1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | /* $Id: int_rat.cc,v 1.12 1999-09-24 08:43:29 Singular Exp $ */ |
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3 | |
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4 | #include <config.h> |
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5 | |
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6 | #include "assert.h" |
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7 | |
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8 | #include "cf_defs.h" |
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9 | #include "int_rat.h" |
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10 | #include "int_int.h" |
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11 | #include "imm.h" |
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12 | #include "canonicalform.h" |
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13 | #include "cf_factory.h" |
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14 | #include "gmpext.h" |
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15 | |
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16 | static int intgcd( int a, int b ) |
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17 | { |
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18 | if ( a < 0 ) a = -a; |
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19 | if ( b < 0 ) b = -b; |
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20 | |
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21 | int c; |
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22 | |
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23 | while ( b != 0 ) { |
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24 | c = a % b; |
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25 | a = b; |
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26 | b = c; |
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27 | } |
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28 | return a; |
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29 | } |
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30 | |
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31 | |
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32 | InternalRational::InternalRational() |
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33 | { |
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34 | mpz_init( &_num ); |
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35 | mpz_init_set_si( &_den, 1 ); |
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36 | } |
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37 | |
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38 | InternalRational::InternalRational( const int i ) |
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39 | { |
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40 | mpz_init_set_si( &_num, i ); |
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41 | mpz_init_set_si( &_den, 1 ); |
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42 | } |
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43 | |
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44 | InternalRational::InternalRational( const int n, const int d ) |
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45 | { |
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46 | ASSERT( d != 0, "divide by zero" ); |
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47 | if ( n == 0 ) { |
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48 | mpz_init_set_si( &_num, 0 ); |
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49 | mpz_init_set_si( &_den, 1 ); |
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50 | } |
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51 | else { |
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52 | int g = intgcd( n, d ); |
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53 | if ( d < 0 ) { |
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54 | mpz_init_set_si( &_num, -n / g ); |
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55 | mpz_init_set_si( &_den, -d / g ); |
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56 | } |
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57 | else { |
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58 | mpz_init_set_si( &_num, n / g ); |
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59 | mpz_init_set_si( &_den, d / g ); |
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60 | } |
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61 | } |
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62 | } |
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63 | |
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64 | InternalRational::InternalRational( const char * ) |
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65 | { |
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66 | // sollte nicht gebraucht werden !!! |
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67 | ASSERT( 0, "fatal error" ); |
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68 | mpz_init( &_num ); |
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69 | mpz_init( &_den ); |
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70 | } |
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71 | |
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72 | InternalRational::InternalRational( const MP_INT &n ) : _num(n) |
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73 | { |
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74 | mpz_init_set_si( &_den, 1 ); |
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75 | } |
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76 | |
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77 | InternalRational::InternalRational( const MP_INT &n, const MP_INT &d ) : _num(n), _den(d) |
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78 | { |
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79 | } |
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80 | |
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81 | InternalRational::~InternalRational() |
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82 | { |
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83 | mpz_clear( &_num ); |
