[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[2dd068] | 2 | |
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[e4fe2b] | 3 | #include "config.h" |
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[9d7aaa] | 4 | |
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[650f2d8] | 5 | #include "cf_assert.h" |
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[718e670] | 6 | |
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[2dd068] | 7 | #include "cf_defs.h" |
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| 8 | #include "int_rat.h" |
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| 9 | #include "int_int.h" |
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| 10 | #include "imm.h" |
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| 11 | #include "canonicalform.h" |
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| 12 | #include "cf_factory.h" |
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| 13 | #include "gmpext.h" |
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| 14 | |
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[8710ff0] | 15 | static long intgcd( long a, long b ) |
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| 16 | { |
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| 17 | if ( a < 0 ) a = -a; |
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| 18 | if ( b < 0 ) b = -b; |
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| 19 | |
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| 20 | long c; |
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| 21 | |
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| 22 | while ( b != 0 ) |
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| 23 | { |
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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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[2dd068] | 31 | |
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| 32 | InternalRational::InternalRational() |
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| 33 | { |
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[a52291] | 34 | mpz_init( _num ); |
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| 35 | mpz_init_set_si( _den, 1 ); |
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[2dd068] | 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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[a52291] | 40 | mpz_init_set_si( _num, i ); |
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| 41 | mpz_init_set_si( _den, 1 ); |
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[2dd068] | 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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[1e6de6] | 47 | if ( n == 0 ) |
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| 48 | { |
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[a52291] | 49 | mpz_init_set_si( _num, 0 ); |
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| 50 | mpz_init_set_si( _den, 1 ); |
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[2dd068] | 51 | } |
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[1e6de6] | 52 | else |
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| 53 | { |
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[1daf0d] | 54 | long g = intgcd( (long) n, (long) d ); |
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[a52291] | 55 | if ( d < 0 ) |
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| 56 | { |
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[1daf0d] | 57 | mpz_init_set_si( _num, -((long)n) / g ); |
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| 58 | mpz_init_set_si( _den, -((long)d) / g ); |
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[a52291] | 59 | } |
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| 60 | else |
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| 61 | { |
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| 62 | mpz_init_set_si( _num, n / g ); |
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| 63 | mpz_init_set_si( _den, d / g ); |
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| 64 | } |
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[2dd068] | 65 | } |
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| 66 | } |
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| 67 | |
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[8710ff0] | 68 | InternalRational::InternalRational( const long i ) |
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| 69 | { |
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| 70 | mpz_init_set_si( _num, i ); |
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| 71 | mpz_init_set_si( _den, 1 ); |
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| 72 | } |
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| 73 | |
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| 74 | InternalRational::InternalRational( const long n, const long d ) |
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| 75 | { |
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| 76 | ASSERT( d != 0, "divide by zero" ); |
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| 77 | if ( n == 0 ) |
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| 78 | { |
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| 79 | mpz_init_set_si( _num, 0 ); |
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| 80 | mpz_init_set_si( _den, 1 ); |
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| 81 | } |
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| 82 | else |
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| 83 | { |
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| 84 | long g = intgcd( n, d ); |
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| 85 | if ( d < 0 ) |
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| 86 | { |
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| 87 | mpz_init_set_si( _num, -n / g ); |
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| 88 | mpz_init_set_si( _den, -d / g ); |
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| 89 | } |
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| 90 | else |
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| 91 | { |
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| 92 | mpz_init_set_si( _num, n / g ); |
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| 93 | mpz_init_set_si( _den, d / g ); |
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| 94 | } |
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| 95 | } |
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| 96 | } |
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| 97 | |
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[2dd068] | 98 | InternalRational::InternalRational( const char * ) |
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| 99 | { |
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| 100 | // sollte nicht gebraucht werden !!! |
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| 101 | ASSERT( 0, "fatal error" ); |
