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 (integers) |
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6 | */ |
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7 | #ifdef HAVE_RINGS |
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8 | #if SI_INTEGER_VARIANT == 3 |
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9 | #define POW_2_28 (1L<<60) |
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10 | |
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11 | //make sure that a small number is an immediate integer |
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12 | //bascially copied from longrat.cc nlShort3 |
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13 | //TODO: is there any point in checking 0 first??? |
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14 | //TODO: it is not clear that this works in 32/64 bit everywhere. |
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15 | // too many hacks. |
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16 | #ifdef LDEBUG |
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17 | #define nrzTest(A) nrzDBTest(A,__FILE__,__LINE__,NULL) |
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18 | BOOLEAN nrzDBTest (number x, const char *f, const int l, const coeffs); |
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19 | #else |
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20 | #define nrzTest(A) |
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21 | #endif |
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22 | |
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23 | #undef CF_DEBUG |
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24 | static inline number nrz_short(number x) |
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25 | { |
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26 | #if CF_DEBUG |
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27 | StringAppendS("short("); |
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28 | nrzWrite(x, NULL); |
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29 | #endif |
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30 | if (mpz_sgn1((mpz_ptr) x)==0) |
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31 | { |
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32 | mpz_clear((mpz_ptr)x); |
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33 | omFreeBin(x, gmp_nrz_bin); |
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34 | #if CF_DEBUG |
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35 | StringAppendS(")=0"); |
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36 | #endif |
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37 | return INT_TO_SR(0); |
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38 | } |
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39 | if (mpz_size1((mpz_ptr)x)<=MP_SMALL) |
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40 | { |
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41 | long ui=mpz_get_si((mpz_ptr)x); |
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42 | if ((((ui<<3)>>3)==ui) |
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43 | && (mpz_cmp_si((mpz_ptr)x,ui)==0)) |
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44 | { |
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45 | mpz_clear((mpz_ptr)x); |
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46 | omFreeBin(x, gmp_nrz_bin); |
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47 | #if CF_DEBUG |
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48 | StringAppendS(")=imm"); |
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49 | #endif |
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50 | return INT_TO_SR(ui); |
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51 | } |
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52 | } |
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53 | #if CF_DEBUG |
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54 | StringAppendS(")"); |
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55 | #endif |
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56 | nrzTest(x); |
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57 | return x; |
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58 | } |
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59 | |
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60 | |
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61 | int nrzSize(number a, const coeffs) |
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62 | { |
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63 | if (a==INT_TO_SR(0)) return 0; |
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64 | if (n_Z_IS_SMALL(a)) return 1; |
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65 | return ((mpz_ptr)a)->_mp_alloc; |
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66 | } |
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67 | |
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68 | |
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69 | /* |
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70 | * Multiply two numbers |
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71 | * check for 0, 1, -1 maybe |
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72 | */ |
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73 | #if CF_DEBUG |
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74 | number _nrzMult(number, number, const coeffs); |
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75 | number nrzMult(number a, number b, const coeffs R) |
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76 | { |
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77 | StringSetS("Mult: "); |
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78 | nrzWrite(a, R); |
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79 | StringAppendS(" by "); |
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80 | nrzWrite(b, R); |
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81 | number c = _nrzMult(a, b, R); |
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82 | StringAppendS(" is "); |
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83 | nrzWrite(c, R); |
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84 | char * s = StringEndS(); |
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85 | Print("%s\n", s); |
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86 | omFree(s); |
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87 | return c; |
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88 | } |
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89 | number _nrzMult (number a, number b, const coeffs R) |
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90 | #else |
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91 | number nrzMult (number a, number b, const coeffs R) |
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92 | #endif |
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93 | { |
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94 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
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95 | { |
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96 | //from longrat.cc |
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97 | if (a==INT_TO_SR(0)) return INT_TO_SR(0); |
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98 | if (b==INT_TO_SR(0)) return INT_TO_SR(0); |
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99 | long r=(long)((unsigned long)(SR_HDL(a)-1L))*((unsigned long)(SR_HDL(b)>>1)); |
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100 | if ((r/(SR_HDL(b)>>1))==(SR_HDL(a)-1L)) |
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101 | { |
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102 | number u=((number) ((r>>1)+SR_INT)); |
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103 | if (((((long)SR_HDL(u))<<1)>>1)==SR_HDL(u)) return (u); |
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104 | return nrzInit(SR_HDL(u)>>2, R); |
