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 2^m |
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6 | */ |
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7 | #include "misc/auxiliary.h" |
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8 | |
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9 | #include "misc/mylimits.h" |
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10 | #include "reporter/reporter.h" |
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11 | |
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12 | #include "coeffs/si_gmp.h" |
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13 | #include "coeffs/coeffs.h" |
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14 | #include "coeffs/numbers.h" |
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15 | #include "coeffs/longrat.h" |
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16 | #include "coeffs/mpr_complex.h" |
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17 | |
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18 | #include "coeffs/rmodulo2m.h" |
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19 | #include "coeffs/rmodulon.h" |
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20 | |
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21 | #include <string.h> |
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22 | |
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23 | #ifdef HAVE_RINGS |
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24 | |
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25 | #ifdef LDEBUG |
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26 | BOOLEAN nr2mDBTest(number a, const char *f, const int l, const coeffs r) |
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27 | { |
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28 | if ((((long)a<0L) || ((long)a>(long)r->mod2mMask)) |
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29 | && (r->mod2mMask!= ~0UL)) |
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30 | { |
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31 | Print("wrong mod 2^n number %ld (m:%ld) at %s,%d\n",(long)a,(long)r->mod2mMask,f,l); |
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32 | return FALSE; |
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33 | } |
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34 | return TRUE; |
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35 | } |
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36 | #endif |
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37 | |
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38 | |
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39 | static inline number nr2mMultM(number a, number b, const coeffs r) |
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40 | { |
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41 | return (number) |
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42 | ((((unsigned long) a) * ((unsigned long) b)) & r->mod2mMask); |
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43 | } |
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44 | |
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45 | static inline void nr2mInpMultM(number &a, number b, const coeffs r) |
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46 | { |
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47 | a= (number) |
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48 | ((((unsigned long) a) * ((unsigned long) b)) & r->mod2mMask); |
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49 | } |
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50 | |
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51 | static inline number nr2mAddM(number a, number b, const coeffs r) |
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52 | { |
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53 | return (number) |
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54 | ((((unsigned long) a) + ((unsigned long) b)) & r->mod2mMask); |
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55 | } |
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56 | |
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57 | static inline void nr2mInpAddM(number &a, number b, const coeffs r) |
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58 | { |
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59 | a= (number) |
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60 | ((((unsigned long) a) + ((unsigned long) b)) & r->mod2mMask); |
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61 | } |
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62 | |
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63 | static inline number nr2mSubM(number a, number b, const coeffs r) |
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64 | { |
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65 | return (number)((unsigned long)a < (unsigned long)b ? |
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66 | r->mod2mMask+1 - (unsigned long)b + (unsigned long)a: |
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67 | (unsigned long)a - (unsigned long)b); |
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68 | } |
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69 | |
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70 | #define nr2mNegM(A,r) (number)((r->mod2mMask+1 - (unsigned long)(A)) & r->mod2mMask) |
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71 | #define nr2mEqualM(A,B) ((A)==(B)) |
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72 | |
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73 | EXTERN_VAR omBin gmp_nrz_bin; /* init in rintegers*/ |
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74 | |
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75 | static char* nr2mCoeffName(const coeffs cf) |
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76 | { |
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77 | STATIC_VAR char n2mCoeffName_buf[37]; |
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78 | if (cf->modExponent>32) /* for 32/64bit arch.*/ |
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79 | snprintf(n2mCoeffName_buf,36,"ZZ/(bigint(2)^%lu)",cf->modExponent); |
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80 | else |
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81 | snprintf(n2mCoeffName_buf,36,"ZZ/(2^%lu)",cf->modExponent); |
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82 | return n2mCoeffName_buf; |
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83 | } |
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84 | |
