include/numerix/interval.hpp File Reference
#include <basix/function.hpp>
#include <numerix/rounded.hpp>
Go to the source code of this file.
Classes
Namespaces
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 >)
- EQUAL_SCALAR_SUGAR (template< typename C, typename V >, interval< C, V >, C)
- COMPARE_SCALAR_SUGAR (template< typename C, typename V >, interval< C, V >, C)
- EQUAL_SCALAR_SUGAR_BIS (template< typename C, typename V >, interval< C, V >, C)
- COMPARE_SCALAR_SUGAR_BIS (template< typename C, typename V >, interval< C, V >, C)
- 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_default (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
Define Documentation
#define Down V::template rnd_helper<C>::DV |
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> |
#define TMPL template<typename C,typename V> |
#define TMPL_DEF template<typename C,typename V=std_interval> |
#define Up V::template rnd_helper<C>::UV |
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(), 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().