1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT: numbers modulo p (<=32749) |
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6 | */ |
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7 | |
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8 | #include "misc/auxiliary.h" |
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9 | #include "omalloc/omalloc.h" |
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10 | |
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11 | #include "factory/factory.h" |
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12 | |
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13 | #include "misc/mylimits.h" |
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14 | #include "misc/sirandom.h" |
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15 | |
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16 | #include "reporter/reporter.h" |
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17 | |
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18 | #include "coeffs/coeffs.h" |
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19 | #include "coeffs/numbers.h" |
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20 | #include "coeffs/mpr_complex.h" |
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21 | |
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22 | #include "coeffs/longrat.h" |
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23 | #include "coeffs/modulop.h" |
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24 | |
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25 | #include <string.h> |
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26 | |
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27 | BOOLEAN npGreaterZero (number k, const coeffs r); |
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28 | number npMult (number a, number b, const coeffs r); |
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29 | number npInit (long i, const coeffs r); |
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30 | long npInt (number &n, const coeffs r); |
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31 | void npPower (number a, int i, number * result,const coeffs r); |
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32 | BOOLEAN npIsZero (number a,const coeffs r); |
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33 | BOOLEAN npIsOne (number a,const coeffs r); |
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34 | BOOLEAN npIsMOne (number a,const coeffs r); |
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35 | number npDiv (number a, number b,const coeffs r); |
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36 | number npNeg (number c,const coeffs r); |
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37 | number npInvers (number c,const coeffs r); |
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38 | BOOLEAN npGreater (number a, number b,const coeffs r); |
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39 | BOOLEAN npEqual (number a, number b,const coeffs r); |
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40 | void npWrite (number a, const coeffs r); |
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41 | void npCoeffWrite (const coeffs r, BOOLEAN details); |
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42 | const char * npRead (const char *s, number *a,const coeffs r); |
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43 | void nvInpMult(number &a, number b, const coeffs r); |
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44 | |
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45 | #ifdef LDEBUG |
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46 | BOOLEAN npDBTest (number a, const char *f, const int l, const coeffs r); |
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47 | #endif |
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48 | |
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49 | nMapFunc npSetMap(const coeffs src, const coeffs dst); |
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50 | |
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51 | #ifdef NV_OPS |
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52 | #pragma GCC diagnostic ignored "-Wlong-long" |
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53 | static inline number nvMultM(number a, number b, const coeffs r) |
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54 | { |
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55 | assume( getCoeffType(r) == n_Zp ); |
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56 | |
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57 | #if SIZEOF_LONG == 4 |
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58 | #define ULONG64 (unsigned long long)(unsigned long) |
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59 | #else |
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60 | #define ULONG64 (unsigned long) |
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61 | #endif |
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62 | return (number) |
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63 | (unsigned long)((ULONG64 a)*(ULONG64 b) % (ULONG64 r->ch)); |
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64 | } |
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65 | number nvMult (number a, number b, const coeffs r); |
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66 | number nvDiv (number a, number b, const coeffs r); |
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67 | number nvInvers (number c, const coeffs r); |
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68 | //void nvPower (number a, int i, number * result, const coeffs r); |
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69 | #endif |
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70 | |
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71 | BOOLEAN npGreaterZero (number k, const coeffs r) |
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72 | { |
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73 | n_Test(k, r); |
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74 | |
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75 | int h = (int)((long) k); |
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76 | return ((int)h !=0) && (h <= (r->ch>>1)); |
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77 | } |
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78 | |
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79 | //unsigned long npMultMod(unsigned long a, unsigned long b, int npPrimeM) |