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[a52291] | 102 | mpz_init( _num ); |
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| 103 | mpz_init( _den ); |
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[2dd068] | 104 | } |
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| 105 | |
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[a52291] | 106 | //InternalRational::InternalRational( const mpz_ptr n ) : _num(n) |
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| 107 | //{ |
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| 108 | // mpz_init_set_si( _den, 1 ); |
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| 109 | //} |
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| 110 | |
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| 111 | InternalRational::InternalRational( const mpz_ptr n ) |
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[2dd068] | 112 | { |
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[a52291] | 113 | _num[0]=*n; |
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| 114 | mpz_init_set_si( _den, 1 ); |
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[2dd068] | 115 | } |
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| 116 | |
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[a52291] | 117 | InternalRational::InternalRational( const mpz_ptr n, const mpz_ptr d ) |
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[2dd068] | 118 | { |
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[a52291] | 119 | _num[0]=*n; |
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| 120 | _den[0]=*d; |
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[2dd068] | 121 | } |
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| 122 | |
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| 123 | InternalRational::~InternalRational() |
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| 124 | { |
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[a52291] | 125 | mpz_clear( _num ); |
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| 126 | mpz_clear( _den ); |
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[2dd068] | 127 | } |
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| 128 | |
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| 129 | InternalCF* InternalRational::deepCopyObject() const |
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| 130 | { |
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[a52291] | 131 | mpz_t dummy_num; |
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| 132 | mpz_t dummy_den; |
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| 133 | mpz_init_set( dummy_num, _num ); |
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| 134 | mpz_init_set( dummy_den, _den ); |
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[2dd068] | 135 | return new InternalRational( dummy_num, dummy_den ); |
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| 136 | } |
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| 137 | |
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[718e670] | 138 | #ifndef NOSTREAMIO |
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[181148] | 139 | void InternalRational::print( OSTREAM & os, char * c ) |
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[2dd068] | 140 | { |
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[a52291] | 141 | char * str = new char[mpz_sizeinbase( _num, 10 ) + 2]; |
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| 142 | str = mpz_get_str( str, 10, _num ); |
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[2dd068] | 143 | os << str << '/'; |
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| 144 | delete [] str; |
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[a52291] | 145 | str = new char[mpz_sizeinbase( _den, 10 ) + 2]; |
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| 146 | str = mpz_get_str( str, 10, _den ); |
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[2dd068] | 147 | os << str << c; |
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| 148 | delete [] str; |
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| 149 | } |
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[718e670] | 150 | #endif /* NOSTREAMIO */ |
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[2dd068] | 151 | |
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| 152 | bool InternalRational::is_imm() const |
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| 153 | { |
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[a52291] | 154 | return mpz_cmp_si( _den, 1 ) == 0 && mpz_is_imm( _num ); |
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[2dd068] | 155 | } |
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| 156 | |
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| 157 | InternalCF* InternalRational::genZero() |
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| 158 | { |
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| 159 | if ( isZero() ) |
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[2b44a1] | 160 | return copyObject(); |
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[2dd068] | 161 | else |
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[2b44a1] | 162 | return new InternalRational(); |
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[2dd068] | 163 | } |
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| 164 | |
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| 165 | InternalCF* InternalRational::genOne() |
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| 166 | { |
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| 167 | if ( isOne() ) |
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[2b44a1] | 168 | return copyObject(); |
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[2dd068] | 169 | else |
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[2b44a1] | 170 | return new InternalRational( 1 ); |
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[2dd068] | 171 | } |
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| 172 | |
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[143cbf2] | 173 | //{{{ InternalCF * InternalRational::num (), den () |
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[516dc8] | 174 | // docu: see CanonicalForm::num(), den() |
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[143cbf2] | 175 | InternalCF * InternalRational::num () |
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[2dd068] | 176 | { |
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[a52291] | 177 | if ( mpz_is_imm( _num ) ) |
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[1e6de6] | 178 | { |
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[a52291] | 179 | InternalCF * res = int2imm( mpz_get_si( _num ) ); |
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[2b44a1] | 180 | return res; |
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[2dd068] | 181 | } |
