[8a150b] | 1 | #ifndef MPR_COMPLEX_H |
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| 2 | #define MPR_COMPLEX_H |
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| 3 | /**************************************** |
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| 4 | * Computer Algebra System SINGULAR * |
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| 5 | ****************************************/ |
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[f543de1] | 6 | /* $Id: mpr_complex.h,v 1.4 1999-06-24 07:46:51 wenk Exp $ */ |
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[8a150b] | 7 | |
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| 8 | /* |
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| 9 | * ABSTRACT - multipolynomial resultants - real floating-point numbers using gmp |
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| 10 | * and complex numbers based on pairs of real floating-point numbers |
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| 11 | * |
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| 12 | */ |
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| 13 | |
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| 14 | //-> include & define stuff |
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| 15 | // must have gmp version >= 2 |
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| 16 | extern "C" { |
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| 17 | #include <gmp.h> |
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| 18 | } |
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| 19 | #include "numbers.h" |
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[f543de1] | 20 | #include "ring.h" |
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[8a150b] | 21 | #include "mpr_global.h" |
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| 22 | |
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| 23 | #define DEFPREC 20 // minimum number of digits (output operations) |
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| 24 | |
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| 25 | #define GMP_DEFAULT_PREC_BITS 512 // size of mantissa of floating-point number |
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| 26 | #define GMP_NEEDEQUAL_BITS 512-64 // a == b for the first gmp_equalupto_bits bits |
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| 27 | //<- |
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| 28 | |
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| 29 | void setGMPFloatPrecBytes( unsigned long int bytes ); |
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| 30 | unsigned long int getGMPFloatPrecBytes(); |
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[f543de1] | 31 | |
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[8a150b] | 32 | void setGMPFloatDigits( size_t digits ); |
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| 33 | size_t getGMPFloatDigits(); |
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| 34 | |
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| 35 | //-> class gmp_float |
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| 36 | /** |
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| 37 | * @short wrapper class for GNU Multi Precision Floats |
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| 38 | */ |
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| 39 | class gmp_float |
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| 40 | { |
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| 41 | public: |
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[f543de1] | 42 | gmp_float( const int v = 0 ) |
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| 43 | { |
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| 44 | mpf_init2( t, gmp_default_prec_bits ); |
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| 45 | mpf_set_si( t, (signed long int) v ); |
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| 46 | } |
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| 47 | gmp_float( const long v ) |
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| 48 | { |
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| 49 | mpf_init2( t, gmp_default_prec_bits ); |
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| 50 | mpf_set_si( t, (signed long int) v ); |
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| 51 | } |
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| 52 | gmp_float( const mprfloat v ) // double |
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| 53 | { |
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| 54 | mpf_init2( t, gmp_default_prec_bits ); |
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| 55 | mpf_set_d( t, (double) v ); |
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| 56 | } |
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| 57 | gmp_float( const mpf_t v ) |
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| 58 | { |
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| 59 | mpf_init2( t, gmp_default_prec_bits ); |
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| 60 | mpf_set( t, v ); |
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| 61 | } |
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| 62 | gmp_float( const mpz_t v ) // gnu mp Z |
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| 63 | { |
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| 64 | mpf_init2( t, gmp_default_prec_bits ); |
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| 65 | mpf_set_z( t, v ); |
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| 66 | } |
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| 67 | gmp_float( const gmp_float & v ) // copy constructor |
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| 68 | { |
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| 69 | //mpf_init2( t, mpf_get_prec( v.t ) ); |
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| 70 | mpf_init2( t, gmp_default_prec_bits ); |
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| 71 | mpf_set( t, v.t ); |
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| 72 | } |
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| 73 | |
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| 74 | ~gmp_float() |
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| 75 | { |
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| 76 | mpf_clear( t ); |
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| 77 | } |
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[8a150b] | 78 | |
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| 79 | friend gmp_float operator + ( const gmp_float & a, const gmp_float & b ); |
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| 80 | friend gmp_float operator - ( const gmp_float & a, const gmp_float & b ); |