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80 | //{ |
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81 | // unsigned long c = a*b; |
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82 | // c = c % npPrimeM; |
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83 | // assume(c == (unsigned long) npMultM((number) a, (number) b, npPrimeM)); |
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84 | // return c; |
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85 | //} |
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86 | |
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87 | number npMult (number a,number b, const coeffs r) |
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88 | { |
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89 | n_Test(a, r); |
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90 | n_Test(b, r); |
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91 | |
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92 | if (((long)a == 0) || ((long)b == 0)) |
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93 | return (number)0; |
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94 | number c = npMultM(a,b, r); |
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95 | n_Test(c, r); |
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96 | return c; |
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97 | } |
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98 | |
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99 | void npInpMult (number &a,number b, const coeffs r) |
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100 | { |
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101 | n_Test(a, r); |
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102 | n_Test(b, r); |
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103 | |
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104 | if (((long)a == 0) || ((long)b == 0)) |
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105 | a=(number)0; |
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106 | else |
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107 | a = npMultM(a,b, r); |
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108 | n_Test(a, r); |
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109 | } |
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110 | |
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111 | /*2 |
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112 | * create a number from int |
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113 | */ |
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114 | number npInit (long i, const coeffs r) |
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115 | { |
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116 | long ii=i % (long)r->ch; |
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117 | if (ii < 0L) ii += (long)r->ch; |
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118 | |
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119 | number c = (number)ii; |
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120 | n_Test(c, r); |
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121 | return c; |
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122 | } |
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123 | |
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124 | |
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125 | /*2 |
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126 | * convert a number to an int in (-p/2 .. p/2] |
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127 | */ |
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128 | long npInt(number &n, const coeffs r) |
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129 | { |
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130 | n_Test(n, r); |
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131 | |
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132 | if ((long)n > (((long)r->ch) >>1)) return ((long)n -((long)r->ch)); |
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133 | else return ((long)n); |
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134 | } |
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135 | |
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136 | BOOLEAN npIsZero (number a, const coeffs r) |
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137 | { |
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138 | n_Test(a, r); |
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139 | |
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140 | return 0 == (long)a; |
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141 | } |
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142 | |
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143 | BOOLEAN npIsOne (number a, const coeffs r) |
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144 | { |
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145 | n_Test(a, r); |
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146 | |
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147 | return 1 == (long)a; |
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148 | } |
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149 | |
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150 | BOOLEAN npIsMOne (number a, const coeffs r) |
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151 | { |
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152 | n_Test(a, r); |
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153 | |
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154 | return ((r->npPminus1M == (long)a) &&(1L!=(long)a))/*for char 2*/; |
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155 | } |
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156 | |
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157 | #ifdef HAVE_DIV_MOD |
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158 | |
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159 | #ifdef USE_NTL_XGCD |
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160 | |
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161 | //ifdef HAVE_NTL // in ntl.a |
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162 | //extern void XGCD(long& d, long& s, long& t, long a, long b); |
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163 | #include <NTL/ZZ.h> |
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164 | #ifdef NTL_CLIENT |
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165 | NTL_CLIENT |
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166 | #endif |