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105 | } |
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106 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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107 | mpz_init_set_si(erg, SR_TO_INT(a)); |
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108 | mpz_mul_si(erg, erg, SR_TO_INT(b)); |
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109 | nrzTest((number)erg); |
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110 | return nrz_short((number) erg); |
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111 | } |
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112 | else if (n_Z_IS_SMALL(a)) |
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113 | { |
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114 | if (a==INT_TO_SR(0)) return INT_TO_SR(0); |
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115 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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116 | mpz_init_set(erg, (mpz_ptr) b); |
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117 | mpz_mul_si(erg, erg, SR_TO_INT(a)); |
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118 | return nrz_short((number) erg); |
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119 | } |
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120 | else if (n_Z_IS_SMALL(b)) |
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121 | { |
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122 | if (b==INT_TO_SR(0)) return INT_TO_SR(0); |
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123 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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124 | mpz_init_set(erg, (mpz_ptr) a); |
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125 | mpz_mul_si(erg, erg, SR_TO_INT(b)); |
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126 | return nrz_short((number) erg); |
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127 | } |
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128 | else |
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129 | { |
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130 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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131 | mpz_init(erg); |
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132 | mpz_mul(erg, (mpz_ptr) a, (mpz_ptr) b); |
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133 | nrzTest((number)erg); |
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134 | return nrz_short((number) erg); |
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135 | } |
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136 | } |
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137 | |
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138 | static long int_gcd(long a, long b) |
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139 | { |
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140 | long r; |
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141 | a = ABS(a); |
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142 | b = ABS(b); |
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143 | if (!a) return b; |
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144 | if (!b) return a; |
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145 | do |
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146 | { |
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147 | r = a % b; |
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148 | a = b; |
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149 | b = r; |
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150 | } while (b); |
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151 | return ABS(a); // % in C does not imply a sign |
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152 | // it would be unlikely to see a negative here |
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153 | // but who knows |
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154 | } |
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155 | |
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156 | /* |
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157 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
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158 | */ |
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159 | static number nrzLcm (number a, number b, const coeffs R) |
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160 | { |
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161 | #ifdef CF_DEBUG |
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162 | PrintS("nrzLcm\n"); |
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163 | #endif |
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164 | mpz_ptr erg; |
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165 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
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166 | { |
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167 | long g = int_gcd(SR_TO_INT(a), SR_TO_INT(b)); |
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168 | return nrzMult(a, INT_TO_SR(SR_TO_INT(b)/g), R); |
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169 | } |
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170 | else |
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171 | { |
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172 | erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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173 | if (n_Z_IS_SMALL(a)) |
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174 | { |
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175 | mpz_init_set(erg, (mpz_ptr) b); |
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176 | unsigned long g = mpz_gcd_ui(NULL, erg, (unsigned long) ABS(SR_TO_INT(a))); |
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177 | mpz_mul_si(erg, erg, SR_TO_INT(a)/g); |
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178 | } |
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179 | else if (n_Z_IS_SMALL(b)) |
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180 | { |
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181 | mpz_init_set(erg, (mpz_ptr) a); |
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182 | unsigned long g = mpz_gcd_ui(NULL, erg, (unsigned long) ABS(SR_TO_INT(b))); |
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183 | mpz_mul_si(erg, erg, SR_TO_INT(b)/g); |
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184 | } |
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185 | else |
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186 | { |
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187 | mpz_init(erg); |
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188 | mpz_lcm(erg, (mpz_ptr) a, (mpz_ptr) b); |
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189 | } |
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190 | } |
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191 | nrzTest((number)erg); |
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192 | return (number) erg; |
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193 | } |
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194 | |
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195 | static number nrzCopy(number a, const coeffs) |
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196 | { |
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197 | if (n_Z_IS_SMALL(a)) return a; |
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198 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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199 | mpz_init_set(erg, (mpz_ptr) a); |
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200 | nrzTest((number)erg); |
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201 | return (number) erg; |
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202 | } |
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203 | |