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85 | static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void * p) |
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86 | { |
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87 | if (n==n_Z2m) |
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88 | { |
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89 | int m=(int)(long)(p); |
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90 | unsigned long mm=r->mod2mMask; |
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91 | if (((mm+1)>>m)==1L) return TRUE; |
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92 | } |
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93 | return FALSE; |
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94 | } |
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95 | |
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96 | static coeffs nr2mQuot1(number c, const coeffs r) |
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97 | { |
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98 | coeffs rr; |
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99 | long ch = r->cfInt(c, r); |
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100 | mpz_t a,b; |
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101 | mpz_init_set(a, r->modNumber); |
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102 | mpz_init_set_ui(b, ch); |
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103 | mpz_ptr gcd; |
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104 | gcd = (mpz_ptr) omAlloc(sizeof(mpz_t)); |
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105 | mpz_init(gcd); |
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106 | mpz_gcd(gcd, a,b); |
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107 | if(mpz_cmp_ui(gcd, 1) == 0) |
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108 | { |
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109 | WerrorS("constant in q-ideal is coprime to modulus in ground ring"); |
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110 | WerrorS("Unable to create qring!"); |
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111 | return NULL; |
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112 | } |
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113 | if(mpz_cmp_ui(gcd, 2) == 0) |
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114 | { |
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115 | rr = nInitChar(n_Zp, (void*)2); |
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116 | } |
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117 | else |
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118 | { |
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119 | int kNew = 1; |
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120 | mpz_t baseTokNew; |
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121 | mpz_init(baseTokNew); |
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122 | mpz_set(baseTokNew, r->modBase); |
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123 | while(mpz_cmp(gcd, baseTokNew) > 0) |
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124 | { |
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125 | kNew++; |
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126 | mpz_mul(baseTokNew, baseTokNew, r->modBase); |
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127 | } |
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128 | mpz_clear(baseTokNew); |
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129 | rr = nInitChar(n_Z2m, (void*)(long)kNew); |
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130 | } |
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131 | return(rr); |
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132 | } |
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133 | |
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134 | /* TRUE iff 0 < k <= 2^m / 2 */ |
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135 | static BOOLEAN nr2mGreaterZero(number k, const coeffs r) |
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136 | { |
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137 | if ((unsigned long)k == 0) return FALSE; |
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138 | if ((unsigned long)k > ((r->mod2mMask >> 1) + 1)) return FALSE; |
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139 | return TRUE; |
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140 | } |
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141 | |
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142 | /* |
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143 | * Multiply two numbers |
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144 | */ |
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145 | static number nr2mMult(number a, number b, const coeffs r) |
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146 | { |
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147 | number n; |
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148 | if (((unsigned long)a == 0) || ((unsigned long)b == 0)) |
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149 | return (number)0; |
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150 | else |
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151 | n=nr2mMultM(a, b, r); |
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152 | n_Test(n,r); |
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153 | return n; |
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154 | } |
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155 | |
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156 | static void nr2mInpMult(number &a, number b, const coeffs r) |
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157 | { |
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158 | if (((unsigned long)a == 0) || ((unsigned long)b == 0)) |
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159 | { a=(number)0; return; } |
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160 | else |
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161 | nr2mInpMultM(a, b, r); |
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162 | n_Test(a,r); |
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163 | } |
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164 | |
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165 | static number nr2mAnn(number b, const coeffs r); |
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166 | /* |
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167 | * Give the smallest k, such that a * x = k = b * y has a solution |
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168 | */ |