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| 81 | friend gmp_float operator * ( const gmp_float & a, const gmp_float & b ); |
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| 82 | friend gmp_float operator / ( const gmp_float & a, const gmp_float & b ); |
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| 83 | |
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[f543de1] | 84 | inline gmp_float & operator += ( const gmp_float & a ); |
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| 85 | inline gmp_float & operator -= ( const gmp_float & a ); |
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| 86 | inline gmp_float & operator *= ( const gmp_float & a ); |
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| 87 | inline gmp_float & operator /= ( const gmp_float & a ); |
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[8a150b] | 88 | |
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| 89 | friend bool operator == ( const gmp_float & a, const gmp_float & b ); |
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| 90 | friend bool operator > ( const gmp_float & a, const gmp_float & b ); |
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| 91 | friend bool operator < ( const gmp_float & a, const gmp_float & b ); |
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| 92 | friend bool operator >= ( const gmp_float & a, const gmp_float & b ); |
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| 93 | friend bool operator <= ( const gmp_float & a, const gmp_float & b ); |
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| 94 | |
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| 95 | friend gmp_float operator - ( const gmp_float & a ); |
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| 96 | |
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| 97 | gmp_float & operator = ( const gmp_float & a ); |
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| 98 | gmp_float & operator = ( const mpz_t & a ); |
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| 99 | gmp_float & operator = ( const mprfloat a ); |
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| 100 | gmp_float & operator = ( const long a ); |
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| 101 | |
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[f543de1] | 102 | inline int sign(); // t>0:+1, t==0:0, t<0:-1 |
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| 103 | inline bool isZero(); // t == 0 ? |
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| 104 | inline bool isOne(); // t == 1 ? |
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| 105 | inline bool isMOne(); // t == -1 ? |
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[8a150b] | 106 | |
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[f543de1] | 107 | inline bool setFromStr( char * in ); |
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[8a150b] | 108 | |
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| 109 | // access |
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| 110 | inline const mpf_t *mpfp() const; |
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| 111 | |
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[f543de1] | 112 | inline operator double(); |
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| 113 | inline operator double() const; |
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[8a150b] | 114 | |
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[f543de1] | 115 | inline operator int(); |
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| 116 | inline operator int() const; |
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[8a150b] | 117 | |
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| 118 | public: |
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| 119 | static void setPrecision( const unsigned long int prec ) |
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| 120 | { gmp_default_prec_bits= prec; } |
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| 121 | static void setEqualBits( const unsigned long int prec ) |
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| 122 | { gmp_needequal_bits= prec; } |
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| 123 | |
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| 124 | static const unsigned long int getPrecision() |
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| 125 | { return gmp_default_prec_bits; } |
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| 126 | static const unsigned long int getEqualBits() |
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| 127 | { return gmp_needequal_bits; } |
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| 128 | |
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| 129 | private: |
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| 130 | static unsigned long int gmp_default_prec_bits; |
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| 131 | static unsigned long int gmp_needequal_bits; |
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| 132 | |
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| 133 | mpf_t t; |
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| 134 | }; |
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| 135 | |
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[f543de1] | 136 | static const gmp_float gmpOne= 1; |
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| 137 | static const gmp_float gmpMOne= -1; |
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| 138 | static const gmp_float gmpZero= 0; |
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| 139 | |
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| 140 | // <gmp_float> operator <gmp_float> |
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| 141 | inline gmp_float & gmp_float::operator += ( const gmp_float & a ) |
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| 142 | { |
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| 143 | mpf_add( t, t, a.t ); |
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| 144 | return *this; |
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| 145 | } |
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| 146 | inline gmp_float & gmp_float::operator -= ( const gmp_float & a ) |
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| 147 | { |
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| 148 | mpf_sub( t, t, a.t ); |
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| 149 | return *this; |
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| 150 | } |
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| 151 | inline gmp_float & gmp_float::operator *= ( const gmp_float & a ) |
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| 152 | { |
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| 153 | mpf_mul( t, t, a.t ); |