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84 | mpz_clear( &_den ); |
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85 | } |
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86 | |
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87 | InternalCF* InternalRational::deepCopyObject() const |
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88 | { |
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89 | MP_INT dummy_num; |
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90 | MP_INT dummy_den; |
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91 | mpz_init_set( &dummy_num, &_num ); |
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92 | mpz_init_set( &dummy_den, &_den ); |
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93 | return new InternalRational( dummy_num, dummy_den ); |
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94 | } |
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95 | |
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96 | #ifndef NOSTREAMIO |
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97 | void InternalRational::print( ostream & os, char * c ) |
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98 | { |
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99 | char * str = new char[mpz_sizeinbase( &_num, 10 ) + 2]; |
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100 | str = mpz_get_str( str, 10, &_num ); |
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101 | os << str << '/'; |
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102 | delete [] str; |
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103 | str = new char[mpz_sizeinbase( &_den, 10 ) + 2]; |
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104 | str = mpz_get_str( str, 10, &_den ); |
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105 | os << str << c; |
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106 | delete [] str; |
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107 | } |
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108 | #endif /* NOSTREAMIO */ |
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109 | |
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110 | bool InternalRational::is_imm() const |
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111 | { |
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112 | return mpz_cmp_si( &_den, 1 ) == 0 && mpz_is_imm( &_num ); |
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113 | } |
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114 | |
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115 | InternalCF* InternalRational::genZero() |
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116 | { |
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117 | if ( isZero() ) |
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118 | return copyObject(); |
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119 | else |
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120 | return new InternalRational(); |
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121 | } |
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122 | |
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123 | InternalCF* InternalRational::genOne() |
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124 | { |
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125 | if ( isOne() ) |
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126 | return copyObject(); |
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127 | else |
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128 | return new InternalRational( 1 ); |
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129 | } |
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130 | |
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131 | //{{{ InternalCF * InternalRational::num (), den () |
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132 | // docu: see CanonicalForm::num(), den() |
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133 | InternalCF * InternalRational::num () |
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134 | { |
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135 | if ( mpz_is_imm( &_num ) ) { |
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136 | InternalCF * res = int2imm( mpz_get_si( &_num ) ); |
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137 | return res; |
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138 | } |
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139 | else { |
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140 | MP_INT dummy; |
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141 | mpz_init_set( &dummy, &_num ); |
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142 | return new InternalInteger( dummy ); |
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143 | } |
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144 | } |
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145 | |
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146 | InternalCF * InternalRational::den () |
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147 | { |
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148 | if ( mpz_is_imm( &_den ) ) { |
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149 | InternalCF * res = int2imm( mpz_get_si( &_den ) ); |
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150 | return res; |
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151 | } |
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152 | else { |
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153 | MP_INT dummy; |
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154 | mpz_init_set( &dummy, &_den ); |
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155 | return new InternalInteger( dummy ); |
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156 | } |
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157 | } |
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158 | //}}} |
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159 | |
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160 | //{{{ InternalCF * InternalRational::neg () |
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161 | // docu: see CanonicalForm::operator -() |
