include/numerix/ball.hpp File Reference

#include <numerix/ball_rounded.hpp>
#include <numerix/ball_rough.hpp>
#include <numerix/ball_infinities.hpp>

Go to the source code of this file.

Classes

class ball< C, R, V >
struct symbolic_type_information< ball< floating<> > >
struct rounding_helper< ball< C, R, V > >
struct projective_helper< ball< C, R, V > >
struct make_ball_helper< ball< C, R, V >, C2, R2 >
struct make_interval_helper< ball< C, R, V >, C2 >
struct binary_helper< ball< C, R, V > >
struct elementary_variant< C, Real, V >
struct elementary_variant< C, C, V >

Namespaces

namespace mmx

Defines

#define Ball_variant(C) typename ball_variant_helper<C>::BV
#define TMPL_DEF
#define TMPL template<typename C,typename R,typename V>
#define Ball ball<C,R,V>
#define Abs_ball ball<Abs_type(C),R,Abs_type(V) >
#define Elementary_variant(C, V) typename elementary_variant<C,Real_type(C),V>::EV
#define mmx_ball(R, C) ball<C >

Functions

UNARY_RETURN_TYPE (template< typename C, typename R, typename V >, center_op, ball< C, R, V >, C)
UNARY_RETURN_TYPE (template< typename C, typename R, typename V >, radius_op, ball< C, R, V >, R)
UNARY_RETURN_TYPE (template< typename C, typename R, typename V >, abs_op, ball< C, R, V >, ball< Abs_type(C), R, Abs_type(V) >)
template<typename C , typename R , typename V > C center (const ball< C, R, V > &z)
template<typename C , typename R , typename V > R radius (const ball< C, R, V > &z)
template<typename C , typename R , typename V > C & center (ball< C, R, V > &z)
template<typename C , typename R , typename V > R & radius (ball< C, R, V > &z)
template<typename C , typename R , typename V > C lower (const ball< C, R, V > &z)
template<typename C , typename R , typename V > C upper (const ball< C, R, V > &z)
template<typename C , typename R , typename V > R abs_down (const ball< C, R, V > &z)
template<typename C , typename R , typename V > R abs_up (const ball< C, R, V > &z)
template<typename C , typename R , typename V > R bnd_down (const ball< C, R, V > &z)
template<typename C , typename R , typename V > R bnd_up (const ball< C, R, V > &z)
template<typename C , typename R , typename V > void add_rounding_error (ball< C, R, V > &z)
template<typename C , typename R , typename V > void add_additive_error (ball< C, R, V > &z)
template<typename C , typename R , typename V > void add_multiplicative_error (ball< C, R, V > &z)
template<typename C , typename R , typename V > void add_elementary_error (ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > copy (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > duplicate (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_exact_zero (const ball< C, R, V > &z)
template<typename Op , typename C , typename R , typename V > nat unary_hash (const ball< C, R, V > &x)
template<typename Op , typename C , typename R , typename V > bool binary_test (const ball< C, R, V > &x1, const ball< C, R, V > &x2)
EXACT_IDENTITY_OP_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >) HARD_IDENTITY_OP_SUGAR(template< typename C
template<typename C , typename R , typename V > ball< C, R, V > syntactic flatten (const ball< C, R, V > &z)
template<typename C , typename R , typename V > syntactic flatten (const ball< C, R, V > &z, xnat dd)
template<typename C , typename R , typename V > syntactic flatten_range (const ball< C, R, V > &z)
template<typename C , typename R , typename V > syntactic flatten_range (const ball< C, R, V > &z, xnat dd)
template<typename R , typename V > syntactic flatten (const ball< double, R, V > &z)
template<typename R , typename V > syntactic flatten (const ball< double, R, V > &z, xnat dd)
template<typename FV , typename R , typename V > syntactic flatten (const ball< floating< FV >, R, V > &z)
template<typename FV , typename R , typename V > syntactic flatten (const ball< floating< FV >, R, V > &z, xnat dd)
template<typename TC , typename TR , typename TV , typename FC , typename FR , typename FV > void set_as (ball< TC, TR, TV > &r, const ball< FC, FR, FV > &z)
template<typename TC , typename TR , typename TV , typename F > void set_as (ball< TC, TR, TV > &r, const F &z)
template<typename C , typename R , typename V > bool is_zero (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_non_zero (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_negative_or_zero (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_negative (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_positive_or_zero (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_positive (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool operator== (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool operator!= (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool operator<= (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool operator< (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool operator>= (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool operator> (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > bool included (const ball< C, R, V > &b1, const ball< C, R, V > &b2)
template<typename C , typename R , typename V > nat hash (const ball< C, R, V > &z)
EQUAL_INT_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >)
COMPARE_INT_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >)
EQUAL_SCALAR_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >, C)
COMPARE_SCALAR_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >, C)
EQUAL_SCALAR_SUGAR_BIS (template< typename C, typename R, typename V >, ball< C, R, V >, C)
COMPARE_SCALAR_SUGAR_BIS (template< typename C, typename R, typename V >, ball< C, R, V >, C)
template<typename C , typename R , typename V > void set_default (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_nan (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_maximal (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_minimal (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_infinity (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_fuzz (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_smallest (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_largest (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_accuracy (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_log2 (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_pi (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_euler (ball< C, R, V > &x)