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[1e6de6] | 182 | else |
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| 183 | { |
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[a52291] | 184 | mpz_t dummy; |
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| 185 | mpz_init_set( dummy, _num ); |
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[2b44a1] | 186 | return new InternalInteger( dummy ); |
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[2dd068] | 187 | } |
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| 188 | } |
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| 189 | |
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[143cbf2] | 190 | InternalCF * InternalRational::den () |
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[2dd068] | 191 | { |
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[a52291] | 192 | if ( mpz_is_imm( _den ) ) |
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[1e6de6] | 193 | { |
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[a52291] | 194 | InternalCF * res = int2imm( mpz_get_si( _den ) ); |
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[2b44a1] | 195 | return res; |
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[2dd068] | 196 | } |
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[1e6de6] | 197 | else |
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| 198 | { |
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[a52291] | 199 | mpz_t dummy; |
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| 200 | mpz_init_set( dummy, _den ); |
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[2b44a1] | 201 | return new InternalInteger( dummy ); |
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[2dd068] | 202 | } |
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| 203 | } |
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[516dc8] | 204 | //}}} |
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[2dd068] | 205 | |
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[6dd289] | 206 | //{{{ InternalCF * InternalRational::neg () |
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| 207 | // docu: see CanonicalForm::operator -() |
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| 208 | InternalCF * |
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| 209 | InternalRational::neg () |
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[2dd068] | 210 | { |
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[1e6de6] | 211 | if ( getRefCount() > 1 ) |
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| 212 | { |
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[2b44a1] | 213 | decRefCount(); |
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[a52291] | 214 | mpz_t dummy_num; |
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| 215 | mpz_t dummy_den; |
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| 216 | mpz_init_set( dummy_num, _num ); |
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| 217 | mpz_init_set( dummy_den, _den ); |
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| 218 | mpz_neg( dummy_num, dummy_num ); |
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[2b44a1] | 219 | return new InternalRational( dummy_num, dummy_den ); |
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[1e6de6] | 220 | } |
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| 221 | else |
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| 222 | { |
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[a52291] | 223 | mpz_neg( _num, _num ); |
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[2b44a1] | 224 | return this; |
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[2dd068] | 225 | } |
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| 226 | } |
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[6dd289] | 227 | //}}} |
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[2dd068] | 228 | |
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| 229 | InternalCF* InternalRational::addsame( InternalCF * c ) |
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| 230 | { |
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| 231 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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[a52291] | 232 | mpz_t n, d, g; |
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[2dd068] | 233 | |
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[a52291] | 234 | mpz_init( g ); mpz_init( n ); mpz_init( d ); |
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| 235 | mpz_gcd( g, _den, MPQDEN( c ) ); |
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[2dd068] | 236 | |
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[a52291] | 237 | if ( mpz_cmp_si( g, 1 ) == 0 ) |
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[1e6de6] | 238 | { |
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[a52291] | 239 | mpz_mul( n, _den, MPQNUM( c ) ); |
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| 240 | mpz_mul( g, _num, MPQDEN( c ) ); |
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| 241 | mpz_add( n, n, g ); |
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| 242 | mpz_mul( d, _den, MPQDEN( c ) ); |
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[2dd068] | 243 | } |
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[1e6de6] | 244 | else |
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| 245 | { |
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[a52291] | 246 | mpz_t tmp1; |
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| 247 | mpz_t tmp2; |
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| 248 | mpz_init( tmp1 ); |
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| 249 | mpz_divexact( tmp1, _den, g ); |
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| 250 | mpz_init( tmp2 ); |
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| 251 | mpz_divexact( tmp2, MPQDEN( c ), g ); |
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| 252 | mpz_mul( d, tmp2, _den ); |
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| 253 | mpz_mul( tmp2, tmp2, _num ); |
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| 254 | mpz_mul( tmp1, tmp1, MPQNUM( c ) ); |
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| 255 | mpz_add( n, tmp1, tmp2 ); |
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| 256 | mpz_gcd( g, n, d ); |
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| 257 | if ( mpz_cmp_si( g, 1 ) != 0 ) |
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[41072b] | 258 | { |
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[a52291] | 259 | mpz_divexact( n, n, g ); |
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| 260 | mpz_divexact( d, d, g ); |
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[41072b] | 261 | } |
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[a52291] | 262 | mpz_clear( tmp1 ); |
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| 263 | mpz_clear( tmp2 ); |