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| 154 | return *this; |
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| 155 | } |
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| 156 | inline gmp_float & gmp_float::operator /= ( const gmp_float & a ) |
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| 157 | { |
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| 158 | mpf_div( t, t, a.t ); |
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| 159 | return *this; |
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| 160 | } |
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| 161 | |
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| 162 | // <gmp_float> = <*> |
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| 163 | inline gmp_float & gmp_float::operator = ( const gmp_float & a ) |
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| 164 | { |
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| 165 | mpf_set( t, a.t ); |
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| 166 | return *this; |
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| 167 | } |
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| 168 | inline gmp_float & gmp_float::operator = ( const mpz_t & a ) |
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| 169 | { |
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| 170 | mpf_set_z( t, a ); |
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| 171 | return *this; |
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| 172 | } |
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| 173 | inline gmp_float & gmp_float::operator = ( const mprfloat a ) |
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| 174 | { |
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| 175 | mpf_set_d( t, (double) a ); |
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| 176 | return *this; |
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| 177 | } |
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| 178 | inline gmp_float & gmp_float::operator = ( const long a ) |
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| 179 | { |
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| 180 | mpf_set_si( t, (signed long int) a ); |
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| 181 | return *this; |
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| 182 | } |
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| 183 | |
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| 184 | // cast to double |
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| 185 | inline gmp_float::operator double() |
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| 186 | { |
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| 187 | return mpf_get_d( t ); |
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| 188 | } |
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| 189 | inline gmp_float::operator double() const |
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| 190 | { |
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| 191 | return mpf_get_d( t ); |
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| 192 | } |
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| 193 | |
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| 194 | // cast to int |
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| 195 | inline gmp_float::operator int() |
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| 196 | { |
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| 197 | return (int)mpf_get_d( t ); |
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| 198 | } |
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| 199 | inline gmp_float::operator int() const |
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| 200 | { |
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| 201 | return (int)mpf_get_d( t ); |
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| 202 | } |
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| 203 | |
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| 204 | // get sign of real number ( -1: t < 0; 0: t==0; 1: t > 0 ) |
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| 205 | inline int gmp_float::sign() |
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| 206 | { |
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| 207 | return mpf_sgn( t ); |
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| 208 | } |
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| 209 | // t == 0 ? |
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| 210 | inline bool gmp_float::isZero() |
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| 211 | { |
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| 212 | #ifdef VARIANTE_1 |
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| 213 | return (mpf_sgn( t ) == 0); |
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| 214 | #else |
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| 215 | return mpf_eq( t , gmpZero.t , gmp_float::gmp_needequal_bits ); |
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| 216 | #endif |
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| 217 | } |
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| 218 | // t == 1 ? |
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| 219 | inline bool gmp_float::isOne() |
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| 220 | { |
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| 221 | #ifdef VARIANTE_1 |
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| 222 | return (mpf_cmp_ui( t , 1 ) == 0); |
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| 223 | #else |
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| 224 | return mpf_eq( t , gmpOne.t , gmp_float::gmp_needequal_bits ); |
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| 225 | #endif |
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| 226 | } |
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| 227 | // t == -1 ? |
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| 228 | inline bool gmp_float::isMOne() |
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| 229 | { |
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| 230 | #ifdef VARIANTE_1 |
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| 231 | return (mpf_cmp_si( t , -1 ) == 0); |
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| 232 | #else |
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| 233 | return mpf_eq( t , gmpMOne.t , gmp_float::gmp_needequal_bits ); |
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| 234 | #endif |
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| 235 | } |
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| 236 | |
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| 237 | inline bool gmp_float::setFromStr( char * in ) |
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| 238 | { |