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167 | |
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168 | #endif |
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169 | |
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170 | static inline long InvMod(long a, const coeffs R) |
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171 | { |
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172 | long d, s, t; |
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173 | |
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174 | #ifdef USE_NTL_XGCD |
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175 | XGCD(d, s, t, a, R->ch); |
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176 | assume (d == 1); |
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177 | #else |
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178 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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179 | |
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180 | assume(a>0); |
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181 | u1=1; u2=0; |
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182 | u = a; v = R->ch; |
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183 | |
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184 | while (v != 0) |
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185 | { |
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186 | q = u / v; |
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187 | r = u % v; |
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188 | u = v; |
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189 | v = r; |
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190 | u0 = u2; |
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191 | u2 = u1 - q*u2; |
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192 | u1 = u0; |
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193 | } |
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194 | |
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195 | assume(u==1); |
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196 | s = u1; |
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197 | #endif |
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198 | if (s < 0) |
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199 | return s + R->ch; |
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200 | else |
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201 | return s; |
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202 | } |
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203 | #endif |
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204 | |
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205 | static inline number npInversM (number c, const coeffs r) |
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206 | { |
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207 | n_Test(c, r); |
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208 | #ifndef HAVE_DIV_MOD |
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209 | number d = (number)(long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]]; |
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210 | #else |
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211 | long inv=(long)r->npInvTable[(long)c]; |
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212 | if (inv==0) |
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213 | { |
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214 | inv=InvMod((long)c,r); |
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215 | r->npInvTable[(long)c]=inv; |
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216 | } |
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217 | number d = (number)inv; |
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218 | #endif |
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219 | n_Test(d, r); |
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220 | return d; |
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221 | |
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222 | } |
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223 | |
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224 | number npDiv (number a,number b, const coeffs r) |
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225 | { |
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226 | n_Test(a, r); |
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227 | n_Test(b, r); |
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228 | |
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229 | //#ifdef NV_OPS |
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230 | // if (r->ch>NV_MAX_PRIME) |
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231 | // return nvDiv(a,b); |
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232 | //#endif |
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233 | if ((long)a==0L) |
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234 | return (number)0L; |
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235 | number d; |
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236 | |
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237 | #ifndef HAVE_DIV_MOD |
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238 | if ((long)b==0L) |
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239 | { |
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240 | WerrorS(nDivBy0); |
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241 | return (number)0L; |
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242 | } |
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243 | |
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244 | int s = r->npLogTable[(long)a] - r->npLogTable[(long)b]; |
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245 | if (s < 0) |
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246 | s += r->npPminus1M; |
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247 | d = (number)(long)r->npExpTable[s]; |
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248 | #else |
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249 | number inv=npInversM(b,r); |
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250 | d = npMultM(a,inv,r); |
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251 | #endif |
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252 | |
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253 | n_Test(d, r); |
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254 | return d; |