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162 | InternalCF * |
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163 | InternalRational::neg () |
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164 | { |
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165 | if ( getRefCount() > 1 ) { |
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166 | decRefCount(); |
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167 | MP_INT dummy_num; |
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168 | MP_INT dummy_den; |
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169 | mpz_init_set( &dummy_num, &_num ); |
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170 | mpz_init_set( &dummy_den, &_den ); |
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171 | mpz_neg( &dummy_num, &dummy_num ); |
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172 | return new InternalRational( dummy_num, dummy_den ); |
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173 | } else { |
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174 | mpz_neg( &_num, &_num ); |
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175 | return this; |
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176 | } |
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177 | } |
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178 | //}}} |
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179 | |
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180 | InternalCF* InternalRational::addsame( InternalCF * c ) |
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181 | { |
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182 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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183 | MP_INT n, d, g; |
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184 | |
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185 | mpz_init( &g ); mpz_init( &n ); mpz_init( &d ); |
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186 | mpz_gcd( &g, &_den, &MPQDEN( c ) ); |
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187 | |
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188 | if ( mpz_cmp_si( &g, 1 ) == 0 ) { |
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189 | mpz_mul( &n, &_den, &MPQNUM( c ) ); |
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190 | mpz_mul( &g, &_num, &MPQDEN( c ) ); |
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191 | mpz_add( &n, &n, &g ); |
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192 | mpz_mul( &d, &_den, &MPQDEN( c ) ); |
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193 | } |
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194 | else { |
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195 | MP_INT tmp1; |
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196 | MP_INT tmp2; |
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197 | mpz_init( &tmp1 ); |
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198 | mpz_div( &tmp1, &_den, &g ); |
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199 | mpz_init( &tmp2 ); |
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200 | mpz_div( &tmp2, &MPQDEN( c ), &g ); |
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201 | mpz_mul( &d, &tmp2, &_den ); |
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202 | mpz_mul( &tmp2, &tmp2, &_num ); |
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203 | mpz_mul( &tmp1, &tmp1, &MPQNUM( c ) ); |
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204 | mpz_add( &n, &tmp1, &tmp2 ); |
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205 | mpz_gcd( &g, &n, &d ); |
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206 | if ( mpz_cmp_si( &g, 1 ) != 0 ) { |
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207 | mpz_div( &n, &n, &g ); |
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208 | mpz_div( &d, &d, &g ); |
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209 | } |
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210 | mpz_clear( &tmp1 ); |
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211 | mpz_clear( &tmp2 ); |
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212 | } |
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213 | mpz_clear( &g ); |
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214 | if ( deleteObject() ) delete this; |
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215 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
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216 | if ( mpz_is_imm( &n ) ) { |
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217 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
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218 | mpz_clear( &n ); mpz_clear( &d ); |
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219 | return res; |
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220 | } |
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221 | else { |
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222 | mpz_clear( &d ); |
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223 | return new InternalInteger( n ); |
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224 | } |
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225 | } |
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226 | else |
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227 | return new InternalRational( n, d ); |
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228 | } |
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229 | |
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230 | InternalCF* InternalRational::subsame( InternalCF * c ) |
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231 | { |
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232 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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233 | MP_INT n, d, g; |
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234 | |
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235 | mpz_init( &g ); mpz_init( &n ); mpz_init( &d ); |
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236 | mpz_gcd( &g, &_den, &MPQDEN( c ) ); |
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237 | |