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[2dd068] | 264 | } |
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[a52291] | 265 | mpz_clear( g ); |
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[2dd068] | 266 | if ( deleteObject() ) delete this; |
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[a52291] | 267 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
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[1e6de6] | 268 | { |
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[a52291] | 269 | mpz_clear( d ); |
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| 270 | if ( mpz_is_imm( n ) ) |
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[41072b] | 271 | { |
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[a52291] | 272 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
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| 273 | mpz_clear( n ); |
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[41072b] | 274 | return res; |
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| 275 | } |
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| 276 | else |
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| 277 | { |
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| 278 | return new InternalInteger( n ); |
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| 279 | } |
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[2dd068] | 280 | } |
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| 281 | else |
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[41072b] | 282 | { |
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| 283 | return new InternalRational( n, d ); |
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| 284 | } |
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[2dd068] | 285 | } |
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| 286 | |
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| 287 | InternalCF* InternalRational::subsame( InternalCF * c ) |
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| 288 | { |
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| 289 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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[a52291] | 290 | mpz_t n, d, g; |
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[2dd068] | 291 | |
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[a52291] | 292 | mpz_init( g ); mpz_init( n ); mpz_init( d ); |
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| 293 | mpz_gcd( g, _den, MPQDEN( c ) ); |
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[2dd068] | 294 | |
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[a52291] | 295 | if ( mpz_cmp_si( g, 1 ) == 0 ) |
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[1e6de6] | 296 | { |
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[a52291] | 297 | mpz_mul( n, _den, MPQNUM( c ) ); |
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| 298 | mpz_mul( g, _num, MPQDEN( c ) ); |
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| 299 | mpz_sub( n, g, n ); |
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| 300 | mpz_mul( d, _den, MPQDEN( c ) ); |
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[2dd068] | 301 | } |
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[1e6de6] | 302 | else |
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| 303 | { |
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[a52291] | 304 | mpz_t tmp1; |
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| 305 | mpz_t tmp2; |
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| 306 | mpz_init( tmp1 ); |
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| 307 | mpz_divexact( tmp1, _den, g ); |
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| 308 | mpz_init( tmp2 ); |
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| 309 | mpz_divexact( tmp2, MPQDEN( c ), g ); |
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| 310 | mpz_mul( d, tmp2, _den ); |
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| 311 | mpz_mul( tmp2, tmp2, _num ); |
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| 312 | mpz_mul( tmp1, tmp1, MPQNUM( c ) ); |
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| 313 | mpz_sub( n, tmp2, tmp1 ); |
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| 314 | mpz_gcd( g, n, d ); |
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| 315 | if ( mpz_cmp_si( g, 1 ) != 0 ) |
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[1e6de6] | 316 | { |
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[a52291] | 317 | mpz_divexact( n, n, g ); |
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| 318 | mpz_divexact( d, d, g ); |
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[2b44a1] | 319 | } |
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[a52291] | 320 | mpz_clear( tmp1 ); |
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| 321 | mpz_clear( tmp2 ); |
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[2dd068] | 322 | } |
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[a52291] | 323 | mpz_clear( g ); |
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[2dd068] | 324 | if ( deleteObject() ) delete this; |
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[a52291] | 325 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
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[1e6de6] | 326 | { |
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[a52291] | 327 | mpz_clear( d ); |
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| 328 | if ( mpz_is_imm( n ) ) |
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[1e6de6] | 329 | { |
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[a52291] | 330 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
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| 331 | mpz_clear( n ); |
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[2b44a1] | 332 | return res; |
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| 333 | } |
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[1e6de6] | 334 | else |
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| 335 | { |
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[2b44a1] | 336 | return new InternalInteger( n ); |
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| 337 | } |
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[2dd068] | 338 | } |
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| 339 | else |
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[2b44a1] | 340 | return new InternalRational( n, d ); |
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[2dd068] | 341 | } |
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| 342 | |
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| 343 | InternalCF* InternalRational::mulsame( InternalCF * c ) |
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| 344 | { |
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| 345 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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[a52291] | 346 | mpz_t n, d; |
