/Users/mourrain/Devel/mmx/numerix/include/numerix/interval.hpp File Reference

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

Go to the source code of this file.

Classes

• struct std_interval
• struct std_interval::rnd_helper< C >
• class interval< C, V >
• struct rounding_helper< interval< C, V > >
• struct make_ball_helper< interval< C, V >, C2, R2 >
• struct make_interval_helper< interval< C, V >, C2 >
• struct binary_helper< interval< C, V > >

Namespaces

• namespace mmx

Defines

• #define TMPL_DEF   template<typename C,typename V=std_interval>
• #define TMPL   template<typename C,typename V>
• #define Interval   interval<C,V>
• #define Up   V::template rnd_helper<C>::UV
• #define Down   V::template rnd_helper<C>::DV

Functions

• template<typename C , typename V > C lower (const interval< C, V > &z)
• template<typename C , typename V > C upper (const interval< C, V > &z)
• DEFINE_UNARY_FORMAT_1 (interval) UNARY_RETURN_TYPE(template< typename C
• UNARY_RETURN_TYPE (template< typename C, typename V >, radius_op, interval< C, V >, C)
• template<typename C , typename V > C center (const interval< C, V > &x)
• template<typename C , typename V > C radius (const interval< C, V > &x)
• template<typename C , typename V > format< C > CF (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > abs (const interval< C, V > &x)
• template<typename C , typename V > C abs_down (const interval< C, V > &x)
• template<typename C , typename V > C abs_up (const interval< C, V > &x)
• template<typename C , typename V > C bnd_down (const interval< C, V > &x)
• template<typename C , typename V > C bnd_up (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > copy (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > duplicate (const interval< C, V > &x)
• template<typename C , typename V > bool is_exact_zero (const interval< C, V > &x)
• template<typename Op , typename C , typename V > nat unary_hash (const interval< C, V > &x)
• template<typename Op , typename C , typename V > bool binary_test (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename S1 , typename D > interval< D > map (const function_1< D, Argument(S1) > &fun, const interval< S1 > &x)
• template<typename S1 , typename D > interval< D > map (D(*fun)(const S1 &), const interval< S1 > &x)
• EXACT_IDENTITY_OP_SUGAR (template< typename C, typename V >, interval< C, V >) HARD_IDENTITY_OP_SUGAR(template< typename C
• template<typename C , typename V > interval< C, V > nat hash (const interval< C, V > &x)
• template<typename C , typename V > syntactic flatten (const interval< C, V > &x)
• template<typename C , typename V > syntactic flatten (const interval< C, V > &x, xnat dd)
• template<typename C , typename V > bool intersect (interval< C, V > &r, const interval< C, V > &a, const interval< C, V > &b)
• template<typename C , typename V > bool is_zero (const interval< C, V > &x)
• template<typename C , typename V > bool is_non_zero (const interval< C, V > &x)
• template<typename C , typename V > bool operator== (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > bool operator!= (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > bool operator<= (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > bool operator< (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > bool operator>= (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > bool operator> (const interval< C, V > &x1, const interval< C, V > &x2)
• EQUAL_INT_SUGAR (template< typename C, typename V >, interval< C, V >)
• COMPARE_INT_SUGAR (template< typename C, typename V >, interval< C, V >)
• template<typename C , typename V > interval< C, V > min (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > max (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > floor (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > trunc (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > ceil (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > round (const interval< C, V > &x)
• template<typename C , typename V > void set_nan (interval< C, V > &x)
• template<typename C , typename V > void set_maximal (interval< C, V > &x)
• template<typename C , typename V > void set_minimal (interval< C, V > &x)
• template<typename C , typename V > void set_infinity (interval< C, V > &x)
• template<typename C , typename V > void set_fuzz (interval< C, V > &x)
• template<typename C , typename V > void set_smallest (interval< C, V > &x)
• template<typename C , typename V > void set_largest (interval< C, V > &x)
• template<typename C , typename V > void set_accuracy (interval< C, V > &x)
• template<typename C , typename V > void set_log2 (interval< C, V > &x)
• template<typename C , typename V > void set_pi (interval< C, V > &x)
• template<typename C , typename V > void set_euler (interval< C, V > &x)
• template<typename C , typename V > void set_catalan (interval< C, V > &x)
• template<typename C , typename V > interval< C, V > times_infinity (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > operator- (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > operator+ (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator+ (const interval< C, V > &x1, const C &x2)
• template<typename C , typename V > interval< C, V > operator+ (const C &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator- (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator- (const interval< C, V > &x1, const C &x2)
• template<typename C , typename V > interval< C, V > operator- (const C &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator* (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator* (const interval< C, V > &x1, const C &x2)
• template<typename C , typename V > interval< C, V > operator* (const C &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > square (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > operator/ (const interval< C, V > &x1, const interval< C, V > &x2)
• template<typename C , typename V > interval< C, V > operator/ (const interval< C, V > &x1, const C &x2)
• template<typename C , typename V > interval< C, V > operator/ (const C &x1, const interval< C, V > &x2)
• ARITH_INT_SUGAR (template< typename C, typename V >, interval< C, V >)
• template<typename C , typename V > interval< C, V > sqrt (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > hypot (const interval< C, V > &x, const interval< C, V > &y)
• template<typename C , typename V > interval< C, V > exp (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > log (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > pow (const interval< C, V > &x, const interval< C, V > &y)
• template<typename C , typename V > interval< C, V > cos (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > sin (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > tan (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > cosh (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > sinh (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > tanh (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > acos (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > asin (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > atan (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > atan2 (const interval< C, V > &y, const interval< C, V > &x)
• INV_TRIGO_SUGAR (template< typename C, typename V >, interval< C, V >) INV_HYPER_SUGAR(template< typename C
• interval< C, V > ARG_HYPER_SUGAR (template< typename C, typename V >, interval< C, V >) template< typename C
• interval< C, V > V bool is_finite (const interval< C, V > &x)
• template<typename C , typename V > bool is_infinite (const interval< C, V > &x)
• template<typename C , typename V > bool is_fuzz (const interval< C, V > &x)
• template<typename C , typename V > bool is_nan (const interval< C, V > &x)
• template<typename C , typename V > bool is_reliable (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > change_precision (const interval< C, V > &x, xnat prec)
• template<typename C , typename V > xnat precision (const interval< C, V > &x)
• template<typename C , typename V > xint exponent (const interval< C, V > &x)
• template<typename C , typename V > double magnitude (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > operator<< (const interval< C, V > &x, const xint &shift)
• template<typename C , typename V > interval< C, V > operator>> (const interval< C, V > &x, const xint &shift)
• template<typename C , typename V > interval< C, V > sharpen (const interval< C, V > &x)
• template<typename C , typename V > interval< C, V > blur (const interval< C, V > &x, const C &r)
• template<typename C , typename V > interval< C, V > blur (const interval< C, V > &x, const interval< C, V > &r)