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204 | /* |
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205 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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206 | * a solution. |
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207 | */ |
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208 | static number nrzGcd (number a,number b,const coeffs R) |
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209 | { |
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210 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
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211 | { |
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212 | long g = int_gcd(SR_TO_INT(a), SR_TO_INT(b)); |
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213 | return INT_TO_SR(g); |
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214 | } |
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215 | else if (n_Z_IS_SMALL(a)) |
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216 | { |
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217 | if (a==INT_TO_SR(0)) |
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218 | return nrzCopy(b, R); |
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219 | unsigned long g = mpz_gcd_ui(NULL, (mpz_ptr)b, (unsigned long) ABS(SR_TO_INT(a))); |
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220 | return INT_TO_SR( g); |
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221 | } |
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222 | else if (n_Z_IS_SMALL(b)) |
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223 | { |
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224 | if (b==INT_TO_SR(0)) |
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225 | return nrzCopy(a, R); |
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226 | unsigned long g = mpz_gcd_ui(NULL, (mpz_ptr)a, (unsigned long) ABS(SR_TO_INT(b))); |
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227 | return INT_TO_SR(g); |
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228 | } |
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229 | else |
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230 | { |
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231 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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232 | mpz_init(erg); |
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233 | mpz_gcd(erg, (mpz_ptr) a, (mpz_ptr) b); |
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234 | nrzTest((number)erg); |
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235 | return (number) erg; |
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236 | } |
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237 | } |
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238 | |
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239 | /* |
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240 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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241 | * a solution and r, s, s.t. k = s*a + t*b |
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242 | */ |
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243 | static long int_extgcd(long a, long b, long * u, long* x, long * v, long* y) |
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244 | { |
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245 | long q, r; |
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246 | if (!a) |
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247 | { |
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248 | *u = 0; |
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249 | *v = 1; |
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250 | *x = -1; |
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251 | *y = 0; |
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252 | return b; |
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253 | } |
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254 | if (!b) |
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255 | { |
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256 | *u = 1; |
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257 | *v = 0; |
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258 | *x = 0; |
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259 | *y = 1; |
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260 | return a; |
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261 | } |
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262 | *u=1; |
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263 | *v=0; |
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264 | *x=0; |
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265 | *y=1; |
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266 | do |
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267 | { |
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268 | q = a/b; |
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269 | r = a%b; |
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270 | assume (q*b+r == a); |
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271 | a = b; |
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272 | b = r; |
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273 | |
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274 | r = -(*v)*q+(*u); |
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275 | (*u) =(*v); |
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276 | (*v) = r; |
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277 | |
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278 | r = -(*y)*q+(*x); |
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279 | (*x) = (*y); |
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280 | (*y) = r; |
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281 | } while (b); |
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282 | |
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283 | return a; |
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284 | } |
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285 | |
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286 | static number nrzExtGcd (number a, number b, number *s, number *t, const coeffs) |
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287 | { |
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288 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
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289 | { |
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290 | long u, v, x, y; |
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291 | long g = int_extgcd(SR_TO_INT(a), SR_TO_INT(b), &u, &v, &x, &y); |
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292 | *s = INT_TO_SR(u); |
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293 | *t = INT_TO_SR(v); |
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294 | return INT_TO_SR(g); |
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295 | } |
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296 | else |
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297 | { |
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298 | mpz_t aa, bb; |
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299 | if (n_Z_IS_SMALL(a)) |
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300 | { |
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301 | mpz_init_set_si(aa, SR_TO_INT(a)); |
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302 | } |
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303 | else |
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304 | { |
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305 | mpz_init_set(aa, (mpz_ptr) a); |
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306 | } |
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307 | if (n_Z_IS_SMALL(b)) |
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308 | { |
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309 | mpz_init_set_si(bb, SR_TO_INT(b)); |
