | mpz_init_set(z->z,(mpz_ptr) from); |
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167 | //mpz_init_set_ui(&z->n,1); |
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168 | z->s = 3; |
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169 | z=nlShort3(z); |
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170 | return z; |
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171 | } |
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172 | |
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173 | /*2 |
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174 | * convert from an machine long |
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175 | */ |
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176 | number nlMapMachineInt(number from, const coeffs src, const coeffs dst) |
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177 | { |
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178 | number z=ALLOC_RNUMBER(); |
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179 | #if defined(LDEBUG) |
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180 | z->debug=123456; |
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181 | #endif |
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182 | mpz_init_set_ui(z->z,(unsigned long) from); |
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183 | z->s = 3; |
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184 | z=nlShort3(z); |
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185 | return z; |
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186 | } |
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187 | #endif |
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188 | |
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189 | |
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190 | #ifdef LDEBUG |
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191 | BOOLEAN nlDBTest(number a, const char *f,const int l, const coeffs r) |
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192 | { |
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193 | if (a==NULL) |
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194 | { |
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195 | Print("!!longrat: NULL in %s:%d\n",f,l); |
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196 | return FALSE; |
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197 | } |
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198 | //if ((int)a==1) Print("!! 0x1 as number ? %s %d\n",f,l); |
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199 | if ((((long)a)&3L)==3L) |
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200 | { |
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201 | Print(" !!longrat:ptr(3) in %s:%d\n",f,l); |
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202 | return FALSE; |
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203 | } |
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204 | if ((((long)a)&3L)==1L) |
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205 | { |
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206 | if (((((LONG)(long)a)<<1)>>1)!=((LONG)(long)a)) |
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207 | { |
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208 | Print(" !!longrat:arith:%lx in %s:%d\n",(long)a, f,l); |
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209 | return FALSE; |
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210 | } |
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211 | return TRUE; |
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212 | } |
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213 | /* TODO: If next line is active, then computations in algebraic field |
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214 | extensions over Q will throw a lot of assume violations although |
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215 | everything is computed correctly and no seg fault appears. |
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216 | Maybe the test is not appropriate in this case. */ |
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217 | //omCheckIf(omCheckAddrSize(a,sizeof(*a)), return FALSE); |
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218 | if (a->debug!=123456) |
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219 | { |
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220 | Print("!!longrat:debug:%d in %s:%d\n",a->debug,f,l); |
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221 | a->debug=123456; |
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222 | return FALSE; |
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223 | } |
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224 | if ((a->s<0)||(a->s>4)) |
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225 | { |
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226 | Print("!!longrat:s=%d in %s:%d\n",a->s,f,l); |
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227 | return FALSE; |
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228 | } |
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229 | /* TODO: If next line is active, then computations in algebraic field |
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230 | extensions over Q will throw a lot of assume violations although |
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231 | everything is computed correctly and no seg fault appears. |
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232 | Maybe the test is not appropriate in this case. */ |
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233 | //omCheckAddrSize(a->z[0]._mp_d,a->z[0]._mp_alloc*BYTES_PER_MP_LIMB); |
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234 | if (a->z[0]._mp_alloc==0) |
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235 | Print("!!longrat:z->alloc=0 in %s:%d\n",f,l); |
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236 | |
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237 | if (a->s<2) |
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238 | { |
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239 | /* TODO: If next line is active, then computations in algebraic field |
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240 | extensions over Q will throw a lot of assume violations although |
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241 | everything is computed correctly and no seg fault appears. |
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242 | Maybe the test is not appropriate in this case. */ |
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243 | //omCheckIf(omCheckAddrSize(a->n[0]._mp_d,a->n[0]._mp_alloc*BYTES_PER_MP_LIMB), return FALSE); |
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244 | if (a->z[0]._mp_alloc==0) |
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245 | Print("!!longrat:n->alloc=0 in %s:%d\n",f,l); |
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246 | if ((mpz_size1(a->n) ==1) && (mpz_cmp_si(a->n,(long)1)==0)) |
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247 | { |
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248 | Print("!!longrat:integer as rational in %s:%d\n",f,l); |
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249 | mpz_clear(a->n); a->s=3; |
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250 | return FALSE; |
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251 | } |
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252 | else if (mpz_isNeg(a->n)) |
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253 | { |
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254 | Print("!!longrat:div. by negative in %s:%d\n",f,l); |
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255 | mpz_neg(a->z,a->z); |
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256 | mpz_neg(a->n,a->n); |
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257 | return FALSE; |
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258 | } |
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259 | return TRUE; |
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260 | } |
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261 | //if (a->s==2) |
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262 | //{ |
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263 | // Print("!!longrat:s=2 in %s:%d\n",f,l); |
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264 | // return FALSE; |
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265 | //} |
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266 | if (mpz_size1(a->z)>MP_SMALL) return TRUE; |
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267 | LONG ui=(int)mpz_get_si(a->z); |
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268 | if ((((ui<<3)>>3)==ui) |
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269 | && (mpz_cmp_si(a->z,(long)ui)==0)) |
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270 | { |
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271 | Print("!!longrat:im int %d in %s:%d\n",ui,f,l); |
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272 | f=NULL; |
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273 | return FALSE; |
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274 | } |
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275 | return TRUE; |
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276 | } |
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277 | #endif |
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278 | |
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279 | #ifdef HAVE_FACTORY |
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280 | CanonicalForm nlConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
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281 | { |
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282 | if (setChar) setCharacteristic( 0 ); |
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283 | |
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284 | CanonicalForm term; |
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285 | if ( SR_HDL(n) & SR_INT ) |
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286 | { |
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287 | term = SR_TO_INT(n); |
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288 | } |
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289 | else |
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290 | { |
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291 | if ( n->s == 3 ) |
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292 | { |
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293 | MP_INT dummy; |
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294 | mpz_init_set( &dummy,n->z ); |
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295 | term = make_cf( dummy ); |
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296 | } |
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297 | else |
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298 | { |
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299 | // assume s==0 or s==1 |