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| 239 | return ( mpf_set_str( t, in, 10 ) == 0 ); |
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| 240 | } |
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| 241 | |
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| 242 | // access pointer |
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| 243 | inline const mpf_t *gmp_float::mpfp() const |
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| 244 | { |
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| 245 | return &t; |
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| 246 | } |
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| 247 | |
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[8a150b] | 248 | // built-in functions of GMP |
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| 249 | gmp_float abs( const gmp_float & ); |
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| 250 | gmp_float sqrt( const gmp_float & ); |
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| 251 | gmp_float hypot( const gmp_float &, const gmp_float & ); |
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| 252 | |
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| 253 | // simulated functions using double functions |
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| 254 | gmp_float sin( const gmp_float & ); |
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| 255 | gmp_float cos( const gmp_float & ); |
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| 256 | gmp_float log( const gmp_float & ); |
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| 257 | gmp_float exp( const gmp_float & ); |
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| 258 | |
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| 259 | gmp_float max( const gmp_float &, const gmp_float & ); |
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| 260 | |
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| 261 | gmp_float numberToFloat( number num ); |
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[f543de1] | 262 | char *floatToStr( const gmp_float & r, const unsigned int oprec ); |
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[8a150b] | 263 | //<- |
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| 264 | |
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[f543de1] | 265 | //-> class gmp_complex |
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[8a150b] | 266 | /** |
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[f543de1] | 267 | * @short gmp_complex numbers based on |
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[8a150b] | 268 | */ |
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[f543de1] | 269 | class gmp_complex |
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[8a150b] | 270 | { |
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[0f0a1d] | 271 | private: |
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[f543de1] | 272 | gmp_float r, i; |
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[0f0a1d] | 273 | |
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[8a150b] | 274 | public: |
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[f543de1] | 275 | gmp_complex( const gmp_float re= 0.0, const gmp_float im= 0.0 ) |
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| 276 | { |
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| 277 | r= re; |
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| 278 | i= im; |
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| 279 | } |
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| 280 | gmp_complex( const mprfloat re, const mprfloat im = 0.0 ) |
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| 281 | { |
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| 282 | r= re; |
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| 283 | i= im; |
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| 284 | } |
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| 285 | gmp_complex( const long re, const long im ) |
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| 286 | { |
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| 287 | r= re; |
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| 288 | i= im; |
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| 289 | } |
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| 290 | gmp_complex( const gmp_complex & v ) |
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| 291 | { |
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| 292 | r= v.r; |
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| 293 | i= v.i; |
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| 294 | } |
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| 295 | ~gmp_complex() {} |
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| 296 | |
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| 297 | friend gmp_complex operator + ( const gmp_complex & a, const gmp_complex & b ); |
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| 298 | friend gmp_complex operator - ( const gmp_complex & a, const gmp_complex & b ); |
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| 299 | friend gmp_complex operator * ( const gmp_complex & a, const gmp_complex & b ); |
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| 300 | friend gmp_complex operator / ( const gmp_complex & a, const gmp_complex & b ); |
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| 301 | |
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| 302 | // gmp_complex <operator> real |
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| 303 | inline friend gmp_complex operator + ( const gmp_complex & a, const gmp_float b_d ); |
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| 304 | inline friend gmp_complex operator - ( const gmp_complex & a, const gmp_float b_d ); |
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| 305 | inline friend gmp_complex operator * ( const gmp_complex & a, const gmp_float b_d ); |
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| 306 | inline friend gmp_complex operator / ( const gmp_complex & a, const gmp_float b_d ); |
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| 307 | |
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| 308 | gmp_complex & operator += ( const gmp_complex & a ); |
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| 309 | gmp_complex & operator -= ( const gmp_complex & a ); |
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| 310 | gmp_complex & operator *= ( const gmp_complex & a ); |
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| 311 | gmp_complex & operator /= ( const gmp_complex & a ); |
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| 312 | |
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| 313 | inline friend bool operator == ( const gmp_complex & a, const gmp_complex & b ); |