Variables

• center_op
• interval< C, V >

---

Define Documentation

#define Down   V::template rnd_helper<C>::DV

Examples:

floating_test.cpp.

Definition at line 22 of file interval.hpp.

Referenced by implementation< ball_rounding, W, ball_rounded >::abs_down(), implementation< ball_elementary, W, ball_rounded >::acos(), implementation< ball_elementary, W, ball_rounded >::asin(), implementation< ball_elementary, W, ball_rounded >::atan(), implementation< ball_rounding, W, ball_rounded >::bnd_down(), implementation< ball_ordered, W, ball_rounded >::ceil(), implementation< ball_elementary, W, ball_rounded >::cos(), implementation< ball_ordered, W, ball_rounded >::floor(), implementation< ball_multiplicative, W, ball_rounded >::invert(), implementation< ball_rounding, W, ball_rounded >::lower(), implementation< ball_ordered, W, ball_rounded >::round(), implementation< ball_elementary, W, ball_rounded >::sin(), implementation< ball_root, W, ball_rounded >::sqrt(), implementation< ball_root, IV, ball_complex< BV > >::sqrt(), and implementation< ball_ordered, W, ball_rounded >::trunc().

#define Interval   interval<C,V>

Definition at line 20 of file interval.hpp.

Referenced by mmx::abs(), mmx::acos(), mmx::asin(), binary_helper< interval< C, V > >::assemble(), mmx::atan(), mmx::atan2(), mmx::blur(), mmx::ceil(), mmx::change_precision(), mmx::copy(), mmx::cos(), mmx::cosh(), mmx::duplicate(), mmx::exp(), mmx::floor(), mmx::hypot(), mmx::intersect(), mmx::log(), mmx::max(), mmx::min(), mmx::operator*(), mmx::operator+(), mmx::operator-(), mmx::operator/(), mmx::operator<<(), mmx::operator>>(), binary_helper< interval< C, V > >::read(), mmx::round(), mmx::set_accuracy(), mmx::set_catalan(), mmx::set_euler(), mmx::set_fuzz(), mmx::set_infinity(), mmx::set_largest(), mmx::set_log2(), mmx::set_maximal(), mmx::set_minimal(), mmx::set_nan(), mmx::set_pi(), mmx::set_smallest(), mmx::sharpen(), mmx::sin(), mmx::sinh(), mmx::sqrt(), mmx::square(), mmx::trunc(), make_interval_helper< interval< C, V >, C2 >::val(), and make_ball_helper< interval< C, V >, C2, R2 >::val().

#define TMPL   template<typename C,typename V>

Definition at line 19 of file interval.hpp.

#define TMPL_DEF   template<typename C,typename V=std_interval>

Definition at line 18 of file interval.hpp.

#define Up   V::template rnd_helper<C>::UV

Examples:

floating_test.cpp.

Definition at line 21 of file interval.hpp.

Referenced by 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(), mmx::blur(), implementation< ball_rounding, W, ball_rounded >::bnd_up(), implementation< ball_ordered, W, ball_rounded >::ceil(), 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(), implementation< ball_ordered, W, ball_rounded >::floor(), 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_elementary, W, ball_rounded >::log(), implementation< ball_elementary, IV, ball_complex< BV > >::log(), implementation< ball_rounding, W, ball_rounded >::make_interval(), implementation< ball_multiplicative, W, ball_rounded >::mul(), implementation< ball_ordered, W, ball_rounded >::round(), 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, IV, ball_complex< BV > >::sqrt(), implementation< ball_multiplicative, W, ball_rounded >::square(), implementation< ball_additive, W, ball_rounded >::sub(), implementation< ball_ordered, W, ball_rounded >::trunc(), implementation< ball_rounding, W, ball_rounded >::upper(), and make_interval_helper< ball< C, R, V >, C2 >::val().