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300 | MP_INT num, den; |
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301 | On(SW_RATIONAL); |
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302 | mpz_init_set( &num, n->z ); |
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303 | mpz_init_set( &den, n->n ); |
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304 | term = make_cf( num, den, ( n->s != 1 )); |
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305 | } |
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306 | } |
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307 | return term; |
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308 | } |
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309 | |
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310 | number nlConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
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311 | { |
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312 | if (n.isImm()) |
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313 | { |
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314 | return nlInit(n.intval(),r); |
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315 | } |
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316 | else |
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317 | { |
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318 | number z=(number)omAllocBin(rnumber_bin); |
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319 | #if defined(LDEBUG) |
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320 | z->debug=123456; |
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321 | #endif |
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322 | gmp_numerator( n, z->z ); |
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323 | if ( n.den().isOne() ) |
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324 | z->s = 3; |
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325 | else |
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326 | { |
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327 | gmp_denominator( n, z->n ); |
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328 | z->s = 0; |
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329 | } |
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330 | nlNormalize(z,r); |
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331 | return z; |
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332 | } |
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333 | } |
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334 | #endif |
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335 | number nlRInit (long i); |
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336 | |
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337 | static number nlMapR(number from, const coeffs src, const coeffs dst) |
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338 | { |
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339 | assume( getCoeffType(dst) == ID ); |
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340 | assume( getCoeffType(src) == n_R ); |
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341 | |
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342 | double f=nrFloat(from); |
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343 | if (f==0.0) return INT_TO_SR(0); |
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344 | int f_sign=1; |
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345 | if (f<0.0) |
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346 | { |
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347 | f_sign=-1; |
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348 | f=-f; |
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349 | } |
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350 | int i=0; |
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351 | mpz_t h1; |
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352 | mpz_init_set_ui(h1,1); |
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353 | while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG) |
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354 | { |
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355 | f*=FLT_RADIX; |
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356 | mpz_mul_ui(h1,h1,FLT_RADIX); |
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357 | i++; |
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358 | } |
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359 | number re=nlRInit(1); |
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360 | mpz_set_d(re->z,f); |
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361 | memcpy(&(re->n),&h1,sizeof(h1)); |
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362 | re->s=0; /* not normalized */ |
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363 | if(f_sign==-1) re=nlNeg(re,dst); |
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364 | nlNormalize(re,dst); |
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365 | return re; |
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366 | } |
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367 | |
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368 | static number nlMapLongR(number from, const coeffs src, const coeffs dst) |
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369 | { |
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370 | assume( getCoeffType(dst) == ID ); |
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371 | assume( getCoeffType(src) == n_long_R ); |
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372 | |
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373 | gmp_float *ff=(gmp_float*)from; |
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374 | mpf_t *f=ff->_mpfp(); |
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375 | number res; |
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376 | mpz_ptr dest,ndest; |
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377 | int size, i,negative; |
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378 | int e,al,bl; |
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379 | mp_ptr qp,dd,nn; |
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380 | |
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381 | size = (*f)[0]._mp_size; |
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382 | if (size == 0) |
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383 | return INT_TO_SR(0); |
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384 | if(size<0) |
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385 | { |
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386 | negative = 1; |
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387 | size = -size; |
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388 | } |
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389 | else |
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390 | negative = 0; |
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391 | |
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392 | qp = (*f)[0]._mp_d; |
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393 | while(qp[0]==0) |
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394 | { |
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395 | qp++; |
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396 | size--; |
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397 | } |
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398 | |
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399 | e=(*f)[0]._mp_exp-size; |
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400 | res = ALLOC_RNUMBER(); |
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401 | #if defined(LDEBUG) |
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402 | res->debug=123456; |
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403 | #endif |
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404 | dest = res->z; |
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405 | |
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406 | if (e<0) |
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407 | { |
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408 | al = dest->_mp_size = size; |
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409 | if (al<2) al = 2; |
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410 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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411 | for (i=0;i<size;i++) dd[i] = qp[i]; |
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412 | bl = 1-e; |
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413 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
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414 | nn[bl-1] = 1; |
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415 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
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416 | ndest = res->n; |
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417 | ndest->_mp_d = nn; |
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418 | ndest->_mp_alloc = ndest->_mp_size = bl; |
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419 | res->s = 0; |
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420 | } |
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421 | else |
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422 | { |
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423 | al = dest->_mp_size = size+e; |
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424 | if (al<2) al = 2; |
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425 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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426 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
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427 | for (i=0;i<e;i++) dd[i] = 0; |
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428 | res->s = 3; |
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429 | } |
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430 | |
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431 | dest->_mp_d = dd; |
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432 | dest->_mp_alloc = al; |
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433 | if (negative) dest->_mp_size = -dest->_mp_size; |
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434 | |
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435 | if (res->s==0) |
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436 | nlNormalize(res,dst); |
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437 | else if (mpz_size1(res->z)<=MP_SMALL) |
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438 | { |
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439 | // res is new, res->ref is 1 |
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440 | res=nlShort3(res); |
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441 | } |
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442 | nlTest(res, dst); |