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310 | } |
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311 | else |
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312 | { |
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313 | mpz_init_set(bb, (mpz_ptr) b); |
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314 | } |
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315 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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316 | mpz_ptr bs = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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317 | mpz_ptr bt = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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318 | mpz_init(erg); |
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319 | mpz_init(bs); |
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320 | mpz_init(bt); |
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321 | mpz_gcdext(erg, bs, bt, aa, bb); |
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322 | *s = nrz_short((number) bs); |
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323 | *t = nrz_short((number) bt); |
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324 | mpz_clear(aa); |
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325 | mpz_clear(bb); |
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326 | return nrz_short((number) erg); |
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327 | } |
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328 | } |
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329 | #if CF_DEBUG |
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330 | static number _nrzXExtGcd(number, number, number *, number *, number *, number *, const coeffs); |
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331 | static number nrzXExtGcd(number a, number b, number *x, number * y, number * u, number * v, const coeffs R) |
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332 | { |
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333 | char * s; |
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334 | StringSetS("XExtGcd: "); |
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335 | nrzWrite(a, R); |
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336 | StringAppendS(" by "); |
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337 | nrzWrite(b, R); |
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338 | number c = _nrzXExtGcd(a, b, x, y, u, v, R); |
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339 | StringAppendS(" is "); |
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340 | nrzWrite(c, R); |
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341 | StringAppendS("[["); |
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342 | nrzWrite(*x, R); |
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343 | StringAppendS(", "); |
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344 | nrzWrite(*y, R); |
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345 | StringAppendS("], "); |
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346 | nrzWrite(*u, R); |
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347 | StringAppendS(", "); |
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348 | nrzWrite(*v, R); |
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349 | s=StringEndS(); |
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350 | Print("%s]]\n", s); |
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351 | omFree(s); |
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352 | return c; |
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353 | } |
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354 | static number _nrzXExtGcd (number a, number b, number *s, number *t, number *u, number *v, const coeffs ) |
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355 | #else |
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356 | static number nrzXExtGcd (number a, number b, number *s, number *t, number *u, number *v, const coeffs ) |
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357 | #endif |
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358 | { |
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359 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
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360 | { |
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361 | long uu, vv, x, y; |
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362 | long g = int_extgcd(SR_TO_INT(a), SR_TO_INT(b), &uu, &vv, &x, &y); |
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363 | *s = INT_TO_SR(uu); |
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364 | *t = INT_TO_SR(vv); |
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365 | *u = INT_TO_SR(x); |
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366 | *v = INT_TO_SR(y); |
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367 | return INT_TO_SR(g); |
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368 | } |
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369 | else |
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370 | { |
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371 | mpz_t aa, bb; |
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372 | if (n_Z_IS_SMALL(a)) |
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373 | { |
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374 | mpz_init_set_si(aa, SR_TO_INT(a)); |
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375 | } |
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376 | else |
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377 | { |
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378 | mpz_init_set(aa, (mpz_ptr) a); |
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379 | } |
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380 | if (n_Z_IS_SMALL(b)) |
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381 | { |
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382 | mpz_init_set_si(bb, SR_TO_INT(b)); |
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383 | } |
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384 | else |
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385 | { |
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386 | mpz_init_set(bb, (mpz_ptr) b); |
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387 | } |
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388 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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389 | mpz_ptr bs = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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390 | mpz_ptr bt = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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391 | mpz_init(erg); |
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392 | mpz_init(bs); |
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393 | mpz_init(bt); |
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394 | |
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395 | mpz_gcdext(erg, bs, bt, aa, bb); |
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396 | |
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397 | mpz_ptr bu = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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398 | mpz_ptr bv = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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399 | |
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400 | mpz_init_set(bu, (mpz_ptr) bb); |
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401 | mpz_init_set(bv, (mpz_ptr) aa); |
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402 | |
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403 | mpz_clear(aa); |
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404 | mpz_clear(bb); |
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405 | assume(mpz_cmp_si(erg, 0)); |
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406 | |