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169 | static number nr2mLcm(number a, number b, const coeffs) |
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170 | { |
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171 | unsigned long res = 0; |
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172 | if ((unsigned long)a == 0) a = (number) 1; |
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173 | if ((unsigned long)b == 0) b = (number) 1; |
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174 | while ((unsigned long)a % 2 == 0) |
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175 | { |
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176 | a = (number)((unsigned long)a / 2); |
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177 | if ((unsigned long)b % 2 == 0) b = (number)((unsigned long)b / 2); |
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178 | res++; |
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179 | } |
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180 | while ((unsigned long)b % 2 == 0) |
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181 | { |
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182 | b = (number)((unsigned long)b / 2); |
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183 | res++; |
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184 | } |
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185 | return (number)(1L << res); // (2**res) |
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186 | } |
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187 | |
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188 | /* |
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189 | * Give the largest k, such that a = x * k, b = y * k has |
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190 | * a solution. |
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191 | */ |
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192 | static number nr2mGcd(number a, number b, const coeffs) |
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193 | { |
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194 | unsigned long res = 0; |
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195 | if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1; |
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196 | while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0) |
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197 | { |
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198 | a = (number)((unsigned long)a / 2); |
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199 | b = (number)((unsigned long)b / 2); |
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200 | res++; |
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201 | } |
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202 | // if ((unsigned long)b % 2 == 0) |
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203 | // { |
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204 | // return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit |
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205 | // } |
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206 | // else |
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207 | // { |
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208 | return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit |
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209 | // } |
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210 | } |
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211 | |
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212 | /* assumes that 'a' is odd, i.e., a unit in Z/2^m, and computes |
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213 | the extended gcd of 'a' and 2^m, in order to find some 's' |
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214 | and 't' such that a * s + 2^m * t = gcd(a, 2^m) = 1; |
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215 | this code will always find a positive 's' */ |
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216 | static void specialXGCD(unsigned long& s, unsigned long a, const coeffs r) |
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217 | { |
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218 | mpz_ptr u = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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219 | mpz_init_set_ui(u, a); |
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220 | mpz_ptr u0 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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221 | mpz_init(u0); |
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222 | mpz_ptr u1 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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223 | mpz_init_set_ui(u1, 1); |
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224 | mpz_ptr u2 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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225 | mpz_init(u2); |
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226 | mpz_ptr v = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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227 | mpz_init_set_ui(v, r->mod2mMask); |
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228 | mpz_add_ui(v, v, 1); /* now: v = 2^m */ |
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229 | mpz_ptr v0 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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230 | mpz_init(v0); |
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231 | mpz_ptr v1 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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232 | mpz_init(v1); |
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233 | mpz_ptr v2 = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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234 | mpz_init_set_ui(v2, 1); |
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235 | mpz_ptr q = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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236 | mpz_init(q); |
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237 | mpz_ptr rr = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
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238 | mpz_init(rr); |
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239 | |
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240 | while (mpz_sgn1(v) != 0) /* i.e., while v != 0 */ |
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241 | { |
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242 | mpz_div(q, u, v); |
