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 n |
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6 | */ |
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7 | #ifdef HAVE_CONFIG_H |
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8 | #include "libpolysconfig.h" |
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9 | #endif /* HAVE_CONFIG_H */ |
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10 | #include <misc/auxiliary.h> |
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11 | |
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12 | #ifdef HAVE_RINGS |
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13 | |
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14 | #include <string.h> |
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15 | #include <misc/mylimits.h> |
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16 | #include <coeffs/coeffs.h> |
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17 | #include <reporter/reporter.h> |
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18 | #include <omalloc/omalloc.h> |
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19 | #include <coeffs/numbers.h> |
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20 | #include <coeffs/longrat.h> |
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21 | #include <coeffs/mpr_complex.h> |
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22 | #include <coeffs/rintegers.h> |
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23 | #include "si_gmp.h" |
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24 | |
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25 | /// Our Type! |
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26 | static const n_coeffType ID = n_Z; |
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27 | |
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28 | omBin gmp_nrz_bin = omGetSpecBin(sizeof(mpz_t)); |
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29 | |
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30 | /* |
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31 | * Multiply two numbers |
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32 | */ |
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33 | number nrzMult (number a, number b, const coeffs) |
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34 | { |
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35 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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36 | mpz_init(erg); |
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37 | mpz_mul(erg, (int_number) a, (int_number) b); |
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38 | return (number) erg; |
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39 | } |
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40 | |
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41 | /* |
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42 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
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43 | */ |
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44 | number nrzLcm (number a,number b,const coeffs) |
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45 | { |
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46 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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47 | mpz_init(erg); |
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48 | mpz_lcm(erg, (int_number) a, (int_number) b); |
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49 | return (number) erg; |
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50 | } |
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51 | |
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52 | /* |
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53 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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54 | * a solution. |
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55 | */ |
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56 | number nrzGcd (number a,number b,const coeffs) |
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57 | { |
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58 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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59 | mpz_init(erg); |
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60 | mpz_gcd(erg, (int_number) a, (int_number) b); |
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61 | return (number) erg; |
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62 | } |
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63 | |
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64 | /* |
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65 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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66 | * a solution and r, s, s.t. k = s*a + t*b |
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67 | */ |
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68 | number nrzExtGcd (number a, number b, number *s, number *t, const coeffs) |
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69 | { |
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70 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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71 | int_number bs = (int_number) omAllocBin(gmp_nrz_bin); |
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72 | int_number bt = (int_number) omAllocBin(gmp_nrz_bin); |
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73 | mpz_init(erg); |
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74 | mpz_init(bs); |
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75 | mpz_init(bt); |
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76 | mpz_gcdext(erg, bs, bt, (int_number) a, (int_number) b); |
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77 | *s = (number) bs; |
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78 | *t = (number) bt; |
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79 | return (number) erg; |
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80 | } |
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81 | |
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82 | void nrzPower (number a, int i, number * result, const coeffs) |
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83 | { |
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84 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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85 | mpz_init(erg); |
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86 | mpz_pow_ui(erg, (int_number) a, i); |
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87 | *result = (number) erg; |
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88 | } |
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89 | |
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90 | /* |
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91 | * create a number from int |
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92 | */ |
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93 | number nrzInit (long i, const coeffs) |
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94 | { |
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95 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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96 | mpz_init_set_si(erg, i); |
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97 | return (number) erg; |
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98 | } |
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99 | |
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100 | void nrzDelete(number *a, const coeffs) |
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101 | { |
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102 | if (*a == NULL) return; |
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103 | mpz_clear((int_number) *a); |
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104 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
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105 | *a = NULL; |
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106 | } |
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107 | |
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108 | number nrzCopy(number a, const coeffs) |
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109 | { |
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110 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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111 | mpz_init_set(erg, (int_number) a); |