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238 | if ( mpz_cmp_si( &g, 1 ) == 0 ) { |
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239 | mpz_mul( &n, &_den, &MPQNUM( c ) ); |
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240 | mpz_mul( &g, &_num, &MPQDEN( c ) ); |
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241 | mpz_sub( &n, &g, &n ); |
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242 | mpz_mul( &d, &_den, &MPQDEN( c ) ); |
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243 | } |
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244 | else { |
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245 | MP_INT tmp1; |
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246 | MP_INT tmp2; |
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247 | mpz_init( &tmp1 ); |
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248 | mpz_div( &tmp1, &_den, &g ); |
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249 | mpz_init( &tmp2 ); |
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250 | mpz_div( &tmp2, &MPQDEN( c ), &g ); |
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251 | mpz_mul( &d, &tmp2, &_den ); |
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252 | mpz_mul( &tmp2, &tmp2, &_num ); |
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253 | mpz_mul( &tmp1, &tmp1, &MPQNUM( c ) ); |
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254 | mpz_sub( &n, &tmp2, &tmp1 ); |
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255 | mpz_gcd( &g, &n, &d ); |
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256 | if ( mpz_cmp_si( &g, 1 ) != 0 ) { |
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257 | mpz_div( &n, &n, &g ); |
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258 | mpz_div( &d, &d, &g ); |
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259 | } |
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260 | mpz_clear( &tmp1 ); |
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261 | mpz_clear( &tmp2 ); |
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262 | } |
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263 | mpz_clear( &g ); |
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264 | if ( deleteObject() ) delete this; |
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265 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
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266 | if ( mpz_is_imm( &n ) ) { |
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267 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
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268 | mpz_clear( &n ); mpz_clear( &d ); |
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269 | return res; |
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270 | } |
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271 | else { |
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272 | mpz_clear( &d ); |
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273 | return new InternalInteger( n ); |
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274 | } |
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275 | } |
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276 | else |
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277 | return new InternalRational( n, d ); |
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278 | } |
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279 | |
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280 | InternalCF* InternalRational::mulsame( InternalCF * c ) |
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281 | { |
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282 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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283 | MP_INT n, d; |
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284 | |
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285 | if ( this == c ) { |
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286 | mpz_init( &n ); mpz_init( &d ); |
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287 | mpz_mul( &n, &_num, &_num ); |
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288 | mpz_mul( &d, &_den, &_den ); |
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289 | } |
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290 | else { |
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291 | MP_INT g1, g2, tmp1, tmp2; |
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292 | mpz_init( &g1 ); mpz_init( &g2 ); |
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293 | mpz_init( &n ); mpz_init( &d ); |
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294 | mpz_gcd( &g1, &_num, &MPQDEN( c ) ); |
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295 | mpz_gcd( &g2, &_den, &MPQNUM( c ) ); |
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296 | bool g1is1 = mpz_cmp_si( &g1, 1 ) == 0; |
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297 | bool g2is1 = mpz_cmp_si( &g2, 1 ) == 0; |
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298 | mpz_init( &tmp1 ); mpz_init( &tmp2 ); |
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299 | if ( ! g1is1 ) |
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300 | mpz_div( &tmp1, &_num, &g1 ); |
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301 | else |
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302 | mpz_set( &tmp1, &_num ); |
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303 | if ( ! g2is1 ) |
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304 | mpz_div( &tmp2, &MPQNUM( c ), &g2 ); |
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305 | else |
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306 | mpz_set( &tmp2, &MPQNUM( c ) ); |
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307 | mpz_mul( &n, &tmp1, &tmp2 ); |
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308 | if ( ! g1is1 ) |
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309 | mpz_div( &tmp1, &MPQDEN( c ), &g1 ); |
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310 | else |
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311 | mpz_set( &tmp1, &MPQDEN( c ) ); |
