1 | #ifndef MODULOP_H |
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2 | #define MODULOP_H |
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3 | /**************************************** |
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4 | * Computer Algebra System SINGULAR * |
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5 | ****************************************/ |
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6 | /* |
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7 | * ABSTRACT: numbers modulo p (<=32749) |
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8 | */ |
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9 | #include "misc/auxiliary.h" |
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10 | #include "factory/factory.h" |
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11 | |
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12 | #ifdef HAVE_NTL |
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13 | #include <NTL/config.h> |
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14 | #ifdef NTL_AVOID_BRANCHING |
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15 | #undef HAVE_GENERIC_ADD |
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16 | #endif |
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17 | #endif |
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18 | |
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19 | |
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20 | // define if a*b is with mod instead of tables |
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21 | //#define HAVE_GENERIC_MULT |
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22 | // define if 1/b is from tables |
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23 | //#define HAVE_INVTABLE |
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24 | // define if an if should be used(NTL does not define NTL_AVOID_BRANCHING) |
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25 | //#define HAVE_GENERIC_ADD |
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26 | |
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27 | //#undef HAVE_GENERIC_ADD |
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28 | //#undef HAVE_GENERIC_MULT |
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29 | //#undef HAVE_INVTABLE |
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30 | |
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31 | //#define HAVE_GENERIC_ADD 1 |
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32 | //#define HAVE_GENERIC_MULT 1 |
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33 | //#define HAVE_INVTABLE 1 |
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34 | |
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35 | // enable large primes (32749 < p < 2^31-) |
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36 | #define NV_OPS |
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37 | #define NV_MAX_PRIME 32749 |
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38 | #define FACTORY_MAX_PRIME 536870909 |
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39 | |
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40 | struct n_Procs_s; typedef struct n_Procs_s *coeffs; |
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41 | struct snumber; typedef struct snumber * number; |
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42 | |
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43 | BOOLEAN npInitChar(coeffs r, void* p); |
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44 | |
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45 | // inline number npMultM(number a, number b, int npPrimeM) |
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46 | // // return (a*b)%n |
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47 | // { |
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48 | // double ab; |
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49 | // long q, res; |
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50 | // |
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51 | // ab = ((double) ((int)a)) * ((double) ((int)b)); |
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52 | // q = (long) (ab/((double) npPrimeM)); // q could be off by (+/-) 1 |
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53 | // res = (long) (ab - ((double) q)*((double) npPrimeM)); |
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54 | // res += (res >> 31) & npPrimeM; |
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55 | // res -= npPrimeM; |
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56 | // res += (res >> 31) & npPrimeM; |
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57 | // return (number)res; |
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58 | // } |
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59 | #ifdef HAVE_GENERIC_MULT |
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60 | static inline number npMultM(number a, number b, const coeffs r) |
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61 | { |
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62 | return (number) |
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63 | ((((unsigned long) a)*((unsigned long) b)) % ((unsigned long) r->ch)); |
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64 | } |
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65 | static inline void npInpMultM(number &a, number b, const coeffs r) |
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66 | { |
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67 | a=(number) |
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68 | ((((unsigned long) a)*((unsigned long) b)) % ((unsigned long) r->ch)); |
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69 | } |
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70 | #else |
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71 | static inline number npMultM(number a, number b, const coeffs r) |
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72 | { |
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73 | long x = (long)r->npLogTable[(long)a]+ r->npLogTable[(long)b]; |
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74 | #ifdef HAVE_GENERIC_ADD |
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75 | if (x>=r->npPminus1M) x-=r->npPminus1M; |
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76 | #else |
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77 | x-=r->npPminus1M; |
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78 | #if SIZEOF_LONG == 8 |
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79 | x += (x >> 63) & r->npPminus1M; |
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80 | #else |
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81 | x += (x >> 31) & r->npPminus1M; |
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82 | #endif |
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83 | #endif |
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84 | return (number)(long)r->npExpTable[x]; |
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85 | } |
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86 | static inline void npInpMultM(number &a, number b, const coeffs r) |
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87 | { |
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88 | long x = (long)r->npLogTable[(long)a]+ r->npLogTable[(long)b]; |
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89 | #ifdef HAVE_GENERIC_ADD |
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90 | if (x>=r->npPminus1M) x-=r->npPminus1M; |
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91 | #else |
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92 | x-=r->npPminus1M; |
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93 | #if SIZEOF_LONG == 8 |
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94 | x += (x >> 63) & r->npPminus1M; |
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95 | #else |
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96 | x += (x >> 31) & r->npPminus1M; |
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97 | #endif |
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98 | #endif |
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99 | a=(number)(long)r->npExpTable[x]; |
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100 | } |
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101 | #endif |
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102 | |
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103 | #if 0 |
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104 | inline number npAddAsm(number a, number b, int m) |
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105 | { |
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106 | number r; |
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107 | asm ("addl %2, %1; cmpl %3, %1; jb 0f; subl %3, %1; 0:" |
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108 | : "=&r" (r) |
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109 | : "%0" (a), "g" (b), "g" (m) |
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110 | : "cc"); |
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111 | return r; |
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112 | } |
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113 | inline number npSubAsm(number a, number b, int m) |
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114 | { |
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115 | number r; |
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116 | asm ("subl %2, %1; jnc 0f; addl %3, %1; 0:" |
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117 | : "=&r" (r) |
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118 | : "%0" (a), "g" (b), "g" (m) |
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119 | : "cc"); |
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120 | return r; |
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121 | } |
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122 | #endif |
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123 | #ifdef HAVE_GENERIC_ADD |
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124 | static inline number npAddM(number a, number b, const coeffs r) |
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125 | { |
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126 | unsigned long R = (unsigned long)a + (unsigned long)b; |
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127 | return (number)(R >= (unsigned long)r->ch ? R - (unsigned long)r->ch : R); |