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112 | return (number) erg; |
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113 | } |
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114 | |
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115 | #if 0 |
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116 | number nrzCopyMap(number a, const coeffs /*src*/, const coeffs dst) |
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117 | { |
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118 | return nrzCopy(a,dst); |
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119 | } |
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120 | #endif |
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121 | |
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122 | int nrzSize(number a, const coeffs) |
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123 | { |
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124 | if (a == NULL) return 0; |
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125 | return sizeof(mpz_t); |
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126 | } |
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127 | |
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128 | /* |
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129 | * convert a number to int |
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130 | */ |
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131 | int nrzInt(number &n, const coeffs) |
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132 | { |
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133 | return (int) mpz_get_si( (int_number)n); |
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134 | } |
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135 | |
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136 | number nrzAdd (number a, number b, const coeffs) |
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137 | { |
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138 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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139 | mpz_init(erg); |
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140 | mpz_add(erg, (int_number) a, (int_number) b); |
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141 | return (number) erg; |
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142 | } |
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143 | |
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144 | number nrzSub (number a, number b, const coeffs) |
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145 | { |
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146 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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147 | mpz_init(erg); |
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148 | mpz_sub(erg, (int_number) a, (int_number) b); |
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149 | return (number) erg; |
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150 | } |
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151 | |
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152 | number nrzGetUnit (number, const coeffs r) |
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153 | { |
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154 | return nrzInit(1, r); |
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155 | } |
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156 | |
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157 | BOOLEAN nrzIsUnit (number a, const coeffs) |
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158 | { |
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159 | return 0 == mpz_cmpabs_ui((int_number) a, 1); |
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160 | } |
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161 | |
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162 | BOOLEAN nrzIsZero (number a, const coeffs) |
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163 | { |
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164 | return 0 == mpz_cmpabs_ui((int_number) a, 0); |
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165 | } |
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166 | |
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167 | BOOLEAN nrzIsOne (number a, const coeffs) |
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168 | { |
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169 | return (a!=NULL) && (0 == mpz_cmp_si((int_number) a, 1)); |
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170 | } |
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171 | |
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172 | BOOLEAN nrzIsMOne (number a, const coeffs) |
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173 | { |
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174 | return (a!=NULL) && (0 == mpz_cmp_si((int_number) a, -1)); |
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175 | } |
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176 | |
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177 | BOOLEAN nrzEqual (number a,number b, const coeffs) |
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178 | { |
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179 | return 0 == mpz_cmp((int_number) a, (int_number) b); |
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180 | } |
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181 | |
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182 | BOOLEAN nrzGreater (number a,number b, const coeffs) |
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183 | { |
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184 | return 0 < mpz_cmp((int_number) a, (int_number) b); |
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185 | } |
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186 | |
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187 | BOOLEAN nrzGreaterZero (number k, const coeffs) |
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188 | { |
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189 | return 0 < mpz_cmp_si((int_number) k, 0); |
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190 | } |
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191 | |
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192 | int nrzDivComp(number a, number b, const coeffs r) |
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193 | { |
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194 | if (nrzDivBy(a, b, r)) |
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195 | { |
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196 | if (nrzDivBy(b, a, r)) return 2; |
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197 | return -1; |
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198 | } |
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199 | if (nrzDivBy(b, a, r)) return 1; |
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200 | return 0; |
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201 | } |
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202 | |
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203 | BOOLEAN nrzDivBy (number a,number b, const coeffs) |
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204 | { |
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205 | return mpz_divisible_p((int_number) a, (int_number) b) != 0; |
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206 | } |
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207 | |
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208 | number nrzDiv (number a,number b, const coeffs R) |
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209 | { |
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210 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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211 | mpz_init(erg); |
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212 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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213 | mpz_init(r); |
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214 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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215 | if (!nrzIsZero((number) r, R)) |
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216 | { |
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217 | WerrorS("Division by non divisible element."); |
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218 | WerrorS("Result is without remainder."); |
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219 | } |
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220 | mpz_clear(r); |