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443 | return res; |
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444 | } |
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445 | |
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446 | //static number nlMapLongR(number from) |
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447 | //{ |
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448 | // gmp_float *ff=(gmp_float*)from; |
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449 | // const mpf_t *f=ff->mpfp(); |
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450 | // int f_size=ABS((*f)[0]._mp_size); |
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451 | // if (f_size==0) |
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452 | // return nlInit(0); |
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453 | // int f_sign=1; |
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454 | // number work=ngcCopy(from); |
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455 | // if (!ngcGreaterZero(work)) |
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456 | // { |
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457 | // f_sign=-1; |
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458 | // work=ngcNeg(work); |
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459 | // } |
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460 | // int i=0; |
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461 | // mpz_t h1; |
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462 | // mpz_init_set_ui(h1,1); |
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463 | // while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG) |
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464 | // { |
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465 | // f*=FLT_RADIX; |
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466 | // mpz_mul_ui(h1,h1,FLT_RADIX); |
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467 | // i++; |
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468 | // } |
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469 | // number r=nlRInit(1); |
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470 | // mpz_set_d(&(r->z),f); |
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471 | // memcpy(&(r->n),&h1,sizeof(h1)); |
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472 | // r->s=0; /* not normalized */ |
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473 | // nlNormalize(r); |
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474 | // return r; |
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475 | // |
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476 | // |
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477 | // number r=nlRInit(1); |
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478 | // int f_shift=f_size+(*f)[0]._mp_exp; |
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479 | // if ( f_shift > 0) |
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480 | // { |
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481 | // r->s=0; |
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482 | // mpz_init(&r->n); |
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483 | // mpz_setbit(&r->n,f_shift*BYTES_PER_MP_LIMB*8); |
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484 | // mpz_setbit(&r->z,f_size*BYTES_PER_MP_LIMB*8-1); |
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485 | // // now r->z has enough space |
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486 | // memcpy(mpz_limb_d(&r->z),((*f)[0]._mp_d),f_size*BYTES_PER_MP_LIMB); |
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487 | // nlNormalize(r); |
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488 | // } |
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489 | // else |
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490 | // { |
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491 | // r->s=3; |
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492 | // if (f_shift==0) |
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493 | // { |
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494 | // mpz_setbit(&r->z,f_size*BYTES_PER_MP_LIMB*8-1); |
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495 | // // now r->z has enough space |
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496 | // memcpy(mpz_limb_d(&r->z),((*f)[0]._mp_d),f_size*BYTES_PER_MP_LIMB); |
---|
497 | // } |
---|
498 | // else /* f_shift < 0 */ |
---|
499 | // { |
---|
500 | // mpz_setbit(&r->z,(f_size-f_shift)*BYTES_PER_MP_LIMB*8-1); |
---|
501 | // // now r->z has enough space |
---|
502 | // memcpy(mpz_limb_d(&r->z)-f_shift,((*f)[0]._mp_d), |
---|
503 | // f_size*BYTES_PER_MP_LIMB); |
---|
504 | // } |
---|
505 | // } |
---|
506 | // if ((*f)[0]._mp_size<0); |
---|
507 | // r=nlNeg(r); |
---|
508 | // return r; |
---|
509 | //} |
---|
510 | |
---|
511 | int nlSize(number a, const coeffs) |
---|
512 | { |
---|
513 | if (a==INT_TO_SR(0)) |
---|
514 | return 0; /* rational 0*/ |
---|
515 | if (SR_HDL(a) & SR_INT) |
---|
516 | return 1; /* immidiate int */ |
---|
517 | int s=a->z[0]._mp_alloc; |
---|
518 | // while ((s>0) &&(a->z._mp_d[s]==0L)) s--; |
---|
519 | //#if SIZEOF_LONG == 8 |
---|
520 | // if (a->z._mp_d[s] < (unsigned long)0x100000000L) s=s*2-1; |
---|
521 | // else s *=2; |
---|
522 | //#endif |
---|
523 | // s++; |
---|
524 | if (a->s<2) |
---|
525 | { |
---|
526 | int d=a->n[0]._mp_alloc; |
---|
527 | // while ((d>0) && (a->n._mp_d[d]==0L)) d--; |
---|
528 | //#if SIZEOF_LONG == 8 |
---|
529 | // if (a->n._mp_d[d] < (unsigned long)0x100000000L) d=d*2-1; |
---|
530 | // else d *=2; |
---|
531 | //#endif |
---|
532 | s+=d; |
---|
533 | } |
---|
534 | return s; |
---|
535 | } |
---|
536 | |
---|
537 | /*2 |
---|
538 | * convert number to int |
---|
539 | */ |
---|
540 | int nlInt(number &i, const coeffs r) |
---|
541 | { |
---|
542 | nlTest(i, r); |
---|
543 | nlNormalize(i,r); |
---|
544 | if (SR_HDL(i) &SR_INT) return SR_TO_INT(i); |
---|
545 | if (i->s==3) |
---|
546 | { |
---|
547 | if(mpz_size1(i->z)>MP_SMALL) return 0; |
---|
548 | int ul=(int)mpz_get_si(i->z); |
---|
549 | if (mpz_cmp_si(i->z,(long)ul)!=0) return 0; |
---|
550 | return ul; |
---|
551 | } |
---|
552 | mpz_t tmp; |
---|
553 | int ul; |
---|
554 | mpz_init(tmp); |
---|
555 | MPZ_DIV(tmp,i->z,i->n); |
---|
556 | if(mpz_size1(tmp)>MP_SMALL) ul=0; |
---|
557 | else |
---|
558 | { |
---|
559 | ul=(int)mpz_get_si(tmp); |
---|
560 | if (mpz_cmp_si(tmp,(long)ul)!=0) ul=0; |
---|
561 | } |
---|
562 | mpz_clear(tmp); |
---|
563 | return ul; |
---|
564 | } |
---|
565 | |
---|
566 | /*2 |
---|
567 | * convert number to bigint |
---|
568 | */ |
---|
569 | number nlBigInt(number &i, const coeffs r) |
---|
570 | { |
---|
571 | nlTest(i, r); |
---|
572 | nlNormalize(i,r); |
---|
573 | if (SR_HDL(i) &SR_INT) return (i); |
---|
574 | if (i->s==3) |
---|
575 | { |
---|
576 | return nlCopy(i,r); |
---|
577 | } |
---|
578 | number tmp=nlRInit(1); |
---|
579 | MPZ_DIV(tmp->z,i->z,i->n); |
---|
580 | tmp=nlShort3(tmp); |
---|
581 | return tmp; |
---|
582 | } |
---|
583 | |
---|
584 | /* |
---|
585 | * 1/a |
---|
586 | */ |
---|
587 | number nlInvers(number a, const coeffs r) |
---|
588 | { |
---|
589 | nlTest(a, r); |
---|
590 | number n; |
---|
591 | if (SR_HDL(a) & SR_INT) |
---|
592 | { |
---|
593 | if ((a==INT_TO_SR(1L)) || (a==INT_TO_SR(-1L))) |
---|
594 | { |
---|
595 | return a; |
---|
596 | } |
---|
597 | if (nlIsZero(a,r)) |
---|
598 | { |
---|
599 | WerrorS(nDivBy0); |
---|
600 | return INT_TO_SR(0); |
---|
601 | } |
---|
602 | n=ALLOC_RNUMBER(); |
---|
603 | #if defined(LDEBUG) |
---|
604 | n->debug=123456; |
---|
605 | #endif |
---|
606 | n->s=1; |
---|
607 | if ((long)a>0L) |
---|
608 | { |
---|
609 | mpz_init_set_si(n->z,(long)1); |
---|
610 | mpz_init_set_si(n->n,(long)SR_TO_INT(a)); |
---|
611 | } |
---|
612 | else |
---|
613 | { |
---|
614 | mpz_init_set_si(n->z,(long)-1); |
---|
615 | mpz_init_set_si(n->n,(long)-SR_TO_INT(a)); |
---|
616 | } |
---|
617 | nlTest(n, r); |
---|
618 | return n; |
---|
619 | } |
---|
620 | n=ALLOC_RNUMBER(); |
---|
621 | #if defined(LDEBUG) |
---|
622 | n->debug=123456; |
---|
623 | #endif |
---|
624 | { |
---|
625 | n->s=a->s; |
---|
626 | mpz_init_set(n->n,a->z); |
---|
627 | switch (a->s) |
---|
628 | { |
---|
629 | case 0: |
---|
630 | case 1: |
---|
631 | mpz_init_set(n->z,a->n); |
---|
632 | if (mpz_isNeg(n->n)) /* && n->s<2*/ |
---|
633 | { |
---|
634 | mpz_neg(n->z,n->z); |
---|
635 | mpz_neg(n->n,n->n); |
---|
636 | } |
---|
637 | if (mpz_cmp_si(n->n,(long)1)==0) |
---|
638 | { |
---|
639 | mpz_clear(n->n); |
---|
640 | n->s=3; |
---|
641 | n=nlShort3(n); |
---|
642 | } |
---|
643 | break; |
---|
644 | case 3: |
---|
645 | n->s=1; |
---|
646 | if (mpz_isNeg(n->n)) /* && n->s<2*/ |
---|
647 | { |
---|
648 | mpz_neg(n->n,n->n); |
---|
649 | mpz_init_set_si(n->z,(long)-1); |
---|
650 | } |
---|
651 | else |
---|
652 | { |
---|
653 | mpz_init_set_si(n->z,(long)1); |
---|
654 | } |
---|
655 | break; |
---|
656 | } |
---|
657 | } |
---|
658 | nlTest(n, r); |
---|
659 | return n; |
---|
660 | } |
---|
661 | |
---|
662 | |
---|
663 | /*2 |
---|
664 | * u := a / b in Z, if b | a (else undefined) |
---|
665 | */ |
---|
666 | number nlExactDiv(number a, number b, const coeffs r) |
---|
667 | { |
---|
668 | if (b==INT_TO_SR(0)) |
---|
669 | { |
---|
670 | WerrorS(nDivBy0); |
---|
671 | return INT_TO_SR(0); |
---|
672 | } |
---|
673 | if (a==INT_TO_SR(0)) |
---|
674 | return INT_TO_SR(0); |
---|
675 | number u; |
---|
676 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
677 | { |
---|
678 | /* the small int -(1<<28) divided by -1 is the large int (1<<28) */ |
---|
679 | if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L))) |
---|
680 | { |
---|
681 | return nlRInit(POW_2_28); |
---|
682 | } |
---|
683 | long aa=SR_TO_INT(a); |
---|
684 | long bb=SR_TO_INT(b); |
---|
685 | return INT_TO_SR(aa/bb); |
---|
686 | } |
---|
687 | number bb=NULL; |
---|
688 | if (SR_HDL(b) & SR_INT) |
---|
689 | { |
---|
690 | bb=nlRInit(SR_TO_INT(b)); |
---|
691 | b=bb; |
---|
692 | } |
---|
693 | u=ALLOC_RNUMBER(); |
---|
694 | #if defined(LDEBUG) |
---|
695 | u->debug=123456; |
---|
696 | #endif |
---|
697 | mpz_init(u->z); |
---|
698 | /* u=a/b */ |
---|
699 | u->s = 3; |
---|
700 | MPZ_EXACTDIV(u->z,a->z,b->z); |
---|
701 | if (bb!=NULL) |
---|
702 | { |
---|
703 | mpz_clear(bb->z); |
---|
704 | #if defined(LDEBUG) |
---|
705 | bb->debug=654324; |
---|
706 | #endif |
---|
707 | omFreeBin((void *)bb, rnumber_bin); |
---|
708 | } |
---|
709 | u=nlShort3(u); |
---|
710 | nlTest(u, r); |
---|
711 | return u; |
---|
712 | } |
---|
713 | |
---|
714 | /*2 |
---|
715 | * u := a / b in Z |
---|
716 | */ |
---|
717 | number nlIntDiv (number a, number b, const coeffs r) |
---|
718 | { |
---|
719 | if (b==INT_TO_SR(0)) |
---|
720 | { |
---|
721 | WerrorS(nDivBy0); |
---|
722 | return INT_TO_SR(0); |
---|
723 | } |
---|
724 | if (a==INT_TO_SR(0)) |
---|
725 | return INT_TO_SR(0); |
---|
726 | number u; |
---|
727 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
