C-XSC - A C++ Class Library for Extended Scientific Computing  2.5.4
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cxsc::l_interval Class Reference

The Multiple-Precision Data Type l_interval. More...

#include <l_interval.hpp>

List of all members.

Public Member Functions

 l_interval () throw ()
 Constructor of class l_interval.
 l_interval (const l_interval &) throw ()
 Constructor of class l_interval.
 l_interval (const l_real &, const l_real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Constructor of class l_interval.
 l_interval (const real &, const l_real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Constructor of class l_interval.
 l_interval (const l_real &, const real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Constructor of class l_interval.
 l_interval (const real &, const real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Constructor of class l_interval.
 l_interval (const dotprecision &) throw ()
 Constructor of class l_interval.
 l_interval (const dotprecision &, const dotprecision &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Constructor of class l_interval.
 l_interval (const idotprecision &) throw ()
 Constructor of class l_interval.
 l_interval (const real &) throw ()
 Constructor of class l_interval.
 l_interval (const l_real &) throw ()
 Constructor of class l_interval.
 l_interval (const l_ivector &) throw ()
 Constructor of class l_interval.
 l_interval (const l_ivector_slice &) throw ()
 Constructor of class l_interval.
 l_interval (const l_imatrix &m) throw ()
 Constructor of class l_interval.
 l_interval (const l_imatrix_slice &m) throw ()
 Constructor of class l_interval.
 l_interval (const interval &) throw ()
 Constructor of class l_interval.
l_interval & operator= (const real &a) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const l_real &a) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const interval &a) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const l_interval &a) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const lx_interval &) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const dotprecision &a) throw ()
 Implementation of standard assigning operator.
l_interval & operator= (const idotprecision &) throw ()
 Implementation of standard assigning operator.
real & operator[] (int) throw ()
 Access to the single components used to store the long data type value.