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221 | omFreeBin(r, gmp_nrz_bin); |
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222 | return (number) erg; |
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223 | } |
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224 | |
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225 | number nrzIntDiv (number a,number b, const coeffs) |
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226 | { |
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227 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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228 | mpz_init(erg); |
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229 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
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230 | return (number) erg; |
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231 | } |
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232 | |
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233 | number nrzIntMod (number a,number b, const coeffs) |
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234 | { |
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235 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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236 | mpz_init(erg); |
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237 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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238 | mpz_init(r); |
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239 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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240 | mpz_clear(erg); |
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241 | return (number) r; |
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242 | } |
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243 | |
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244 | number nrzInvers (number c, const coeffs r) |
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245 | { |
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246 | if (!nrzIsUnit((number) c, r)) |
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247 | { |
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248 | WerrorS("Non invertible element."); |
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249 | return (number)0; //TODO |
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250 | } |
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251 | return nrzCopy(c,r); |
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252 | } |
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253 | |
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254 | number nrzNeg (number c, const coeffs) |
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255 | { |
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256 | // nNeg inplace !!! |
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257 | mpz_mul_si((int_number) c, (int_number) c, -1); |
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258 | return c; |
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259 | } |
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260 | |
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261 | number nrzMapMachineInt(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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262 | { |
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263 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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264 | mpz_init_set_ui(erg, (NATNUMBER) from); |
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265 | return (number) erg; |
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266 | } |
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267 | |
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268 | number nrzMapZp(number from, const coeffs /*src*/, const coeffs /*dst*/) |
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269 | { |
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270 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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271 | mpz_init_set_si(erg, (long) from); |
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272 | return (number) erg; |
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273 | } |
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274 | |
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275 | number nrzMapQ(number from, const coeffs src, const coeffs /*dst*/) |
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276 | { |
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277 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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278 | mpz_init(erg); |
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279 | nlGMP(from, (number) erg, src); |
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280 | return (number) erg; |
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281 | } |
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282 | |
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283 | nMapFunc nrzSetMap(const coeffs src, const coeffs /*dst*/) |
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284 | { |
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285 | /* dst = currRing */ |
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286 | if (nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_ModN(src) || nCoeff_is_Ring_PtoM(src)) |
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287 | { |
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288 | return ndCopyMap; //nrzCopyMap; |
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289 | } |
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290 | if (nCoeff_is_Ring_2toM(src)) |
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291 | { |
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292 | return nrzMapMachineInt; |
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293 | } |
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294 | if (nCoeff_is_Zp(src)) |
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295 | { |
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296 | return nrzMapZp; |
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297 | } |
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298 | if (nCoeff_is_Q(src)) |
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299 | { |
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300 | return nrzMapQ; |
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301 | } |
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302 | return NULL; // default |
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303 | } |
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304 | |
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305 | |
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306 | /* |
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307 | * set the exponent (allocate and init tables) (TODO) |
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308 | */ |
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309 | |
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310 | void nrzSetExp(int, coeffs) |
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311 | { |
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312 | } |
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313 | |
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314 | void nrzInitExp(int, coeffs) |
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315 | { |
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316 | } |
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317 | |
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318 | #ifdef LDEBUG |
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319 | BOOLEAN nrzDBTest (number, const char *, const int, const coeffs) |
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320 | { |
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321 | return TRUE;//TODO |
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322 | } |
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323 | #endif |
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324 | |
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325 | void nrzWrite (number &a, const coeffs) |
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326 | { |
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327 | char *s,*z; |
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328 | if (a==NULL) |
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329 | { |