728 | { |
---|
729 | /* the small int -(1<<28) divided by -1 is the large int (1<<28) */ |
---|
730 | if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L))) |
---|
731 | { |
---|
732 | return nlRInit(POW_2_28); |
---|
733 | } |
---|
734 | long aa=SR_TO_INT(a); |
---|
735 | long bb=SR_TO_INT(b); |
---|
736 | return INT_TO_SR(aa/bb); |
---|
737 | } |
---|
738 | if (SR_HDL(a) & SR_INT) |
---|
739 | { |
---|
740 | /* the small int -(1<<28) divided by 2^28 is 1 */ |
---|
741 | if (a==INT_TO_SR(-(POW_2_28))) |
---|
742 | { |
---|
743 | if(mpz_cmp_si(b->z,(POW_2_28))==0) |
---|
744 | { |
---|
745 | return INT_TO_SR(-1); |
---|
746 | } |
---|
747 | } |
---|
748 | /* a is a small and b is a large int: -> 0 */ |
---|
749 | return INT_TO_SR(0); |
---|
750 | } |
---|
751 | number bb=NULL; |
---|
752 | if (SR_HDL(b) & SR_INT) |
---|
753 | { |
---|
754 | bb=nlRInit(SR_TO_INT(b)); |
---|
755 | b=bb; |
---|
756 | } |
---|
757 | u=ALLOC_RNUMBER(); |
---|
758 | #if defined(LDEBUG) |
---|
759 | u->debug=123456; |
---|
760 | #endif |
---|
761 | assume(a->s==3); |
---|
762 | assume(b->s==3); |
---|
763 | mpz_init_set(u->z,a->z); |
---|
764 | /* u=u/b */ |
---|
765 | u->s = 3; |
---|
766 | MPZ_DIV(u->z,u->z,b->z); |
---|
767 | if (bb!=NULL) |
---|
768 | { |
---|
769 | mpz_clear(bb->z); |
---|
770 | #if defined(LDEBUG) |
---|
771 | bb->debug=654324; |
---|
772 | #endif |
---|
773 | omFreeBin((void *)bb, rnumber_bin); |
---|
774 | } |
---|
775 | u=nlShort3(u); |
---|
776 | nlTest(u, r); |
---|
777 | return u; |
---|
778 | } |
---|
779 | |
---|
780 | /*2 |
---|
781 | * u := a mod b in Z, u>=0 |
---|
782 | */ |
---|
783 | number nlIntMod (number a, number b, const coeffs r) |
---|
784 | { |
---|
785 | if (b==INT_TO_SR(0)) |
---|
786 | { |
---|
787 | WerrorS(nDivBy0); |
---|
788 | return INT_TO_SR(0); |
---|
789 | } |
---|
790 | if (a==INT_TO_SR(0)) |
---|
791 | return INT_TO_SR(0); |
---|
792 | number u; |
---|
793 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
794 | { |
---|
795 | if ((long)a>0L) |
---|
796 | { |
---|
797 | if ((long)b>0L) |
---|
798 | return INT_TO_SR(SR_TO_INT(a)%SR_TO_INT(b)); |
---|
799 | else |
---|
800 | return INT_TO_SR(SR_TO_INT(a)%(-SR_TO_INT(b))); |
---|
801 | } |
---|
802 | else |
---|
803 | { |
---|
804 | if ((long)b>0L) |
---|
805 | { |
---|
806 | long i=(-SR_TO_INT(a))%SR_TO_INT(b); |
---|
807 | if ( i != 0L ) i = (SR_TO_INT(b))-i; |
---|
808 | return INT_TO_SR(i); |
---|
809 | } |
---|
810 | else |
---|
811 | { |
---|
812 | long i=(-SR_TO_INT(a))%(-SR_TO_INT(b)); |
---|
813 | if ( i != 0L ) i = (-SR_TO_INT(b))-i; |
---|
814 | return INT_TO_SR(i); |
---|
815 | } |
---|
816 | } |
---|
817 | } |
---|
818 | if (SR_HDL(a) & SR_INT) |
---|
819 | { |
---|
820 | /* a is a small and b is a large int: -> a or (a+b) or (a-b) */ |
---|
821 | if ((long)a<0L) |
---|
822 | { |
---|
823 | if (mpz_isNeg(b->z)) |
---|
824 | return nlSub(a,b,r); |
---|
825 | /*else*/ |
---|
826 | return nlAdd(a,b,r); |
---|
827 | } |
---|
828 | /*else*/ |
---|
829 | return a; |
---|
830 | } |
---|
831 | number bb=NULL; |
---|
832 | if (SR_HDL(b) & SR_INT) |
---|
833 | { |
---|
834 | bb=nlRInit(SR_TO_INT(b)); |
---|
835 | b=bb; |
---|
836 | } |
---|
837 | u=ALLOC_RNUMBER(); |
---|
838 | #if defined(LDEBUG) |
---|
839 | u->debug=123456; |
---|
840 | #endif |
---|
841 | mpz_init(u->z); |
---|
842 | u->s = 3; |
---|
843 | mpz_mod(u->z,a->z,b->z); |
---|
844 | if (bb!=NULL) |
---|
845 | { |
---|
846 | mpz_clear(bb->z); |
---|
847 | #if defined(LDEBUG) |
---|
848 | bb->debug=654324; |
---|
849 | #endif |
---|
850 | omFreeBin((void *)bb, rnumber_bin); |
---|
851 | } |
---|
852 | if (mpz_isNeg(u->z)) |
---|
853 | { |
---|
854 | if (mpz_isNeg(b->z)) |
---|
855 | mpz_sub(u->z,u->z,b->z); |
---|
856 | else |
---|
857 | mpz_add(u->z,u->z,b->z); |
---|
858 | } |
---|
859 | u=nlShort3(u); |
---|
860 | nlTest(u, r); |
---|
861 | return u; |
---|
862 | } |
---|
863 | |
---|
864 | /*2 |
---|
865 | * u := a / b |
---|
866 | */ |
---|
867 | number nlDiv (number a, number b, const coeffs r) |
---|
868 | { |
---|
869 | number u; |
---|
870 | if (nlIsZero(b,r)) |
---|
871 | { |
---|
872 | WerrorS(nDivBy0); |
---|
873 | return INT_TO_SR(0); |
---|
874 | } |
---|
875 | u=ALLOC_RNUMBER(); |
---|
876 | u->s=0; |
---|
877 | #if defined(LDEBUG) |
---|
878 | u->debug=123456; |
---|
879 | #endif |
---|
880 | // ---------- short / short ------------------------------------ |
---|
881 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
882 | { |
---|
883 | long i=SR_TO_INT(a); |
---|
884 | long j=SR_TO_INT(b); |
---|
885 | if ((i==-POW_2_28) && (j== -1L)) |
---|
886 | { |
---|
887 | FREE_RNUMBER(u); |
---|
888 | return nlRInit(POW_2_28); |
---|
889 | } |
---|
890 | long r=i%j; |
---|
891 | if (r==0) |
---|
892 | { |
---|
893 | omFreeBin((void *)u, rnumber_bin); |
---|
894 | return INT_TO_SR(i/j); |
---|
895 | } |
---|
896 | mpz_init_set_si(u->z,(long)i); |
---|
897 | mpz_init_set_si(u->n,(long)j); |
---|
898 | } |
---|
899 | else |
---|
900 | { |
---|
901 | mpz_init(u->z); |
---|
902 | // ---------- short / long ------------------------------------ |
---|
903 | if (SR_HDL(a) & SR_INT) |
---|
904 | { |
---|
905 | // short a / (z/n) -> (a*n)/z |
---|
906 | if (b->s<2) |
---|
907 | { |
---|
908 | mpz_mul_si(u->z,b->n,SR_TO_INT(a)); |
---|
909 | } |
---|
910 | else |
---|
911 | // short a / long z -> a/z |
---|
912 | { |
---|
913 | mpz_set_si(u->z,SR_TO_INT(a)); |
---|
914 | } |
---|
915 | if (mpz_cmp(u->z,b->z)==0) |
---|
916 | { |
---|
917 | mpz_clear(u->z); |
---|
918 | FREE_RNUMBER(u); |
---|
919 | return INT_TO_SR(1); |
---|
920 | } |
---|
921 | mpz_init_set(u->n,b->z); |
---|
922 | } |
---|
923 | // ---------- long / short ------------------------------------ |
---|
924 | else if (SR_HDL(b) & SR_INT) |
---|
925 | { |
---|
926 | mpz_set(u->z,a->z); |
---|
927 | // (z/n) / b -> z/(n*b) |
---|
928 | if (a->s<2) |
---|
929 | { |
---|
930 | mpz_init_set(u->n,a->n); |
---|
931 | if ((long)b>0L) |
---|
932 | mpz_mul_ui(u->n,u->n,SR_TO_INT(b)); |
---|
933 | else |
---|
934 | { |
---|
935 | mpz_mul_ui(u->n,u->n,-SR_TO_INT(b)); |
---|
936 | mpz_neg(u->z,u->z); |
---|
937 | } |
---|
938 | } |
---|
939 | else |
---|
940 | // long z / short b -> z/b |
---|
941 | { |
---|
942 | //mpz_set(u->z,a->z); |
---|
943 | mpz_init_set_si(u->n,SR_TO_INT(b)); |
---|
944 | } |
---|
945 | } |
---|
946 | // ---------- long / long ------------------------------------ |
---|
947 | else |
---|
948 | { |
---|
949 | mpz_set(u->z,a->z); |
---|
950 | mpz_init_set(u->n,b->z); |
---|
951 | if (a->s<2) mpz_mul(u->n,u->n,a->n); |
---|
952 | if (b->s<2) mpz_mul(u->z,u->z,b->n); |
---|
953 | } |
---|
954 | } |
---|
955 | if (mpz_isNeg(u->n)) |
---|
956 | { |
---|
957 | mpz_neg(u->z,u->z); |
---|
958 | mpz_neg(u->n,u->n); |
---|
959 | } |
---|
960 | if (mpz_cmp_si(u->n,(long)1)==0) |
---|
961 | { |
---|
962 | mpz_clear(u->n); |
---|
963 | u->s=3; |
---|
964 | u=nlShort3(u); |
---|
965 | } |
---|
966 | nlTest(u, r); |
---|
967 | return u; |
---|
968 | } |
---|
969 | |
---|
970 | /*2 |
---|
971 | * u:= x ^ exp |
---|
972 | */ |
---|
973 | void nlPower (number x,int exp,number * u, const coeffs r) |
---|
974 | { |
---|
975 | *u = INT_TO_SR(0); // 0^e, e!=0 |
---|
976 | if (!nlIsZero(x,r)) |
---|
977 | { |
---|
978 | nlTest(x, r); |
---|
979 | number aa=NULL; |
---|
980 | if (SR_HDL(x) & SR_INT) |
---|
981 | { |
---|
982 | aa=nlRInit(SR_TO_INT(x)); |
---|
983 | x=aa; |
---|
984 | } |
---|
985 | else if (x->s==0) |
---|
986 | nlNormalize(x,r); |
---|
987 | *u=ALLOC_RNUMBER(); |
---|
988 | #if defined(LDEBUG) |
---|
989 | (*u)->debug=123456; |
---|
990 | #endif |
---|
991 | mpz_init((*u)->z); |
---|
992 | mpz_pow_ui((*u)->z,x->z,(unsigned long)exp); |
---|
993 | if (x->s<2) |
---|
994 | { |
---|
995 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
996 | { |
---|
997 | x->s=3; |
---|
998 | mpz_clear(x->n); |
---|
999 | } |
---|
1000 | else |
---|
1001 | { |
---|
1002 | mpz_init((*u)->n); |
---|
1003 | mpz_pow_ui((*u)->n,x->n,(unsigned long)exp); |
---|
1004 | } |
---|
1005 | } |
---|
1006 | (*u)->s = x->s; |
---|
1007 | if ((*u)->s==3) *u=nlShort3(*u); |
---|
1008 | if (aa!=NULL) |
---|
1009 | { |
---|
1010 | mpz_clear(aa->z); |
---|
1011 | FREE_RNUMBER(aa); |
---|
1012 | } |
---|
1013 | } |
---|
1014 | else if (exp==0) |
---|
1015 | *u = INT_TO_SR(1); // 0^0 |
---|
1016 | #ifdef LDEBUG |
---|
1017 | if (exp<0) Print("nlPower: neg. exp. %d\n",exp); |
---|
1018 | nlTest(*u, r); |
---|
1019 | #endif |
---|
1020 | } |
---|
1021 | |
---|
1022 | |
---|
1023 | /*2 |
---|
1024 | * za >= 0 ? |
---|
1025 | */ |
---|
1026 | BOOLEAN nlGreaterZero (number a, const coeffs r) |
---|
1027 | { |
---|
1028 | nlTest(a, r); |
---|
1029 | if (SR_HDL(a) & SR_INT) return SR_HDL(a)>1L /* represents number(0) */; |
---|
1030 | return (!mpz_isNeg(a->z)); |
---|
1031 | } |
---|
1032 | |
---|
1033 | /*2 |
---|
1034 | * a > b ? |
---|
1035 | */ |
---|
1036 | BOOLEAN nlGreater (number a, number b, const coeffs r) |
---|
1037 | { |
---|
1038 | nlTest(a, r); |
---|
1039 | nlTest(b, r); |
---|
1040 | number re; |
---|
1041 | BOOLEAN rr; |
---|
1042 | re=nlSub(a,b,r); |
---|
1043 | rr=(!nlIsZero(re,r)) && (nlGreaterZero(re,r)); |
---|
1044 | nlDelete(&re,r); |
---|
1045 | return rr; |
---|
1046 | } |
---|
1047 | |
---|
1048 | /*2 |
---|
1049 | * a == -1 ? |
---|
1050 | */ |
---|
1051 | BOOLEAN nlIsMOne (number a, const coeffs r) |
---|
1052 | { |
---|
1053 | #ifdef LDEBUG |
---|
1054 | if (a==NULL) return FALSE; |
---|
1055 | nlTest(a, r); |
---|
1056 | #endif |
---|
1057 | //if (SR_HDL(a) & SR_INT) return (a==INT_TO_SR(-1L)); |
---|
1058 | //return FALSE; |
---|
1059 | return (a==INT_TO_SR(-1L)); |
---|
1060 | } |
---|
1061 | |
---|
1062 | /*2 |
---|
1063 | * result =gcd(a,b) |
---|
1064 | */ |
---|
1065 | number nlGcd(number a, number b, const coeffs r) |
---|
1066 | { |
---|
1067 | number result; |
---|
1068 | nlTest(a, r); |
---|
1069 | nlTest(b, r); |
---|
1070 | //nlNormalize(a); |
---|
1071 | //nlNormalize(b); |
---|
1072 | if ((a==INT_TO_SR(1L))||(a==INT_TO_SR(-1L)) |
---|
1073 | || (b==INT_TO_SR(1L))||(b==INT_TO_SR(-1L))) |
---|
1074 | return INT_TO_SR(1L); |
---|
1075 | if (a==INT_TO_SR(0)) /* gcd(0,b) ->b */ |
---|
1076 | return nlCopy(b,r); |
---|
1077 | if (b==INT_TO_SR(0)) /* gcd(a,0) -> a */ |
---|
1078 | return nlCopy(a,r); |
---|
1079 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
1080 | { |
---|
1081 | long i=SR_TO_INT(a); |
---|
1082 | long j=SR_TO_INT(b); |
---|
1083 | if((i==0L)||(j==0L)) |
---|
1084 | return INT_TO_SR(1); |
---|
1085 | long l; |
---|
1086 | i=ABS(i); |
---|
1087 | j=ABS(j); |
---|
1088 | do |
---|
1089 | { |
---|
1090 | l=i%j; |
---|
1091 | i=j; |
---|
1092 | j=l; |
---|
1093 | } while (l!=0L); |
---|
1094 | if (i==POW_2_28) |
---|
1095 | result=nlRInit(POW_2_28); |
---|
1096 | else |
---|
1097 | result=INT_TO_SR(i); |
---|
1098 | nlTest(result,r); |
---|
1099 | return result; |
---|
1100 | } |
---|
1101 | if (((!(SR_HDL(a) & SR_INT))&&(a->s<2)) |
---|
1102 | || ((!(SR_HDL(b) & SR_INT))&&(b->s<2))) return INT_TO_SR(1); |
---|
1103 | if (SR_HDL(a) & SR_INT) |
---|
1104 | { |
---|
1105 | LONG aa=ABS(SR_TO_INT(a)); |
---|