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243 | mpz_mod(rr, u, v); |
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244 | mpz_set(u, v); |
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245 | mpz_set(v, rr); |
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246 | mpz_set(u0, u2); |
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247 | mpz_set(v0, v2); |
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248 | mpz_mul(u2, u2, q); mpz_sub(u2, u1, u2); /* u2 = u1 - q * u2 */ |
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249 | mpz_mul(v2, v2, q); mpz_sub(v2, v1, v2); /* v2 = v1 - q * v2 */ |
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250 | mpz_set(u1, u0); |
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251 | mpz_set(v1, v0); |
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252 | } |
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253 | |
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254 | while (mpz_sgn1(u1) < 0) /* i.e., while u1 < 0 */ |
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255 | { |
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256 | /* we add 2^m = (2^m - 1) + 1 to u1: */ |
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257 | mpz_add_ui(u1, u1, r->mod2mMask); |
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258 | mpz_add_ui(u1, u1, 1); |
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259 | } |
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260 | s = mpz_get_ui(u1); /* now: 0 <= s <= 2^m - 1 */ |
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261 | |
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262 | mpz_clear(u); omFreeBinAddr((ADDRESS)u); |
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263 | mpz_clear(u0); omFreeBinAddr((ADDRESS)u0); |
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264 | mpz_clear(u1); omFreeBinAddr((ADDRESS)u1); |
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265 | mpz_clear(u2); omFreeBinAddr((ADDRESS)u2); |
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266 | mpz_clear(v); omFreeBinAddr((ADDRESS)v); |
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267 | mpz_clear(v0); omFreeBinAddr((ADDRESS)v0); |
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268 | mpz_clear(v1); omFreeBinAddr((ADDRESS)v1); |
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269 | mpz_clear(v2); omFreeBinAddr((ADDRESS)v2); |
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270 | mpz_clear(q); omFreeBinAddr((ADDRESS)q); |
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271 | mpz_clear(rr); omFreeBinAddr((ADDRESS)rr); |
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272 | } |
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273 | |
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274 | static unsigned long InvMod(unsigned long a, const coeffs r) |
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275 | { |
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276 | assume((unsigned long)a % 2 != 0); |
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277 | unsigned long s; |
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278 | specialXGCD(s, a, r); |
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279 | return s; |
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280 | } |
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281 | |
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282 | static inline number nr2mInversM(number c, const coeffs r) |
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283 | { |
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284 | assume((unsigned long)c % 2 != 0); |
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285 | // Table !!! |
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286 | unsigned long inv; |
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287 | inv = InvMod((unsigned long)c,r); |
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288 | return (number)inv; |
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289 | } |
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290 | |
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291 | static number nr2mInvers(number c, const coeffs r) |
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292 | { |
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293 | if ((unsigned long)c % 2 == 0) |
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294 | { |
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295 | WerrorS("division by zero divisor"); |
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296 | return (number)0; |
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297 | } |
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298 | return nr2mInversM(c, r); |
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299 | } |
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300 | |
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301 | /* |
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302 | * Give the largest k, such that a = x * k, b = y * k has |
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303 | * a solution. |
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304 | */ |
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305 | static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r) |
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306 | { |
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307 | unsigned long res = 0; |
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308 | if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1; |
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309 | while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0) |
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310 | { |
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311 | a = (number)((unsigned long)a / 2); |
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312 | b = (number)((unsigned long)b / 2); |
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313 | res++; |
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314 | } |
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315 | if ((unsigned long)b % 2 == 0) |
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316 | { |
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317 | *t = NULL; |
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318 | *s = nr2mInvers(a,r); |
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319 | return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit |
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320 | } |
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321 | else |