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255 | |
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256 | } |
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257 | number npInvers (number c, const coeffs r) |
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258 | { |
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259 | n_Test(c, r); |
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260 | |
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261 | if ((long)c==0L) |
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262 | { |
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263 | WerrorS("1/0"); |
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264 | return (number)0L; |
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265 | } |
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266 | number d = npInversM(c,r); |
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267 | |
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268 | n_Test(d, r); |
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269 | return d; |
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270 | } |
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271 | |
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272 | number npNeg (number c, const coeffs r) |
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273 | { |
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274 | n_Test(c, r); |
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275 | |
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276 | if ((long)c==0L) return c; |
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277 | |
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278 | #if 0 |
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279 | number d = npNegM(c,r); |
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280 | n_Test(d, r); |
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281 | return d; |
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282 | #else |
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283 | c = npNegM(c,r); |
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284 | n_Test(c, r); |
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285 | return c; |
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286 | #endif |
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287 | } |
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288 | |
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289 | BOOLEAN npGreater (number a,number b, const coeffs r) |
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290 | { |
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291 | n_Test(a, r); |
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292 | n_Test(b, r); |
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293 | |
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294 | //return (long)a != (long)b; |
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295 | return ((long)a) > ((long)b); |
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296 | } |
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297 | |
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298 | BOOLEAN npEqual (number a,number b, const coeffs r) |
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299 | { |
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300 | n_Test(a, r); |
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301 | n_Test(b, r); |
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302 | |
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303 | // return (long)a == (long)b; |
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304 | |
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305 | return npEqualM(a,b,r); |
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306 | } |
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307 | |
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308 | void npWrite (number a, const coeffs r) |
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309 | { |
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310 | n_Test(a, r); |
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311 | |
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312 | if ((long)a>(((long)r->ch) >>1)) StringAppend("-%d",(int)(((long)r->ch)-((long)a))); |
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313 | else StringAppend("%d",(int)((long)a)); |
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314 | } |
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315 | |
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316 | #if 0 |
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317 | void npPower (number a, int i, number * result, const coeffs r) |
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318 | { |
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319 | n_Test(a, r); |
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320 | |
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321 | if (i==0) |
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322 | { |
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323 | //npInit(1,result); |
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324 | *(long *)result = 1; |
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325 | } |
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326 | else if (i==1) |
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327 | { |
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328 | *result = a; |
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329 | } |
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330 | else |
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331 | { |
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332 | npPower(a,i-1,result,r); |
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333 | *result = npMultM(a,*result,r); |
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334 | } |
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335 | } |
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336 | #endif |
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337 | |
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338 | static const char* npEati(const char *s, int *i, const coeffs r) |
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339 | { |
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340 | if (((*s) >= '0') && ((*s) <= '9')) |
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341 | { |
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342 | unsigned long ii=0L; |
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343 | do |
