include/numerix/affine.hpp File Reference

#include <basix/function.hpp>
#include <numerix/ball.hpp>

Go to the source code of this file.

Classes

• struct affine_limits_helper< C, VC >
• class affine< C, VC >
• struct rounding_helper< affine< C, VC > >
• struct binary_helper< affine< C, VC > >

Namespaces

• namespace mmx

Defines

• #define TMPL_DEF   template<typename C, typename VC= C>
• #define TMPL   template<typename C, typename VC>
• #define R   Radius_type(C)
• #define VR   typename affine_limits_helper<C,VC>::VT
• #define Affine   affine<C,VC>
• #define Affine_rep   affine_rep<C,VC>
• #define Abs_affine   affine<Abs_type(C),Abs_type(VC) >
• #define Real_affine   affine<Real_type(C),Real_type(VC) >

Functions

• template<typename C , typename VC > C base (const affine< C, VC > &z)
• template<typename C , typename VC > VC slope (const affine< C, VC > &z)
• template<typename C , typename VC > affine_limits_helper< C, VC >::VT limits (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > operator- (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C > C dot (const C &x, const C &y)
• DEFINE_BINARY_FORMAT_2 (affine) template< typename C
• STYPE_TO_TYPE (template< typename C, typename VC >, scalar_type, affine< C, VC >, C)
• UNARY_RETURN_TYPE (template< typename C, typename VC >, Re_op, affine< C, VC >, affine< Real_type(C), Real_type(VC) >)
• UNARY_RETURN_TYPE (template< typename C, typename VC >, abs_op, affine< C, VC >, affine< Abs_type(C), Abs_type(VC) >)
• template<typename C , typename VC > format< C > CF1 (const affine< C, VC > &z)
• template<typename C , typename VC > format< VC > CF2 (const affine< C, VC > &z)
• template<typename C , typename VC > C truncate (const affine< C, VC > &z)
• template<typename C , typename VC > affine_limits_helper< C, VC >::VT common_limits (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > make_affine (const C &cst, const VC &lin, const VC &dom)
• template<typename C , typename VC > VC domain (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > copy (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > duplicate (const affine< C, VC > &z)
• template<typename Op , typename C , typename VC > nat unary_hash (const affine< C, VC > &x)
• template<typename Op , typename C , typename VC > bool binary_test (const affine< C, VC > &x1, const affine< C, VC > &x2)
• template<typename CS , typename CD , typename DS , typename DD , typename FunC , typename FunD > affine< CD, DD > map (const FunC &funC, const FunD &funD, const affine< CS, DS > &z, const format< CD > &fmC, const format< DD > &fmD)
• TRUE_IDENTITY_OP_SUGAR (template< typename C, typename VC >, affine< C, VC >) EXACT_IDENTITY_OP_SUGAR(template< typename C
• affine< C, VC > VC syntactic flatten (const affine< C, VC > &z)
• template<typename C , typename VC > void set_default (affine< C, VC > &x)
• template<typename C , typename VC > void set_nan (affine< C, VC > &x)
• template<typename C , typename VC > void set_maximal (affine< C, VC > &x)
• template<typename C , typename VC > void set_minimal (affine< C, VC > &x)
• template<typename C , typename VC > void set_infinity (affine< C, VC > &x)
• template<typename C , typename VC > void set_fuzz (affine< C, VC > &x)
• template<typename C , typename VC > void set_smallest (affine< C, VC > &x)
• template<typename C , typename VC > void set_largest (affine< C, VC > &x)
• template<typename C , typename VC > void set_accuracy (affine< C, VC > &x)
• template<typename C , typename VC > void set_log2 (affine< C, VC > &x)
• template<typename C , typename VC > void set_pi (affine< C, VC > &x)
• template<typename C , typename VC > void set_euler (affine< C, VC > &x)
• template<typename C , typename VC > void set_imaginary (affine< C, VC > &x)
• template<typename C , typename VC > affine< C, VC > times_infinity (const affine< C, VC > &x)
• template<typename C , typename VC > affine< C, VC > operator- (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > operator+ (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator+ (const C &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator+ (const affine< C, VC > &z1, const C &z2)
• template<typename C , typename VC > affine< C, VC > operator- (const C &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator- (const affine< C, VC > &z1, const C &z2)
• template<typename C , typename VC > affine< C, VC > operator* (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator* (const C &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator* (const affine< C, VC > &z1, const C &z2)
• template<typename C , typename VC > affine< C, VC > square (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > invert (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > operator/ (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator/ (const C &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > operator/ (const affine< C, VC > &z1, const C &z2)
• ARITH_INT_SUGAR (template< typename C, typename VC >, affine< C, VC >)
• template<typename C , typename VC > bool operator<= (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > bool operator< (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > bool operator>= (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > bool operator> (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > min (const affine< C, VC > &z1, const affine< C, VC > &z2)
• template<typename C , typename VC > affine< C, VC > max (const affine< C, VC > &z1, const affine< C, VC > &z2)
• EQUAL_INT_SUGAR (template< typename C, typename VC >, affine< C, VC >)
• COMPARE_INT_SUGAR (template< typename C, typename VC >, affine< C, VC >)
• template<typename C , typename VC > bool is_finite (const affine< C, VC > &z)
• template<typename C , typename VC > bool is_nan (const affine< C, VC > &z)
• template<typename C , typename VC > bool is_infinite (const affine< C, VC > &z)
• template<typename C , typename VC > bool is_fuzz (const affine< C, VC > &z)
• template<typename C , typename VC > bool is_reliable (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > change_precision (const affine< C, VC > &z, xnat prec)
• template<typename C , typename VC > xnat precision (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > additive_error (const affine< C, VC > &z)
• template<typename C , typename VC > double magnitude (const affine< C, VC > &z)
• template<typename C , typename VC > xint exponent (const affine< C, VC > &z)
• template<typename C , typename VC > affine< C, VC > operator<< (const affine< C, VC > &z, const xint &s)
• template<typename C , typename VC > affine< C, VC > operator>> (const affine< C, VC > &z, const xint &s)
• template<typename C , typename VC > affine< C, VC > sharpen (const affine< C, VC > &z)
• template<typename C , typename VC , typename C2 , typename VC2 > affine< C, VC > blur (const affine< C, VC > &z, const affine< C2, VC2 > &r)
• template<typename C , typename VC > affine< Abs_type(C), Abs_type(VC) > abs (const affine< C, VC > &z)
• template<typename C , typename VC > affine< Real_type(C),
  Real_type(VC) > Re (const affine< C, VC > &z)
• template<typename C , typename VC > affine< Real_type(C),
  Real_type(VC) > Im (const affine< C, VC > &z)