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322 | { |
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323 | *s = NULL; |
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324 | *t = nr2mInvers(b,r); |
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325 | return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit |
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326 | } |
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327 | } |
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328 | |
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329 | static void nr2mPower(number a, int i, number * result, const coeffs r) |
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330 | { |
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331 | if (i == 0) |
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332 | { |
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333 | *(unsigned long *)result = 1; |
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334 | } |
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335 | else if (i == 1) |
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336 | { |
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337 | *result = a; |
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338 | } |
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339 | else |
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340 | { |
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341 | nr2mPower(a, i-1, result, r); |
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342 | *result = nr2mMultM(a, *result, r); |
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343 | } |
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344 | } |
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345 | |
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346 | /* |
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347 | * create a number from int |
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348 | */ |
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349 | static number nr2mInit(long i, const coeffs r) |
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350 | { |
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351 | if (i == 0) return (number)(unsigned long)0; |
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352 | |
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353 | long ii = i; |
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354 | unsigned long j = (unsigned long)1; |
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355 | if (ii < 0) { j = r->mod2mMask; ii = -ii; } |
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356 | unsigned long k = (unsigned long)ii; |
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357 | k = k & r->mod2mMask; |
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358 | /* now we have: i = j * k mod 2^m */ |
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359 | return nr2mMult((number)j, (number)k, r); |
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360 | } |
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361 | |
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362 | /* |
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363 | * convert a number to an int in ]-k/2 .. k/2], |
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364 | * where k = 2^m; i.e., an int in ]-2^(m-1) .. 2^(m-1)]; |
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365 | */ |
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366 | static long nr2mInt(number &n, const coeffs r) |
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367 | { |
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368 | unsigned long nn = (unsigned long)n; |
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369 | unsigned long l = r->mod2mMask >> 1; l++; /* now: l = 2^(m-1) */ |
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370 | if ((unsigned long)nn > l) |
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371 | return (long)((unsigned long)nn - r->mod2mMask - 1); |
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372 | else |
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373 | return (long)((unsigned long)nn); |
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374 | } |
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375 | |
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376 | static number nr2mAdd(number a, number b, const coeffs r) |
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377 | { |
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378 | number n=nr2mAddM(a, b, r); |
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379 | n_Test(n,r); |
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380 | return n; |
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381 | } |
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382 | |
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383 | static void nr2mInpAdd(number &a, number b, const coeffs r) |
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384 | { |
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385 | nr2mInpAddM(a, b, r); |
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386 | n_Test(a,r); |
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387 | } |
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388 | |
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389 | static number nr2mSub(number a, number b, const coeffs r) |
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390 | { |
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391 | number n=nr2mSubM(a, b, r); |
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392 | n_Test(n,r); |
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393 | return n; |
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394 | } |
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395 | |
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396 | static BOOLEAN nr2mIsUnit(number a, const coeffs) |
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397 | { |
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398 | return ((unsigned long)a % 2 == 1); |
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399 | } |
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400 | |
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401 | static number nr2mGetUnit(number k, const coeffs) |
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402 | { |
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403 | if (k == NULL) return (number)1; |
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404 | unsigned long erg = (unsigned long)k; |
