1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT: numbers modulo n |
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7 | */ |
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8 | |
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9 | #include <string.h> |
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10 | #include "mod2.h" |
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11 | #include <mylimits.h> |
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12 | #include "structs.h" |
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13 | #include "febase.h" |
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14 | #include "omalloc.h" |
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15 | #include "numbers.h" |
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16 | #include "longrat.h" |
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17 | #include "mpr_complex.h" |
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18 | #include "ring.h" |
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19 | #include "rintegers.h" |
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20 | #include "si_gmp.h" |
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21 | |
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22 | #ifdef HAVE_RINGS |
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23 | |
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24 | omBin gmp_nrz_bin = omGetSpecBin(sizeof(MP_INT)); |
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25 | |
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26 | /* |
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27 | * Multiply two numbers |
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28 | */ |
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29 | number nrzMult (number a, number b) |
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30 | { |
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31 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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32 | mpz_init(erg); |
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33 | mpz_mul(erg, (int_number) a, (int_number) b); |
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34 | return (number) erg; |
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35 | } |
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36 | |
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37 | /* |
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38 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
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39 | */ |
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40 | number nrzLcm (number a,number b,ring r) |
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41 | { |
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42 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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43 | mpz_init(erg); |
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44 | mpz_lcm(erg, (int_number) a, (int_number) b); |
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45 | return (number) erg; |
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46 | } |
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47 | |
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48 | /* |
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49 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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50 | * a solution. |
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51 | */ |
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52 | number nrzGcd (number a,number b,ring r) |
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53 | { |
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54 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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55 | mpz_init(erg); |
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56 | mpz_gcd(erg, (int_number) a, (int_number) b); |
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57 | return (number) erg; |
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58 | } |
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59 | |
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60 | /* |
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61 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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62 | * a solution and r, s, s.t. k = s*a + t*b |
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63 | */ |
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64 | number nrzExtGcd (number a, number b, number *s, number *t) |
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65 | { |
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66 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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67 | int_number bs = (int_number) omAllocBin(gmp_nrz_bin); |
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68 | int_number bt = (int_number) omAllocBin(gmp_nrz_bin); |
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69 | mpz_init(erg); |
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70 | mpz_init(bs); |
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71 | mpz_init(bt); |
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72 | mpz_gcdext(erg, bs, bt, (int_number) a, (int_number) b); |
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73 | *s = (number) bs; |
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74 | *t = (number) bt; |
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75 | return (number) erg; |
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76 | } |
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77 | |
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78 | void nrzPower (number a, int i, number * result) |
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79 | { |
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80 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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81 | mpz_init(erg); |
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82 | mpz_pow_ui(erg, (int_number) a, i); |
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83 | *result = (number) erg; |
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84 | } |
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85 | |
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86 | /* |
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87 | * create a number from int |
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88 | */ |
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89 | number nrzInit (int i, const ring r) |
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90 | { |
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91 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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92 | mpz_init_set_si(erg, i); |
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93 | return (number) erg; |
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94 | } |
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95 | |
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96 | void nrzDelete(number *a, const ring r) |
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97 | { |
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98 | if (*a == NULL) return; |
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99 | mpz_clear((int_number) *a); |
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100 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
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101 | *a = NULL; |
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102 | } |
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103 | |
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104 | number nrzCopy(number a) |
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105 | { |
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106 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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107 | mpz_init_set(erg, (int_number) a); |
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108 | return (number) erg; |
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109 | } |
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110 | |
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111 | number cfrzCopy(number a, const ring r) |
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112 | { |
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113 | return nrzCopy(a); |
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114 | } |
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115 | |
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116 | int nrzSize(number a) |
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117 | { |
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118 | if (a == NULL) return 0; |
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119 | return sizeof(MP_INT); |
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120 | } |
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121 | |
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122 | /* |
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123 | * convert a number to int |
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124 | */ |
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125 | int nrzInt(number &n, const ring r) |