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344 | { |
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345 | ii *= 10; |
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346 | ii += *s++ - '0'; |
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347 | if (ii >= (MAX_INT_VAL / 10)) ii = ii % r->ch; |
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348 | } |
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349 | while (((*s) >= '0') && ((*s) <= '9')); |
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350 | if (ii >= (unsigned long)r->ch) ii = ii % r->ch; |
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351 | *i=(int)ii; |
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352 | } |
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353 | else (*i) = 1; |
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354 | return s; |
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355 | } |
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356 | |
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357 | const char * npRead (const char *s, number *a, const coeffs r) |
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358 | { |
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359 | int z; |
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360 | int n=1; |
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361 | |
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362 | s = npEati(s, &z, r); |
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363 | if ((*s) == '/') |
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364 | { |
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365 | s++; |
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366 | s = npEati(s, &n, r); |
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367 | } |
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368 | if (n == 1) |
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369 | *a = (number)(long)z; |
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370 | else |
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371 | { |
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372 | if ((z==0)&&(n==0)) WerrorS(nDivBy0); |
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373 | else |
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374 | { |
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375 | #ifdef NV_OPS |
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376 | if (r->ch>NV_MAX_PRIME) |
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377 | *a = nvDiv((number)(long)z,(number)(long)n,r); |
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378 | else |
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379 | #endif |
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380 | *a = npDiv((number)(long)z,(number)(long)n,r); |
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381 | } |
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382 | } |
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383 | n_Test(*a, r); |
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384 | return s; |
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385 | } |
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386 | |
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387 | /*2 |
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388 | * set the charcteristic (allocate and init tables) |
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389 | */ |
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390 | |
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391 | void npKillChar(coeffs r) |
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392 | { |
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393 | #ifdef HAVE_DIV_MOD |
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394 | if (r->npInvTable!=NULL) |
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395 | omFreeSize( (void *)r->npInvTable, r->ch*sizeof(unsigned short) ); |
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396 | r->npInvTable=NULL; |
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397 | #else |
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398 | if (r->npExpTable!=NULL) |
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399 | { |
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400 | omFreeSize( (void *)r->npExpTable, r->ch*sizeof(unsigned short) ); |
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401 | omFreeSize( (void *)r->npLogTable, r->ch*sizeof(unsigned short) ); |
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402 | r->npExpTable=NULL; r->npLogTable=NULL; |
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403 | } |
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404 | #endif |
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405 | } |
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406 | |
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407 | static BOOLEAN npCoeffsEqual(const coeffs r, n_coeffType n, void * parameter) |
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408 | { |
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409 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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410 | return (n==n_Zp) && (r->ch==(int)(long)parameter); |
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411 | } |
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412 | CanonicalForm npConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
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413 | { |
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414 | if (setChar) setCharacteristic( r->ch ); |
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415 | CanonicalForm term(npInt( n,r )); |
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416 | return term; |
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417 | } |
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418 | |
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419 | number npConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
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420 | { |
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421 | if (n.isImm()) |
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422 | { |
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423 | return npInit(n.intval(),r); |
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424 | } |
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425 | else |
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426 | { |
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427 | assume(0); |