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| 347 | mpz_init( n ); mpz_init( d ); |
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[2dd068] | 348 | |
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[1e6de6] | 349 | if ( this == c ) |
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| 350 | { |
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[a52291] | 351 | mpz_mul( n, _num, _num ); |
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| 352 | mpz_mul( d, _den, _den ); |
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[2dd068] | 353 | } |
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[1e6de6] | 354 | else |
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| 355 | { |
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[a52291] | 356 | mpz_t g1, g2, tmp1, tmp2; |
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| 357 | mpz_init( g1 ); mpz_init( g2 ); |
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| 358 | mpz_gcd( g1, _num, MPQDEN( c ) ); |
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| 359 | mpz_gcd( g2, _den, MPQNUM( c ) ); |
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| 360 | bool g1is1 = mpz_cmp_si( g1, 1 ) == 0; |
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| 361 | bool g2is1 = mpz_cmp_si( g2, 1 ) == 0; |
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| 362 | mpz_init( tmp1 ); mpz_init( tmp2 ); |
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[2b44a1] | 363 | if ( ! g1is1 ) |
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[a52291] | 364 | mpz_divexact( tmp1, _num, g1 ); |
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[2b44a1] | 365 | else |
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[a52291] | 366 | mpz_set( tmp1, _num ); |
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[2b44a1] | 367 | if ( ! g2is1 ) |
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[a52291] | 368 | mpz_divexact( tmp2, MPQNUM( c ), g2 ); |
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[2b44a1] | 369 | else |
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[a52291] | 370 | mpz_set( tmp2, MPQNUM( c ) ); |
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| 371 | mpz_mul( n, tmp1, tmp2 ); |
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[2b44a1] | 372 | if ( ! g1is1 ) |
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[a52291] | 373 | mpz_divexact( tmp1, MPQDEN( c ), g1 ); |
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[2b44a1] | 374 | else |
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[a52291] | 375 | mpz_set( tmp1, MPQDEN( c ) ); |
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[2b44a1] | 376 | if ( ! g2is1 ) |
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[a52291] | 377 | mpz_divexact( tmp2, _den, g2 ); |
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[2b44a1] | 378 | else |
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[a52291] | 379 | mpz_set( tmp2, _den ); |
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| 380 | mpz_mul( d, tmp1, tmp2 ); |
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| 381 | mpz_clear( tmp1 ); mpz_clear( tmp2 ); |
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| 382 | mpz_clear( g1 ); mpz_clear( g2 ); |
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[2dd068] | 383 | } |
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| 384 | if ( deleteObject() ) delete this; |
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[a52291] | 385 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
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[1e6de6] | 386 | { |
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[a52291] | 387 | mpz_clear( d ); |
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| 388 | if ( mpz_is_imm( n ) ) |
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[1e6de6] | 389 | { |
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[a52291] | 390 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
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| 391 | mpz_clear( n ); |
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[2b44a1] | 392 | return res; |
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| 393 | } |
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[1e6de6] | 394 | else |
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| 395 | { |
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[2b44a1] | 396 | return new InternalInteger( n ); |
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| 397 | } |
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[2dd068] | 398 | } |
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| 399 | else |
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[2b44a1] | 400 | return new InternalRational( n, d ); |
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[2dd068] | 401 | } |
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| 402 | |
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| 403 | InternalCF* InternalRational::dividesame( InternalCF * c ) |
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| 404 | { |
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| 405 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "illegal domain" ); |
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| 406 | |
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[1e6de6] | 407 | if ( this == c ) |
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| 408 | { |
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[2b44a1] | 409 | if ( deleteObject() ) delete this; |
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[8710ff0] | 410 | return CFFactory::basic( 1L ); |
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[2dd068] | 411 | } |
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[1e6de6] | 412 | else |
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| 413 | { |
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[a52291] | 414 | mpz_t n, d; |
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| 415 | mpz_t g1, g2, tmp1, tmp2; |
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| 416 | mpz_init( n ); mpz_init( d ); |
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| 417 | mpz_init( g1 ); mpz_init( g2 ); |
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| 418 | mpz_gcd( g1, _num, MPQNUM( c ) ); |
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| 419 | mpz_gcd( g2, _den, MPQDEN( c ) ); |
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| 420 | bool g1is1 = mpz_cmp_si( g1, 1 ) == 0; |
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| 421 | bool g2is1 = mpz_cmp_si( g2, 1 ) == 0; |
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| 422 | mpz_init( tmp1 ); mpz_init( tmp2 ); |
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[2b44a1] | 423 | if ( ! g1is1 ) |
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[a52291] | 424 | mpz_divexact( tmp1, _num, g1 ); |
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[2b44a1] | 425 | else |