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405 | while (erg % 2 == 0) erg = erg / 2; |
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406 | return (number)erg; |
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407 | } |
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408 | |
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409 | static BOOLEAN nr2mIsZero(number a, const coeffs) |
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410 | { |
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411 | return 0 == (unsigned long)a; |
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412 | } |
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413 | |
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414 | static BOOLEAN nr2mIsOne(number a, const coeffs) |
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415 | { |
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416 | return 1 == (unsigned long)a; |
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417 | } |
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418 | |
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419 | static BOOLEAN nr2mIsMOne(number a, const coeffs r) |
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420 | { |
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421 | return ((r->mod2mMask == (unsigned long)a) &&(1L!=(long)a))/*for char 2^1*/; |
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422 | } |
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423 | |
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424 | static BOOLEAN nr2mEqual(number a, number b, const coeffs) |
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425 | { |
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426 | return (a == b); |
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427 | } |
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428 | |
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429 | static number nr2mDiv(number a, number b, const coeffs r) |
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430 | { |
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431 | if ((unsigned long)a == 0) return (number)0; |
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432 | else if ((unsigned long)b % 2 == 0) |
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433 | { |
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434 | if ((unsigned long)b != 0) |
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435 | { |
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436 | while (((unsigned long)b % 2 == 0) && ((unsigned long)a % 2 == 0)) |
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437 | { |
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438 | a = (number)((unsigned long)a / 2); |
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439 | b = (number)((unsigned long)b / 2); |
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440 | } |
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441 | } |
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442 | if ((long)b==0L) |
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443 | { |
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444 | WerrorS(nDivBy0); |
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445 | return (number)0L; |
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446 | } |
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447 | else if ((unsigned long)b % 2 == 0) |
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448 | { |
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449 | WerrorS("Division not possible, even by cancelling zero divisors."); |
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450 | WerrorS("Result is integer division without remainder."); |
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451 | return (number) ((unsigned long) a / (unsigned long) b); |
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452 | } |
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453 | } |
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454 | number n=nr2mMult(a, nr2mInversM(b,r),r); |
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455 | n_Test(n,r); |
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456 | return n; |
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457 | } |
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458 | |
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459 | /* Is 'a' divisible by 'b'? There are two cases: |
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460 | 1) a = 0 mod 2^m; then TRUE iff b = 0 or b is a power of 2 |
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461 | 2) a, b <> 0; then TRUE iff b/gcd(a, b) is a unit mod 2^m */ |
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462 | static BOOLEAN nr2mDivBy (number a, number b, const coeffs r) |
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463 | { |
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464 | if (a == NULL) |
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465 | { |
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466 | unsigned long c = r->mod2mMask + 1; |
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467 | if (c != 0) /* i.e., if no overflow */ |
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468 | return (c % (unsigned long)b) == 0; |
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469 | else |
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470 | { |
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471 | /* overflow: we need to check whether b |
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472 | is zero or a power of 2: */ |
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473 | c = (unsigned long)b; |
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474 | while (c != 0) |
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475 | { |
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476 | if ((c % 2) != 0) return FALSE; |
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477 | c = c >> 1; |
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478 | } |
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479 | return TRUE; |
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480 | } |
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481 | } |
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482 | else |
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483 | { |
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484 | number n = nr2mGcd(a, b, r); |
---|
485 | n = nr2mDiv(b, n, r); |
---|
486 | return nr2mIsUnit(n, r); |
---|
487 | } |
---|
488 | } |
---|
489 | |
---|
490 | static BOOLEAN nr2mGreater(number a, number b, const coeffs r) |