1106 | unsigned long t=mpz_gcd_ui(NULL,b->z,(long)aa); |
---|
1107 | if (t==POW_2_28) |
---|
1108 | result=nlRInit(POW_2_28); |
---|
1109 | else |
---|
1110 | result=INT_TO_SR(t); |
---|
1111 | } |
---|
1112 | else |
---|
1113 | if (SR_HDL(b) & SR_INT) |
---|
1114 | { |
---|
1115 | LONG bb=ABS(SR_TO_INT(b)); |
---|
1116 | unsigned long t=mpz_gcd_ui(NULL,a->z,(long)bb); |
---|
1117 | if (t==POW_2_28) |
---|
1118 | result=nlRInit(POW_2_28); |
---|
1119 | else |
---|
1120 | result=INT_TO_SR(t); |
---|
1121 | } |
---|
1122 | else |
---|
1123 | { |
---|
1124 | result=ALLOC_RNUMBER(); |
---|
1125 | mpz_init(result->z); |
---|
1126 | mpz_gcd(result->z,a->z,b->z); |
---|
1127 | result->s = 3; |
---|
1128 | #ifdef LDEBUG |
---|
1129 | result->debug=123456; |
---|
1130 | #endif |
---|
1131 | result=nlShort3(result); |
---|
1132 | } |
---|
1133 | nlTest(result, r); |
---|
1134 | return result; |
---|
1135 | } |
---|
1136 | |
---|
1137 | number nlShort1(number x) // assume x->s==0/1 |
---|
1138 | { |
---|
1139 | assume(x->s<2); |
---|
1140 | if (mpz_cmp_ui(x->z,(long)0)==0) |
---|
1141 | { |
---|
1142 | _nlDelete_NoImm(&x); |
---|
1143 | return INT_TO_SR(0); |
---|
1144 | } |
---|
1145 | if (x->s<2) |
---|
1146 | { |
---|
1147 | if (mpz_cmp(x->z,x->n)==0) |
---|
1148 | { |
---|
1149 | _nlDelete_NoImm(&x); |
---|
1150 | return INT_TO_SR(1); |
---|
1151 | } |
---|
1152 | } |
---|
1153 | return x; |
---|
1154 | } |
---|
1155 | /*2 |
---|
1156 | * simplify x |
---|
1157 | */ |
---|
1158 | void nlNormalize (number &x, const coeffs r) |
---|
1159 | { |
---|
1160 | if ((SR_HDL(x) & SR_INT) ||(x==NULL)) |
---|
1161 | return; |
---|
1162 | if (x->s==3) |
---|
1163 | { |
---|
1164 | x=nlShort3_noinline(x); |
---|
1165 | nlTest(x,r); |
---|
1166 | return; |
---|
1167 | } |
---|
1168 | else if (x->s==0) |
---|
1169 | { |
---|
1170 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
1171 | { |
---|
1172 | mpz_clear(x->n); |
---|
1173 | x->s=3; |
---|
1174 | x=nlShort3(x); |
---|
1175 | } |
---|
1176 | else |
---|
1177 | { |
---|
1178 | mpz_t gcd; |
---|
1179 | mpz_init(gcd); |
---|
1180 | mpz_gcd(gcd,x->z,x->n); |
---|
1181 | x->s=1; |
---|
1182 | if (mpz_cmp_si(gcd,(long)1)!=0) |
---|
1183 | { |
---|
1184 | mpz_t r; |
---|
1185 | mpz_init(r); |
---|
1186 | MPZ_EXACTDIV(r,x->z,gcd); |
---|
1187 | mpz_set(x->z,r); |
---|
1188 | MPZ_EXACTDIV(r,x->n,gcd); |
---|
1189 | mpz_set(x->n,r); |
---|
1190 | mpz_clear(r); |
---|
1191 | if (mpz_cmp_si(x->n,(long)1)==0) |
---|
1192 | { |
---|
1193 | mpz_clear(x->n); |
---|
1194 | x->s=3; |
---|
1195 | x=nlShort3_noinline(x); |
---|
1196 | } |
---|
1197 | } |
---|
1198 | mpz_clear(gcd); |
---|
1199 | } |
---|
1200 | } |
---|
1201 | nlTest(x, r); |
---|
1202 | } |
---|
1203 | |
---|
1204 | /*2 |
---|
1205 | * returns in result->z the lcm(a->z,b->n) |
---|
1206 | */ |
---|
1207 | number nlLcm(number a, number b, const coeffs r) |
---|
1208 | { |
---|
1209 | number result; |
---|
1210 | nlTest(a, r); |
---|
1211 | nlTest(b, r); |
---|
1212 | if ((SR_HDL(b) & SR_INT) |
---|
1213 | || (b->s==3)) |
---|
1214 | { |
---|
1215 | // b is 1/(b->n) => b->n is 1 => result is a |
---|
1216 | return nlCopy(a,r); |
---|
1217 | } |
---|
1218 | result=ALLOC_RNUMBER(); |
---|
1219 | #if defined(LDEBUG) |
---|
1220 | result->debug=123456; |
---|
1221 | #endif |
---|
1222 | result->s=3; |
---|
1223 | mpz_t gcd; |
---|
1224 | mpz_init(gcd); |
---|
1225 | mpz_init(result->z); |
---|
1226 | if (SR_HDL(a) & SR_INT) |
---|
1227 | mpz_gcd_ui(gcd,b->n,ABS(SR_TO_INT(a))); |
---|
1228 | else |
---|
1229 | mpz_gcd(gcd,a->z,b->n); |
---|
1230 | if (mpz_cmp_si(gcd,(long)1)!=0) |
---|
1231 | { |
---|
1232 | mpz_t bt; |
---|
1233 | mpz_init_set(bt,b->n); |
---|
1234 | MPZ_EXACTDIV(bt,bt,gcd); |
---|
1235 | if (SR_HDL(a) & SR_INT) |
---|
1236 | mpz_mul_si(result->z,bt,SR_TO_INT(a)); |
---|
1237 | else |
---|
1238 | mpz_mul(result->z,bt,a->z); |
---|
1239 | mpz_clear(bt); |
---|
1240 | } |
---|
1241 | else |
---|
1242 | if (SR_HDL(a) & SR_INT) |
---|
1243 | mpz_mul_si(result->z,b->n,SR_TO_INT(a)); |
---|
1244 | else |
---|
1245 | mpz_mul(result->z,b->n,a->z); |
---|
1246 | mpz_clear(gcd); |
---|
1247 | result=nlShort3(result); |
---|
1248 | nlTest(result, r); |
---|
1249 | return result; |
---|
1250 | } |
---|
1251 | |
---|
1252 | int nlModP(number n, int p, const coeffs r) |
---|
1253 | { |
---|
1254 | if (SR_HDL(n) & SR_INT) |
---|
1255 | { |
---|
1256 | long i=SR_TO_INT(n); |
---|
1257 | if (i<0L) return (((long)p)-((-i)%((long)p))); |
---|
1258 | return i%((long)p); |
---|
1259 | } |
---|
1260 | int iz=(int)mpz_fdiv_ui(n->z,(unsigned long)p); |
---|
1261 | if (n->s!=3) |
---|
1262 | { |
---|
1263 | int in=mpz_fdiv_ui(n->n,(unsigned long)p); |
---|
1264 | #ifdef NV_OPS |
---|
1265 | if (p>NV_MAX_PRIME) |
---|
1266 | return (int)((long)nvDiv((number)iz,(number)in,(const coeffs)r)); |
---|
1267 | #endif |
---|
1268 | return (int)((long)npDiv((number)iz,(number)in,(const coeffs)r)); |
---|
1269 | } |
---|
1270 | return iz; |
---|
1271 | } |
---|
1272 | |
---|
1273 | #ifdef HAVE_RINGS |
---|
1274 | /*2 |
---|
1275 | * convert number i (from Q) to GMP and warn if denom != 1 |
---|
1276 | */ |
---|
1277 | void nlGMP(number &i, number n, const coeffs r) |
---|
1278 | { |
---|
1279 | // Hier brauche ich einfach die GMP Zahl |
---|
1280 | nlTest(i, r); |
---|
1281 | nlNormalize(i, r); |
---|
1282 | if (SR_HDL(i) & SR_INT) |
---|
1283 | { |
---|
1284 | mpz_set_si((mpz_ptr) n, SR_TO_INT(i)); |
---|
1285 | return; |
---|
1286 | } |
---|
1287 | if (i->s!=3) |
---|
1288 | { |
---|
1289 | WarnS("Omitted denominator during coefficient mapping !"); |
---|
1290 | } |
---|
1291 | mpz_set((mpz_ptr) n, i->z); |
---|
1292 | } |
---|
1293 | #endif |
---|
1294 | |
---|
1295 | /*2 |
---|
1296 | * acces to denominator, other 1 for integers |
---|
1297 | */ |
---|
1298 | number nlGetDenom(number &n, const coeffs r) |
---|
1299 | { |
---|
1300 | if (!(SR_HDL(n) & SR_INT)) |
---|
1301 | { |
---|
1302 | if (n->s==0) |
---|
1303 | { |
---|
1304 | nlNormalize(n,r); |
---|
1305 | } |
---|
1306 | if (!(SR_HDL(n) & SR_INT)) |
---|
1307 | { |
---|
1308 | if (n->s!=3) |
---|
1309 | { |
---|
1310 | number u=ALLOC_RNUMBER(); |
---|
1311 | u->s=3; |
---|
1312 | #if defined(LDEBUG) |
---|
1313 | u->debug=123456; |
---|
1314 | #endif |
---|
1315 | mpz_init_set(u->z,n->n); |
---|
1316 | u=nlShort3_noinline(u); |
---|
1317 | return u; |
---|
1318 | } |
---|
1319 | } |
---|
1320 | } |
---|
1321 | return INT_TO_SR(1); |
---|
1322 | } |
---|
1323 | |
---|
1324 | /*2 |
---|
1325 | * acces to Nominator, nlCopy(n) for integers |
---|
1326 | */ |
---|
1327 | number nlGetNumerator(number &n, const coeffs r) |
---|
1328 | { |
---|
1329 | if (!(SR_HDL(n) & SR_INT)) |
---|
1330 | { |
---|
1331 | if (n->s==0) |
---|
1332 | { |
---|
1333 | nlNormalize(n,r); |
---|
1334 | } |
---|
1335 | if (!(SR_HDL(n) & SR_INT)) |
---|
1336 | { |
---|
1337 | number u=ALLOC_RNUMBER(); |
---|
1338 | #if defined(LDEBUG) |
---|
1339 | u->debug=123456; |
---|
1340 | #endif |
---|
1341 | u->s=3; |
---|
1342 | mpz_init_set(u->z,n->z); |
---|
1343 | if (n->s!=3) |
---|
1344 | { |
---|
1345 | u=nlShort3_noinline(u); |
---|
1346 | } |
---|
1347 | return u; |
---|
1348 | } |
---|
1349 | } |
---|
1350 | return n; // imm. int |
---|
1351 | } |
---|
1352 | |
---|
1353 | /*************************************************************** |
---|
1354 | * |
---|
1355 | * routines which are needed by Inline(d) routines |
---|
1356 | * |
---|
1357 | *******************************************************************/ |
---|
1358 | BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b) |
---|
1359 | { |
---|
1360 | assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT)); |
---|
1361 | // long - short |
---|
1362 | BOOLEAN bo; |
---|
1363 | if (SR_HDL(b) & SR_INT) |
---|
1364 | { |
---|
1365 | if (a->s!=0) return FALSE; |
---|
1366 | number n=b; b=a; a=n; |
---|
1367 | } |
---|
1368 | // short - long |
---|
1369 | if (SR_HDL(a) & SR_INT) |
---|
1370 | { |
---|
1371 | if (b->s!=0) |
---|
1372 | return FALSE; |
---|
1373 | if (((long)a > 0L) && (mpz_isNeg(b->z))) |
---|
1374 | return FALSE; |
---|
1375 | if (((long)a < 0L) && (!mpz_isNeg(b->z))) |
---|
1376 | return FALSE; |
---|
1377 | mpz_t bb; |
---|
1378 | mpz_init_set(bb,b->n); |
---|
1379 | mpz_mul_si(bb,bb,(long)SR_TO_INT(a)); |
---|
1380 | bo=(mpz_cmp(bb,b->z)==0); |
---|
1381 | mpz_clear(bb); |
---|
1382 | return bo; |
---|
1383 | } |
---|
1384 | // long - long |
---|
1385 | if (((a->s==1) && (b->s==3)) |
---|
1386 | || ((b->s==1) && (a->s==3))) |
---|
1387 | return FALSE; |
---|
1388 | if (mpz_isNeg(a->z)&&(!mpz_isNeg(b->z))) |
---|
1389 | return FALSE; |
---|
1390 | if (mpz_isNeg(b->z)&&(!mpz_isNeg(a->z))) |
---|
1391 | return FALSE; |
---|
1392 | mpz_t aa; |
---|
1393 | mpz_t bb; |
---|
1394 | mpz_init_set(aa,a->z); |
---|
1395 | mpz_init_set(bb,b->z); |
---|
1396 | if (a->s<2) mpz_mul(bb,bb,a->n); |
---|
1397 | if (b->s<2) mpz_mul(aa,aa,b->n); |
---|
1398 | bo=(mpz_cmp(aa,bb)==0); |
---|
1399 | mpz_clear(aa); |
---|
1400 | mpz_clear(bb); |
---|
1401 | return bo; |
---|
1402 | } |
---|
1403 | |
---|
1404 | // copy not immediate number a |
---|
1405 | number _nlCopy_NoImm(number a) |
---|
1406 | { |
---|
1407 | assume(!((SR_HDL(a) & SR_INT)||(a==NULL))); |
---|
1408 | //nlTest(a, r); |
---|
1409 | number b=ALLOC_RNUMBER(); |
---|
1410 | #if defined(LDEBUG) |
---|
1411 | b->debug=123456; |
---|
1412 | #endif |
---|
1413 | switch (a->s) |
---|
1414 | { |
---|
1415 | case 0: |
---|
1416 | case 1: |
---|
1417 | mpz_init_set(b->n,a->n); |
---|
1418 | case 3: |
---|
1419 | mpz_init_set(b->z,a->z); |
---|
1420 | break; |
---|
1421 | } |
---|
1422 | b->s = a->s; |
---|
1423 | return b; |
---|
1424 | } |
---|
1425 | |
---|
1426 | void _nlDelete_NoImm(number *a) |
---|
1427 | { |
---|
1428 | { |
---|
1429 | switch ((*a)->s) |
---|
1430 | { |
---|
1431 | case 0: |
---|
1432 | case 1: |
---|
1433 | mpz_clear((*a)->n); |
---|
1434 | case 3: |
---|
1435 | mpz_clear((*a)->z); |
---|
1436 | #ifdef LDEBUG |
---|
1437 | (*a)->s=2; |
---|
1438 | #endif |
---|
1439 | } |
---|
1440 | omFreeBin((void *) *a, rnumber_bin); |
---|
1441 | } |
---|
1442 | } |
---|
1443 | |
---|
1444 | number _nlNeg_NoImm(number a) |
---|
1445 | { |
---|
1446 | { |
---|
1447 | mpz_neg(a->z,a->z); |
---|
1448 | if (a->s==3) |
---|
1449 | { |
---|
1450 | a=nlShort3(a); |
---|
1451 | } |
---|
1452 | } |
---|
1453 | return a; |
---|
1454 | } |
---|
1455 | |
---|
1456 | number _nlAdd_aNoImm_OR_bNoImm(number a, number b) |
---|
1457 | { |
---|
1458 | number u=ALLOC_RNUMBER(); |
---|
1459 | #if defined(LDEBUG) |
---|
1460 | u->debug=123456; |
---|
1461 | #endif |
---|
1462 | mpz_init(u->z); |
---|
1463 | if (SR_HDL(b) & SR_INT) |
---|
1464 | { |
---|
1465 | number x=a; |
---|
1466 | a=b; |
---|
1467 | b=x; |
---|
1468 | } |
---|
1469 | if (SR_HDL(a) & SR_INT) |
---|
1470 | { |
---|
1471 | switch (b->s) |
---|
1472 | { |
---|
1473 | case 0: |
---|
1474 | case 1:/* a:short, b:1 */ |
---|
1475 | { |
---|
1476 | mpz_t x; |
---|
1477 | mpz_init(x); |
---|
1478 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
1479 | mpz_add(u->z,b->z,x); |
---|
1480 | mpz_clear(x); |
---|