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[a52291] | 426 | mpz_set( tmp1, _num ); |
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[2b44a1] | 427 | if ( ! g2is1 ) |
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[a52291] | 428 | mpz_divexact( tmp2, MPQDEN( c ), g2 ); |
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[2b44a1] | 429 | else |
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[a52291] | 430 | mpz_set( tmp2, MPQDEN( c ) ); |
---|
| 431 | mpz_mul( n, tmp1, tmp2 ); |
---|
[2b44a1] | 432 | if ( ! g1is1 ) |
---|
[a52291] | 433 | mpz_divexact( tmp1, MPQNUM( c ), g1 ); |
---|
[2b44a1] | 434 | else |
---|
[a52291] | 435 | mpz_set( tmp1, MPQNUM( c ) ); |
---|
[2b44a1] | 436 | if ( ! g2is1 ) |
---|
[a52291] | 437 | mpz_divexact( tmp2, _den, g2 ); |
---|
[2b44a1] | 438 | else |
---|
[a52291] | 439 | mpz_set( tmp2, _den ); |
---|
| 440 | mpz_mul( d, tmp1, tmp2 ); |
---|
| 441 | mpz_clear( tmp1 ); mpz_clear( tmp2 ); |
---|
| 442 | mpz_clear( g1 ); mpz_clear( g2 ); |
---|
[2b44a1] | 443 | if ( deleteObject() ) delete this; |
---|
[a52291] | 444 | if ( mpz_cmp_si( d, 0 ) < 0 ) |
---|
[cc4553] | 445 | { |
---|
[a52291] | 446 | mpz_neg( d, d ); |
---|
| 447 | mpz_neg( n, n ); |
---|
[2b44a1] | 448 | } |
---|
[a52291] | 449 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
---|
[1e6de6] | 450 | { |
---|
[a52291] | 451 | mpz_clear( d ); |
---|
| 452 | if ( mpz_is_imm( n ) ) |
---|
[1e6de6] | 453 | { |
---|
[a52291] | 454 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
---|
| 455 | mpz_clear( n ); |
---|
[2b44a1] | 456 | return res; |
---|
| 457 | } |
---|
[1e6de6] | 458 | else |
---|
| 459 | { |
---|
[2b44a1] | 460 | return new InternalInteger( n ); |
---|
| 461 | } |
---|
| 462 | } |
---|
| 463 | else |
---|
| 464 | return new InternalRational( n, d ); |
---|
[2dd068] | 465 | } |
---|
| 466 | } |
---|
| 467 | |
---|
| 468 | InternalCF* InternalRational::divsame( InternalCF * c ) |
---|
| 469 | { |
---|
| 470 | return dividesame( c ); |
---|
| 471 | } |
---|
| 472 | |
---|
| 473 | InternalCF* InternalRational::modulosame( InternalCF * c ) |
---|
| 474 | { |
---|
| 475 | return modsame( c ); |
---|
| 476 | } |
---|
| 477 | |
---|
| 478 | InternalCF* InternalRational::modsame( InternalCF * ) |
---|
| 479 | { |
---|
| 480 | if ( deleteObject() ) delete this; |
---|
[8710ff0] | 481 | return CFFactory::basic( 0L ); |
---|
[2dd068] | 482 | } |
---|
| 483 | |
---|
| 484 | void InternalRational::divremsame( InternalCF * c, InternalCF*& quot, InternalCF*& rem ) |
---|
| 485 | { |
---|
| 486 | quot = copyObject(); |
---|
| 487 | quot = quot->dividesame( c ); |
---|
[8710ff0] | 488 | rem = CFFactory::basic( 0L ); |
---|
[2dd068] | 489 | } |
---|
| 490 | |
---|
| 491 | bool InternalRational::divremsamet( InternalCF* c, InternalCF*& quot, InternalCF*& rem ) |
---|
| 492 | { |
---|
| 493 | divremsame( c, quot, rem ); |
---|
| 494 | return true; |
---|
| 495 | } |
---|
| 496 | |
---|
[1aeb9a7] | 497 | //{{{ int InternalRational::comparesame, comparecoeff ( InternalCF * c ) |
---|
| 498 | //{{{ docu |
---|
| 499 | // |
---|
| 500 | // comparesame(), comparecoeff() - compare with an |
---|
| 501 | // InternalRational. |
---|
| 502 | // |
---|
| 503 | // comparesame() compares the CO=a/b and c=p/q using the |
---|
| 504 | // equivalence a/b < p/q iff a*q < p*b. |
---|
| 505 | // |
---|
| 506 | // comparecoeff() compares the CO=a/b and the integer c using the |
---|
| 507 | // equivalence a/b < c iff a < c*b. |
---|
| 508 | // |
---|
| 509 | // Note: Both operations may be relatively expensive due to the |
---|
| 510 | // multiplications. |
---|
| 511 | // |
---|
[07dec4] | 512 | // See also: CanonicalForm::operator <(), CanonicalForm::operator ==() |
---|
[1aeb9a7] | 513 | // |
---|
| 514 | //}}} |
---|
| 515 | int |
---|
| 516 | InternalRational::comparesame ( InternalCF * c ) |
---|
| 517 | { |
---|
| 518 | ASSERT( ! ::is_imm( c ) && c->levelcoeff() == RationalDomain, "incompatible base coefficients" ); |
---|
[a52291] | 519 | mpz_t dummy1, dummy2; |
---|
| 520 | mpz_init( dummy1 ); mpz_init( dummy2 ); |
---|
| 521 | mpz_mul( dummy1, _num, MPQDEN( c ) ); |
---|
| 522 | mpz_mul( dummy2, _den, MPQNUM( c ) ); |
---|
| 523 | int result = mpz_cmp( dummy1, dummy2 ); |
---|
| 524 | mpz_clear( dummy1 ); mpz_clear( dummy2 ); |
---|
[1aeb9a7] | 525 | return result; |
---|
| 526 | } |
---|
| 527 | |
---|
| 528 | int |
---|
| 529 | InternalRational::comparecoeff ( InternalCF* c ) |
---|
[2dd068] | 530 | { |
---|
[1e6de6] | 531 | if ( ::is_imm( c ) ) |
---|
| 532 | { |
---|
[2b44a1] | 533 | ASSERT( ::is_imm( c ) == INTMARK, "incompatible base coefficients" ); |
---|
[a52291] | 534 | mpz_t dummy; |
---|
| 535 | mpz_init_set_si( dummy, imm2int( c ) ); |
---|
| 536 | mpz_mul( dummy, dummy, _den ); |
---|
| 537 | int result = mpz_cmp( _num, dummy ); |
---|
| 538 | mpz_clear( dummy ); |
---|
[2b44a1] | 539 | return result; |
---|
[2dd068] | 540 | } |
---|
[1e6de6] | 541 | else |
---|
| 542 | { |
---|
[2b44a1] | 543 | ASSERT( c->levelcoeff() == IntegerDomain, "incompatible base coefficients" ); |
---|
[a52291] | 544 | mpz_t dummy; |
---|
| 545 | mpz_init( dummy ); |
---|
| 546 | mpz_mul( dummy, _den, InternalInteger::MPI( c ) ); |
---|
| 547 | int result = mpz_cmp( _num, dummy ); |
---|
| 548 | mpz_clear( dummy ); |
---|
[2b44a1] | 549 | return result; |
---|
[2dd068] | 550 | } |
---|
| 551 | } |
---|
[1aeb9a7] | 552 | //}}} |
---|
[2dd068] | 553 | |
---|
| 554 | InternalCF* InternalRational::addcoeff( InternalCF* c ) |
---|
| 555 | { |
---|
| 556 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
[a52291] | 557 | mpz_t n, d; |
---|
[1e6de6] | 558 | if ( ::is_imm( c ) ) |
---|
| 559 | { |
---|
[8710ff0] | 560 | long cc = imm2int( c ); |
---|
[2b44a1] | 561 | if ( cc == 0 ) |
---|
| 562 | return this; |
---|
[41072b] | 563 | else |
---|
| 564 | { |
---|
[a52291] | 565 | mpz_init( n ); |
---|
[41072b] | 566 | if ( cc < 0 ) |
---|
| 567 | { |
---|
[a52291] | 568 | mpz_mul_ui( n, _den, -cc ); |
---|
| 569 | mpz_sub( n, _num, n ); |
---|
[41072b] | 570 | } |
---|
| 571 | else |
---|
| 572 | { |
---|
[a52291] | 573 | mpz_mul_ui( n, _den, cc ); |
---|
| 574 | mpz_add( n, _num, n ); |
---|
[41072b] | 575 | } |
---|
| 576 | } |
---|
[2dd068] | 577 | } |
---|
[1e6de6] | 578 | else |
---|
| 579 | { |
---|
[2b44a1] | 580 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
[a52291] | 581 | mpz_init( n ); |
---|
| 582 | mpz_mul( n, _den, InternalInteger::MPI( c ) ); |
---|
| 583 | mpz_add( n, _num, n ); |
---|
[2dd068] | 584 | } |
---|
[a52291] | 585 | mpz_init_set( d, _den ); |
---|
[2dd068] | 586 | // at this point there is no way that the result is not a true rational |
---|
| 587 | if ( deleteObject() ) delete this; |
---|
| 588 | return new InternalRational( n, d ); |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | InternalCF* InternalRational::subcoeff( InternalCF* c, bool negate ) |
---|
| 592 | { |
---|
| 593 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