---|
491 | { |
---|
492 | return nr2mDivBy(a, b,r); |
---|
493 | } |
---|
494 | |
---|
495 | static int nr2mDivComp(number as, number bs, const coeffs) |
---|
496 | { |
---|
497 | unsigned long a = (unsigned long)as; |
---|
498 | unsigned long b = (unsigned long)bs; |
---|
499 | assume(a != 0 && b != 0); |
---|
500 | while (a % 2 == 0 && b % 2 == 0) |
---|
501 | { |
---|
502 | a = a / 2; |
---|
503 | b = b / 2; |
---|
504 | } |
---|
505 | if (a % 2 == 0) |
---|
506 | { |
---|
507 | return -1; |
---|
508 | } |
---|
509 | else |
---|
510 | { |
---|
511 | if (b % 2 == 1) |
---|
512 | { |
---|
513 | return 2; |
---|
514 | } |
---|
515 | else |
---|
516 | { |
---|
517 | return 1; |
---|
518 | } |
---|
519 | } |
---|
520 | } |
---|
521 | |
---|
522 | static number nr2mMod(number a, number b, const coeffs r) |
---|
523 | { |
---|
524 | /* |
---|
525 | We need to return the number rr which is uniquely determined by the |
---|
526 | following two properties: |
---|
527 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
---|
528 | (2) There exists some k in the integers Z such that a = k * b + rr. |
---|
529 | Consider g := gcd(2^m, |b|). Note that then |b|/g is a unit in Z/2^m. |
---|
530 | Now, there are three cases: |
---|
531 | (a) g = 1 |
---|
532 | Then |b| is a unit in Z/2^m, i.e. |b| (and also b) divides a. |
---|
533 | Thus rr = 0. |
---|
534 | (b) g <> 1 and g divides a |
---|
535 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
---|
536 | (c) g <> 1 and g does not divide a |
---|
537 | Let's denote the division with remainder of a by g as follows: |
---|
538 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
---|
539 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
---|
540 | in this third case, rr is the remainder of division of a by g in Z. |
---|
541 | This algorithm is the same as for the case Z/n, except that we may |
---|
542 | compute the gcd of |b| and 2^m "by hand": We just extract the highest |
---|
543 | power of 2 (<= 2^m) that is contained in b. |
---|
544 | */ |
---|
545 | assume((unsigned long) b != 0); |
---|
546 | unsigned long g = 1; |
---|
547 | unsigned long b_div = (unsigned long) b; |
---|
548 | |
---|
549 | /* |
---|
550 | * b_div is unsigned, so that (b_div < 0) evaluates false at compile-time |
---|
551 | * |
---|
552 | if (b_div < 0) b_div = -b_div; // b_div now represents |b|, BUT b_div is unsigned! |
---|
553 | */ |
---|
554 | |
---|
555 | unsigned long rr = 0; |
---|
556 | while ((g < r->mod2mMask ) && (b_div > 0) && (b_div % 2 == 0)) |
---|
557 | { |
---|
558 | b_div = b_div >> 1; |
---|
559 | g = g << 1; |
---|
560 | } // g is now the gcd of 2^m and |b| |
---|
561 | |
---|
562 | if (g != 1) rr = (unsigned long)a % g; |
---|
563 | return (number)rr; |
---|
564 | } |
---|
565 | |
---|
566 | #if 0 |
---|
567 | // unused |
---|
568 | static number nr2mIntDiv(number a, number b, const coeffs r) |
---|
569 | { |
---|
570 | if ((unsigned long)a == 0) |
---|
571 | { |
---|
572 | if ((unsigned long)b == 0) |
---|
573 | return (number)1; |
---|
574 | if ((unsigned long)b == 1) |
---|
575 | return (number)0; |
---|
576 | unsigned long c = r->mod2mMask + 1; |
---|
577 | if (c != 0) /* i.e., if no overflow */ |
---|
578 | return (number)(c / (unsigned long)b); |
---|
579 | else |
---|
580 | { |
---|
581 | /* overflow: c = 2^32 resp. 2^64, depending on platform */ |
---|
582 | mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
---|
583 | mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1); |
---|
584 | mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b); |
---|
585 | unsigned long s = mpz_get_ui(cc); |
---|
586 | mpz_clear(cc); omFree((ADDRESS)cc); |
---|
587 | return (number)(unsigned long)s; |
---|
588 | } |
---|
589 | } |
---|
590 | else |
---|
591 | { |
---|
592 | if ((unsigned long)b == 0) |
---|
593 | return (number)0; |
---|
594 | return (number)((unsigned long) a / (unsigned long) b); |
---|
595 | } |
---|
596 | } |
---|
597 | #endif |
---|
598 | |
---|
599 | static number nr2mAnn(number b, const coeffs r) |
---|
600 | { |
---|
601 | if ((unsigned long)b == 0) |
---|
602 | return NULL; |
---|
603 | if ((unsigned long)b == 1) |
---|
604 | return NULL; |
---|
605 | unsigned long c = r->mod2mMask + 1; |
---|
606 | if (c != 0) /* i.e., if no overflow */ |
---|
607 | return (number)(c / (unsigned long)b); |
---|
608 | else |
---|
609 | { |
---|
610 | /* overflow: c = 2^32 resp. 2^64, depending on platform */ |
---|
611 | mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
---|
612 | mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1); |
---|
613 | mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b); |
---|
614 | unsigned long s = mpz_get_ui(cc); |
---|
615 | mpz_clear(cc); omFreeBinAddr((ADDRESS)cc); |
---|
616 | return (number)(unsigned long)s; |
---|
617 | } |
---|
618 | } |
---|
619 | |
---|
620 | static number nr2mNeg(number c, const coeffs r) |
---|
621 | { |
---|
622 | if ((unsigned long)c == 0) return c; |
---|
623 | number n=nr2mNegM(c, r); |
---|
624 | n_Test(n,r); |
---|
625 | return n; |
---|
626 | } |
---|
627 | |
---|
628 | static number nr2mMapMachineInt(number from, const coeffs /*src*/, const coeffs dst) |
---|
629 | { |
---|
630 | unsigned long i = ((unsigned long)from) % (dst->mod2mMask + 1) ; |
---|
631 | return (number)i; |
---|
632 | } |
---|
633 | |
---|
634 | static number nr2mMapProject(number from, const coeffs /*src*/, const coeffs dst) |
---|
635 | { |
---|
636 | unsigned long i = ((unsigned long)from) % (dst->mod2mMask + 1); |
---|
637 | return (number)i; |
---|
638 | } |
---|
639 | |
---|
640 | number nr2mMapZp(number from, const coeffs /*src*/, const coeffs dst) |
---|
641 | { |
---|
642 | unsigned long j = (unsigned long)1; |
---|
643 | long ii = (long)from; |
---|
644 | if (ii < 0) { j = dst->mod2mMask; ii = -ii; } |
---|
645 | unsigned long i = (unsigned long)ii; |
---|
646 | i = i & dst->mod2mMask; |
---|
647 | /* now we have: from = j * i mod 2^m */ |
---|
648 | return nr2mMult((number)i, (number)j, dst); |
---|
649 | } |
---|
650 | |
---|
651 | static number nr2mMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
652 | { |
---|
653 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
654 | mpz_init(erg); |
---|
655 | mpz_ptr k = (mpz_ptr)omAlloc(sizeof(mpz_t)); |
---|
656 | mpz_init_set_ui(k, dst->mod2mMask); |
---|
657 | |
---|
658 | mpz_and(erg, (mpz_ptr)from, k); |
---|
659 | number res = (number) mpz_get_ui(erg); |
---|
660 | |
---|
661 | mpz_clear(erg); omFreeBinAddr((ADDRESS)erg); |
---|
662 | mpz_clear(k); omFreeBinAddr((ADDRESS)k); |
---|
663 | |
---|
664 | return (number)res; |
---|
665 | } |
---|
666 | |
---|
667 | static number nr2mMapQ(number from, const coeffs src, const coeffs dst) |