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407 | mpz_div(bu, bu, erg); |
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408 | mpz_div(bv, bv, erg); |
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409 | |
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410 | mpz_mul_si(bu, bu, -1); |
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411 | *u = nrz_short((number) bu); |
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412 | *v = nrz_short((number) bv); |
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413 | |
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414 | *s = nrz_short((number) bs); |
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415 | *t = nrz_short((number) bt); |
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416 | return nrz_short((number) erg); |
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417 | } |
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418 | } |
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419 | #if CF_DEBUG |
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420 | static number _nrzQuotRem(number, number, number *, const coeffs); |
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421 | static number nrzQuotRem(number a, number b, number * r, const coeffs R) |
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422 | { |
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423 | StringSetS("QuotRem: "); |
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424 | nrzWrite(a, R); |
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425 | StringAppendS(" by "); |
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426 | nrzWrite(b, R); |
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427 | number c = _nrzQuotRem(a, b, r, R); |
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428 | StringAppendS(" is "); |
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429 | nrzWrite(c, R); |
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430 | if (r) { |
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431 | StringAppendS("+R("); |
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432 | nrzWrite(*r, R); |
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433 | StringAppendS(")"); |
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434 | } |
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435 | char * s = StringEndS(); |
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436 | Print("%s\n", s); |
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437 | omFree(s); |
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438 | return c; |
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439 | } |
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440 | static number _nrzQuotRem (number a, number b, number * r, const coeffs ) |
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441 | #else |
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442 | static number nrzQuotRem (number a, number b, number * r, const coeffs ) |
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443 | #endif |
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444 | { |
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445 | mpz_ptr qq = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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446 | mpz_init(qq); |
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447 | mpz_ptr rr = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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448 | mpz_init(rr); |
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449 | mpz_t bb; |
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450 | mpz_t aa; |
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451 | int gsign; |
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452 | if (SR_HDL(b) & SR_INT) |
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453 | { |
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454 | if (SR_HDL(b)<0) gsign=-1; |
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455 | else gsign=1; |
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456 | mpz_init_set_si(bb,SR_TO_INT(b)); |
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457 | } |
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458 | else |
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459 | { |
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460 | gsign = mpz_sgn((mpz_ptr) b); |
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461 | mpz_init_set(bb,(mpz_ptr) b); |
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462 | } |
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463 | if (SR_HDL(a) & SR_INT) |
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464 | { |
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465 | mpz_init_set_si(aa,SR_TO_INT(a)); |
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466 | } |
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467 | else |
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468 | { |
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469 | mpz_init_set(aa,(mpz_ptr) a); |
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470 | } |
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471 | mpz_t gg, ghalf; |
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472 | mpz_init(gg); |
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473 | mpz_init(ghalf); |
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474 | mpz_abs(gg, bb); |
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475 | mpz_fdiv_qr(qq, rr, aa, gg); |
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476 | mpz_tdiv_q_2exp(ghalf, gg, 1); |
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477 | if (mpz_cmp(rr, ghalf) > 0) // r > ghalf |
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478 | { |
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479 | mpz_sub(rr, rr, gg); |
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480 | mpz_add_ui(qq, qq, 1); |
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481 | } |
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482 | if (gsign < 0) mpz_neg(qq, qq); |
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483 | |
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484 | mpz_clear(ghalf); |
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485 | mpz_clear(gg); |
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486 | mpz_clear(aa); |
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487 | mpz_clear(bb); |
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488 | if (r==NULL) |
---|
489 | { |
---|
490 | mpz_clear(rr); |
---|
491 | omFreeBin(rr,gmp_nrz_bin); |
---|
492 | } |
---|
493 | else |
---|
494 | { |
---|
495 | *r=nrz_short((number)rr); |
---|
496 | } |
---|
497 | return nrz_short((number)qq); |
---|
498 | } |
---|
499 | |
---|
500 | static void nrzPower (number a, int i, number * result, const coeffs) |
---|
501 | { |
---|
502 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
503 | mpz_init(erg); |
---|
504 | mpz_t aa; |
---|
505 | if (n_Z_IS_SMALL(a)) |
---|
506 | mpz_init_set_si(aa, SR_TO_INT(a)); |
---|
507 | else |
---|
508 | mpz_init_set(aa, (mpz_ptr) a); |
---|
509 | mpz_pow_ui(erg, aa, i); |
---|
510 | *result = nrz_short((number) erg); |
---|
511 | } |
---|
512 | |
---|
513 | /* |
---|
514 | * create a number from int |
---|
515 | * TODO: do not create an mpz if not necessary |
---|
516 | */ |
---|
517 | number nrzInit (long i, const coeffs) |
---|
518 | { |
---|
519 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
520 | mpz_init_set_si(erg, i); |
---|
521 | return nrz_short((number) erg); |
---|
522 | } |
---|
523 | |
---|
524 | static number nrzInitMPZ(mpz_t m, const coeffs) |
---|
525 | { |
---|
526 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
527 | mpz_init_set(erg, m); |
---|
528 | return nrz_short((number) erg); |
---|
529 | } |
---|
530 | |
---|
531 | |
---|
532 | void nrzDelete(number *a, const coeffs) |
---|
533 | { |
---|
534 | if (*a == NULL) return; |
---|
535 | if (n_Z_IS_SMALL(*a)==0) |
---|