1481 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1482 | { |
---|
1483 | mpz_clear(u->z); |
---|
1484 | FREE_RNUMBER(u); |
---|
1485 | return INT_TO_SR(0); |
---|
1486 | } |
---|
1487 | if (mpz_cmp(u->z,b->n)==0) |
---|
1488 | { |
---|
1489 | mpz_clear(u->z); |
---|
1490 | FREE_RNUMBER(u); |
---|
1491 | return INT_TO_SR(1); |
---|
1492 | } |
---|
1493 | mpz_init_set(u->n,b->n); |
---|
1494 | u->s = 0; |
---|
1495 | break; |
---|
1496 | } |
---|
1497 | case 3: |
---|
1498 | { |
---|
1499 | if ((long)a>0L) |
---|
1500 | mpz_add_ui(u->z,b->z,SR_TO_INT(a)); |
---|
1501 | else |
---|
1502 | mpz_sub_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
1503 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1504 | { |
---|
1505 | mpz_clear(u->z); |
---|
1506 | FREE_RNUMBER(u); |
---|
1507 | return INT_TO_SR(0); |
---|
1508 | } |
---|
1509 | u->s = 3; |
---|
1510 | u=nlShort3(u); |
---|
1511 | break; |
---|
1512 | } |
---|
1513 | } |
---|
1514 | } |
---|
1515 | else |
---|
1516 | { |
---|
1517 | switch (a->s) |
---|
1518 | { |
---|
1519 | case 0: |
---|
1520 | case 1: |
---|
1521 | { |
---|
1522 | switch(b->s) |
---|
1523 | { |
---|
1524 | case 0: |
---|
1525 | case 1: |
---|
1526 | { |
---|
1527 | mpz_t x; |
---|
1528 | mpz_init(x); |
---|
1529 | |
---|
1530 | mpz_mul(x,b->z,a->n); |
---|
1531 | mpz_mul(u->z,a->z,b->n); |
---|
1532 | mpz_add(u->z,u->z,x); |
---|
1533 | mpz_clear(x); |
---|
1534 | |
---|
1535 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1536 | { |
---|
1537 | mpz_clear(u->z); |
---|
1538 | FREE_RNUMBER(u); |
---|
1539 | return INT_TO_SR(0); |
---|
1540 | } |
---|
1541 | mpz_init(u->n); |
---|
1542 | mpz_mul(u->n,a->n,b->n); |
---|
1543 | if (mpz_cmp(u->z,u->n)==0) |
---|
1544 | { |
---|
1545 | mpz_clear(u->z); |
---|
1546 | mpz_clear(u->n); |
---|
1547 | FREE_RNUMBER(u); |
---|
1548 | return INT_TO_SR(1); |
---|
1549 | } |
---|
1550 | u->s = 0; |
---|
1551 | break; |
---|
1552 | } |
---|
1553 | case 3: /* a:1 b:3 */ |
---|
1554 | { |
---|
1555 | mpz_mul(u->z,b->z,a->n); |
---|
1556 | mpz_add(u->z,u->z,a->z); |
---|
1557 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1558 | { |
---|
1559 | mpz_clear(u->z); |
---|
1560 | FREE_RNUMBER(u); |
---|
1561 | return INT_TO_SR(0); |
---|
1562 | } |
---|
1563 | if (mpz_cmp(u->z,a->n)==0) |
---|
1564 | { |
---|
1565 | mpz_clear(u->z); |
---|
1566 | FREE_RNUMBER(u); |
---|
1567 | return INT_TO_SR(1); |
---|
1568 | } |
---|
1569 | mpz_init_set(u->n,a->n); |
---|
1570 | u->s = 0; |
---|
1571 | break; |
---|
1572 | } |
---|
1573 | } /*switch (b->s) */ |
---|
1574 | break; |
---|
1575 | } |
---|
1576 | case 3: |
---|
1577 | { |
---|
1578 | switch(b->s) |
---|
1579 | { |
---|
1580 | case 0: |
---|
1581 | case 1:/* a:3, b:1 */ |
---|
1582 | { |
---|
1583 | mpz_mul(u->z,a->z,b->n); |
---|
1584 | mpz_add(u->z,u->z,b->z); |
---|
1585 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1586 | { |
---|
1587 | mpz_clear(u->z); |
---|
1588 | FREE_RNUMBER(u); |
---|
1589 | return INT_TO_SR(0); |
---|
1590 | } |
---|
1591 | if (mpz_cmp(u->z,b->n)==0) |
---|
1592 | { |
---|
1593 | mpz_clear(u->z); |
---|
1594 | FREE_RNUMBER(u); |
---|
1595 | return INT_TO_SR(1); |
---|
1596 | } |
---|
1597 | mpz_init_set(u->n,b->n); |
---|
1598 | u->s = 0; |
---|
1599 | break; |
---|
1600 | } |
---|
1601 | case 3: |
---|
1602 | { |
---|
1603 | mpz_add(u->z,a->z,b->z); |
---|
1604 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1605 | { |
---|
1606 | mpz_clear(u->z); |
---|
1607 | FREE_RNUMBER(u); |
---|
1608 | return INT_TO_SR(0); |
---|
1609 | } |
---|
1610 | u->s = 3; |
---|
1611 | u=nlShort3(u); |
---|
1612 | break; |
---|
1613 | } |
---|
1614 | } |
---|
1615 | break; |
---|
1616 | } |
---|
1617 | } |
---|
1618 | } |
---|
1619 | return u; |
---|
1620 | } |
---|
1621 | |
---|
1622 | number _nlSub_aNoImm_OR_bNoImm(number a, number b) |
---|
1623 | { |
---|
1624 | number u=ALLOC_RNUMBER(); |
---|
1625 | #if defined(LDEBUG) |
---|
1626 | u->debug=123456; |
---|
1627 | #endif |
---|
1628 | mpz_init(u->z); |
---|
1629 | if (SR_HDL(a) & SR_INT) |
---|
1630 | { |
---|
1631 | switch (b->s) |
---|
1632 | { |
---|
1633 | case 0: |
---|
1634 | case 1:/* a:short, b:1 */ |
---|
1635 | { |
---|
1636 | mpz_t x; |
---|
1637 | mpz_init(x); |
---|
1638 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
1639 | mpz_sub(u->z,x,b->z); |
---|
1640 | mpz_clear(x); |
---|
1641 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1642 | { |
---|
1643 | mpz_clear(u->z); |
---|
1644 | FREE_RNUMBER(u); |
---|
1645 | return INT_TO_SR(0); |
---|
1646 | } |
---|
1647 | if (mpz_cmp(u->z,b->n)==0) |
---|
1648 | { |
---|
1649 | mpz_clear(u->z); |
---|
1650 | FREE_RNUMBER(u); |
---|
1651 | return INT_TO_SR(1); |
---|
1652 | } |
---|
1653 | mpz_init_set(u->n,b->n); |
---|
1654 | u->s = 0; |
---|
1655 | break; |
---|
1656 | } |
---|
1657 | case 3: |
---|
1658 | { |
---|
1659 | if ((long)a>0L) |
---|
1660 | { |
---|
1661 | mpz_sub_ui(u->z,b->z,SR_TO_INT(a)); |
---|
1662 | mpz_neg(u->z,u->z); |
---|
1663 | } |
---|
1664 | else |
---|
1665 | { |
---|
1666 | mpz_add_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
1667 | mpz_neg(u->z,u->z); |
---|
1668 | } |
---|
1669 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1670 | { |
---|
1671 | mpz_clear(u->z); |
---|
1672 | FREE_RNUMBER(u); |
---|
1673 | return INT_TO_SR(0); |
---|
1674 | } |
---|
1675 | u->s = 3; |
---|
1676 | u=nlShort3(u); |
---|
1677 | break; |
---|
1678 | } |
---|
1679 | } |
---|
1680 | } |
---|
1681 | else if (SR_HDL(b) & SR_INT) |
---|
1682 | { |
---|
1683 | switch (a->s) |
---|
1684 | { |
---|
1685 | case 0: |
---|
1686 | case 1:/* b:short, a:1 */ |
---|
1687 | { |
---|
1688 | mpz_t x; |
---|
1689 | mpz_init(x); |
---|
1690 | mpz_mul_si(x,a->n,SR_TO_INT(b)); |
---|
1691 | mpz_sub(u->z,a->z,x); |
---|
1692 | mpz_clear(x); |
---|
1693 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1694 | { |
---|
1695 | mpz_clear(u->z); |
---|
1696 | FREE_RNUMBER(u); |
---|
1697 | return INT_TO_SR(0); |
---|
1698 | } |
---|
1699 | if (mpz_cmp(u->z,a->n)==0) |
---|
1700 | { |
---|
1701 | mpz_clear(u->z); |
---|
1702 | FREE_RNUMBER(u); |
---|
1703 | return INT_TO_SR(1); |
---|
1704 | } |
---|
1705 | mpz_init_set(u->n,a->n); |
---|
1706 | u->s = 0; |
---|
1707 | break; |
---|
1708 | } |
---|
1709 | case 3: |
---|
1710 | { |
---|
1711 | if ((long)b>0L) |
---|
1712 | { |
---|
1713 | mpz_sub_ui(u->z,a->z,SR_TO_INT(b)); |
---|
1714 | } |
---|
1715 | else |
---|
1716 | { |
---|
1717 | mpz_add_ui(u->z,a->z,-SR_TO_INT(b)); |
---|
1718 | } |
---|
1719 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1720 | { |
---|
1721 | mpz_clear(u->z); |
---|
1722 | FREE_RNUMBER(u); |
---|
1723 | return INT_TO_SR(0); |
---|
1724 | } |
---|
1725 | u->s = 3; |
---|
1726 | u=nlShort3(u); |
---|
1727 | break; |
---|
1728 | } |
---|
1729 | } |
---|
1730 | } |
---|
1731 | else |
---|
1732 | { |
---|
1733 | switch (a->s) |
---|
1734 | { |
---|
1735 | case 0: |
---|
1736 | case 1: |
---|
1737 | { |
---|
1738 | switch(b->s) |
---|
1739 | { |
---|
1740 | case 0: |
---|
1741 | case 1: |
---|
1742 | { |
---|
1743 | mpz_t x; |
---|
1744 | mpz_t y; |
---|
1745 | mpz_init(x); |
---|
1746 | mpz_init(y); |
---|
1747 | mpz_mul(x,b->z,a->n); |
---|
1748 | mpz_mul(y,a->z,b->n); |
---|
1749 | mpz_sub(u->z,y,x); |
---|
1750 | mpz_clear(x); |
---|
1751 | mpz_clear(y); |
---|
1752 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1753 | { |
---|
1754 | mpz_clear(u->z); |
---|
1755 | FREE_RNUMBER(u); |
---|
1756 | return INT_TO_SR(0); |
---|
1757 | } |
---|
1758 | mpz_init(u->n); |
---|
1759 | mpz_mul(u->n,a->n,b->n); |
---|
1760 | if (mpz_cmp(u->z,u->n)==0) |
---|
1761 | { |
---|
1762 | mpz_clear(u->z); |
---|
1763 | mpz_clear(u->n); |
---|
1764 | FREE_RNUMBER(u); |
---|
1765 | return INT_TO_SR(1); |
---|
1766 | } |
---|
1767 | u->s = 0; |
---|
1768 | break; |
---|
1769 | } |
---|
1770 | case 3: /* a:1, b:3 */ |
---|
1771 | { |
---|
1772 | mpz_t x; |
---|
1773 | mpz_init(x); |
---|
1774 | mpz_mul(x,b->z,a->n); |
---|
1775 | mpz_sub(u->z,a->z,x); |
---|
1776 | mpz_clear(x); |
---|
1777 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1778 | { |
---|
1779 | mpz_clear(u->z); |
---|
1780 | FREE_RNUMBER(u); |
---|
1781 | return INT_TO_SR(0); |
---|
1782 | } |
---|
1783 | if (mpz_cmp(u->z,a->n)==0) |
---|
1784 | { |
---|
1785 | mpz_clear(u->z); |
---|
1786 | FREE_RNUMBER(u); |
---|
1787 | return INT_TO_SR(1); |
---|
1788 | } |
---|
1789 | mpz_init_set(u->n,a->n); |
---|
1790 | u->s = 0; |
---|
1791 | break; |
---|
1792 | } |
---|
1793 | } |
---|
1794 | break; |
---|
1795 | } |
---|
1796 | case 3: |
---|
1797 | { |
---|
1798 | switch(b->s) |
---|
1799 | { |
---|
1800 | case 0: |
---|
1801 | case 1: /* a:3, b:1 */ |
---|
1802 | { |
---|
1803 | mpz_t x; |
---|
1804 | mpz_init(x); |
---|
1805 | mpz_mul(x,a->z,b->n); |
---|
1806 | mpz_sub(u->z,x,b->z); |
---|
1807 | mpz_clear(x); |
---|
1808 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1809 | { |
---|
1810 | mpz_clear(u->z); |
---|
1811 | FREE_RNUMBER(u); |
---|
1812 | return INT_TO_SR(0); |
---|
1813 | } |
---|
1814 | if (mpz_cmp(u->z,b->n)==0) |
---|
1815 | { |
---|
1816 | mpz_clear(u->z); |
---|
1817 | FREE_RNUMBER(u); |
---|
1818 | return INT_TO_SR(1); |
---|
1819 | } |
---|
1820 | mpz_init_set(u->n,b->n); |
---|
1821 | u->s = 0; |
---|
1822 | break; |
---|
1823 | } |
---|
1824 | case 3: /* a:3 , b:3 */ |
---|
1825 | { |
---|
1826 | mpz_sub(u->z,a->z,b->z); |
---|
1827 | if (mpz_cmp_ui(u->z,(long)0)==0) |
---|
1828 | { |
---|
1829 | mpz_clear(u->z); |
---|
1830 | FREE_RNUMBER(u); |
---|
1831 | return INT_TO_SR(0); |
---|
1832 | } |
---|
1833 | u->s = 3; |
---|
1834 | u=nlShort3(u); |
---|
1835 | break; |
---|
1836 | } |
---|
1837 | } |
---|
1838 | break; |
---|
1839 | } |
---|
1840 | } |
---|
1841 | } |
---|
1842 | return u; |
---|
1843 | } |
---|
1844 | |
---|
1845 | // a and b are intermediate, but a*b not |
---|
1846 | number _nlMult_aImm_bImm_rNoImm(number a, number b) |
---|
1847 | { |
---|
1848 | number u=ALLOC_RNUMBER(); |
---|
1849 | #if defined(LDEBUG) |
---|
1850 | u->debug=123456; |
---|
1851 | #endif |
---|
1852 | u->s=3; |
---|
1853 | mpz_init_set_si(u->z,SR_TO_INT(a)); |
---|
1854 | mpz_mul_si(u->z,u->z,SR_TO_INT(b)); |
---|
1855 | return u; |
---|
1856 | } |
---|
1857 | |
---|
1858 | // a or b are not immediate |
---|
1859 | number _nlMult_aNoImm_OR_bNoImm(number a, number b) |
---|
1860 | { |
---|
1861 | assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT)); |
---|
1862 | number u=ALLOC_RNUMBER(); |
---|
1863 | #if defined(LDEBUG) |
---|
1864 | u->debug=123456; |
---|
1865 | #endif |
---|
1866 | mpz_init(u->z); |
---|
1867 | if (SR_HDL(b) & SR_INT) |
---|
1868 | { |
---|
1869 | number x=a; |
---|
1870 | a=b; |
---|
1871 | b=x; |
---|
1872 | } |
---|
1873 | if (SR_HDL(a) & SR_INT) |
---|
1874 | { |
---|
1875 | u->s=b->s; |
---|
1876 | if (u->s==1) u->s=0; |
---|
1877 | if ((long)a>0L) |
---|
1878 | { |
---|
1879 | mpz_mul_ui(u->z,b->z,(unsigned long)SR_TO_INT(a)); |
---|
1880 | } |
---|
1881 | else |
---|
1882 | { |
---|
1883 | if (a==INT_TO_SR(-1)) |
---|
1884 | { |
---|
1885 | mpz_set(u->z,b->z); |
---|
1886 | mpz_neg(u->z,u->z); |
---|
1887 | u->s=b->s; |
---|
1888 | } |