Variables

• VC
• affine< C, VC > HARD_IDENTITY_OP_SUGAR (template< typename C, typename VC >, affine< C, VC >) template< typename C

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Define Documentation

#define Abs_affine   affine<Abs_type(C),Abs_type(VC) >

Definition at line 24 of file affine.hpp.

#define Affine   affine<C,VC>

Definition at line 22 of file affine.hpp.

Referenced by binary_helper< affine< C, VC > >::assemble(), and binary_helper< affine< C, VC > >::read().

#define Affine_rep   affine_rep<C,VC>

Definition at line 23 of file affine.hpp.

#define R   Radius_type(C)

Definition at line 20 of file affine.hpp.

Referenced by implementation< ball_rounding, W, ball_rounded >::abs_down(), implementation< ball_rounding, W, ball_rounded >::abs_up(), implementation< ball_elementary, W, ball_rounded >::acos(), implementation< ball_additive, W, ball_rounded >::add(), implementation< ball_rounding, W, ball_rounded >::add_additive_error(), implementation< ball_rounding, W, ball_rounded >::add_elementary_error(), implementation< ball_rounding, W, ball_rounded >::add_multiplicative_error(), implementation< ball_rounding, W, ball_rounded >::add_rounding_error(), implementation< ball_elementary, W, ball_rounded >::asin(), implementation< ball_elementary, W, ball_rounded >::atan(), implementation< ball_elementary, W, ball_rounded >::atan2(), ball< C, R, V >::ball(), implementation< ball_rounding, W, ball_rounded >::bnd_down(), implementation< ball_rounding, W, ball_rounded >::bnd_up(), implementation< ball_elementary, W, ball_rounded >::cos(), implementation< ball_elementary, IV, ball_complex< BV > >::cos(), implementation< ball_elementary, W, ball_rounded >::cosh(), implementation< ball_elementary, IV, ball_complex< BV > >::cosh(), implementation< ball_elementary, W, ball_rounded >::exp(), implementation< ball_elementary, IV, ball_complex< BV > >::exp(), binary_helper< ball< C, R, V > >::full_type_name(), implementation< ball_complex_construct, IV, ball_complex< BV > >::gauss(), implementation< ball_root, W, ball_rounded >::hypot(), implementation< ball_multiplicative, W, ball_rounded >::invert(), implementation< ball_multiplicative, W, ball_rough >::invert(), implementation< ball_elementary, W, ball_rounded >::log(), implementation< ball_elementary, IV, ball_complex< BV > >::log(), implementation< ball_multiplicative, W, ball_rounded >::mul(), implementation< ball_multiplicative, W, ball_rough >::mul(), binary_helper< ball< C, R, V > >::read(), rnd_floating< V, R >::rnd(), implementation< ball_shift, W, ball_rough >::shiftl(), implementation< ball_shift, W, ball_rough >::shiftr(), binary_helper< ball< C, R, V > >::short_type_name(), implementation< ball_elementary, W, ball_rounded >::sin(), implementation< ball_elementary, IV, ball_complex< BV > >::sin(), implementation< ball_elementary, W, ball_rounded >::sinh(), implementation< ball_elementary, IV, ball_complex< BV > >::sinh(), implementation< ball_root, W, ball_rounded >::sqrt(), implementation< ball_root, W, ball_rough >::sqrt(), implementation< ball_root, IV, ball_complex< BV > >::sqrt(), implementation< ball_multiplicative, W, ball_rounded >::square(), implementation< ball_multiplicative, W, ball_rough >::square(), implementation< ball_additive, W, ball_rounded >::sub(), and make_interval_helper< ball< C, R, V >, C2 >::val().

#define Real_affine   affine<Real_type(C),Real_type(VC) >

Definition at line 25 of file affine.hpp.

#define TMPL   template<typename C, typename VC>

Definition at line 19 of file affine.hpp.

#define TMPL_DEF   template<typename C, typename VC= C>

Definition at line 18 of file affine.hpp.

#define VR   typename affine_limits_helper<C,VC>::VT

Definition at line 21 of file affine.hpp.

Referenced by binary_helper< affine< C, VC > >::read().