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312 | if ( ! g2is1 ) |
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313 | mpz_div( &tmp2, &_den, &g2 ); |
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314 | else |
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315 | mpz_set( &tmp2, &_den ); |
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316 | mpz_mul( &d, &tmp1, &tmp2 ); |
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317 | mpz_clear( &tmp1 ); mpz_clear( &tmp2 ); |
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318 | mpz_clear( &g1 ); mpz_clear( &g2 ); |
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319 | } |
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320 | if ( deleteObject() ) delete this; |
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321 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
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322 | if ( mpz_is_imm( &n ) ) { |
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323 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
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324 | mpz_clear( &n ); mpz_clear( &d ); |
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325 | return res; |
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326 | } |
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327 | else { |
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328 | mpz_clear( &d ); |
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329 | return new InternalInteger( n ); |
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330 | } |
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331 | } |
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332 | else |
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333 | return new InternalRational( n, d ); |
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334 | } |
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335 | |
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336 | InternalCF* InternalRational::dividesame( InternalCF * c ) |
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337 | { |
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338 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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339 | |
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340 | if ( this == c ) { |
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341 | if ( deleteObject() ) delete this; |
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342 | return CFFactory::basic( 1 ); |
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343 | } |
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344 | else { |
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345 | MP_INT n, d; |
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346 | MP_INT g1, g2, tmp1, tmp2; |
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347 | mpz_init( &n ); mpz_init( &d ); |
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348 | mpz_init( &g1 ); mpz_init( &g2 ); |
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349 | mpz_gcd( &g1, &_num, &MPQNUM( c ) ); |
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350 | mpz_gcd( &g2, &_den, &MPQDEN( c ) ); |
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351 | bool g1is1 = mpz_cmp_si( &g1, 1 ) == 0; |
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352 | bool g2is1 = mpz_cmp_si( &g2, 1 ) == 0; |
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353 | mpz_init( &tmp1 ); mpz_init( &tmp2 ); |
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354 | if ( ! g1is1 ) |
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355 | mpz_div( &tmp1, &_num, &g1 ); |
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356 | else |
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357 | mpz_set( &tmp1, &_num ); |
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358 | if ( ! g2is1 ) |
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359 | mpz_div( &tmp2, &MPQDEN( c ), &g2 ); |
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360 | else |
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361 | mpz_set( &tmp2, &MPQDEN( c ) ); |
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362 | mpz_mul( &n, &tmp1, &tmp2 ); |
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363 | if ( ! g1is1 ) |
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364 | mpz_div( &tmp1, &MPQNUM( c ), &g1 ); |
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365 | else |
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366 | mpz_set( &tmp1, &MPQNUM( c ) ); |
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367 | if ( ! g2is1 ) |
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368 | mpz_div( &tmp2, &_den, &g2 ); |
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369 | else |
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370 | mpz_set( &tmp2, &_den ); |
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371 | mpz_mul( &d, &tmp1, &tmp2 ); |
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372 | mpz_clear( &tmp1 ); mpz_clear( &tmp2 ); |
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373 | mpz_clear( &g1 ); mpz_clear( &g2 ); |
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374 | if ( deleteObject() ) delete this; |
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375 | if ( mpz_cmp_si( &d, 0 ) < 0 ) { |
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376 | mpz_neg( &d, &d ); |
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377 | mpz_neg( &n, &n ); |
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378 | } |
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379 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
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380 | if ( mpz_is_imm( &n ) ) { |
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381 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
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382 | mpz_clear( &n ); mpz_clear( &d ); |
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383 | return res; |
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384 | } |
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385 | else { |
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386 | mpz_clear( &d ); |