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| 314 | |
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| 315 | inline gmp_complex & operator = ( const gmp_complex & a ); |
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[8a150b] | 316 | |
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[f543de1] | 317 | // access to real and imaginary part |
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| 318 | inline gmp_float real() const { return r; } |
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| 319 | inline gmp_float imag() const { return i; } |
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[8a150b] | 320 | |
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[f543de1] | 321 | inline void real( gmp_float val ) { r = val; } |
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| 322 | inline void imag( gmp_float val ) { i = val; } |
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| 323 | }; |
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[8a150b] | 324 | |
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[f543de1] | 325 | // <gmp_complex> = <gmp_complex> operator <gmp_float> |
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| 326 | // |
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| 327 | inline gmp_complex operator + ( const gmp_complex & a, const gmp_float b_d ) |
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| 328 | { |
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| 329 | return gmp_complex( a.r + b_d, a.i ); |
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| 330 | } |
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| 331 | inline gmp_complex operator - ( const gmp_complex & a, const gmp_float b_d ) |
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| 332 | { |
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| 333 | return gmp_complex( a.r - b_d, a.i ); |
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| 334 | } |
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| 335 | inline gmp_complex operator * ( const gmp_complex & a, const gmp_float b_d ) |
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| 336 | { |
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| 337 | return gmp_complex( a.r * b_d, a.i * b_d ); |
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| 338 | } |
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| 339 | inline gmp_complex operator / ( const gmp_complex & a, const gmp_float b_d ) |
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| 340 | { |
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| 341 | return gmp_complex( a.r / b_d, a.i / b_d ); |
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| 342 | } |
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[8a150b] | 343 | |
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[f543de1] | 344 | // <gmp_complex> == <gmp_complex> ? |
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| 345 | inline bool operator == ( const gmp_complex & a, const gmp_complex & b ) |
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| 346 | { |
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| 347 | return ( b.real() == a.real() ) && ( b.imag() == a.imag() ); |
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| 348 | } |
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[8a150b] | 349 | |
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[f543de1] | 350 | // <gmp_complex> = <gmp_complex> |
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| 351 | inline gmp_complex & gmp_complex::operator = ( const gmp_complex & a ) |
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| 352 | { |
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| 353 | r= a.r; |
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| 354 | i= a.i; |
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| 355 | return *this; |
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| 356 | } |
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[8a150b] | 357 | |
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[f543de1] | 358 | // Returns absolute value of a gmp_complex number |
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| 359 | // |
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| 360 | inline gmp_float abs( const gmp_complex & c ) |
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| 361 | { |
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| 362 | return hypot(c.real(),c.imag()); |
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| 363 | } |
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[8a150b] | 364 | |
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[f543de1] | 365 | gmp_complex sqrt( const gmp_complex & x ); |
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[8a150b] | 366 | |
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[f543de1] | 367 | inline gmp_complex numberToGmp_Complex( number num ) |
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[0f0a1d] | 368 | { |
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[f543de1] | 369 | if (rField_is_long_C()) { |
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| 370 | return *(gmp_complex*)num; |
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| 371 | } else { |
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| 372 | return gmp_complex( numberToFloat(num) ); |
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| 373 | } |
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[0f0a1d] | 374 | } |
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[f543de1] | 375 | |
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| 376 | char *complexToStr( const gmp_complex & c, const unsigned int oprec ); |
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[8a150b] | 377 | //<- |
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| 378 | |
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| 379 | #endif MPR_COMPLEX_H |
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| 380 | |
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| 381 | // local Variables: *** |
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| 382 | // folded-file: t *** |
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| 383 | // compile-command-1: "make installg" *** |
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| 384 | // compile-command-2: "make install" *** |
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| 385 | // End: *** |
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[f543de1] | 386 | |
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| 387 | |
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| 388 | |
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| 389 | |
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| 390 | |
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