---|
668 | { |
---|
669 | mpz_ptr gmp = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
670 | nlMPZ(gmp, from, src); |
---|
671 | number res=nr2mMapGMP((number)gmp,src,dst); |
---|
672 | mpz_clear(gmp); omFreeBinAddr((ADDRESS)gmp); |
---|
673 | return res; |
---|
674 | } |
---|
675 | |
---|
676 | static number nr2mMapZ(number from, const coeffs src, const coeffs dst) |
---|
677 | { |
---|
678 | if (SR_HDL(from) & SR_INT) |
---|
679 | { |
---|
680 | long f_i=SR_TO_INT(from); |
---|
681 | return nr2mInit(f_i,dst); |
---|
682 | } |
---|
683 | return nr2mMapGMP(from,src,dst); |
---|
684 | } |
---|
685 | |
---|
686 | static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst) |
---|
687 | { |
---|
688 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src) |
---|
689 | && (src->mod2mMask < dst->mod2mMask)) |
---|
690 | { /* i.e. map an integer mod 2^s into Z mod 2^t, where t < s */ |
---|
691 | return nr2mMapMachineInt; |
---|
692 | } |
---|
693 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src) |
---|
694 | && (src->mod2mMask > dst->mod2mMask)) |
---|
695 | { /* i.e. map an integer mod 2^s into Z mod 2^t, where t > s */ |
---|
696 | // to be done |
---|
697 | return nr2mMapProject; |
---|
698 | } |
---|
699 | if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src)) |
---|
700 | { |
---|
701 | return nr2mMapGMP; |
---|
702 | } |
---|
703 | if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/) |
---|
704 | { |
---|
705 | return nr2mMapZ; |
---|
706 | } |
---|
707 | if ((src->rep==n_rep_gap_rat) && (nCoeff_is_Q(src)||nCoeff_is_Z(src))) |
---|
708 | { |
---|
709 | return nr2mMapQ; |
---|
710 | } |
---|
711 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) && (src->ch == 2)) |
---|
712 | { |
---|
713 | return nr2mMapZp; |
---|
714 | } |
---|
715 | if ((src->rep==n_rep_gmp) && |
---|
716 | (nCoeff_is_Ring_PtoM(src) || nCoeff_is_Zn(src))) |
---|
717 | { |
---|
718 | if (mpz_divisible_2exp_p(src->modNumber,dst->modExponent)) |
---|
719 | return nr2mMapGMP; |
---|
720 | } |
---|
721 | return NULL; // default |
---|
722 | } |
---|
723 | |
---|
724 | /* |
---|
725 | * set the exponent |
---|
726 | */ |
---|
727 | |
---|
728 | static void nr2mSetExp(int m, coeffs r) |
---|
729 | { |
---|
730 | if (m > 1) |
---|
731 | { |
---|
732 | /* we want mod2mMask to be the bit pattern |
---|
733 | '111..1' consisting of m one's: */ |
---|
734 | r->modExponent= m; |
---|
735 | r->mod2mMask = 1; |
---|
736 | for (int i = 1; i < m; i++) r->mod2mMask = (r->mod2mMask << 1) + 1; |
---|
737 | } |
---|
738 | else |
---|
739 | { |
---|
740 | r->modExponent= 2; |
---|
741 | /* code unexpectedly called with m = 1; we continue with m = 2: */ |
---|
742 | r->mod2mMask = 3; /* i.e., '11' in binary representation */ |
---|
743 | } |
---|
744 | } |
---|
745 | |
---|
746 | static void nr2mInitExp(int m, coeffs r) |
---|
747 | { |
---|
748 | nr2mSetExp(m, r); |
---|
749 | if (m < 2) |
---|
750 | WarnS("nr2mInitExp unexpectedly called with m = 1 (we continue with Z/2^2"); |
---|
751 | } |
---|
752 | |
---|
753 | static void nr2mWrite (number a, const coeffs r) |
---|
754 | { |
---|
755 | long i = nr2mInt(a, r); |
---|
756 | StringAppend("%ld", i); |
---|
757 | } |
---|
758 | |
---|
759 | static const char* nr2mEati(const char *s, int *i, const coeffs r) |
---|
760 | { |
---|
761 | |
---|
762 | if (((*s) >= '0') && ((*s) <= '9')) |
---|
763 | { |
---|
764 | (*i) = 0; |
---|
765 | do |
---|
766 | { |
---|
767 | (*i) *= 10; |
---|
768 | (*i) += *s++ - '0'; |
---|
769 | if ((*i) >= (MAX_INT_VAL / 10)) (*i) = (*i) & r->mod2mMask; |
---|
770 | } |
---|
771 | while (((*s) >= '0') && ((*s) <= '9')); |
---|
772 | (*i) = (*i) & r->mod2mMask; |
---|
773 | } |
---|
774 | else (*i) = 1; |
---|
775 | return s; |
---|
776 | } |
---|
777 | |
---|
778 | static const char * nr2mRead (const char *s, number *a, const coeffs r) |
---|
779 | { |
---|
780 | int z; |
---|
781 | int n=1; |
---|
782 | |
---|
783 | s = nr2mEati(s, &z,r); |
---|
784 | if ((*s) == '/') |
---|
785 | { |
---|
786 | s++; |
---|
787 | s = nr2mEati(s, &n,r); |
---|
788 | } |
---|
789 | if (n == 1) |
---|
790 | *a = (number)(long)z; |
---|
791 | else |
---|
792 | *a = nr2mDiv((number)(long)z,(number)(long)n,r); |
---|
793 | return s; |
---|
794 | } |
---|
795 | |
---|
796 | /* for initializing function pointers */ |
---|
797 | BOOLEAN nr2mInitChar (coeffs r, void* p) |
---|
798 | { |
---|
799 | assume( getCoeffType(r) == n_Z2m ); |
---|
800 | nr2mInitExp((int)(long)(p), r); |
---|
801 | |
---|
802 | r->is_field=FALSE; |
---|
803 | r->is_domain=FALSE; |
---|
804 | r->rep=n_rep_int; |
---|
805 | |
---|
806 | //r->cfKillChar = ndKillChar; /* dummy*/ |
---|
807 | r->nCoeffIsEqual = nr2mCoeffIsEqual; |
---|
808 | |
---|
809 | r->modBase = (mpz_ptr) omAllocBin (gmp_nrz_bin); |
---|
810 | mpz_init_set_si (r->modBase, 2L); |
---|
811 | r->modNumber= (mpz_ptr) omAllocBin (gmp_nrz_bin); |
---|
812 | mpz_init (r->modNumber); |
---|
813 | mpz_pow_ui (r->modNumber, r->modBase, r->modExponent); |
---|
814 | |
---|
815 | /* next cast may yield an overflow as mod2mMask is an unsigned long */ |
---|
816 | r->ch = (int)r->mod2mMask + 1; |
---|
817 | |
---|
818 | r->cfInit = nr2mInit; |
---|
819 | //r->cfCopy = ndCopy; |
---|
820 | r->cfInt = nr2mInt; |
---|
821 | r->cfAdd = nr2mAdd; |
---|
822 | r->cfInpAdd = nr2mInpAdd; |
---|
823 | r->cfSub = nr2mSub; |
---|
824 | r->cfMult = nr2mMult; |
---|
825 | r->cfInpMult = nr2mInpMult; |
---|
826 | r->cfDiv = nr2mDiv; |
---|
827 | r->cfAnn = nr2mAnn; |
---|
828 | r->cfIntMod = nr2mMod; |
---|
829 | r->cfExactDiv = nr2mDiv; |
---|
830 | r->cfInpNeg = nr2mNeg; |
---|
831 | r->cfInvers = nr2mInvers; |
---|
832 | r->cfDivBy = nr2mDivBy; |
---|
833 | r->cfDivComp = nr2mDivComp; |
---|
834 | r->cfGreater = nr2mGreater; |
---|
835 | r->cfEqual = nr2mEqual; |
---|
836 | r->cfIsZero = nr2mIsZero; |
---|
837 | r->cfIsOne = nr2mIsOne; |
---|
838 | r->cfIsMOne = nr2mIsMOne; |
---|
839 | r->cfGreaterZero = nr2mGreaterZero; |
---|
840 | r->cfWriteLong = nr2mWrite; |
---|
841 | r->cfRead = nr2mRead; |
---|
842 | r->cfPower = nr2mPower; |
---|
843 | r->cfSetMap = nr2mSetMap; |
---|
844 | // r->cfNormalize = ndNormalize; // default |
---|
845 | r->cfLcm = nr2mLcm; |
---|
846 | r->cfGcd = nr2mGcd; |
---|
847 | r->cfIsUnit = nr2mIsUnit; |
---|
848 | r->cfGetUnit = nr2mGetUnit; |
---|
849 | r->cfExtGcd = nr2mExtGcd; |
---|
850 | r->cfCoeffName = nr2mCoeffName; |
---|
851 | r->cfQuot1 = nr2mQuot1; |
---|
852 | #ifdef LDEBUG |
---|
853 | r->cfDBTest = nr2mDBTest; |
---|
854 | #endif |
---|
855 | r->has_simple_Alloc=TRUE; |
---|
856 | return FALSE; |
---|
857 | } |
---|
858 | |
---|
859 | #endif |
---|
860 | /* #ifdef HAVE_RINGS */ |
---|