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387 | return new InternalInteger( n ); |
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388 | } |
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389 | } |
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390 | else |
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391 | return new InternalRational( n, d ); |
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392 | } |
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393 | } |
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394 | |
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395 | InternalCF* InternalRational::divsame( InternalCF * c ) |
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396 | { |
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397 | return dividesame( c ); |
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398 | } |
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399 | |
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400 | InternalCF* InternalRational::modulosame( InternalCF * c ) |
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401 | { |
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402 | return modsame( c ); |
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403 | } |
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404 | |
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405 | InternalCF* InternalRational::modsame( InternalCF * ) |
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406 | { |
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407 | if ( deleteObject() ) delete this; |
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408 | return CFFactory::basic( 0 ); |
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409 | } |
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410 | |
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411 | void InternalRational::divremsame( InternalCF * c, InternalCF*& quot, InternalCF*& rem ) |
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412 | { |
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413 | quot = copyObject(); |
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414 | quot = quot->dividesame( c ); |
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415 | rem = CFFactory::basic( 0 ); |
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416 | } |
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417 | |
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418 | bool InternalRational::divremsamet( InternalCF* c, InternalCF*& quot, InternalCF*& rem ) |
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419 | { |
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420 | divremsame( c, quot, rem ); |
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421 | return true; |
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422 | } |
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423 | |
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424 | //{{{ int InternalRational::comparesame, comparecoeff ( InternalCF * c ) |
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425 | //{{{ docu |
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426 | // |
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427 | // comparesame(), comparecoeff() - compare with an |
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428 | // InternalRational. |
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429 | // |
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430 | // comparesame() compares the CO=a/b and c=p/q using the |
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431 | // equivalence a/b < p/q iff a*q < p*b. |
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432 | // |
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433 | // comparecoeff() compares the CO=a/b and the integer c using the |
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434 | // equivalence a/b < c iff a < c*b. |
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435 | // |
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436 | // Note: Both operations may be relatively expensive due to the |
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437 | // multiplications. |
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438 | // |
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439 | // See also: CanonicalForm::operator <(), CanonicalForm::operator ==() |
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440 | // |
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441 | //}}} |
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442 | int |
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443 | InternalRational::comparesame ( InternalCF * c ) |
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444 | { |
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445 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "incompatible base coefficients" ); |
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446 | MP_INT dummy1, dummy2; |
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447 | mpz_init( &dummy1 ); mpz_init( &dummy2 ); |
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448 | mpz_mul( &dummy1, &_num, &MPQDEN( c ) ); |
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449 | mpz_mul( &dummy2, &_den, &MPQNUM( c ) ); |
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450 | int result = mpz_cmp( &dummy1, &dummy2 ); |
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451 | mpz_clear( &dummy1 ); mpz_clear( &dummy2 ); |
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452 | return result; |
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453 | } |
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454 | |
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455 | int |
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456 | InternalRational::comparecoeff ( InternalCF* c ) |
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457 | { |
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458 | if ( ::is_imm( c ) ) { |
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459 | ASSERT( ::is_imm( c ) == INTMARK, "incompatible base coefficients" ); |
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460 | MP_INT dummy; |