[a52291] | 594 | mpz_t n, d; |
---|
[1e6de6] | 595 | if ( ::is_imm( c ) ) |
---|
| 596 | { |
---|
[8710ff0] | 597 | long cc = imm2int( c ); |
---|
[2b44a1] | 598 | if ( cc == 0 ) |
---|
[ac8e1a] | 599 | { |
---|
[1e6de6] | 600 | if ( negate ) |
---|
| 601 | { |
---|
| 602 | if ( getRefCount() == 1 ) |
---|
| 603 | { |
---|
[a52291] | 604 | mpz_neg( _num, _num ); |
---|
[2b44a1] | 605 | return this; |
---|
| 606 | } |
---|
[1e6de6] | 607 | else |
---|
| 608 | { |
---|
[2b44a1] | 609 | decRefCount(); |
---|
[a52291] | 610 | mpz_init_set( d, _den ); |
---|
| 611 | mpz_init_set( n, _num ); |
---|
| 612 | mpz_neg( n, n ); |
---|
[2b44a1] | 613 | return new InternalRational( n, d ); |
---|
| 614 | } |
---|
| 615 | } |
---|
| 616 | else |
---|
| 617 | return this; |
---|
[ac8e1a] | 618 | } |
---|
[a52291] | 619 | mpz_init( n ); |
---|
[1e6de6] | 620 | if ( cc < 0 ) |
---|
| 621 | { |
---|
[a52291] | 622 | mpz_mul_ui( n, _den, -cc ); |
---|
| 623 | mpz_neg( n, n ); |
---|
[2b44a1] | 624 | } |
---|
| 625 | else |
---|
[a52291] | 626 | mpz_mul_ui( n, _den, cc ); |
---|
[2b44a1] | 627 | if ( negate ) |
---|
[a52291] | 628 | mpz_sub( n, n, _num ); |
---|
[2b44a1] | 629 | else |
---|
[a52291] | 630 | mpz_sub( n, _num, n ); |
---|
[2dd068] | 631 | } |
---|
[1e6de6] | 632 | else |
---|
| 633 | { |
---|
[2b44a1] | 634 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
[a52291] | 635 | mpz_init( n ); |
---|
| 636 | mpz_mul( n, _den, InternalInteger::MPI( c ) ); |
---|
[2b44a1] | 637 | if ( negate ) |
---|
[a52291] | 638 | mpz_sub( n, n, _num ); |
---|
[2b44a1] | 639 | else |
---|
[a52291] | 640 | mpz_sub( n, _num, n ); |
---|
[2dd068] | 641 | } |
---|
[a52291] | 642 | mpz_init_set( d, _den ); |
---|
[2dd068] | 643 | // at this point there is no way that the result is not a true rational |
---|
| 644 | if ( deleteObject() ) delete this; |
---|
| 645 | return new InternalRational( n, d ); |
---|
| 646 | } |
---|
| 647 | |
---|
| 648 | InternalCF* InternalRational::mulcoeff( InternalCF* c ) |
---|
| 649 | { |
---|
| 650 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
[a52291] | 651 | mpz_t n, d, g; |
---|
[1e6de6] | 652 | if ( ::is_imm( c ) ) |
---|
| 653 | { |
---|
[8710ff0] | 654 | long cc = imm2int( c ); |
---|
[1e6de6] | 655 | if ( cc == 0 ) |
---|
| 656 | { |
---|
[2b44a1] | 657 | if ( deleteObject() ) delete this; |
---|
[8710ff0] | 658 | return CFFactory::basic( 0L ); |
---|
[2b44a1] | 659 | } |
---|
[a52291] | 660 | mpz_init_set_si( n, cc ); |
---|
[2dd068] | 661 | } |
---|
[1e6de6] | 662 | else |
---|
| 663 | { |
---|
[2b44a1] | 664 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
[a52291] | 665 | mpz_init_set( n, InternalInteger::MPI( c ) ); |
---|
[2dd068] | 666 | } |
---|
[a52291] | 667 | mpz_init( g ); |
---|
| 668 | mpz_gcd( g, n, _den ); |
---|
| 669 | if ( mpz_cmp_si( g, 1 ) == 0 ) |
---|
[1e6de6] | 670 | { |
---|
[a52291] | 671 | mpz_mul( n, n, _num ); |
---|
| 672 | mpz_init_set( d, _den ); |
---|
[2dd068] | 673 | } |
---|
[1e6de6] | 674 | else |
---|
| 675 | { |
---|
[a52291] | 676 | mpz_divexact( n, n, g ); |
---|
| 677 | mpz_mul( n, n, _num ); |
---|
| 678 | mpz_init( d ); |
---|
| 679 | mpz_divexact( d, _den, g ); |
---|
[2dd068] | 680 | } |
---|
[a52291] | 681 | mpz_clear( g ); |
---|
[2dd068] | 682 | if ( deleteObject() ) delete this; |
---|
[a52291] | 683 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
---|
[1e6de6] | 684 | { |
---|
[a52291] | 685 | mpz_clear( d ); |
---|
| 686 | if ( mpz_is_imm( n ) ) |
---|
[1e6de6] | 687 | { |
---|
[a52291] | 688 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
---|
| 689 | mpz_clear( n ); |
---|
[2b44a1] | 690 | return res; |
---|
| 691 | } |
---|
[1e6de6] | 692 | else |
---|
| 693 | { |
---|
[2b44a1] | 694 | return new InternalInteger( n ); |
---|
| 695 | } |
---|
[2dd068] | 696 | } |
---|
| 697 | else |
---|
[2b44a1] | 698 | return new InternalRational( n, d ); |
---|
[2dd068] | 699 | } |
---|
| 700 | |
---|
| 701 | InternalCF* InternalRational::dividecoeff( InternalCF* c, bool invert ) |
---|
| 702 | { |
---|
| 703 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "expected integer" ); |
---|
[a52291] | 704 | mpz_t n, d, g; |
---|
[1e6de6] | 705 | if ( ::is_imm( c ) ) |
---|
| 706 | { |
---|
[8710ff0] | 707 | long cc = imm2int( c ); |
---|
[2b44a1] | 708 | ASSERT( c != 0 || invert, "divide by zero" ); |
---|
[1e6de6] | 709 | if ( cc == 0 ) |
---|
| 710 | { |
---|
[2b44a1] | 711 | // => invert |
---|
| 712 | if ( deleteObject() ) delete this; |
---|
[8710ff0] | 713 | return CFFactory::basic( 0L ); |
---|
[2b44a1] | 714 | } |
---|
[1e6de6] | 715 | if ( invert ) |
---|
| 716 | { |
---|
[a52291] | 717 | mpz_init_set_si( n, cc ); |
---|
| 718 | mpz_mul( n, n, _den ); |
---|
| 719 | mpz_init_set( d, _num ); |
---|
[2b44a1] | 720 | } |
---|
[1e6de6] | 721 | else |
---|
| 722 | { |
---|
[a52291] | 723 | mpz_init_set_si( d, cc ); |
---|
| 724 | mpz_mul( d, d, _den ); |
---|
| 725 | mpz_init_set( n, _num ); |
---|
[2b44a1] | 726 | } |
---|
[2dd068] | 727 | } |
---|
[1e6de6] | 728 | else |
---|
| 729 | { |
---|
[2b44a1] | 730 | ASSERT( c->levelcoeff() == IntegerDomain, "expected integer" ); |
---|
[1e6de6] | 731 | if ( invert ) |
---|
| 732 | { |
---|
[a52291] | 733 | mpz_init_set( n, InternalInteger::MPI( c ) ); |
---|
| 734 | mpz_mul( n, n, _den ); |
---|
| 735 | mpz_init_set( d, _num ); |
---|
[2b44a1] | 736 | } |
---|
[1e6de6] | 737 | else |
---|
| 738 | { |
---|
[a52291] | 739 | mpz_init_set( d, InternalInteger::MPI( c ) ); |
---|
| 740 | mpz_mul( d, d, _den ); |
---|
| 741 | mpz_init_set( n, _num ); |
---|
[2b44a1] | 742 | } |
---|
[2dd068] | 743 | } |
---|
[a52291] | 744 | if ( mpz_cmp_si( d, 0 ) < 0 ) |
---|
[1e6de6] | 745 | { |
---|
[a52291] | 746 | mpz_neg( d, d ); |
---|
| 747 | mpz_neg( n, n ); |
---|
[2dd068] | 748 | } |
---|
[a52291] | 749 | mpz_init( g ); |
---|
| 750 | mpz_gcd( g, n, d ); |
---|
| 751 | if ( mpz_cmp_si( g, 1 ) != 0 ) |
---|
[1e6de6] | 752 | { |
---|
[a52291] | 753 | mpz_divexact( d, d, g ); |
---|
| 754 | mpz_divexact( n, n, g ); |
---|
[2dd068] | 755 | } |
---|
[a52291] | 756 | mpz_clear( g ); |
---|
[2dd068] | 757 | if ( deleteObject() ) delete this; |
---|
[1e6de6] | 758 | if ( ! invert ) |
---|
| 759 | { |
---|
[2b44a1] | 760 | // then there was no way for the result to become an integer |
---|
| 761 | return new InternalRational( n, d ); |
---|
[2dd068] | 762 | } |
---|
[a52291] | 763 | if ( mpz_cmp_si( d, 1 ) == 0 ) |
---|
[1e6de6] | 764 | { |
---|
[a52291] | 765 | mpz_clear( d ); |
---|
| 766 | if ( mpz_is_imm( n ) ) |
---|
[1e6de6] | 767 | { |
---|
[a52291] | 768 | InternalCF * res = int2imm( mpz_get_si( n ) ); |
---|
| 769 | mpz_clear( n ); |
---|
[2b44a1] | 770 | return res; |
---|
| 771 | } |
---|
[1e6de6] | 772 | else |
---|
| 773 | { |
---|
[2b44a1] | 774 | return new InternalInteger( n ); |
---|
| 775 | } |
---|
[2dd068] | 776 | } |
---|
| 777 | else |
---|
[2b44a1] | 778 | return new InternalRational( n, d ); |
---|
[2dd068] | 779 | } |
---|
| 780 | |
---|