---|
1889 | else |
---|
1890 | { |
---|
1891 | mpz_mul_ui(u->z,b->z,(unsigned long)-SR_TO_INT(a)); |
---|
1892 | mpz_neg(u->z,u->z); |
---|
1893 | } |
---|
1894 | } |
---|
1895 | if (u->s<2) |
---|
1896 | { |
---|
1897 | if (mpz_cmp(u->z,b->n)==0) |
---|
1898 | { |
---|
1899 | mpz_clear(u->z); |
---|
1900 | FREE_RNUMBER(u); |
---|
1901 | return INT_TO_SR(1); |
---|
1902 | } |
---|
1903 | mpz_init_set(u->n,b->n); |
---|
1904 | } |
---|
1905 | else //u->s==3 |
---|
1906 | { |
---|
1907 | u=nlShort3(u); |
---|
1908 | } |
---|
1909 | } |
---|
1910 | else |
---|
1911 | { |
---|
1912 | mpz_mul(u->z,a->z,b->z); |
---|
1913 | u->s = 0; |
---|
1914 | if(a->s==3) |
---|
1915 | { |
---|
1916 | if(b->s==3) |
---|
1917 | { |
---|
1918 | u->s = 3; |
---|
1919 | } |
---|
1920 | else |
---|
1921 | { |
---|
1922 | if (mpz_cmp(u->z,b->n)==0) |
---|
1923 | { |
---|
1924 | mpz_clear(u->z); |
---|
1925 | FREE_RNUMBER(u); |
---|
1926 | return INT_TO_SR(1); |
---|
1927 | } |
---|
1928 | mpz_init_set(u->n,b->n); |
---|
1929 | } |
---|
1930 | } |
---|
1931 | else |
---|
1932 | { |
---|
1933 | if(b->s==3) |
---|
1934 | { |
---|
1935 | if (mpz_cmp(u->z,a->n)==0) |
---|
1936 | { |
---|
1937 | mpz_clear(u->z); |
---|
1938 | FREE_RNUMBER(u); |
---|
1939 | return INT_TO_SR(1); |
---|
1940 | } |
---|
1941 | mpz_init_set(u->n,a->n); |
---|
1942 | } |
---|
1943 | else |
---|
1944 | { |
---|
1945 | mpz_init(u->n); |
---|
1946 | mpz_mul(u->n,a->n,b->n); |
---|
1947 | if (mpz_cmp(u->z,u->n)==0) |
---|
1948 | { |
---|
1949 | mpz_clear(u->z); |
---|
1950 | mpz_clear(u->n); |
---|
1951 | FREE_RNUMBER(u); |
---|
1952 | return INT_TO_SR(1); |
---|
1953 | } |
---|
1954 | } |
---|
1955 | } |
---|
1956 | } |
---|
1957 | return u; |
---|
1958 | } |
---|
1959 | |
---|
1960 | /*2 |
---|
1961 | * copy a to b for mapping |
---|
1962 | */ |
---|
1963 | number nlCopyMap(number a, const coeffs src, const coeffs dst) |
---|
1964 | { |
---|
1965 | assume( getCoeffType(dst) == ID ); |
---|
1966 | assume( getCoeffType(src) == ID ); |
---|
1967 | |
---|
1968 | if ((SR_HDL(a) & SR_INT)||(a==NULL)) |
---|
1969 | { |
---|
1970 | return a; |
---|
1971 | } |
---|
1972 | return _nlCopy_NoImm(a); |
---|
1973 | } |
---|
1974 | |
---|
1975 | nMapFunc nlSetMap(const coeffs src, const coeffs dst) |
---|
1976 | { |
---|
1977 | assume( getCoeffType(dst) == ID ); |
---|
1978 | // assume( getCoeffType(src) == ID ); |
---|
1979 | |
---|
1980 | if (nCoeff_is_Q(src)) |
---|
1981 | { |
---|
1982 | return nlCopyMap; |
---|
1983 | } |
---|
1984 | if (nCoeff_is_Zp(src)) |
---|
1985 | { |
---|
1986 | return nlMapP; |
---|
1987 | } |
---|
1988 | if (nCoeff_is_R(src)) |
---|
1989 | { |
---|
1990 | return nlMapR; |
---|
1991 | } |
---|
1992 | if (nCoeff_is_long_R(src)) |
---|
1993 | { |
---|
1994 | return nlMapLongR; /* long R -> Q */ |
---|
1995 | } |
---|
1996 | #ifdef HAVE_RINGS |
---|
1997 | if (nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src)) |
---|
1998 | { |
---|
1999 | return nlMapGMP; |
---|
2000 | } |
---|
2001 | if (nCoeff_is_Ring_2toM(src)) |
---|
2002 | { |
---|
2003 | return nlMapMachineInt; |
---|
2004 | } |
---|
2005 | #endif |
---|
2006 | return NULL; |
---|
2007 | } |
---|
2008 | /*2 |
---|
2009 | * z := i |
---|
2010 | */ |
---|
2011 | number nlRInit (long i) |
---|
2012 | { |
---|
2013 | number z=ALLOC_RNUMBER(); |
---|
2014 | #if defined(LDEBUG) |
---|
2015 | z->debug=123456; |
---|
2016 | #endif |
---|
2017 | mpz_init_set_si(z->z,i); |
---|
2018 | z->s = 3; |
---|
2019 | return z; |
---|
2020 | } |
---|
2021 | |
---|
2022 | /*2 |
---|
2023 | * z := i/j |
---|
2024 | */ |
---|
2025 | number nlInit2 (int i, int j, const coeffs r) |
---|
2026 | { |
---|
2027 | number z=ALLOC_RNUMBER(); |
---|
2028 | #if defined(LDEBUG) |
---|
2029 | z->debug=123456; |
---|
2030 | #endif |
---|
2031 | mpz_init_set_si(z->z,(long)i); |
---|
2032 | mpz_init_set_si(z->n,(long)j); |
---|
2033 | z->s = 0; |
---|
2034 | nlNormalize(z,r); |
---|
2035 | return z; |
---|
2036 | } |
---|
2037 | |
---|
2038 | number nlInit2gmp (mpz_t i, mpz_t j, const coeffs r) |
---|
2039 | { |
---|
2040 | number z=ALLOC_RNUMBER(); |
---|
2041 | #if defined(LDEBUG) |
---|
2042 | z->debug=123456; |
---|
2043 | #endif |
---|
2044 | mpz_init_set(z->z,i); |
---|
2045 | mpz_init_set(z->n,j); |
---|
2046 | z->s = 0; |
---|
2047 | nlNormalize(z,r); |
---|
2048 | return z; |
---|
2049 | } |
---|
2050 | |
---|
2051 | #else // DO_LINLINE |
---|
2052 | |
---|
2053 | // declare immedate routines |
---|
2054 | number nlRInit (int i); |
---|
2055 | BOOLEAN _nlEqual_aNoImm_OR_bNoImm(number a, number b); |
---|
2056 | number _nlCopy_NoImm(number a); |
---|
2057 | number _nlNeg_NoImm(number a); |
---|
2058 | number _nlAdd_aNoImm_OR_bNoImm(number a, number b); |
---|
2059 | number _nlSub_aNoImm_OR_bNoImm(number a, number b); |
---|
2060 | number _nlMult_aNoImm_OR_bNoImm(number a, number b); |
---|
2061 | number _nlMult_aImm_bImm_rNoImm(number a, number b); |
---|
2062 | |
---|
2063 | #endif |
---|
2064 | |
---|
2065 | /*************************************************************** |
---|
2066 | * |
---|
2067 | * Routines which might be inlined by p_Numbers.h |
---|
2068 | * |
---|
2069 | *******************************************************************/ |
---|
2070 | #if defined(DO_LINLINE) || !defined(P_NUMBERS_H) |
---|
2071 | |
---|
2072 | // routines which are always inlined/static |
---|
2073 | |
---|
2074 | /*2 |
---|
2075 | * a = b ? |
---|
2076 | */ |
---|
2077 | LINLINE BOOLEAN nlEqual (number a, number b, const coeffs r) |
---|
2078 | { |
---|
2079 | nlTest(a, r); |
---|
2080 | nlTest(b, r); |
---|
2081 | // short - short |
---|
2082 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) return a==b; |
---|
2083 | return _nlEqual_aNoImm_OR_bNoImm(a, b); |
---|
2084 | } |
---|
2085 | |
---|
2086 | |
---|
2087 | LINLINE number nlInit (int i, const coeffs r) |
---|
2088 | { |
---|
2089 | number n; |
---|
2090 | LONG ii=(LONG)i; |
---|
2091 | if ( ((ii << 3) >> 3) == ii ) n=INT_TO_SR(ii); |
---|
2092 | else n=nlRInit(ii); |
---|
2093 | nlTest(n, r); |
---|
2094 | return n; |
---|
2095 | } |
---|
2096 | |
---|
2097 | |
---|
2098 | /*2 |
---|
2099 | * a == 1 ? |
---|
2100 | */ |
---|
2101 | LINLINE BOOLEAN nlIsOne (number a, const coeffs r) |
---|
2102 | { |
---|
2103 | #ifdef LDEBUG |
---|
2104 | if (a==NULL) return FALSE; |
---|
2105 | nlTest(a, r); |
---|
2106 | #endif |
---|
2107 | return (a==INT_TO_SR(1)); |
---|
2108 | } |
---|
2109 | |
---|
2110 | LINLINE BOOLEAN nlIsZero (number a, const coeffs) |
---|
2111 | { |
---|
2112 | return (a==INT_TO_SR(0)); |
---|
2113 | //return (mpz_cmp_si(a->z,(long)0)==0); |
---|
2114 | } |
---|
2115 | |
---|
2116 | /*2 |
---|
2117 | * copy a to b |
---|
2118 | */ |
---|
2119 | LINLINE number nlCopy(number a, const coeffs) |
---|
2120 | { |
---|
2121 | if ((SR_HDL(a) & SR_INT)||(a==NULL)) |
---|
2122 | { |
---|
2123 | return a; |
---|
2124 | } |
---|
2125 | return _nlCopy_NoImm(a); |
---|
2126 | } |
---|
2127 | |
---|
2128 | |
---|
2129 | /*2 |
---|
2130 | * delete a |
---|
2131 | */ |
---|
2132 | LINLINE void nlDelete (number * a, const coeffs r) |
---|
2133 | { |
---|
2134 | if (*a!=NULL) |
---|
2135 | { |
---|
2136 | nlTest(*a, r); |
---|
2137 | if ((SR_HDL(*a) & SR_INT)==0) |
---|
2138 | { |
---|
2139 | _nlDelete_NoImm(a); |
---|
2140 | } |
---|
2141 | *a=NULL; |
---|
2142 | } |
---|
2143 | } |
---|
2144 | |
---|
2145 | /*2 |
---|
2146 | * za:= - za |
---|
2147 | */ |
---|
2148 | LINLINE number nlNeg (number a, const coeffs R) |
---|
2149 | { |
---|
2150 | nlTest(a, R); |
---|
2151 | if(SR_HDL(a) &SR_INT) |
---|
2152 | { |
---|
2153 | int r=SR_TO_INT(a); |
---|
2154 | if (r==(-(POW_2_28))) a=nlRInit(POW_2_28); |
---|
2155 | else a=INT_TO_SR(-r); |
---|
2156 | return a; |
---|
2157 | } |
---|
2158 | a = _nlNeg_NoImm(a); |
---|
2159 | nlTest(a, R); |
---|
2160 | return a; |
---|
2161 | |
---|
2162 | } |
---|
2163 | |
---|
2164 | /*2 |
---|
2165 | * u:= a + b |
---|
2166 | */ |
---|
2167 | LINLINE number nlAdd (number a, number b, const coeffs R) |
---|
2168 | { |
---|
2169 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
2170 | { |
---|
2171 | LONG r=SR_HDL(a)+SR_HDL(b)-1L; |
---|
2172 | if ( ((r << 1) >> 1) == r ) |
---|
2173 | return (number)(long)r; |
---|
2174 | else |
---|
2175 | return nlRInit(SR_TO_INT(r)); |
---|
2176 | } |
---|
2177 | number u = _nlAdd_aNoImm_OR_bNoImm(a, b); |
---|
2178 | nlTest(u, R); |
---|
2179 | return u; |
---|
2180 | } |
---|
2181 | |
---|
2182 | number nlShort1(number a); |
---|
2183 | number nlShort3_noinline(number x); |
---|
2184 | |
---|
2185 | LINLINE number nlInpAdd_(number a, number b, const coeffs r) |
---|
2186 | { |
---|
2187 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
2188 | { |
---|
2189 | LONG r=SR_HDL(a)+SR_HDL(b)-1L; |
---|
2190 | if ( ((r << 1) >> 1) == r ) |
---|
2191 | return (number)(long)r; |
---|
2192 | else |
---|
2193 | return nlRInit(SR_TO_INT(r)); |
---|
2194 | } |
---|
2195 | // a=a+b |
---|
2196 | if (SR_HDL(b) & SR_INT) |
---|
2197 | { |
---|
2198 | switch (a->s) |
---|
2199 | { |
---|
2200 | case 0: |
---|
2201 | case 1:/* b:short, a:1 */ |
---|
2202 | { |
---|
2203 | mpz_t x; |
---|
2204 | mpz_init(x); |
---|
2205 | mpz_mul_si(x,a->n,SR_TO_INT(b)); |
---|
2206 | mpz_add(a->z,a->z,x); |
---|
2207 | mpz_clear(x); |
---|
2208 | a->s = 0; |
---|
2209 | a=nlShort1(a); |
---|
2210 | break; |
---|
2211 | } |
---|
2212 | case 3: |
---|
2213 | { |
---|
2214 | if ((long)b>0L) |
---|
2215 | mpz_add_ui(a->z,a->z,SR_TO_INT(b)); |
---|
2216 | else |
---|
2217 | mpz_sub_ui(a->z,a->z,-SR_TO_INT(b)); |
---|
2218 | a->s = 3; |
---|
2219 | a=nlShort3_noinline(a); |
---|
2220 | break; |
---|
2221 | } |
---|
2222 | } |
---|
2223 | return a; |
---|
2224 | } |
---|
2225 | if (SR_HDL(a) & SR_INT) |
---|
2226 | { |
---|
2227 | number u=ALLOC_RNUMBER(); |
---|
2228 | #if defined(LDEBUG) |
---|
2229 | u->debug=123456; |
---|
2230 | #endif |
---|
2231 | mpz_init(u->z); |
---|
2232 | switch (b->s) |
---|
2233 | { |
---|
2234 | case 0: |
---|
2235 | case 1:/* a:short, b:1 */ |
---|
2236 | { |
---|
2237 | mpz_t x; |
---|
2238 | mpz_init(x); |
---|
2239 | |
---|
2240 | mpz_mul_si(x,b->n,SR_TO_INT(a)); |
---|
2241 | mpz_add(u->z,b->z,x); |
---|
2242 | mpz_clear(x); |
---|
2243 | // result cannot be 0, if coeffs are normalized |
---|
2244 | mpz_init_set(u->n,b->n); |
---|
2245 | u->s = 0; |
---|
2246 | u=nlShort1(u); |
---|
2247 | break; |
---|
2248 | } |
---|
2249 | case 3: |
---|
2250 | { |
---|
2251 | if ((long)a>0L) |
---|
2252 | mpz_add_ui(u->z,b->z,SR_TO_INT(a)); |
---|
2253 | else |
---|
2254 | mpz_sub_ui(u->z,b->z,-SR_TO_INT(a)); |
---|
2255 | // result cannot be 0, if coeffs are normalized |
---|
2256 | u->s = 3; |
---|
2257 | u=nlShort3_noinline(u); |
---|
2258 | break; |
---|
2259 | } |
---|
2260 | } |
---|
2261 | nlTest(u, r); |
---|
2262 | return u; |
---|
2263 | } |
---|
2264 | else |
---|
2265 | { |
---|
2266 | switch (a->s) |
---|
2267 | { |
---|
2268 | case 0: |
---|
2269 | case 1: |
---|
2270 | { |
---|
2271 | switch(b->s) |
---|
2272 | { |
---|
2273 | case 0: |
---|
2274 | case 1: /* a:1 b:1 */ |
---|
2275 | { |
---|
2276 | mpz_t x; |
---|
2277 | mpz_t y; |
---|
2278 | mpz_init(x); |