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461 | mpz_init_set_si( &dummy, imm2int( c ) ); |
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462 | mpz_mul( &dummy, &dummy, &_den ); |
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463 | int result = mpz_cmp( &_num, &dummy ); |
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464 | mpz_clear( &dummy ); |
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465 | return result; |
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466 | } |
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467 | else { |
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468 | ASSERT( c->levelcoeff() == IntegerDomain, "incompatible base coefficients" ); |
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469 | MP_INT dummy; |
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470 | mpz_init( &dummy ); |
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471 | mpz_mul( &dummy, &_den, &InternalInteger::MPI( c ) ); |
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472 | int result = mpz_cmp( &_num, &dummy ); |
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473 | mpz_clear( &dummy ); |
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474 | return result; |
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475 | } |
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476 | } |
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477 | //}}} |
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478 | |
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479 | InternalCF* InternalRational::addcoeff( InternalCF* c ) |
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480 | { |
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481 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
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482 | MP_INT n, d; |
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483 | if ( ::is_imm( c ) ) { |
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484 | int cc = imm2int( c ); |
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485 | if ( cc == 0 ) |
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486 | return this; |
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487 | else if ( cc < 0 ) { |
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488 | mpz_init( &n ); |
---|
489 | mpz_mul_ui( &n, &_den, -cc ); |
---|
490 | mpz_sub( &n, &_num, &n ); |
---|
491 | } |
---|
492 | else { |
---|
493 | mpz_init( &n ); |
---|
494 | mpz_mul_ui( &n, &_den, cc ); |
---|
495 | mpz_add( &n, &_num, &n ); |
---|
496 | } |
---|
497 | } |
---|
498 | else { |
---|
499 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
500 | mpz_init( &n ); |
---|
501 | mpz_mul( &n, &_den, &InternalInteger::MPI( c ) ); |
---|
502 | mpz_add( &n, &_num, &n ); |
---|
503 | } |
---|
504 | mpz_init_set( &d, &_den ); |
---|
505 | // at this point there is no way that the result is not a true rational |
---|
506 | if ( deleteObject() ) delete this; |
---|
507 | return new InternalRational( n, d ); |
---|
508 | } |
---|
509 | |
---|
510 | InternalCF* InternalRational::subcoeff( InternalCF* c, bool negate ) |
---|
511 | { |
---|
512 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
513 | MP_INT n, d; |
---|
514 | if ( ::is_imm( c ) ) { |
---|
515 | int cc = imm2int( c ); |
---|
516 | if ( cc == 0 ) |
---|
517 | if ( negate ) { |
---|
518 | if ( getRefCount() == 1 ) { |
---|
519 | mpz_neg( &_num, &_num ); |
---|
520 | return this; |
---|
521 | } |
---|
522 | else { |
---|
523 | decRefCount(); |
---|
524 | mpz_init_set( &d, &_den ); |
---|
525 | mpz_init_set( &n, &_num ); |
---|
526 | mpz_neg( &n, &n ); |
---|
527 | return new InternalRational( n, d ); |
---|
528 | } |
---|
529 | } |
---|
530 | else |
---|
531 | return this; |
---|
532 | mpz_init( &n ); |
---|
533 | if ( cc < 0 ) { |
---|
534 | mpz_mul_ui( &n, &_den, -cc ); |
---|
535 | mpz_neg( &n, &n ); |
---|
536 | } |
---|
537 | else |
---|
538 | mpz_mul_ui( &n, &_den, cc ); |
---|
539 | if ( negate ) |
---|
540 | mpz_sub( &n, &n, &_num ); |
---|
541 | else |
---|
542 | mpz_sub( &n, &_num, &n ); |
---|
543 | } |
---|
544 | else { |
---|
545 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
546 | mpz_init( &n ); |
---|
547 | mpz_mul( &n, &_den, &InternalInteger::MPI( c ) ); |
---|
548 | if ( negate ) |
---|
549 | mpz_sub( &n, &n, &_num ); |
---|
550 | else |
---|
551 | mpz_sub( &n, &_num, &n ); |
---|
552 | } |
---|
553 | mpz_init_set( &d, &_den ); |
---|
554 | // at this point there is no way that the result is not a true rational |
---|
555 | if ( deleteObject() ) delete this; |
---|
556 | return new InternalRational( n, d ); |
---|
557 | } |
---|
558 | |
---|
559 | InternalCF* InternalRational::mulcoeff( InternalCF* c ) |
---|
560 | { |
---|
561 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
562 | MP_INT n, d, g; |
---|
563 | if ( ::is_imm( c ) ) { |
---|
564 | int cc = imm2int( c ); |
---|
565 | if ( cc == 0 ) { |
---|
566 | if ( deleteObject() ) delete this; |
---|
567 | return CFFactory::basic( 0 ); |
---|
568 | } |
---|
569 | mpz_init_set_si( &n, cc ); |
---|
570 | } |
---|
571 | else { |
---|
572 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
573 | mpz_init_set( &n, &InternalInteger::MPI( c ) ); |
---|
574 | } |
---|
575 | mpz_init( &g ); |
---|
576 | mpz_gcd( &g, &n, &_den ); |
---|
577 | if ( mpz_cmp_si( &g, 1 ) == 0 ) { |
---|
578 | mpz_mul( &n, &n, &_num ); |
---|
579 | mpz_init_set( &d, &_den ); |
---|
580 | } |
---|
581 | else { |
---|
582 | mpz_div( &n, &n, &g ); |
---|
583 | mpz_mul( &n, &n, &_num ); |
---|
584 | mpz_init( &d ); |
---|
585 | mpz_div( &d, &_den, &g ); |
---|
586 | } |
---|
587 | mpz_clear( &g ); |
---|
588 | if ( deleteObject() ) delete this; |
---|
589 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
---|
590 | if ( mpz_is_imm( &n ) ) { |
---|
591 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
---|
592 | mpz_clear( &n ); mpz_clear( &d ); |
---|
593 | return res; |
---|
594 | } |
---|
595 | else { |
---|
596 | mpz_clear( &d ); |
---|
597 | return new InternalInteger( n ); |
---|
598 | } |
---|
599 | } |
---|
600 | else |
---|
601 | return new InternalRational( n, d ); |
---|
602 | } |
---|
603 | |
---|