| 781 | InternalCF* InternalRational::divcoeff( InternalCF* c, bool invert ) |
---|
| 782 | { |
---|
| 783 | return dividecoeff( c, invert ); |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | InternalCF* InternalRational::modulocoeff( InternalCF* c, bool invert ) |
---|
| 787 | { |
---|
| 788 | return modcoeff( c, invert ); |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | InternalCF* InternalRational::modcoeff( InternalCF* c, bool invert ) |
---|
| 792 | { |
---|
| 793 | ASSERT( ::is_imm( c ) == INTMARK || ! ::is_imm( c ), "integer expected" ); |
---|
| 794 | ASSERT( invert || ! ::is_imm( c ) || imm2int( c ) != 0, "divide by zero" ); |
---|
| 795 | if ( deleteObject() ) delete this; |
---|
[8710ff0] | 796 | return CFFactory::basic( 0L ); |
---|
[2dd068] | 797 | } |
---|
| 798 | |
---|
| 799 | void InternalRational::divremcoeff( InternalCF* c, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
| 800 | { |
---|
| 801 | quot = copyObject(); |
---|
| 802 | quot = quot->dividecoeff( c, invert ); |
---|
[8710ff0] | 803 | rem = CFFactory::basic( 0L ); |
---|
[2dd068] | 804 | } |
---|
| 805 | |
---|
| 806 | bool InternalRational::divremcoefft( InternalCF* c, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
| 807 | { |
---|
| 808 | divremcoeff( c, quot, rem, invert ); |
---|
| 809 | return true; |
---|
| 810 | } |
---|
| 811 | |
---|
[05d0b3] | 812 | //{{{ InternalCF * InternalRational::bgcdsame, bgcdcoeff ( const InternalCF * const ) |
---|
| 813 | // docu: see CanonicalForm::bgcd() |
---|
| 814 | InternalCF * |
---|
| 815 | InternalRational::bgcdsame ( const InternalCF * const ) const |
---|
| 816 | { |
---|
| 817 | return int2imm( 1 ); |
---|
| 818 | } |
---|
| 819 | |
---|
| 820 | InternalCF * |
---|
| 821 | InternalRational::bgcdcoeff ( const InternalCF * const ) |
---|
| 822 | { |
---|
| 823 | return int2imm( 1 ); |
---|
| 824 | } |
---|
| 825 | //}}} |
---|
| 826 | |
---|
| 827 | //{{{ InternalCF * InternalRational::bextgcdsame ( InternalCF * c, CanonicalForm & a, CanonicalForm & b ) |
---|
| 828 | // docu: see CanonicalForm::bextgcd() |
---|
| 829 | InternalCF * |
---|
| 830 | InternalRational::bextgcdsame ( InternalCF *, CanonicalForm & a, CanonicalForm & b ) |
---|
| 831 | { |
---|
| 832 | a = 1/CanonicalForm( copyObject() ); b = 0; |
---|
| 833 | return int2imm( 1 ); |
---|
| 834 | } |
---|
| 835 | |
---|
| 836 | InternalCF * |
---|
| 837 | InternalRational::bextgcdcoeff ( InternalCF *, CanonicalForm & a, CanonicalForm & b ) |
---|
| 838 | { |
---|
| 839 | a = 1/CanonicalForm( copyObject() ); b = 0; |
---|
| 840 | return int2imm( 1 ); |
---|
| 841 | } |
---|
| 842 | //}}} |
---|
| 843 | |
---|
[2dd068] | 844 | InternalCF * InternalRational::normalize_myself() |
---|
| 845 | { |
---|
| 846 | ASSERT( getRefCount() == 1, "illegal operation" ); |
---|
[a52291] | 847 | mpz_t g; |
---|
| 848 | mpz_init( g ); |
---|
| 849 | mpz_gcd( g, _num, _den ); |
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| 850 | if ( mpz_cmp_si( g, 1 ) != 0 ) |
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[2b44a1] | 851 | { |
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[a52291] | 852 | mpz_divexact( _num, _num, g ); |
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| 853 | mpz_divexact( _den, _den, g ); |
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[2dd068] | 854 | } |
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[2b44a1] | 855 | // Hier brauchen wir ein mpz_clear, J.M. |
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[a52291] | 856 | mpz_clear( g ); |
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| 857 | if ( mpz_cmp_si( _den, 0 ) < 0 ) |
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[2b44a1] | 858 | { |
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[a52291] | 859 | mpz_neg( _num, _num ); |
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| 860 | mpz_neg( _den, _den ); |
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[2dd068] | 861 | } |
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[a52291] | 862 | if ( mpz_cmp_si( _den, 1 ) == 0 ) |
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[1e6de6] | 863 | { |
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[a52291] | 864 | if ( mpz_is_imm( _num ) ) |
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[2b44a1] | 865 | { |
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[a52291] | 866 | InternalCF * res = int2imm( mpz_get_si( _num ) ); |
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[2b44a1] | 867 | delete this; |
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| 868 | return res; |
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| 869 | } |
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| 870 | else |
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| 871 | { |
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[a52291] | 872 | mpz_t res; |
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| 873 | mpz_init_set( res, _num ); |
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[2b44a1] | 874 | delete this; |
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| 875 | return new InternalInteger( res ); |
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| 876 | } |
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[1e6de6] | 877 | } |
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[2dd068] | 878 | else |
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[2b44a1] | 879 | return this; |
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[2dd068] | 880 | } |
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| 881 | |
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| 882 | |
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[8710ff0] | 883 | long InternalRational::intval() const |
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[2dd068] | 884 | { |
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[8710ff0] | 885 | |
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[a52291] | 886 | ASSERT( mpz_cmp_si( _den, 1 ) == 0, "illegal operation" ); |
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[8710ff0] | 887 | return mpz_get_si( _num ); |
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| 888 | |
---|
[2dd068] | 889 | } |
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| 890 | |
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[ede528] | 891 | //{{{ int InternalRational::sign () const |
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| 892 | // docu: see CanonicalForm::sign() |
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| 893 | int |
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| 894 | InternalRational::sign () const |
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[2dd068] | 895 | { |
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[a52291] | 896 | return mpz_sgn( _num ); |
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[2dd068] | 897 | } |
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[ede528] | 898 | //}}} |
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