---|
2279 | mpz_init(y); |
---|
2280 | mpz_mul(x,b->z,a->n); |
---|
2281 | mpz_mul(y,a->z,b->n); |
---|
2282 | mpz_add(a->z,x,y); |
---|
2283 | mpz_clear(x); |
---|
2284 | mpz_clear(y); |
---|
2285 | mpz_mul(a->n,a->n,b->n); |
---|
2286 | a->s = 0; |
---|
2287 | break; |
---|
2288 | } |
---|
2289 | case 3: /* a:1 b:3 */ |
---|
2290 | { |
---|
2291 | mpz_t x; |
---|
2292 | mpz_init(x); |
---|
2293 | mpz_mul(x,b->z,a->n); |
---|
2294 | mpz_add(a->z,a->z,x); |
---|
2295 | mpz_clear(x); |
---|
2296 | a->s = 0; |
---|
2297 | break; |
---|
2298 | } |
---|
2299 | } /*switch (b->s) */ |
---|
2300 | a=nlShort1(a); |
---|
2301 | break; |
---|
2302 | } |
---|
2303 | case 3: |
---|
2304 | { |
---|
2305 | switch(b->s) |
---|
2306 | { |
---|
2307 | case 0: |
---|
2308 | case 1:/* a:3, b:1 */ |
---|
2309 | { |
---|
2310 | mpz_t x; |
---|
2311 | mpz_init(x); |
---|
2312 | mpz_mul(x,a->z,b->n); |
---|
2313 | mpz_add(a->z,b->z,x); |
---|
2314 | mpz_clear(x); |
---|
2315 | mpz_init_set(a->n,b->n); |
---|
2316 | a->s = 0; |
---|
2317 | a=nlShort1(a); |
---|
2318 | break; |
---|
2319 | } |
---|
2320 | case 3: |
---|
2321 | { |
---|
2322 | mpz_add(a->z,a->z,b->z); |
---|
2323 | a->s = 3; |
---|
2324 | a=nlShort3_noinline(a); |
---|
2325 | break; |
---|
2326 | } |
---|
2327 | } |
---|
2328 | break; |
---|
2329 | } |
---|
2330 | } |
---|
2331 | nlTest(a, r); |
---|
2332 | return a; |
---|
2333 | } |
---|
2334 | } |
---|
2335 | |
---|
2336 | LINLINE void nlInpAdd(number &a, number b, const coeffs r) |
---|
2337 | { |
---|
2338 | a = nlInpAdd_(a, b, r); |
---|
2339 | } |
---|
2340 | |
---|
2341 | |
---|
2342 | LINLINE number nlMult (number a, number b, const coeffs R) |
---|
2343 | { |
---|
2344 | nlTest(a, R); |
---|
2345 | nlTest(b, R); |
---|
2346 | if (a==INT_TO_SR(0)) return INT_TO_SR(0); |
---|
2347 | if (b==INT_TO_SR(0)) return INT_TO_SR(0); |
---|
2348 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
2349 | { |
---|
2350 | LONG r=(SR_HDL(a)-1L)*(SR_HDL(b)>>1); |
---|
2351 | if ((r/(SR_HDL(b)>>1))==(SR_HDL(a)-1L)) |
---|
2352 | { |
---|
2353 | number u=((number) ((r>>1)+SR_INT)); |
---|
2354 | if (((((LONG)SR_HDL(u))<<1)>>1)==SR_HDL(u)) return (u); |
---|
2355 | return nlRInit(SR_HDL(u)>>2); |
---|
2356 | } |
---|
2357 | number u = _nlMult_aImm_bImm_rNoImm(a, b); |
---|
2358 | nlTest(u, R); |
---|
2359 | return u; |
---|
2360 | |
---|
2361 | } |
---|
2362 | number u = _nlMult_aNoImm_OR_bNoImm(a, b); |
---|
2363 | nlTest(u, R); |
---|
2364 | return u; |
---|
2365 | |
---|
2366 | } |
---|
2367 | |
---|
2368 | |
---|
2369 | /*2 |
---|
2370 | * u:= a - b |
---|
2371 | */ |
---|
2372 | LINLINE number nlSub (number a, number b, const coeffs r) |
---|
2373 | { |
---|
2374 | if (SR_HDL(a) & SR_HDL(b) & SR_INT) |
---|
2375 | { |
---|
2376 | LONG r=SR_HDL(a)-SR_HDL(b)+1; |
---|
2377 | if ( ((r << 1) >> 1) == r ) |
---|
2378 | { |
---|
2379 | return (number)(long)r; |
---|
2380 | } |
---|
2381 | else |
---|
2382 | return nlRInit(SR_TO_INT(r)); |
---|
2383 | } |
---|
2384 | number u = _nlSub_aNoImm_OR_bNoImm(a, b); |
---|
2385 | nlTest(u, r); |
---|
2386 | return u; |
---|
2387 | |
---|
2388 | } |
---|
2389 | |
---|
2390 | LINLINE void nlInpMult(number &a, number b, const coeffs r) |
---|
2391 | { |
---|
2392 | number aa=a; |
---|
2393 | if (((SR_HDL(b)|SR_HDL(aa))&SR_INT)) |
---|
2394 | { |
---|
2395 | number n=nlMult(aa,b,r); |
---|
2396 | nlDelete(&a,r); |
---|
2397 | a=n; |
---|
2398 | } |
---|
2399 | else |
---|
2400 | { |
---|
2401 | mpz_mul(aa->z,a->z,b->z); |
---|
2402 | if (aa->s==3) |
---|
2403 | { |
---|
2404 | if(b->s!=3) |
---|
2405 | { |
---|
2406 | mpz_init_set(a->n,b->n); |
---|
2407 | a->s=0; |
---|
2408 | } |
---|
2409 | } |
---|
2410 | else |
---|
2411 | { |
---|
2412 | if(b->s!=3) |
---|
2413 | { |
---|
2414 | mpz_mul(a->n,a->n,b->n); |
---|
2415 | } |
---|
2416 | a->s=0; |
---|
2417 | } |
---|
2418 | } |
---|
2419 | } |
---|
2420 | #endif // DO_LINLINE |
---|
2421 | |
---|
2422 | #ifndef P_NUMBERS_H |
---|
2423 | |
---|
2424 | void nlInpGcd(number &a, number b, const coeffs r) |
---|
2425 | { |
---|
2426 | if ((SR_HDL(b)|SR_HDL(a))&SR_INT) |
---|
2427 | { |
---|
2428 | number n=nlGcd(a,b,r); |
---|
2429 | nlDelete(&a,r); |
---|
2430 | a=n; |
---|
2431 | } |
---|
2432 | else |
---|
2433 | { |
---|
2434 | mpz_gcd(a->z,a->z,b->z); |
---|
2435 | a=nlShort3_noinline(a); |
---|
2436 | } |
---|
2437 | } |
---|
2438 | void nlInpIntDiv(number &a, number b, const coeffs r) |
---|
2439 | { |
---|
2440 | if ((SR_HDL(b)|SR_HDL(a))&SR_INT) |
---|
2441 | { |
---|
2442 | number n=nlIntDiv(a,b, r); |
---|
2443 | nlDelete(&a,r); |
---|
2444 | a=n; |
---|
2445 | } |
---|
2446 | else |
---|
2447 | { |
---|
2448 | if (mpz_isNeg(a->z)) |
---|
2449 | { |
---|
2450 | if (mpz_isNeg(b->z)) |
---|
2451 | { |
---|
2452 | mpz_add(a->z,a->z,b->z); |
---|
2453 | } |
---|
2454 | else |
---|
2455 | { |
---|
2456 | mpz_sub(a->z,a->z,b->z); |
---|
2457 | } |
---|
2458 | mpz_add_ui(a->z,a->z,1); |
---|
2459 | } |
---|
2460 | else |
---|
2461 | { |
---|
2462 | if (mpz_isNeg(b->z)) |
---|
2463 | { |
---|
2464 | mpz_sub(a->z,a->z,b->z); |
---|
2465 | } |
---|
2466 | else |
---|
2467 | { |
---|
2468 | mpz_add(a->z,a->z,b->z); |
---|
2469 | } |
---|
2470 | mpz_sub_ui(a->z,a->z,1); |
---|
2471 | } |
---|
2472 | MPZ_DIV(a->z,a->z,b->z); |
---|
2473 | a=nlShort3_noinline(a); |
---|
2474 | } |
---|
2475 | } |
---|
2476 | |
---|
2477 | number nlFarey(number nN, number nP, const coeffs r) |
---|
2478 | { |
---|
2479 | mpz_t tmp; mpz_init(tmp); |
---|
2480 | mpz_t A,B,C,D,E,N,P; |
---|
2481 | if (SR_HDL(nN) & SR_INT) mpz_init_set_si(N,SR_TO_INT(nN)); |
---|
2482 | else mpz_init_set(N,nN->z); |
---|
2483 | if (SR_HDL(nP) & SR_INT) mpz_init_set_si(P,SR_TO_INT(nP)); |
---|
2484 | else mpz_init_set(P,nP->z); |
---|
2485 | assume(!mpz_isNeg(P)); |
---|
2486 | if (mpz_isNeg(N)) mpz_add(N,N,P); |
---|
2487 | mpz_init_set_si(A,(long)0); |
---|
2488 | mpz_init_set_ui(B,(unsigned long)1); |
---|
2489 | mpz_init_set_si(C,(long)0); |
---|
2490 | mpz_init(D); |
---|
2491 | mpz_init_set(E,P); |
---|
2492 | number z=INT_TO_SR(0); |
---|
2493 | while(mpz_cmp_si(N,(long)0)!=0) |
---|
2494 | { |
---|
2495 | mpz_mul(tmp,N,N); |
---|
2496 | mpz_add(tmp,tmp,tmp); |
---|
2497 | if (mpz_cmp(tmp,P)<0) |
---|
2498 | { |
---|
2499 | // return N/B |
---|
2500 | z=ALLOC_RNUMBER(); |
---|
2501 | #ifdef LDEBUG |
---|
2502 | z->debug=123456; |
---|
2503 | #endif |
---|
2504 | if (mpz_isNeg(B)) |
---|
2505 | { |
---|
2506 | mpz_neg(B,B); |
---|
2507 | mpz_neg(N,N); |
---|
2508 | } |
---|
2509 | mpz_init_set(z->z,N); |
---|
2510 | mpz_init_set(z->n,B); |
---|
2511 | z->s = 0; |
---|
2512 | nlNormalize(z,r); |
---|
2513 | break; |
---|
2514 | } |
---|
2515 | mpz_mod(D,E,N); |
---|
2516 | mpz_div(tmp,E,N); |
---|
2517 | mpz_mul(tmp,tmp,B); |
---|
2518 | mpz_sub(C,A,tmp); |
---|
2519 | mpz_set(E,N); |
---|
2520 | mpz_set(N,D); |
---|
2521 | mpz_set(A,B); |
---|
2522 | mpz_set(B,C); |
---|
2523 | } |
---|
2524 | mpz_clear(tmp); |
---|
2525 | mpz_clear(A); |
---|
2526 | mpz_clear(B); |
---|
2527 | mpz_clear(C); |
---|
2528 | mpz_clear(D); |
---|
2529 | mpz_clear(E); |
---|
2530 | mpz_clear(N); |
---|
2531 | mpz_clear(P); |
---|
2532 | return z; |
---|
2533 | } |
---|
2534 | |
---|
2535 | void nlCoeffWrite (const coeffs r) |
---|
2536 | { |
---|
2537 | PrintS("// characteristic : 0\n"); |
---|
2538 | } |
---|
2539 | |
---|
2540 | BOOLEAN nlInitChar(coeffs r, void* p) |
---|
2541 | { |
---|
2542 | const int ch = (int)(long)(p); |
---|
2543 | |
---|
2544 | r->cfKillChar=NULL; |
---|
2545 | r->cfSetChar=NULL; |
---|
2546 | r->nCoeffIsEqual=ndCoeffIsEqual; |
---|
2547 | r->cfKillChar = ndKillChar; /* dummy */ |
---|
2548 | |
---|
2549 | r->cfMult = nlMult; |
---|
2550 | r->cfSub = nlSub; |
---|
2551 | r->cfAdd = nlAdd; |
---|
2552 | r->cfDiv = nlDiv; |
---|
2553 | r->cfIntDiv= nlIntDiv; |
---|
2554 | r->cfIntMod= nlIntMod; |
---|
2555 | r->cfExactDiv= nlExactDiv; |
---|
2556 | r->cfInit = nlInit; |
---|
2557 | //r->cfPar = ndPar; |
---|
2558 | //r->cfParDeg = ndParDeg; |
---|
2559 | r->cfSize = nlSize; |
---|
2560 | r->cfInt = nlInt; |
---|
2561 | #ifdef HAVE_RINGS |
---|
2562 | //r->cfDivComp = NULL; // only for ring stuff |
---|
2563 | //r->cfIsUnit = NULL; // only for ring stuff |
---|
2564 | //r->cfGetUnit = NULL; // only for ring stuff |
---|
2565 | //r->cfExtGcd = NULL; // only for ring stuff |
---|
2566 | //r->cfDivBy = NULL; // only for ring stuff |
---|
2567 | #endif |
---|
2568 | r->cfNeg = nlNeg; |
---|
2569 | r->cfInvers= nlInvers; |
---|
2570 | r->cfCopy = nlCopy; |
---|
2571 | r->cfRePart = nlCopy; |
---|
2572 | //r->cfImPart = ndReturn0; |
---|
2573 | r->cfWrite = nlWrite; |
---|
2574 | r->cfRead = nlRead; |
---|
2575 | r->cfNormalize=nlNormalize; |
---|
2576 | r->cfGreater = nlGreater; |
---|
2577 | r->cfEqual = nlEqual; |
---|
2578 | r->cfIsZero = nlIsZero; |
---|
2579 | r->cfIsOne = nlIsOne; |
---|
2580 | r->cfIsMOne = nlIsMOne; |
---|
2581 | r->cfGreaterZero = nlGreaterZero; |
---|
2582 | r->cfPower = nlPower; |
---|
2583 | r->cfGetDenom = nlGetDenom; |
---|
2584 | r->cfGetNumerator = nlGetNumerator; |
---|
2585 | r->cfGcd = nlGcd; |
---|
2586 | r->cfLcm = nlLcm; |
---|
2587 | r->cfDelete= nlDelete; |
---|
2588 | r->cfSetMap = nlSetMap; |
---|
2589 | //r->cfName = ndName; |
---|
2590 | r->cfInpMult=nlInpMult; |
---|
2591 | r->cfInit_bigint=nlCopyMap; |
---|
2592 | r->cfCoeffWrite=nlCoeffWrite; |
---|
2593 | #ifdef LDEBUG |
---|
2594 | // debug stuff |
---|
2595 | r->cfDBTest=nlDBTest; |
---|
2596 | #endif |
---|
2597 | |
---|
2598 | // the variables: general stuff (required) |
---|
2599 | r->nNULL = INT_TO_SR(0); |
---|
2600 | //r->type = n_Q; |
---|
2601 | r->ch = 0; |
---|
2602 | r->has_simple_Alloc=FALSE; |
---|
2603 | r->has_simple_Inverse=FALSE; |
---|
2604 | |
---|
2605 | // variables for this type of coeffs: |
---|
2606 | // (none) |
---|
2607 | return FALSE; |
---|
2608 | } |
---|
2609 | #if 0 |
---|
2610 | number nlMod(number a, number b) |
---|
2611 | { |
---|
2612 | if (((SR_HDL(b)&SR_HDL(a))&SR_INT) |
---|
2613 | { |
---|
2614 | int bi=SR_TO_INT(b); |
---|
2615 | int ai=SR_TO_INT(a); |
---|
2616 | int bb=ABS(bi); |
---|
2617 | int c=ai%bb; |
---|
2618 | if (c<0) c+=bb; |
---|
2619 | return (INT_TO_SR(c)); |
---|
2620 | } |
---|
2621 | number al; |
---|
2622 | number bl; |
---|
2623 | if (SR_HDL(a))&SR_INT) |
---|
2624 | al=nlRInit(SR_TO_INT(a)); |
---|
2625 | else |
---|
2626 | al=nlCopy(a); |
---|
2627 | if (SR_HDL(b))&SR_INT) |
---|
2628 | bl=nlRInit(SR_TO_INT(b)); |
---|
2629 | else |
---|
2630 | bl=nlCopy(b); |
---|
2631 | number r=nlRInit(0); |
---|
2632 | mpz_mod(r->z,al->z,bl->z); |
---|
2633 | nlDelete(&al); |
---|
2634 | nlDelete(&bl); |
---|
2635 | if (mpz_size1(&r->z)<=MP_SMALL) |
---|
2636 | { |
---|
2637 | LONG ui=(int)mpz_get_si(&r->z); |
---|
2638 | if ((((ui<<3)>>3)==ui) |
---|
2639 | && (mpz_cmp_si(x->z,(long)ui)==0)) |
---|
2640 | { |
---|
2641 | mpz_clear(&r->z); |
---|
2642 | omFreeBin((void *)r, rnumber_bin); |
---|
2643 | r=INT_TO_SR(ui); |
---|
2644 | } |
---|
2645 | } |
---|
2646 | return r; |
---|
2647 | } |
---|
2648 | #endif |
---|
2649 | #endif // not P_NUMBERS_H |
---|
2650 | #endif // LONGRAT_CC |
---|