604 | InternalCF* InternalRational::dividecoeff( InternalCF* c, bool invert ) |
---|
605 | { |
---|
606 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
607 | MP_INT n, d, g; |
---|
608 | if ( ::is_imm( c ) ) { |
---|
609 | int cc = imm2int( c ); |
---|
610 | ASSERT( c != 0 || invert, "divide by zero" ); |
---|
611 | if ( cc == 0 ) { |
---|
612 | // => invert |
---|
613 | if ( deleteObject() ) delete this; |
---|
614 | return CFFactory::basic( 0 ); |
---|
615 | } |
---|
616 | if ( invert ) { |
---|
617 | mpz_init_set_si( &n, cc ); |
---|
618 | mpz_mul( &n, &n, &_den ); |
---|
619 | mpz_init_set( &d, &_num ); |
---|
620 | } |
---|
621 | else { |
---|
622 | mpz_init_set_si( &d, cc ); |
---|
623 | mpz_mul( &d, &d, &_den ); |
---|
624 | mpz_init_set( &n, &_num ); |
---|
625 | } |
---|
626 | } |
---|
627 | else { |
---|
628 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
629 | if ( invert ) { |
---|
630 | mpz_init_set( &n, &InternalInteger::MPI( c ) ); |
---|
631 | mpz_mul( &n, &n, &_den ); |
---|
632 | mpz_init_set( &d, &_num ); |
---|
633 | } |
---|
634 | else { |
---|
635 | mpz_init_set( &d, &InternalInteger::MPI( c ) ); |
---|
636 | mpz_mul( &d, &d, &_den ); |
---|
637 | mpz_init_set( &n, &_num ); |
---|
638 | } |
---|
639 | } |
---|
640 | if ( mpz_cmp_si( &d, 0 ) < 0 ) { |
---|
641 | mpz_neg( &d, &d ); |
---|
642 | mpz_neg( &n, &n ); |
---|
643 | } |
---|
644 | mpz_init( &g ); |
---|
645 | mpz_gcd( &g, &n, &d ); |
---|
646 | if ( mpz_cmp_si( &g, 1 ) != 0 ) { |
---|
647 | mpz_div( &d, &d, &g ); |
---|
648 | mpz_div( &n, &n, &g ); |
---|
649 | } |
---|
650 | mpz_clear( &g ); |
---|
651 | if ( deleteObject() ) delete this; |
---|
652 | if ( ! invert ) { |
---|
653 | // then there was no way for the result to become an integer |
---|
654 | return new InternalRational( n, d ); |
---|
655 | } |
---|
656 | if ( mpz_cmp_si( &d, 1 ) == 0 ) { |
---|
657 | if ( mpz_is_imm( &n ) ) { |
---|
658 | InternalCF * res = int2imm( mpz_get_si( &n ) ); |
---|
659 | mpz_clear( &n ); mpz_clear( &d ); |
---|
660 | return res; |
---|
661 | } |
---|
662 | else { |
---|
663 | mpz_clear( &d ); |
---|
664 | return new InternalInteger( n ); |
---|
665 | } |
---|
666 | } |
---|
667 | else |
---|
668 | return new InternalRational( n, d ); |
---|
669 | } |
---|
670 | |
---|
671 | InternalCF* InternalRational::divcoeff( InternalCF* c, bool invert ) |
---|
672 | { |
---|
673 | return dividecoeff( c, invert ); |
---|
674 | } |
---|
675 | |
---|
676 | InternalCF* InternalRational::modulocoeff( InternalCF* c, bool invert ) |
---|
677 | { |
---|
678 | return modcoeff( c, invert ); |
---|
679 | } |
---|
680 | |
---|
681 | InternalCF* InternalRational::modcoeff( InternalCF* c, bool invert ) |
---|
682 | { |
---|
683 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "integer expected" ); |
---|
684 | ASSERT( invert || ! ::is_imm( c ) || imm2int( c ) != 0, "divide by zero" ); |
---|
685 | if ( deleteObject() ) delete this; |
---|
686 | return CFFactory::basic( 0 ); |
---|
687 | } |
---|
688 | |
---|
689 | void InternalRational::divremcoeff( InternalCF* c, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
690 | { |
---|
691 | quot = copyObject(); |
---|
692 | quot = quot->dividecoeff( c, invert ); |
---|
693 | rem = CFFactory::basic( 0 ); |
---|
694 | } |
---|
695 | |
---|
696 | bool InternalRational::divremcoefft( InternalCF* c, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
697 | { |
---|
698 | divremcoeff( c, quot, rem, invert ); |
---|
699 | return true; |
---|
700 | } |
---|
701 | |
---|
702 | //{{{ InternalCF * InternalRational::bgcdsame, bgcdcoeff ( const InternalCF * const ) |
---|
703 | // docu: see CanonicalForm::bgcd() |
---|
704 | InternalCF * |
---|
705 | InternalRational::bgcdsame ( const InternalCF * const ) const |
---|
706 | { |
---|
707 | return int2imm( 1 ); |
---|
708 | } |
---|
709 | |
---|
710 | InternalCF * |
---|
711 | InternalRational::bgcdcoeff ( const InternalCF * const ) |
---|
712 | { |
---|
713 | return int2imm( 1 ); |
---|
714 | } |
---|
715 | //}}} |
---|
716 | |
---|
717 | //{{{ InternalCF * InternalRational::bextgcdsame ( InternalCF * c, CanonicalForm & a, CanonicalForm & b ) |
---|
718 | // docu: see CanonicalForm::bextgcd() |
---|
719 | InternalCF * |
---|
720 | InternalRational::bextgcdsame ( InternalCF *, CanonicalForm & a, CanonicalForm & b ) |
---|
721 | { |
---|
722 | a = 1/CanonicalForm( copyObject() ); b = 0; |
---|
723 | return int2imm( 1 ); |
---|
724 | } |
---|
725 | |
---|
726 | InternalCF * |
---|
727 | InternalRational::bextgcdcoeff ( InternalCF *, CanonicalForm & a, CanonicalForm & b ) |
---|
728 | { |
---|
729 | a = 1/CanonicalForm( copyObject() ); b = 0; |
---|
730 | return int2imm( 1 ); |
---|
731 | } |
---|
732 | //}}} |
---|
733 | |
---|
734 | InternalCF * InternalRational::normalize_myself() |
---|
735 | { |
---|
736 | ASSERT( getRefCount() == 1, "illegal operation" ); |
---|
737 | MP_INT g; |
---|
738 | mpz_init( &g ); |
---|
739 | mpz_gcd( &g, &_num, &_den ); |
---|
740 | if ( mpz_cmp_si( &g, 1 ) != 0 ) { |
---|
741 | mpz_div( &_num, &_num, &g ); |
---|
742 | mpz_div( &_den, &_den, &g ); |
---|
743 | } |
---|
744 | // Hier brauchen wir ein mpz_clear, J.M. |
---|
745 | mpz_clear( &g ); |
---|
746 | if ( mpz_cmp_si( &_den, 0 ) < 0 ) { |
---|
747 | mpz_neg( &_num, &_num ); |
---|
748 | mpz_neg( &_den, &_den ); |
---|
749 | } |
---|
750 | if ( mpz_cmp_si( &_den, 1 ) == 0 ) |
---|
751 | if ( mpz_is_imm( &_num ) ) { |
---|
752 | InternalCF * res = int2imm( mpz_get_si( &_num ) ); |
---|
753 | delete this; |
---|
754 | return res; |
---|
755 | } |
---|
756 | else { |
---|
757 | MP_INT res; |
---|
758 | mpz_init_set( &res, &_num ); |
---|
759 | delete this; |
---|
760 | return new InternalInteger( res ); |
---|
761 | } |
---|
762 | else |
---|
763 | return this; |
---|
764 | } |
---|
765 | |
---|
766 | |
---|
767 | int InternalRational::intval() const |
---|
768 | { |
---|
769 | ASSERT( mpz_cmp_si( &_den, 1 ) == 0, "illegal operation" ); |
---|
770 | return (int)mpz_get_si( &_num ); |
---|
771 | } |
---|
772 | |
---|
773 | //{{{ int InternalRational::sign () const |
---|
774 | // docu: see CanonicalForm::sign() |
---|
775 | int |
---|
776 | InternalRational::sign () const |
---|
777 | { |
---|
778 | return mpz_sgn( &_num ); |
---|
779 | } |
---|
780 | //}}} |
---|