536 | { |
---|
537 | mpz_clear((mpz_ptr) *a); |
---|
538 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
---|
539 | } |
---|
540 | *a = NULL; |
---|
541 | } |
---|
542 | |
---|
543 | /* |
---|
544 | * convert a number to int |
---|
545 | */ |
---|
546 | static long nrzInt(number &n, const coeffs) |
---|
547 | { |
---|
548 | if (n_Z_IS_SMALL(n)) return SR_TO_INT(n); |
---|
549 | return mpz_get_si( (mpz_ptr)n); |
---|
550 | } |
---|
551 | #if CF_DEBUG |
---|
552 | static number _nrzAdd(number, number, const coeffs); |
---|
553 | static number nrzAdd(number a, number b, const coeffs R) |
---|
554 | { |
---|
555 | StringSetS("Add: "); |
---|
556 | nrzWrite(a, R); |
---|
557 | StringAppendS(" to "); |
---|
558 | nrzWrite(b, R); |
---|
559 | number c = _nrzAdd(a, b, R); |
---|
560 | StringAppendS(" is "); |
---|
561 | nrzWrite(c, R); |
---|
562 | char * s = StringEndS(); |
---|
563 | Print("%s\n", s); |
---|
564 | omFree(s); |
---|
565 | return c; |
---|
566 | } |
---|
567 | static number _nrzAdd (number a, number b, const coeffs ) |
---|
568 | #else |
---|
569 | static number nrzAdd (number a, number b, const coeffs ) |
---|
570 | #endif |
---|
571 | { |
---|
572 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
573 | { |
---|
574 | long c = SR_HDL(a)+SR_HDL(b)-1L; |
---|
575 | if (INT_IS_SMALL(c)) |
---|
576 | return (number)c; |
---|
577 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
578 | mpz_init_set_si(erg,SR_TO_INT(a)); |
---|
579 | if (SR_HDL(b)>0) |
---|
580 | mpz_add_ui(erg, erg, (unsigned long)SR_TO_INT(b)); |
---|
581 | else |
---|
582 | mpz_sub_ui(erg, erg, (unsigned long)-(SR_TO_INT(b))); |
---|
583 | return nrz_short((number)erg); |
---|
584 | } |
---|
585 | else if (n_Z_IS_SMALL(a)) |
---|
586 | { |
---|
587 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
588 | mpz_init(erg); |
---|
589 | if (SR_HDL(a)>0) |
---|
590 | mpz_add_ui(erg, (mpz_ptr) b, (unsigned long)SR_TO_INT(a)); |
---|
591 | else |
---|
592 | mpz_sub_ui(erg, (mpz_ptr) b, (unsigned long)-(SR_TO_INT(a))); |
---|
593 | return nrz_short((number) erg); |
---|
594 | } |
---|
595 | else if (n_Z_IS_SMALL(b)) |
---|
596 | { |
---|
597 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
598 | mpz_init(erg); |
---|
599 | if (SR_HDL(b)>0) |
---|
600 | mpz_add_ui(erg, (mpz_ptr) a, (unsigned long)SR_TO_INT(b)); |
---|
601 | else |
---|
602 | mpz_sub_ui(erg, (mpz_ptr) a, (unsigned long)-(SR_TO_INT(b))); |
---|
603 | return nrz_short((number) erg); |
---|
604 | } |
---|
605 | else |
---|
606 | { |
---|
607 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
608 | mpz_init(erg); |
---|
609 | mpz_add(erg, (mpz_ptr) a, (mpz_ptr) b); |
---|
610 | return nrz_short((number) erg); |
---|
611 | } |
---|
612 | } |
---|
613 | |
---|
614 | static number nrzSub (number a, number b, const coeffs ) |
---|
615 | { |
---|
616 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
617 | { |
---|
618 | long c = SR_HDL(a)-SR_HDL(b)+1; |
---|
619 | if (INT_IS_SMALL(c)) |
---|
620 | return number(c); |
---|
621 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
622 | mpz_init_set_si(erg,SR_TO_INT(a)); |
---|
623 | if (SR_HDL(b)>0) |
---|
624 | mpz_sub_ui(erg, erg, (unsigned long)SR_TO_INT(b)); |
---|
625 | else |
---|
626 | mpz_add_ui(erg, erg, (unsigned long)-(SR_TO_INT(b))); |
---|
627 | return nrz_short((number)erg); |
---|
628 | } |
---|
629 | else if (n_Z_IS_SMALL(a)) |
---|
630 | { |
---|
631 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
632 | mpz_init_set_si(erg,SR_TO_INT(a)); |
---|
633 | mpz_sub(erg, erg, (mpz_ptr) b); |
---|
634 | return nrz_short((number) erg); |
---|
635 | } |
---|
636 | else if (n_Z_IS_SMALL(b)) |
---|
637 | { |
---|
638 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
639 | mpz_init(erg); |
---|
640 | if (SR_HDL(b)>0) |
---|
641 | mpz_sub_ui(erg, (mpz_ptr) a, (unsigned long)SR_TO_INT(b)); |
---|
642 | else |
---|
643 | mpz_add_ui(erg, (mpz_ptr) a, (unsigned long)-SR_TO_INT(b)); |
---|
644 | return nrz_short((number) erg); |
---|
645 | } |
---|
646 | else |
---|
647 | { |
---|
648 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
649 | mpz_init(erg); |
---|
650 | mpz_sub(erg, (mpz_ptr) a, (mpz_ptr) b); |
---|
651 | return nrz_short((number) erg); |
---|
652 | } |
---|
653 | } |
---|
654 | |
---|
655 | static BOOLEAN nrzGreater (number a,number b, const coeffs) |
---|
656 | { |
---|
657 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
658 | return ((long)a)>((long)b); |
---|
659 | else if (n_Z_IS_SMALL(a)) |
---|
660 | return 0 > mpz_cmp_si((mpz_ptr)b,SR_TO_INT(a)); |
---|
661 | else if (n_Z_IS_SMALL(b)) |
---|
662 | return 0 < mpz_cmp_si((mpz_ptr)a,SR_TO_INT(b)); |
---|
663 | return 0 < mpz_cmp((mpz_ptr) a, (mpz_ptr) b); |
---|
664 | } |
---|
665 | |
---|
666 | static BOOLEAN nrzGreaterZero (number k, const coeffs C) |
---|
667 | { |
---|
668 | return nrzGreater(k, INT_TO_SR(0), C); |
---|
669 | } |
---|
670 | |
---|
671 | static number nrzGetUnit (number n, const coeffs r) |
---|
672 | { |
---|
673 | if (nrzGreaterZero(n, r)) |
---|
674 | return INT_TO_SR(1); |
---|
675 | /*else*/ |
---|
676 | return INT_TO_SR(-1); |
---|
677 | } |
---|
678 | |
---|
679 | static number nrzAnn(number n, const coeffs) |
---|
680 | { |
---|
681 | if (SR_TO_INT(n)) // in Z: the annihilator of !=0 is 0 |
---|
682 | return INT_TO_SR(0); |
---|
683 | else |
---|
684 | return INT_TO_SR(1); |
---|
685 | } |
---|
686 | |
---|
687 | static BOOLEAN nrzIsUnit (number a, const coeffs) |
---|
688 | { |
---|
689 | return ABS(SR_TO_INT(a))==1; |
---|
690 | } |
---|
691 | |
---|
692 | static BOOLEAN nrzIsZero (number a, const coeffs) |
---|
693 | { |
---|
694 | return (a==INT_TO_SR(0)); |
---|
695 | } |
---|
696 | |
---|
697 | static BOOLEAN nrzIsOne (number a, const coeffs) |
---|
698 | { |
---|
699 | return a==INT_TO_SR(1); |
---|
700 | } |
---|
701 | |
---|
702 | static BOOLEAN nrzIsMOne (number a, const coeffs) |
---|
703 | { |
---|
704 | return a==INT_TO_SR(-1); |
---|
705 | } |
---|
706 | |
---|
707 | static BOOLEAN nrzEqual (number a,number b, const coeffs) |
---|
708 | { |
---|
709 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
710 | return a==b; |
---|
711 | else if (n_Z_IS_SMALL(a) || n_Z_IS_SMALL(b)) |
---|
712 | return FALSE; |
---|
713 | else |
---|
714 | return 0 == mpz_cmp((mpz_ptr) a, (mpz_ptr) b); |
---|
715 | } |
---|
716 | |
---|
717 | static BOOLEAN nrzDivBy (number a,number b, const coeffs) |
---|
718 | { |
---|
719 | if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
720 | { |
---|
721 | return SR_TO_INT(a) %SR_TO_INT(b) ==0; |
---|
722 | } |
---|
723 | else if (n_Z_IS_SMALL(a)) |
---|
724 | { |
---|
725 | return a==INT_TO_SR(0); |
---|
726 | } |
---|
727 | else if (n_Z_IS_SMALL(b)) |
---|
728 | { |
---|
729 | return mpz_divisible_ui_p((mpz_ptr)a, (unsigned long)ABS(SR_TO_INT(b))) != 0; |
---|
730 | } |
---|
731 | else |
---|
732 | return mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b) != 0; |
---|
733 | } |
---|
734 | |
---|
735 | static int nrzDivComp(number a, number b, const coeffs r) |
---|
736 | { |
---|
737 | if (nrzDivBy(a, b, r)) |
---|
738 | { |
---|
739 | if (nrzDivBy(b, a, r)) return 2; |
---|
740 | return -1; |
---|
741 | } |
---|
742 | if (nrzDivBy(b, a, r)) return 1; |
---|
743 | return 0; |
---|
744 | } |
---|
745 | |
---|
746 | static number nrzDiv (number a,number b, const coeffs cf) |
---|
747 | { |
---|
748 | if (nrzIsZero(b,cf)) |
---|
749 | { |
---|
750 | WerrorS(nDivBy0); |
---|
751 | return INT_TO_SR(0); |
---|
752 | } |
---|
753 | else if (n_Z_IS_SMALL(a) && n_Z_IS_SMALL(b)) |
---|
754 | { |
---|
755 | long i=SR_TO_INT(a); |
---|
756 | long j=SR_TO_INT(b); |
---|
757 | if (j==1L) return a; |
---|
758 | if ((i==-POW_2_28) && (j== -1L)) |
---|
759 | { |
---|
760 | return nrzInit(POW_2_28,cf); |
---|
761 | } |
---|
762 | //if (SR_TO_INT(a) % SR_TO_INT(b)) |
---|
763 | //{ |
---|
764 | // WerrorS("1:Division by non divisible element."); |
---|
765 | // WerrorS("Result is without remainder."); |
---|
766 | //} |
---|
767 | return INT_TO_SR(i/j); |
---|
768 | } |
---|
769 | else if (n_Z_IS_SMALL(a)) |
---|
770 | { |
---|