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428 | return NULL; |
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429 | } |
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430 | } |
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431 | |
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432 | static char* npCoeffName(const coeffs cf) |
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433 | { |
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434 | static char npCoeffName_buf[15]; |
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435 | snprintf(npCoeffName_buf,14,"ZZ/%d",cf->ch); |
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436 | return npCoeffName_buf; |
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437 | } |
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438 | |
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439 | static char* npCoeffString(const coeffs cf) |
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440 | { |
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441 | return omStrDup(npCoeffName(cf)); |
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442 | } |
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443 | |
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444 | static void npWriteFd(number n, FILE* f, const coeffs) |
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445 | { |
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446 | fprintf(f,"%d ",(int)(long)n); |
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447 | } |
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448 | |
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449 | static number npReadFd(s_buff f, const coeffs) |
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450 | { |
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451 | // read int |
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452 | int dd; |
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453 | dd=s_readint(f); |
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454 | return (number)(long)dd; |
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455 | } |
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456 | |
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457 | static number npRandom(siRandProc p, number, number, const coeffs cf) |
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458 | { |
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459 | return npInit(p(),cf); |
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460 | } |
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461 | |
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462 | BOOLEAN npInitChar(coeffs r, void* p) |
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463 | { |
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464 | assume( getCoeffType(r) == n_Zp ); |
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465 | const int c = (int) (long) p; |
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466 | |
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467 | assume( c > 0 ); |
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468 | |
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469 | int i, w; |
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470 | |
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471 | r->is_field=TRUE; |
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472 | r->is_domain=TRUE; |
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473 | r->rep=n_rep_int; |
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474 | |
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475 | r->ch = c; |
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476 | r->npPminus1M = c /*r->ch*/ - 1; |
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477 | |
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478 | //r->cfInitChar=npInitChar; |
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479 | r->cfKillChar=npKillChar; |
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480 | r->nCoeffIsEqual=npCoeffsEqual; |
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481 | r->cfCoeffString=npCoeffString; |
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482 | r->cfCoeffName=npCoeffName; |
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483 | r->cfCoeffWrite=npCoeffWrite; |
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484 | |
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485 | r->cfMult = npMult; |
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486 | r->cfInpMult = npInpMult; |
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487 | r->cfSub = npSubM; |
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488 | r->cfAdd = npAddM; |
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489 | r->cfInpAdd = npInpAddM; |
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490 | r->cfDiv = npDiv; |
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491 | r->cfInit = npInit; |
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492 | //r->cfSize = ndSize; |
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493 | r->cfInt = npInt; |
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494 | #ifdef HAVE_RINGS |
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495 | //r->cfDivComp = NULL; // only for ring stuff |
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496 | //r->cfIsUnit = NULL; // only for ring stuff |
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497 | //r->cfGetUnit = NULL; // only for ring stuff |
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498 | //r->cfExtGcd = NULL; // only for ring stuff |
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499 | // r->cfDivBy = NULL; // only for ring stuff |
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500 | #endif |
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501 | r->cfInpNeg = npNeg; |
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502 | r->cfInvers= npInvers; |
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503 | //r->cfCopy = ndCopy; |
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504 | //r->cfRePart = ndCopy; |
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505 | //r->cfImPart = ndReturn0; |
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506 | r->cfWriteLong = npWrite; |
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507 | r->cfRead = npRead; |
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508 | //r->cfNormalize=ndNormalize; |
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509 | r->cfGreater = npGreater; |