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330 | StringAppendS("o"); |
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331 | } |
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332 | else |
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333 | { |
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334 | int l=mpz_sizeinbase((int_number) a, 10) + 2; |
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335 | s=(char*)omAlloc(l); |
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336 | z=mpz_get_str(s,10,(int_number) a); |
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337 | StringAppendS(z); |
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338 | omFreeSize((ADDRESS)s,l); |
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339 | } |
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340 | } |
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341 | |
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342 | /*2 |
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343 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
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344 | */ |
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345 | static const char * nlEatLongC(char *s, mpz_ptr i) |
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346 | { |
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347 | const char * start=s; |
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348 | |
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349 | if (*s<'0' || *s>'9') |
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350 | { |
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351 | mpz_set_si(i,1); |
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352 | return s; |
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353 | } |
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354 | while (*s >= '0' && *s <= '9') s++; |
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355 | if (*s=='\0') |
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356 | { |
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357 | mpz_set_str(i,start,10); |
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358 | } |
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359 | else |
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360 | { |
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361 | char c=*s; |
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362 | *s='\0'; |
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363 | mpz_set_str(i,start,10); |
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364 | *s=c; |
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365 | } |
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366 | return s; |
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367 | } |
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368 | |
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369 | const char * nrzRead (const char *s, number *a, const coeffs) |
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370 | { |
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371 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
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372 | { |
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373 | mpz_init(z); |
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374 | s = nlEatLongC((char *) s, z); |
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375 | } |
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376 | *a = (number) z; |
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377 | return s; |
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378 | } |
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379 | |
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380 | void nrzCoeffWrite (const coeffs, BOOLEAN /*details*/) |
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381 | { |
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382 | PrintS("// coeff. ring is : Integers\n"); |
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383 | } |
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384 | |
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385 | |
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386 | BOOLEAN nrzInitChar(coeffs r, void *) |
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387 | { |
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388 | assume( getCoeffType(r) == ID ); |
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389 | r->nCoeffIsEqual = ndCoeffIsEqual; |
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390 | r->cfKillChar = ndKillChar; |
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391 | r->cfMult = nrzMult; |
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392 | r->cfSub = nrzSub; |
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393 | r->cfAdd = nrzAdd; |
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394 | r->cfDiv = nrzDiv; |
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395 | r->cfIntDiv= nrzDiv; |
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396 | r->cfIntMod= nrzIntMod; |
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397 | r->cfExactDiv= nrzDiv; |
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398 | r->cfInit = nrzInit; |
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399 | r->cfSize = nrzSize; |
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400 | r->cfInt = nrzInt; |
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401 | //#ifdef HAVE_RINGS |
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402 | r->cfDivComp = nrzDivComp; // only for ring stuff |
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403 | r->cfIsUnit = nrzIsUnit; // only for ring stuff |
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404 | r->cfGetUnit = nrzGetUnit; // only for ring stuff |
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405 | r->cfExtGcd = nrzExtGcd; // only for ring stuff |
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406 | r->cfDivBy = nrzDivBy; // only for ring stuff |
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407 | r->cfInit_bigint = nrzMapQ; |
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408 | //#endif |
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409 | r->cfNeg = nrzNeg; |
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410 | r->cfInvers= nrzInvers; |
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411 | r->cfCopy = nrzCopy; |
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412 | r->cfWriteLong = nrzWrite; |
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413 | r->cfRead = nrzRead; |
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414 | r->cfGreater = nrzGreater; |
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415 | r->cfEqual = nrzEqual; |
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416 | r->cfIsZero = nrzIsZero; |
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417 | r->cfIsOne = nrzIsOne; |
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418 | r->cfIsMOne = nrzIsMOne; |
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419 | r->cfGreaterZero = nrzGreaterZero; |
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420 | r->cfPower = nrzPower; |
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421 | r->cfGcd = nrzGcd; |
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422 | r->cfLcm = nrzLcm; |
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423 | r->cfDelete= nrzDelete; |
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424 | r->cfSetMap = nrzSetMap; |
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425 | r->cfCoeffWrite = nrzCoeffWrite; |
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426 | // debug stuff |
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427 | |
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428 | #ifdef LDEBUG |
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429 | r->cfDBTest=nrzDBTest; |
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430 | #endif |
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431 | |
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432 | r->nNULL = 0; |
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433 | r->ch = 0; |
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434 | r->has_simple_Alloc=FALSE; |
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435 | r->has_simple_Inverse=FALSE; |
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436 | return FALSE; |
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437 | } |
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438 | |
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439 | #endif |
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