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126 | { |
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127 | return (int) mpz_get_si( (int_number)n); |
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128 | } |
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129 | |
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130 | number nrzAdd (number a, number b) |
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131 | { |
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132 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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133 | mpz_init(erg); |
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134 | mpz_add(erg, (int_number) a, (int_number) b); |
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135 | return (number) erg; |
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136 | } |
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137 | |
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138 | number nrzSub (number a, number b) |
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139 | { |
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140 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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141 | mpz_init(erg); |
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142 | mpz_sub(erg, (int_number) a, (int_number) b); |
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143 | return (number) erg; |
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144 | } |
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145 | |
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146 | number nrzGetUnit (number a) |
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147 | { |
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148 | return nrzInit(1, currRing); |
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149 | } |
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150 | |
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151 | BOOLEAN nrzIsUnit (number a) |
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152 | { |
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153 | return 0 == mpz_cmpabs_ui((int_number) a, 1); |
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154 | } |
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155 | |
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156 | BOOLEAN nrzIsZero (number a) |
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157 | { |
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158 | return 0 == mpz_cmpabs_ui((int_number) a, 0); |
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159 | } |
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160 | |
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161 | BOOLEAN nrzIsOne (number a) |
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162 | { |
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163 | return 0 == mpz_cmp_si((int_number) a, 1); |
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164 | } |
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165 | |
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166 | BOOLEAN nrzIsMOne (number a) |
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167 | { |
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168 | return 0 == mpz_cmp_si((int_number) a, -1); |
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169 | } |
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170 | |
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171 | BOOLEAN nrzEqual (number a,number b) |
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172 | { |
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173 | return 0 == mpz_cmp((int_number) a, (int_number) b); |
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174 | } |
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175 | |
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176 | BOOLEAN nrzGreater (number a,number b) |
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177 | { |
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178 | return 0 < mpz_cmp((int_number) a, (int_number) b); |
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179 | } |
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180 | |
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181 | BOOLEAN nrzGreaterZero (number k) |
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182 | { |
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183 | return 0 < mpz_cmp_si((int_number) k, 0); |
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184 | } |
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185 | |
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186 | int nrzDivComp(number a, number b) |
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187 | { |
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188 | if (nrzEqual(a, b)) return 0; |
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189 | if (nrzDivBy(a, b)) return -1; |
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190 | if (nrzDivBy(b, a)) return 1; |
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191 | return 2; |
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192 | } |
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193 | |
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194 | BOOLEAN nrzDivBy (number a,number b) |
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195 | { |
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196 | return mpz_divisible_p((int_number) a, (int_number) b) != 0; |
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197 | } |
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198 | |
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199 | number nrzDiv (number a,number b) |
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200 | { |
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201 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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202 | mpz_init(erg); |
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203 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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204 | mpz_init(r); |
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205 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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206 | if (!nrzIsZero((number) r)) |
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207 | { |
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208 | WerrorS("Division by non divisible element."); |
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209 | WerrorS("Result is without remainder."); |
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210 | } |
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211 | mpz_clear(r); |
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212 | omFreeBin(r, gmp_nrz_bin); |
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213 | return (number) erg; |
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214 | } |
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215 | |
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216 | number nrzIntDiv (number a,number b) |
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217 | { |
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218 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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219 | mpz_init(erg); |
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220 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
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221 | return (number) erg; |
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222 | } |
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223 | |
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224 | number nrzIntMod (number a,number b) |
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225 | { |
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226 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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227 | mpz_init(erg); |
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228 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); |
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229 | mpz_init(r); |
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230 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
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231 | mpz_clear(erg); |
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232 | return (number) r; |
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233 | } |
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234 | |
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235 | number nrzInvers (number c) |
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236 | { |
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237 | if (!nrzIsUnit((number) c)) |
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238 | { |
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239 | WerrorS("Non invertible element."); |
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240 | return (number)0; //TODO |
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241 | } |
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242 | return nrzCopy(c); |
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243 | } |
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244 | |
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245 | number nrzNeg (number c) |