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510 | r->cfEqual = npEqual; |
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511 | r->cfIsZero = npIsZero; |
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512 | r->cfIsOne = npIsOne; |
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513 | r->cfIsMOne = npIsMOne; |
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514 | r->cfGreaterZero = npGreaterZero; |
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515 | //r->cfPower = npPower; |
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516 | //r->cfGetDenom = ndGetDenom; |
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517 | //r->cfGetNumerator = ndGetNumerator; |
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518 | //r->cfGcd = ndGcd; |
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519 | //r->cfLcm = ndGcd; |
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520 | //r->cfDelete= ndDelete; |
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521 | r->cfSetMap = npSetMap; |
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522 | //r->cfName = ndName; |
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523 | //r->cfInpMult=ndInpMult; |
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524 | r->convSingNFactoryN=npConvSingNFactoryN; |
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525 | r->convFactoryNSingN=npConvFactoryNSingN; |
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526 | r->cfRandom=npRandom; |
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527 | #ifdef LDEBUG |
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528 | // debug stuff |
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529 | r->cfDBTest=npDBTest; |
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530 | #endif |
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531 | |
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532 | // io via ssi |
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533 | r->cfWriteFd=npWriteFd; |
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534 | r->cfReadFd=npReadFd; |
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535 | |
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536 | // the variables: |
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537 | r->type = n_Zp; |
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538 | r->has_simple_Alloc=TRUE; |
---|
539 | r->has_simple_Inverse=TRUE; |
---|
540 | |
---|
541 | // the tables |
---|
542 | #ifdef NV_OPS |
---|
543 | if (r->ch <=NV_MAX_PRIME) |
---|
544 | #endif |
---|
545 | { |
---|
546 | #ifdef HAVE_DIV_MOD |
---|
547 | r->npInvTable=(unsigned short*)omAlloc0( r->ch*sizeof(unsigned short) ); |
---|
548 | #elif (!defined(HAVE_MULT_MOD)||(!HAVE_DIV_MOD)) |
---|
549 | r->npExpTable=(unsigned short *)omAlloc0( r->ch*sizeof(unsigned short) ); |
---|
550 | r->npLogTable=(unsigned short *)omAlloc0( r->ch*sizeof(unsigned short) ); |
---|
551 | r->npExpTable[0] = 1; |
---|
552 | r->npLogTable[0] = 0; |
---|
553 | if (r->ch > 2) |
---|
554 | { |
---|
555 | w = 1; |
---|
556 | loop |
---|
557 | { |
---|
558 | r->npLogTable[1] = 0; |
---|
559 | w++; |
---|
560 | i = 0; |
---|
561 | loop |
---|
562 | { |
---|
563 | i++; |
---|
564 | r->npExpTable[i] =(int)(((long)w * (long)r->npExpTable[i-1]) % r->ch); |
---|
565 | r->npLogTable[r->npExpTable[i]] = i; |
---|
566 | if /*(i == r->ch - 1 ) ||*/ (/*(*/ r->npExpTable[i] == 1 /*)*/) |
---|
567 | break; |
---|
568 | } |
---|
569 | if (i == r->ch - 1) |
---|
570 | break; |
---|
571 | } |
---|
572 | } |
---|
573 | else |
---|
574 | { |
---|
575 | r->npExpTable[1] = 1; |
---|
576 | r->npLogTable[1] = 0; |
---|
577 | } |
---|
578 | #endif |
---|
579 | } |
---|
580 | #ifdef NV_OPS |
---|
581 | else /*if (c>NV_MAX_PRIME)*/ |
---|
582 | { |
---|
583 | r->cfMult = nvMult; |
---|
584 | r->cfDiv = nvDiv; |
---|
585 | r->cfExactDiv = nvDiv; |
---|
586 | r->cfInvers = nvInvers; |
---|
587 | r->cfInpMult = nvInpMult; |
---|
588 | //r->cfPower= nvPower; |
---|
589 | //if (c>FACTORY_MAX_PRIME) // factory will catch this error |
---|
590 | //{ |
---|
591 | // r->convSingNFactoryN=ndConvSingNFactoryN; |
---|
592 | //} |
---|
593 | } |
---|
594 | #endif |
---|
595 | return FALSE; |
---|
596 | } |
---|
597 | |
---|
598 | #ifdef LDEBUG |
---|
599 | BOOLEAN npDBTest (number a, const char *f, const int l, const coeffs r) |
---|
600 | { |
---|
601 | if (((long)a<0L) || ((long)a>(long)r->ch)) |
---|
602 | { |
---|
603 | Print("wrong mod p number %ld at %s,%d\n",(long)a,f,l); |
---|
604 | return FALSE; |
---|
605 | } |
---|
606 | return TRUE; |
---|
607 | } |
---|
608 | #endif |
---|
609 | |
---|
610 | static number npMapP(number from, const coeffs src, const coeffs dst_r) |
---|
611 | { |
---|
612 | long i = (long)from; |
---|
613 | if (i>src->ch/2) |
---|
614 | { |
---|
615 | i-=src->ch; |
---|
616 | while (i < 0) i+=dst_r->ch; |
---|
617 | } |
---|
618 | i%=dst_r->ch; |
---|
619 | return (number)i; |
---|
620 | } |
---|
621 | |
---|
622 | static number npMapLongR(number from, const coeffs /*src*/, const coeffs dst_r) |
---|
623 | { |
---|
624 | gmp_float *ff=(gmp_float*)from; |
---|
625 | mpf_t *f=ff->_mpfp(); |
---|
626 | number res; |
---|
627 | mpz_ptr dest,ndest; |
---|
628 | int size,i; |
---|
629 | int e,al,bl; |
---|
630 | long iz; |
---|
631 | mp_ptr qp,dd,nn; |
---|
632 | |
---|
633 | size = (*f)[0]._mp_size; |
---|
634 | if (size == 0) |
---|
635 | return npInit(0,dst_r); |
---|
636 | if(size<0) |
---|
637 | size = -size; |
---|
638 | |
---|
639 | qp = (*f)[0]._mp_d; |
---|
640 | while(qp[0]==0) |
---|
641 | { |
---|
642 | qp++; |
---|
643 | size--; |
---|
644 | } |
---|
645 | |
---|
646 | if(dst_r->ch>2) |
---|
647 | e=(*f)[0]._mp_exp-size; |
---|
648 | else |
---|
649 | e=0; |
---|
650 | res = ALLOC_RNUMBER(); |
---|
651 | #if defined(LDEBUG) |
---|
652 | res->debug=123456; |
---|
653 | #endif |
---|
654 | dest = res->z; |
---|
655 | |
---|
656 | long in=0; |
---|
657 | if (e<0) |
---|
658 | { |
---|
659 | al = dest->_mp_size = size; |
---|
660 | if (al<2) al = 2; |
---|
661 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
662 | for (i=0;i<size;i++) dd[i] = qp[i]; |
---|
663 | bl = 1-e; |
---|
664 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
---|
665 | nn[bl-1] = 1; |
---|
666 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
---|
667 | ndest = res->n; |
---|
668 | ndest->_mp_d = nn; |
---|
669 | ndest->_mp_alloc = ndest->_mp_size = bl; |
---|
670 | res->s = 0; |
---|
671 | in=mpz_fdiv_ui(ndest,dst_r->ch); |
---|
672 | mpz_clear(ndest); |
---|
673 | } |
---|
674 | else |
---|