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128 | } |
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129 | static inline void npInpAddM(number &a, number b, const coeffs r) |
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130 | { |
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131 | unsigned long R = (unsigned long)a + (unsigned long)b; |
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132 | a=(number)(R >= (unsigned long)r->ch ? R - (unsigned long)r->ch : R); |
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133 | } |
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134 | static inline number npSubM(number a, number b, const coeffs r) |
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135 | { |
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136 | return (number)((long)a<(long)b ? |
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137 | r->ch-(long)b+(long)a : (long)a-(long)b); |
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138 | } |
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139 | #else |
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140 | static inline number npAddM(number a, number b, const coeffs r) |
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141 | { |
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142 | unsigned long res = ((unsigned long)a + (unsigned long)b); |
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143 | res -= r->ch; |
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144 | #if SIZEOF_LONG == 8 |
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145 | res += ((long)res >> 63) & r->ch; |
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146 | #else |
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147 | res += ((long)res >> 31) & r->ch; |
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148 | #endif |
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149 | return (number)res; |
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150 | } |
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151 | static inline void npInpAddM(number &a, number b, const coeffs r) |
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152 | { |
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153 | unsigned long res = ((unsigned long)a + (unsigned long)b); |
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154 | res -= r->ch; |
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155 | #if SIZEOF_LONG == 8 |
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156 | res += ((long)res >> 63) & r->ch; |
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157 | #else |
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158 | res += ((long)res >> 31) & r->ch; |
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159 | #endif |
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160 | a=(number)res; |
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161 | } |
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162 | static inline number npSubM(number a, number b, const coeffs r) |
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163 | { |
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164 | long res = ((long)a - (long)b); |
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165 | #if SIZEOF_LONG == 8 |
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166 | res += (res >> 63) & r->ch; |
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167 | #else |
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168 | res += (res >> 31) & r->ch; |
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169 | #endif |
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170 | return (number)res; |
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171 | } |
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172 | #endif |
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173 | |
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174 | static inline number npNegM(number a, const coeffs r) |
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175 | { |
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176 | return (number)((long)(r->ch)-(long)(a)); |
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177 | } |
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178 | |
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179 | static inline BOOLEAN npIsOne (number a, const coeffs) |
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180 | { |
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181 | return 1 == (long)a; |
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182 | } |
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183 | |
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184 | static inline long npInvMod(long a, const coeffs R) |
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185 | { |
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186 | long s; |
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187 | |
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188 | long u, v, u0, u1, u2, q, r; |
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189 | |
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190 | assume(a>0); |
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191 | u1=1; u2=0; |
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192 | u = a; v = R->ch; |
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193 | |
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194 | do |
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195 | { |
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196 | q = u / v; |
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197 | //r = u % v; |
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198 | r = u - q*v; |
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199 | u = v; |
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200 | v = r; |
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201 | u0 = u2; |
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202 | u2 = u1 - q*u2; |
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203 | u1 = u0; |
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204 | } while (v != 0); |
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205 | |
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206 | assume(u==1); |
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207 | s = u1; |
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208 | #ifdef HAVE_GENERIC_ADD |
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209 | if (s < 0) |
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210 | return s + R->ch; |
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211 | else |
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212 | return s; |
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213 | #else |
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214 | #if SIZEOF_LONG == 8 |
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215 | s += (s >> 63) & R->ch; |
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216 | #else |
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217 | s += (s >> 31) & R->ch; |
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218 | #endif |
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219 | return s; |
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220 | #endif |
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221 | } |
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222 | |
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223 | static inline number npInversM (number c, const coeffs r) |
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224 | { |
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225 | n_Test(c, r); |
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226 | #ifndef HAVE_GENERIC_MULT |
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227 | #ifndef HAVE_INVTABLE |
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228 | number d = (number)(long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]]; |
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229 | #else |
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230 | long inv=(long)r->npInvTable[(long)c]; |
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231 | if (inv==0) |
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232 | { |
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233 | inv = (long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]]; |
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234 | r->npInvTable[(long)c]=inv; |
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235 | } |
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236 | number d = (number)inv; |
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237 | #endif |
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238 | #else |
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239 | #ifdef HAVE_INVTABLE |
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240 | long inv=(long)r->npInvTable[(long)c]; |
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241 | if (inv==0) |
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242 | { |
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243 | inv=npInvMod((long)c,r); |
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244 | r->npInvTable[(long)c]=inv; |
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245 | } |
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246 | #else |
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247 | long inv=npInvMod((long)c,r); |
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248 | #endif |
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249 | number d = (number)inv; |
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250 | #endif |
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251 | n_Test(d, r); |
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252 | return d; |
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253 | } |
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254 | |
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255 | |
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256 | // The folloing is reused inside gnumpc.cc, gnumpfl.cc and longrat.cc |
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257 | long npInt (number &n, const coeffs r); |
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258 | |
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259 | #define npEqualM(A,B,r) ((A)==(B)) |
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260 | |
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261 | #endif |
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