771 | //if (SR_TO_INT(a)) |
---|
772 | //{ |
---|
773 | // WerrorS("2:Division by non divisible element."); |
---|
774 | // WerrorS("Result is without remainder."); |
---|
775 | //} |
---|
776 | return INT_TO_SR(0); |
---|
777 | } |
---|
778 | else if (n_Z_IS_SMALL(b)) |
---|
779 | { |
---|
780 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
781 | mpz_t r; |
---|
782 | mpz_init(r); |
---|
783 | mpz_init(erg); |
---|
784 | if (mpz_divmod_ui(erg, r, (mpz_ptr) a, (unsigned long)ABS(SR_TO_INT(b)))) { |
---|
785 | // WerrorS("3:Division by non divisible element."); |
---|
786 | // WerrorS("Result is without remainder."); |
---|
787 | } |
---|
788 | mpz_clear(r); |
---|
789 | if (SR_HDL(b)<0) |
---|
790 | mpz_neg(erg, erg); |
---|
791 | return nrz_short((number) erg); |
---|
792 | } |
---|
793 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
794 | mpz_init(erg); |
---|
795 | mpz_t r; |
---|
796 | mpz_init(r); |
---|
797 | mpz_tdiv_qr(erg, r, (mpz_ptr) a, (mpz_ptr) b); |
---|
798 | #if CF_DEBUG |
---|
799 | StringSetS("division of"); |
---|
800 | nrzWrite(a, R); |
---|
801 | StringAppendS(" by "); |
---|
802 | nrzWrite(b, R); |
---|
803 | StringAppendS(" is "); |
---|
804 | number du; |
---|
805 | nrzWrite(du = (number)erg, R); |
---|
806 | StringAppendS(" rest "); |
---|
807 | nrzWrite(du = (number)r, R); |
---|
808 | char * s = StringEndS(); |
---|
809 | Print("%s\n", s); |
---|
810 | omFree(s); |
---|
811 | #endif |
---|
812 | |
---|
813 | if (mpz_sgn1(r)!=0) |
---|
814 | { |
---|
815 | //WerrorS("4:Division by non divisible element."); |
---|
816 | //WerrorS("Result is without remainder."); |
---|
817 | } |
---|
818 | mpz_clear(r); |
---|
819 | return nrz_short((number) erg); |
---|
820 | } |
---|
821 | |
---|
822 | static number nrzExactDiv (number a,number b, const coeffs cf) |
---|
823 | { |
---|
824 | assume(SR_TO_INT(b)); |
---|
825 | mpz_t aa, bb; |
---|
826 | if (nrzIsZero(b,cf)) |
---|
827 | { |
---|
828 | WerrorS(nDivBy0); |
---|
829 | return INT_TO_SR(0); |
---|
830 | } |
---|
831 | else if (n_Z_IS_SMALL(a)) |
---|
832 | mpz_init_set_si(aa, SR_TO_INT(a)); |
---|
833 | else |
---|
834 | mpz_init_set(aa, (mpz_ptr) a); |
---|
835 | if (n_Z_IS_SMALL(b)) |
---|
836 | mpz_init_set_si(bb, SR_TO_INT(b)); |
---|
837 | else |
---|
838 | mpz_init_set(bb, (mpz_ptr) b); |
---|
839 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
840 | mpz_init(erg); |
---|
841 | mpz_tdiv_q(erg, (mpz_ptr) aa, (mpz_ptr) bb); |
---|
842 | mpz_clear(aa); |
---|
843 | mpz_clear(bb); |
---|
844 | return nrz_short((number) erg); |
---|
845 | } |
---|
846 | |
---|
847 | static number nrzIntMod (number a,number b, const coeffs) |
---|
848 | { |
---|
849 | mpz_t aa, bb; |
---|
850 | assume(SR_TO_INT(b)); |
---|
851 | if (n_Z_IS_SMALL(a)) |
---|
852 | mpz_init_set_si(aa, SR_TO_INT(a)); |
---|
853 | else |
---|
854 | mpz_init_set(aa, (mpz_ptr) a); |
---|
855 | if (n_Z_IS_SMALL(b)) |
---|
856 | mpz_init_set_si(bb, SR_TO_INT(b)); |
---|
857 | else |
---|
858 | mpz_init_set(bb, (mpz_ptr) b); |
---|
859 | |
---|
860 | mpz_t erg; |
---|
861 | mpz_init(erg); |
---|
862 | mpz_ptr r = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
863 | mpz_init(r); |
---|
864 | mpz_tdiv_qr(erg, r, (mpz_ptr) aa, (mpz_ptr) bb); |
---|
865 | mpz_clear(erg); |
---|
866 | mpz_clear(aa); |
---|
867 | mpz_clear(bb); |
---|
868 | |
---|
869 | return nrz_short((number) r); |
---|
870 | } |
---|
871 | |
---|
872 | static number nrzInvers (number c, const coeffs r) |
---|
873 | { |
---|
874 | if (!nrzIsUnit((number) c, r)) |
---|
875 | { |
---|
876 | WerrorS("Non invertible element."); |
---|
877 | return nrzInit(0,r); |
---|
878 | } |
---|
879 | return c; // has to be 1 or -1.... |
---|
880 | } |
---|
881 | |
---|
882 | static number nrzNeg (number c, const coeffs) |
---|
883 | { |
---|
884 | // nNeg inplace !!! |
---|
885 | if (n_Z_IS_SMALL(c)) |
---|
886 | return INT_TO_SR(-SR_TO_INT(c)); |
---|
887 | mpz_mul_si((mpz_ptr) c, (mpz_ptr) c, -1); |
---|
888 | return c; |
---|
889 | } |
---|
890 | |
---|
891 | static number nrzFarey(number r, number N, const coeffs R) |
---|
892 | { |
---|
893 | number a0 = nrzCopy(N, R); |
---|
894 | number b0 = nrzInit(0, R); |
---|
895 | number a1 = nrzCopy(r, R); |
---|
896 | number b1 = nrzInit(1, R); |
---|
897 | number two = nrzInit(2, R); |
---|
898 | #if 0 |
---|
899 | PrintS("Farey start with "); |
---|
900 | n_Print(r, R); |
---|
901 | PrintS(" mod "); |
---|
902 | n_Print(N, R); |
---|
903 | PrintLn(); |
---|
904 | #endif |
---|
905 | while (1) |
---|
906 | { |
---|
907 | number as = nrzMult(a1, a1, R); |
---|
908 | n_InpMult(as, two, R); |
---|
909 | if (nrzGreater(N, as, R)) |
---|
910 | { |
---|
911 | nrzDelete(&as, R); |
---|
912 | break; |
---|
913 | } |
---|
914 | nrzDelete(&as, R); |
---|
915 | number q = nrzDiv(a0, a1, R); |
---|
916 | number t = nrzMult(a1, q, R), |
---|
917 | s = nrzSub(a0, t, R); |
---|
918 | nrzDelete(&a0, R); |
---|
919 | a0 = a1; |
---|
920 | a1 = s; |
---|
921 | nrzDelete(&t, R); |
---|
922 | |
---|
923 | t = nrzMult(b1, q, R); |
---|
924 | s = nrzSub(b0, t, R); |
---|
925 | nrzDelete(&b0, R); |
---|
926 | b0 = b1; |
---|
927 | b1 = s; |
---|
928 | nrzDelete(&t, R); |
---|
929 | nrzDelete(&q, R); |
---|
930 | } |
---|
931 | number as = nrzMult(b1, b1, R); |
---|
932 | n_InpMult(as, two, R); |
---|
933 | nrzDelete(&two, R); |
---|
934 | if (nrzGreater(as, N, R)) |
---|
935 | { |
---|
936 | nrzDelete(&a0, R); |
---|
937 | nrzDelete(&a1, R); |
---|
938 | nrzDelete(&b0, R); |
---|
939 | nrzDelete(&b1, R); |
---|
940 | nrzDelete(&as, R); |
---|
941 | return NULL; |
---|
942 | } |
---|
943 | nrzDelete(&as, R); |
---|
944 | nrzDelete(&a0, R); |
---|
945 | nrzDelete(&b0, R); |
---|
946 | |
---|
947 | number a, b, ab; |
---|
948 | coeffs Q = nInitChar(n_Q, 0); |
---|
949 | nMapFunc f = n_SetMap(R, Q); |
---|
950 | a = f(a1, R, Q); |
---|
951 | b = f(b1, R, Q); |
---|
952 | ab = n_Div(a, b, Q); |
---|
953 | n_Delete(&a, Q); |
---|
954 | n_Delete(&b, Q); |
---|
955 | nKillChar(Q); |
---|
956 | |
---|
957 | nrzDelete(&a1, R); |
---|
958 | nrzDelete(&b1, R); |
---|
959 | nrzTest(ab); |
---|
960 | return ab; |
---|
961 | } |
---|
962 | |
---|
963 | static number nrzMapMachineInt(number from, const coeffs /*src*/, const coeffs /*dst*/) |
---|
964 | { |
---|
965 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
966 | mpz_init_set_ui(erg, (unsigned long) from); |
---|
967 | return nrz_short((number) erg); |
---|
968 | } |
---|
969 | |
---|
970 | static number nrzMapZp(number from, const coeffs /*src*/, const coeffs /*dst*/) |
---|
971 | { |
---|
972 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
973 | mpz_init_set_si(erg, (long) from); |
---|
974 | return nrz_short((number) erg); |
---|
975 | } |
---|
976 | |
---|
977 | static number nrzModNMap(number from, const coeffs /* src */, const coeffs /*dst*/) |
---|
978 | { |
---|
979 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
980 | mpz_init_set(erg, (mpz_ptr) from); |
---|
981 | return nrz_short((number) erg); |
---|
982 | } |
---|
983 | |
---|
984 | static number nrzMapQ(number from, const coeffs /* src */, const coeffs dst) |
---|
985 | { |
---|
986 | if (SR_HDL(from) & SR_INT) |
---|
987 | return nrzInit(SR_TO_INT(from),dst); |
---|
988 | if (from->s!=3) |
---|
989 | { |
---|
990 | WerrorS("rational in map to integer"); |
---|
991 | return NULL; |
---|
992 | } |
---|
993 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
994 | mpz_init_set(erg, from->z); |
---|
995 | return nrz_short((number) erg); |
---|
996 | } |
---|
997 | |
---|
998 | static nMapFunc nrzSetMap(const coeffs src, const coeffs /*dst*/) |
---|
999 | { |
---|
1000 | /* dst = rintegers */ |
---|
1001 | if (src->rep==n_rep_gmp) //nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src)) |
---|
1002 | return nrzModNMap; |
---|
1003 | |
---|
1004 | if ((src->rep==n_rep_gap_gmp) && nCoeff_is_Z(src)) |
---|
1005 | { |
---|
1006 | return ndCopyMap; //nrzCopyMap; |
---|
1007 | } |
---|
1008 | if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Z(src)) Q, bigint*/ |
---|
1009 | { |
---|
1010 | return nrzMapQ; |
---|
1011 | } |
---|