675 | { |
---|
676 | al = dest->_mp_size = size+e; |
---|
677 | if (al<2) al = 2; |
---|
678 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
679 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
---|
680 | for (i=0;i<e;i++) dd[i] = 0; |
---|
681 | res->s = 3; |
---|
682 | } |
---|
683 | |
---|
684 | dest->_mp_d = dd; |
---|
685 | dest->_mp_alloc = al; |
---|
686 | iz=mpz_fdiv_ui(dest,dst_r->ch); |
---|
687 | mpz_clear(dest); |
---|
688 | if(res->s==0) |
---|
689 | iz=(long)npDiv((number)iz,(number)in,dst_r); |
---|
690 | FREE_RNUMBER(res); // Q!? |
---|
691 | return (number)iz; |
---|
692 | } |
---|
693 | |
---|
694 | #ifdef HAVE_RINGS |
---|
695 | /*2 |
---|
696 | * convert from a GMP integer |
---|
697 | */ |
---|
698 | static number npMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
699 | { |
---|
700 | mpz_ptr erg = (mpz_ptr) omAlloc(sizeof(mpz_t)); // evtl. spaeter mit bin |
---|
701 | mpz_init(erg); |
---|
702 | |
---|
703 | mpz_mod_ui(erg, (mpz_ptr) from, dst->ch); |
---|
704 | number r = (number) mpz_get_si(erg); |
---|
705 | |
---|
706 | mpz_clear(erg); |
---|
707 | omFree((void *) erg); |
---|
708 | return (number) r; |
---|
709 | } |
---|
710 | |
---|
711 | static number npMapZ(number from, const coeffs src, const coeffs dst) |
---|
712 | { |
---|
713 | if (SR_HDL(from) & SR_INT) |
---|
714 | { |
---|
715 | long f_i=SR_TO_INT(from); |
---|
716 | return npInit(f_i,dst); |
---|
717 | } |
---|
718 | return npMapGMP(from,src,dst); |
---|
719 | } |
---|
720 | |
---|
721 | /*2 |
---|
722 | * convert from an machine long |
---|
723 | */ |
---|
724 | static number npMapMachineInt(number from, const coeffs /*src*/,const coeffs dst) |
---|
725 | { |
---|
726 | long i = (long) (((unsigned long) from) % dst->ch); |
---|
727 | return (number) i; |
---|
728 | } |
---|
729 | #endif |
---|
730 | |
---|
731 | static number npMapCanonicalForm (number a, const coeffs /*src*/, const coeffs dst) |
---|
732 | { |
---|
733 | setCharacteristic (dst ->ch); |
---|
734 | CanonicalForm f= CanonicalForm ((InternalCF*)(a)); |
---|
735 | return (number) (f.intval()); |
---|
736 | } |
---|
737 | |
---|
738 | nMapFunc npSetMap(const coeffs src, const coeffs dst) |
---|
739 | { |
---|
740 | #ifdef HAVE_RINGS |
---|
741 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)) |
---|
742 | { |
---|
743 | return npMapMachineInt; |
---|
744 | } |
---|
745 | if (src->rep==n_rep_gmp) //nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src)) |
---|
746 | { |
---|
747 | return npMapGMP; |
---|
748 | } |
---|
749 | if (src->rep==n_rep_gap_gmp) //nCoeff_is_Ring_Z(src) |
---|
750 | { |
---|
751 | return npMapZ; |
---|
752 | } |
---|
753 | #endif |
---|
754 | if (src->rep==n_rep_gap_rat) /* Q, Z */ |
---|
755 | { |
---|
756 | return nlModP; // npMap0; // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp // FIXME! |
---|
757 | } |
---|
758 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) ) |
---|
759 | { |
---|
760 | if (n_GetChar(src) == n_GetChar(dst)) |
---|
761 | { |
---|
762 | return ndCopyMap; |
---|
763 | } |
---|
764 | else |
---|
765 | { |
---|
766 | return npMapP; |
---|
767 | } |
---|
768 | } |
---|
769 | if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src)) |
---|
770 | { |
---|
771 | return npMapLongR; |
---|
772 | } |
---|
773 | if (nCoeff_is_CF (src)) |
---|
774 | { |
---|
775 | return npMapCanonicalForm; |
---|
776 | } |
---|
777 | return NULL; /* default */ |
---|
778 | } |
---|
779 | |
---|
780 | // ----------------------------------------------------------- |
---|
781 | // operation for very large primes (32749< p < 2^31-1) |
---|
782 | // ---------------------------------------------------------- |
---|
783 | #ifdef NV_OPS |
---|
784 | |
---|
785 | number nvMult (number a,number b, const coeffs r) |
---|
786 | { |
---|
787 | //if (((long)a == 0) || ((long)b == 0)) |
---|
788 | // return (number)0; |
---|
789 | //else |
---|
790 | return nvMultM(a,b,r); |
---|
791 | } |
---|
792 | |
---|
793 | void nvInpMult(number &a, number b, const coeffs r) |
---|
794 | { |
---|
795 | number n=nvMultM(a,b,r); |
---|
796 | a=n; |
---|
797 | } |
---|
798 | |
---|
799 | static inline long nvInvMod(long a, const coeffs R) |
---|
800 | { |
---|
801 | #ifdef HAVE_DIV_MOD |
---|
802 | return InvMod(a, R); |
---|
803 | #else |
---|
804 | /// TODO: use "long InvMod(long a, const coeffs R)"?! |
---|
805 | |
---|
806 | long s; |
---|
807 | |
---|
808 | long u, u0, u1, u2, q, r; // v0, v1, v2, |
---|
809 | |
---|
810 | u1=1; // v1=0; |
---|
811 | u2=0; // v2=1; |
---|
812 | u = a; |
---|
813 | |
---|
814 | long v = R->ch; |
---|
815 | |
---|
816 | while (v != 0) |
---|
817 | { |
---|
818 | q = u / v; |
---|
819 | r = u % v; |
---|
820 | u = v; |
---|
821 | v = r; |
---|
822 | u0 = u2; |
---|
823 | // v0 = v2; |
---|
824 | u2 = u1 - q*u2; |
---|
825 | // v2 = v1 - q*v2; |
---|
826 | u1 = u0; |
---|
827 | // v1 = v0; |
---|
828 | } |
---|
829 | |
---|
830 | s = u1; |
---|
831 | //t = v1; |
---|
832 | if (s < 0) |
---|
833 | return s + R->ch; |
---|
834 | else |
---|
835 | return s; |
---|
836 | #endif |
---|
837 | } |
---|
838 | |
---|
839 | static inline number nvInversM (number c, const coeffs r) |
---|
840 | { |
---|
841 | long inv=nvInvMod((long)c,r); |
---|
842 | return (number)inv; |
---|
843 | } |
---|
844 | |
---|
845 | number nvDiv (number a,number b, const coeffs r) |
---|
846 | { |
---|
847 | if ((long)a==0L) |
---|
848 | return (number)0L; |
---|
849 | else if ((long)b==0L) |
---|
850 | { |
---|
851 | WerrorS(nDivBy0); |
---|
852 | return (number)0L; |
---|
853 | } |
---|
854 | else |
---|
855 | { |
---|
856 | number inv=nvInversM(b,r); |
---|
857 | return nvMultM(a,inv,r); |
---|
858 | } |
---|
859 | } |
---|
860 | number nvInvers (number c, const coeffs r) |
---|
861 | { |
---|
862 | if ((long)c==0L) |
---|
863 | { |
---|
864 | WerrorS(nDivBy0); |
---|
865 | return (number)0L; |
---|
866 | } |
---|
867 | return nvInversM(c,r); |
---|
868 | } |
---|
869 | #if 0 |
---|
870 | void nvPower (number a, int i, number * result, const coeffs r) |
---|
871 | { |
---|
872 | if (i==0) |
---|
873 | { |
---|
874 | //npInit(1,result); |
---|
875 | *(long *)result = 1; |
---|
876 | } |
---|
877 | else if (i==1) |
---|
878 | { |
---|
879 | *result = a; |
---|
880 | } |
---|
881 | else |
---|
882 | { |
---|
883 | nvPower(a,i-1,result,r); |
---|
884 | *result = nvMultM(a,*result,r); |
---|
885 | } |
---|
886 | } |
---|
887 | #endif |
---|
888 | #endif |
---|
889 | |
---|
890 | void npCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
---|
891 | { |
---|
892 | Print("ZZ/%d",r->ch); |
---|
893 | } |
---|
894 | |
---|