template<typename C , typename R , typename V > void set_imaginary (ball< C, R, V > &x)
template<typename C , typename R , typename V > ball< C, R, V > times_infinity (const ball< C, R, V > &x)
template<typename C , typename R , typename V > ball< C, R, V > operator- (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > operator+ (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator+ (const ball< C, R, V > &z1, const C &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator+ (const C &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator- (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator- (const ball< C, R, V > &z1, const C &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator- (const C &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator* (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator* (const ball< C, R, V > &z1, const C &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator* (const C &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > square (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > invert (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > operator/ (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator/ (const ball< C, R, V > &z1, const C &z2)
template<typename C , typename R , typename V > ball< C, R, V > operator/ (const C &z1, const ball< C, R, V > &z2)
ARITH_INT_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >)
template<typename C , typename R , typename V > ball< C, R, V > sqrt (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > hypot (const ball< C, R, V > &x, const ball< C, R, V > &y)
template<typename C , typename R , typename V > ball< C, R, V > exp (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > log (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > pow (const ball< C, R, V > &z, const ball< C, R, V > &y)
template<typename C , typename R , typename V > ball< C, R, V > pow (const ball< C, R, V > &z, const int &y)
template<typename C , typename R , typename V > ball< C, R, V > pow (const int &z, const ball< C, R, V > &y)
template<typename C , typename R , typename V > ball< C, R, V > cos (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > sin (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > tan (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > cosh (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > sinh (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > tanh (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > acos (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > asin (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > atan (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > atan2 (const ball< C, R, V > &y, const ball< C, R, V > &x)
INV_TRIGO_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >) INV_HYPER_SUGAR(template< typename C
ball< C, R, V > V ball
< Abs_type(C), R, Abs_type(V) > abs (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > min (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > max (const ball< C, R, V > &z1, const ball< C, R, V > &z2)
template<typename C , typename R , typename V > ball< C, R, V > floor (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > trunc (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > ceil (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > round (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_finite (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_infinite (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_fuzz (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_nan (const ball< C, R, V > &z)
template<typename C , typename R , typename V > bool is_reliable (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > change_precision (const ball< C, R, V > &z, xnat prec)
template<typename C , typename R , typename V > xnat precision (const ball< C, R, V > &x)
template<typename C , typename R , typename V > ball< Abs_type(C), R, Abs_type(V) > additive_error (const ball< C, R, V > &x)
template<typename C , typename R , typename V > ball< Abs_type(C), R, Abs_type(V) > multiplicative_error (const ball< C, R, V > &x)
template<typename C , typename R , typename V > ball< Abs_type(C), R, Abs_type(V) > elementary_error (const ball< C, R, V > &x)
template<typename C , typename R , typename V > xint exponent (const ball< C, R, V > &z)
template<typename C , typename R , typename V > double magnitude (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > operator<< (const ball< C, R, V > &z, const xint &shift)
template<typename C , typename R , typename V > ball< C, R, V > operator>> (const ball< C, R, V > &z, const xint &shift)
template<typename C , typename R , typename V > ball< C, R, V > next_above (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > next_below (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > sharpen (const ball< C, R, V > &z)
template<typename C , typename R , typename V > ball< C, R, V > blur (const ball< C, R, V > &z, const R &r)
template<typename C , typename R , typename V , typename K > ball< C, R, V > blur (const ball< C, R, V > &z, const ball< K, R, V > &r)
template<typename R , typename C > ball< C > make_mmx_ball (const C &c, const R &r)
template<typename C > ball< C > make_mmx_ball (const C &c)
template<typename C > Abs_type (C) mmx_radius(const ball< C > &z)

Variables

R
V
ball< C, R, V > ARG_HYPER_SUGAR (template< typename C, typename R, typename V >, ball< C, R, V >) template< typename C

Define Documentation

#define Abs_ball ball<Abs_type(C),R,Abs_type(V) >

Definition at line 25 of file ball.hpp.

#define Ball ball<C,R,V>

Definition at line 24 of file ball.hpp.

#define Ball_variant ( C ) typename ball_variant_helper<C>::BV

Definition at line 19 of file ball.hpp.

#define Elementary_variant	(	C,
		V		)	typename elementary_variant<C,Real_type(C),V>::EV

Definition at line 468 of file ball.hpp.

#define mmx_ball	(	R,
		C		)	ball<C >

Definition at line 702 of file ball.hpp.

#define TMPL template<typename C,typename R,typename V>

Definition at line 23 of file ball.hpp.

#define TMPL_DEF

Value:

template<typename C, \
  typename R=Default_radius_type(C),  \
  typename V=Ball_variant(C) >

Definition at line 20 of file ball.hpp.