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246 | { |
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247 | // nNeg inplace !!! |
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248 | mpz_mul_si((int_number) c, (int_number) c, -1); |
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249 | return c; |
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250 | } |
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251 | |
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252 | number nrzMapMachineInt(number from) |
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253 | { |
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254 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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255 | mpz_init_set_ui(erg, (NATNUMBER) from); |
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256 | return (number) erg; |
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257 | } |
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258 | |
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259 | number nrzMapZp(number from) |
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260 | { |
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261 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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262 | mpz_init_set_si(erg, (long) from); |
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263 | return (number) erg; |
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264 | } |
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265 | |
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266 | number nrzMapQ(number from) |
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267 | { |
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268 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); |
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269 | mpz_init(erg); |
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270 | nlGMP(from, (number) erg); |
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271 | return (number) erg; |
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272 | } |
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273 | |
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274 | nMapFunc nrzSetMap(const ring src, const ring dst) |
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275 | { |
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276 | /* dst = currRing */ |
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277 | if (rField_is_Ring_Z(src) || rField_is_Ring_ModN(src) || rField_is_Ring_PtoM(src)) |
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278 | { |
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279 | return nrzCopy; |
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280 | } |
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281 | if (rField_is_Ring_2toM(src)) |
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282 | { |
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283 | return nrzMapMachineInt; |
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284 | } |
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285 | if (rField_is_Zp(src)) |
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286 | { |
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287 | return nrzMapZp; |
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288 | } |
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289 | if (rField_is_Q(src)) |
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290 | { |
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291 | return nrzMapQ; |
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292 | } |
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293 | return NULL; // default |
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294 | } |
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295 | |
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296 | |
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297 | /* |
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298 | * set the exponent (allocate and init tables) (TODO) |
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299 | */ |
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300 | |
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301 | void nrzSetExp(int m, ring r) |
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302 | { |
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303 | } |
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304 | |
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305 | void nrzInitExp(int m, ring r) |
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306 | { |
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307 | } |
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308 | |
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309 | #ifdef LDEBUG |
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310 | //BOOLEAN nrzDBTest (number a, const char *f, const int l) |
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311 | //{ |
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312 | // return TRUE;//TODO |
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313 | //} |
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314 | #endif |
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315 | |
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316 | void nrzWrite (number &a, const ring r) |
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317 | { |
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318 | char *s,*z; |
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319 | if (a==NULL) |
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320 | { |
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321 | StringAppendS("o"); |
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322 | } |
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323 | else |
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324 | { |
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325 | int l=mpz_sizeinbase((int_number) a, 10) + 2; |
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326 | s=(char*)omAlloc(l); |
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327 | z=mpz_get_str(s,10,(int_number) a); |
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328 | StringAppendS(z); |
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329 | omFreeSize((ADDRESS)s,l); |
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330 | } |
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331 | } |
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332 | |
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333 | /*2 |
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334 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
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335 | */ |
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336 | static const char * nlEatLongC(char *s, MP_INT *i) |
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337 | { |
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338 | const char * start=s; |
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339 | |
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340 | if (*s<'0' || *s>'9') |
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341 | { |
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342 | mpz_set_si(i,1); |
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343 | return s; |
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344 | } |
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345 | while (*s >= '0' && *s <= '9') s++; |
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346 | if (*s=='\0') |
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347 | { |
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348 | mpz_set_str(i,start,10); |
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349 | } |
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350 | else |
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351 | { |
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352 | char c=*s; |
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353 | *s='\0'; |
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354 | mpz_set_str(i,start,10); |
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355 | *s=c; |
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356 | } |
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357 | return s; |
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358 | } |
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359 | |
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360 | const char * nrzRead (const char *s, number *a) |
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361 | { |
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362 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); |
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363 | { |
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364 | mpz_init(z); |
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365 | s = nlEatLongC((char *) s, z); |
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366 | } |
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367 | *a = (number) z; |
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368 | return s; |
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369 | } |
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370 | #endif |
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