1012 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)) |
---|
1013 | { |
---|
1014 | return nrzMapMachineInt; |
---|
1015 | } |
---|
1016 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src)) |
---|
1017 | { |
---|
1018 | return nrzMapZp; |
---|
1019 | } |
---|
1020 | return NULL; // default |
---|
1021 | } |
---|
1022 | |
---|
1023 | |
---|
1024 | #ifdef LDEBUG |
---|
1025 | BOOLEAN nrzDBTest (number x, const char *f, const int l, const coeffs) |
---|
1026 | { |
---|
1027 | if (SR_HDL(x) & SR_INT) return TRUE; |
---|
1028 | if (mpz_sgn1((mpz_ptr) x)==0) |
---|
1029 | { |
---|
1030 | Print("gmp-0 %s:%d\n",f,l); |
---|
1031 | return FALSE; |
---|
1032 | } |
---|
1033 | if (mpz_size1((mpz_ptr)x)<=MP_SMALL) |
---|
1034 | { |
---|
1035 | long ui=mpz_get_si((mpz_ptr)x); |
---|
1036 | if ((((ui<<3)>>3)==ui) |
---|
1037 | && (mpz_cmp_si((mpz_ptr)x,ui)==0)) |
---|
1038 | { |
---|
1039 | Print("gmp-small %s:%d\n",f,l); |
---|
1040 | return FALSE; |
---|
1041 | } |
---|
1042 | } |
---|
1043 | return TRUE; |
---|
1044 | } |
---|
1045 | #endif |
---|
1046 | |
---|
1047 | void nrzWrite (number a, const coeffs) |
---|
1048 | { |
---|
1049 | char *s,*z; |
---|
1050 | if (a==NULL) |
---|
1051 | { |
---|
1052 | StringAppendS("o"); |
---|
1053 | } |
---|
1054 | else |
---|
1055 | { |
---|
1056 | if (n_Z_IS_SMALL(a)) |
---|
1057 | { |
---|
1058 | StringAppend("%d", SR_TO_INT(a)); |
---|
1059 | } |
---|
1060 | else |
---|
1061 | { |
---|
1062 | int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2; |
---|
1063 | s=(char*)omAlloc(l); |
---|
1064 | z=mpz_get_str(s,10,(mpz_ptr) a); |
---|
1065 | StringAppendS(z); |
---|
1066 | omFreeSize((ADDRESS)s,l); |
---|
1067 | } |
---|
1068 | } |
---|
1069 | } |
---|
1070 | |
---|
1071 | /*2 |
---|
1072 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
1073 | */ |
---|
1074 | static const char * nlEatLongC(char *s, mpz_ptr i) |
---|
1075 | { |
---|
1076 | const char * start=s; |
---|
1077 | |
---|
1078 | if (*s<'0' || *s>'9') |
---|
1079 | { |
---|
1080 | mpz_set_ui(i,1); |
---|
1081 | return s; |
---|
1082 | } |
---|
1083 | while (*s >= '0' && *s <= '9') s++; |
---|
1084 | if (*s=='\0') |
---|
1085 | { |
---|
1086 | mpz_set_str(i,start,10); |
---|
1087 | } |
---|
1088 | else |
---|
1089 | { |
---|
1090 | char c=*s; |
---|
1091 | *s='\0'; |
---|
1092 | mpz_set_str(i,start,10); |
---|
1093 | *s=c; |
---|
1094 | } |
---|
1095 | return s; |
---|
1096 | } |
---|
1097 | |
---|
1098 | static const char * nrzRead (const char *s, number *a, const coeffs) |
---|
1099 | { |
---|
1100 | mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
1101 | { |
---|
1102 | mpz_init(z); |
---|
1103 | s = nlEatLongC((char *) s, z); |
---|
1104 | } |
---|
1105 | *a = nrz_short((number) z); |
---|
1106 | return s; |
---|
1107 | } |
---|
1108 | |
---|
1109 | static CanonicalForm nrzConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs /*r*/ ) |
---|
1110 | { |
---|
1111 | if (setChar) setCharacteristic( 0 ); |
---|
1112 | |
---|
1113 | CanonicalForm term; |
---|
1114 | if ( n_Z_IS_SMALL(n)) |
---|
1115 | { |
---|
1116 | term = SR_TO_INT(n); |
---|
1117 | } |
---|
1118 | else |
---|
1119 | { |
---|
1120 | mpz_t dummy; |
---|
1121 | mpz_init_set( dummy,n->z ); |
---|
1122 | term = make_cf( dummy ); |
---|
1123 | } |
---|
1124 | return term; |
---|
1125 | } |
---|
1126 | |
---|
1127 | static number nrzConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
---|
1128 | { |
---|
1129 | if (n.isImm()) |
---|
1130 | { |
---|
1131 | return nrzInit(n.intval(),r); |
---|
1132 | } |
---|
1133 | else |
---|
1134 | { |
---|
1135 | if ( !n.den().isOne() ) |
---|
1136 | { |
---|
1137 | WerrorS("rational in conversion to integer"); |
---|
1138 | return NULL; |
---|
1139 | } |
---|
1140 | mpz_ptr z = (mpz_ptr) omAlloc0Bin(gmp_nrz_bin); |
---|
1141 | gmp_numerator( n,z); |
---|
1142 | return nrz_short((number)z); |
---|
1143 | } |
---|
1144 | } |
---|
1145 | |
---|
1146 | static void nrzMPZ(mpz_t res, number &a, const coeffs) |
---|
1147 | { |
---|
1148 | if (n_Z_IS_SMALL(a)) |
---|
1149 | mpz_init_set_si(res, SR_TO_INT(a)); |
---|
1150 | else |
---|
1151 | mpz_init_set(res, (mpz_ptr) a); |
---|
1152 | } |
---|
1153 | |
---|
1154 | static number nrzEucNorm (number a, const coeffs ) |
---|
1155 | { |
---|
1156 | if (n_Z_IS_SMALL(a)) |
---|
1157 | { |
---|
1158 | long aa=ABS(SR_TO_INT(a)); |
---|
1159 | return INT_TO_SR(aa); |
---|
1160 | } |
---|
1161 | else |
---|
1162 | { |
---|
1163 | mpz_ptr abs = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
1164 | mpz_init(abs); |
---|
1165 | mpz_abs(abs, (mpz_ptr)a); |
---|
1166 | nrzTest((number)abs); |
---|
1167 | return (number) abs; |
---|
1168 | } |
---|
1169 | } |
---|
1170 | |
---|
1171 | static coeffs nrzQuot1(number c, const coeffs r) |
---|
1172 | { |
---|
1173 | mpz_t dummy; |
---|
1174 | if(n_Z_IS_SMALL(c)) |
---|
1175 | { |
---|
1176 | long ch = r->cfInt(c, r); |
---|
1177 | mpz_init_set_ui(dummy, ch); |
---|
1178 | } |
---|
1179 | else |
---|
1180 | { |
---|
1181 | mpz_init_set(dummy, (mpz_ptr)c); |
---|
1182 | } |
---|
1183 | ZnmInfo info; |
---|
1184 | info.base = dummy; |
---|
1185 | info.exp = (unsigned long) 1; |
---|
1186 | coeffs rr = nInitChar(n_Zn, (void*)&info); |
---|
1187 | mpz_clear(dummy); |
---|
1188 | return(rr); |
---|
1189 | } |
---|
1190 | |
---|
1191 | number nlReadFd(const ssiInfo *d, const coeffs); |
---|
1192 | void nlWriteFd(number n, const ssiInfo* d, const coeffs); |
---|
1193 | |
---|
1194 | BOOLEAN nrzInitChar(coeffs r, void *) |
---|
1195 | { |
---|
1196 | assume( getCoeffType(r) == n_Z ); |
---|
1197 | |
---|
1198 | r->is_field=FALSE; |
---|
1199 | r->is_domain=TRUE; |
---|
1200 | r->rep=n_rep_gap_gmp; |
---|
1201 | |
---|
1202 | //r->nCoeffIsEqual = ndCoeffIsEqual; |
---|
1203 | r->cfCoeffName = nrzCoeffName; |
---|
1204 | //r->cfKillChar = ndKillChar; |
---|
1205 | r->cfMult = nrzMult; |
---|
1206 | r->cfSub = nrzSub; |
---|
1207 | r->cfAdd = nrzAdd; |
---|
1208 | r->cfDiv = nrzDiv; |
---|
1209 | r->cfIntMod= nrzIntMod; |
---|
1210 | r->cfExactDiv= nrzExactDiv; |
---|
1211 | r->cfInit = nrzInit; |
---|
1212 | r->cfInitMPZ = nrzInitMPZ; |
---|
1213 | r->cfSize = nrzSize; |
---|
1214 | r->cfInt = nrzInt; |
---|
1215 | //#ifdef HAVE_RINGS |
---|
1216 | r->cfDivComp = nrzDivComp; // only for ring stuff |
---|
1217 | r->cfIsUnit = nrzIsUnit; // only for ring stuff |
---|
1218 | r->cfGetUnit = nrzGetUnit; // only for ring stuff |
---|
1219 | r->cfAnn = nrzAnn; |
---|
1220 | r->cfExtGcd = nrzExtGcd; // only for ring stuff |
---|
1221 | r->cfXExtGcd = nrzXExtGcd; // only for ring stuff |
---|
1222 | r->cfEucNorm = nrzEucNorm; |
---|
1223 | r->cfQuotRem = nrzQuotRem; |
---|
1224 | r->cfDivBy = nrzDivBy; // only for ring stuff |
---|
1225 | //#endif |
---|
1226 | r->cfInpNeg = nrzNeg; |
---|
1227 | r->cfInvers= nrzInvers; |
---|
1228 | r->cfCopy = nrzCopy; |
---|
1229 | r->cfWriteLong = nrzWrite; |
---|
1230 | r->cfRead = nrzRead; |
---|
1231 | r->cfGreater = nrzGreater; |
---|
1232 | r->cfEqual = nrzEqual; |
---|
1233 | r->cfIsZero = nrzIsZero; |
---|
1234 | r->cfIsOne = nrzIsOne; |
---|
1235 | r->cfIsMOne = nrzIsMOne; |
---|
1236 | r->cfGreaterZero = nrzGreaterZero; |
---|
1237 | r->cfPower = nrzPower; |
---|
1238 | r->cfGcd = nrzGcd; |
---|
1239 | r->cfLcm = nrzLcm; |
---|
1240 | r->cfDelete= nrzDelete; |
---|
1241 | r->cfSetMap = nrzSetMap; |
---|
1242 | r->convSingNFactoryN = nrzConvSingNFactoryN; |
---|
1243 | r->convFactoryNSingN = nrzConvFactoryNSingN; |
---|
1244 | r->cfMPZ = nrzMPZ; |
---|
1245 | r->cfFarey = nrzFarey; |
---|
1246 | r->cfWriteFd=nlWriteFd; |
---|
1247 | r->cfReadFd=nlReadFd; |
---|
1248 | |
---|
1249 | r->cfQuot1 = nrzQuot1; |
---|
1250 | // requires conversion to factory: |
---|
1251 | r->cfChineseRemainder=nlChineseRemainderSym; |
---|
1252 | // debug stuff |
---|
1253 | |
---|
1254 | #ifdef LDEBUG |
---|
1255 | r->cfDBTest=nrzDBTest; |
---|
1256 | #endif |
---|
1257 | |
---|
1258 | r->ch = 0; |
---|
1259 | r->has_simple_Alloc=FALSE; |
---|
1260 | r->has_simple_Inverse=FALSE; |
---|
1261 | return FALSE; |
---|
1262 | } |
---|
1263 | #endif |
---|
1264 | #endif |
---|