Friends

interval _l_interval (const l_ivector &) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _l_interval (const l_ivector_slice &) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _l_interval (const l_imatrix &m) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _l_interval (const l_imatrix_slice &m) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
l_interval abs (const l_interval &a) throw ()
 Returns the absolute value of the interval.
void accumulate (idotprecision &, const real &, const l_interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_interval &, const real &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const interval &, const l_real &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_real &, const interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_interval &, const l_real &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_real &, const l_interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_interval &, const interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const interval &, const l_interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
void accumulate (idotprecision &, const l_interval &, const l_interval &) throw ()
 The accurate scalar product of the last two arguments added to the value of the first argument.
l_interval acos (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \arccos([x]) $.
l_interval acosh (const l_interval &) throw ()
 Calculates $ \mbox{arccosh}([x]) $.
l_interval acot (const l_interval &) throw ()
 Calculates $ \mbox{arccot}([x]) $.
l_interval acoth (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \mbox{arccoth}([x]) $.
l_interval adjust (const l_interval &) throw ()
 Sets the precision of a specific long datatype value.
l_interval asin (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \arcsin([x]) $.
l_interval asinh (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \mbox{arcsinh}([x]) $.
l_interval atan (const l_interval &) throw ()
 Calculates $ \arctan([x]) $.
l_interval atanh (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \mbox{arctanh}([x]) $.
l_interval Catalan_l_interval () throw ()
 Enclosure-Interval for Catalan Numbers.
void ConvexHull (const l_interval &, const l_interval &, l_interval &, l_interval &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval cos (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \cos([x]) $.
l_interval cosh (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \cosh([x]) $.
l_interval cot (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \cot([x]) $.
l_interval coth (const l_interval &) throw ()
 Calculates $ \coth([x]) $.
l_real diam (const l_interval &a) throw ()
 Returns the rounded diameter of the interval.
l_interval E_l_interval () throw ()
 Enclosure-Interval for $ e $.
l_interval Ep2_l_interval () throw ()
 Enclosure-Interval for $ e^2 $.
l_interval Ep2Pi_l_interval () throw ()
 Enclosure-Interval for $ e^{2\pi} $.
l_interval Ep2r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{e^2} $.
l_interval EpPi_l_interval () throw ()
 Enclosure-Interval for $ e^\pi $.
l_interval EpPid2_l_interval () throw ()
 Enclosure-Interval for $ e^{\frac{\pi}{2}} $.
l_interval EpPid4_l_interval () throw ()
 Enclosure-Interval for $ e^{\frac{\pi}{4}} $.
l_interval Er_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{e} $.
l_interval EulerGa_l_interval () throw ()
 Enclosure-Interval for Euler Gamma.
l_interval exp (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \exp([x]) $.
l_interval exp10 (const l_interval &)
 Calculates $ \exp10([x]) $.
l_interval exp2 (const l_interval &)
 Calculates $ \exp2([x]) $.
int expo_gr (const l_interval &)
 Returns the maximum of the expo-function.
int expo_sm (const l_interval &)
 Returns the minimum of the expo-function.
l_real Inf (const l_interval &) throw ()
 Returns the infimum of an interval.
void Intersection (const l_interval &, const l_interval &, l_interval &, l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval li_ln10 ()
 Enclosure-Interval for $ \ln 10 $.
l_interval li_ln2 ()
 Enclosure-Interval for $ \ln 2 $.
l_interval li_pi4 ()
 Enclosure-Interval for $ \frac{\pi}{4} $.
l_interval li_Rln10 ()
 Enclosure-Interval for $ \frac{1}{\ln 10} $.
l_interval li_sqrt2 ()
 Enclosure-Interval for $ \sqrt{2} $.
l_interval ln (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \ln([x]) $.
l_interval Ln10_l_interval () throw ()
 Enclosure-Interval for $ \ln 10 $.
l_interval Ln10r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\ln 10} $.
l_interval Ln2_l_interval () throw ()
 Enclosure-Interval for $ \ln 2 $.
l_interval Ln2Pi_l_interval () throw ()
 Enclosure-Interval for $ \ln 2\pi $.
l_interval Ln2r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\ln 2} $.
l_interval LnPi_l_interval () throw ()
 Enclosure-Interval for $ \ln \pi $.
l_interval log10 (const l_interval &)
 Calculates $ \log10([x]) $.
l_interval log2 (const l_interval &)
 Calculates $ \log2([x]) $.
l_real mid (const l_interval &a) throw ()
 Returns the rounded middle of the interval.
bool operator! (const l_interval &) throw ()
 Implementation of standard negation operation.
bool operator!= (const l_interval &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_real &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_interval &, const l_real &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_interval &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const real &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_interval &, const real &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const idotprecision &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_interval &, const idotprecision &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const dotprecision &, const l_interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const l_interval &, const dotprecision &) throw ()
 Implementation of standard negated equality operation.
l_interval operator& (const l_interval &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL,ERROR_LINTERVAL_IN_EXACT_CH_OR_IS)
 Returns the intersection of the arguments.
idotprecision operator& (const idotprecision &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
idotprecision operator& (const l_interval &, const idotprecision &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const l_real &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const l_interval &, const l_real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const interval &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const l_interval &, const interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const real &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const l_interval &, const real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const interval &, const l_real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval operator& (const l_real &, const interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
l_interval & operator&= (l_interval &, const l_interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval & operator&= (l_interval &, const idotprecision &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval & operator&= (l_interval &, const l_real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval & operator&= (l_interval &, const interval &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval & operator&= (l_interval &, const real &) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
l_interval operator* (const l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const l_interval &, const l_real &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const l_real &, const l_interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const l_interval &, const interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const interval &, const l_interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const l_interval &, const real &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const real &, const l_interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const l_real &, const interval &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval operator* (const interval &, const l_real &) throw ()
 Implementation of standard algebraic multiplication operation.
l_interval & operator*= (l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
l_interval & operator*= (l_interval &, const l_real &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
l_interval & operator*= (l_interval &, const interval &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
l_interval & operator*= (l_interval &, const real &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
l_interval operator+ (const l_interval &) throw ()
 Implementation of standard algebraic positive sign operation.
l_interval operator+ (const l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic addition operation.
idotprecision operator+ (const l_interval &, const idotprecision &) throw ()
 Implementation of standard algebraic addition operation.
idotprecision operator+ (const idotprecision &, const l_interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const l_interval &, const l_real &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const l_real &, const l_interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const l_interval &, const interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const interval &, const l_interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const l_interval &, const real &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const real &, const l_interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const l_real &, const interval &) throw ()
 Implementation of standard algebraic addition operation.
l_interval operator+ (const interval &, const l_real &) throw ()
 Implementation of standard algebraic addition operation.
l_interval & operator+= (l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic addition and allocation operation.
l_interval & operator+= (l_interval &, const l_real &) throw ()
 Implementation of standard algebraic addition and allocation operation.
l_interval & operator+= (l_interval &, const interval &) throw ()
 Implementation of standard algebraic addition and allocation operation.
l_interval & operator+= (l_interval &, const real &) throw ()
 Implementation of standard algebraic addition and allocation operation.
l_interval operator- (const l_interval &) throw ()
 Implementation of standard algebraic negative sign operation.
l_interval operator- (const l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction operation.
idotprecision operator- (const l_interval &, const idotprecision &) throw ()
 Implementation of standard algebraic subtraction operation.
idotprecision operator- (const idotprecision &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const l_interval &, const l_real &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const l_real &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const l_interval &, const interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const interval &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const l_interval &, const real &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const real &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const l_real &, const interval &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval operator- (const interval &, const l_real &) throw ()
 Implementation of standard algebraic subtraction operation.
l_interval & operator-= (l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
l_interval & operator-= (l_interval &, const l_real &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
l_interval & operator-= (l_interval &, const interval &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
l_interval & operator-= (l_interval &, const real &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
l_interval operator/ (const l_interval &, const l_interval &) throw (ERROR_LINTERVAL_DIV_BY_ZERO)
 Implementation of standard algebraic division operation.
l_interval operator/ (const l_interval &, const l_real &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const l_real &, const l_interval &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const l_interval &, const interval &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const interval &, const l_interval &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const l_interval &, const real &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const real &, const l_interval &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const l_real &, const interval &) throw ()
 Implementation of standard algebraic division operation.
l_interval operator/ (const interval &, const l_real &) throw ()
 Implementation of standard algebraic division operation.
l_interval & operator/= (l_interval &, const l_interval &) throw ()
 Implementation of standard algebraic division and allocation operation.
l_interval & operator/= (l_interval &, const l_real &) throw ()
 Implementation of standard algebraic division and allocation operation.
l_interval & operator/= (l_interval &, const interval &) throw ()
 Implementation of standard algebraic division and allocation operation.
l_interval & operator/= (l_interval &, const real &) throw ()
 Implementation of standard algebraic division and allocation operation.
bool operator< (const l_interval &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_real &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_interval &, const l_real &) throw ()
 Implementation of standard less-than operation.
bool operator< (const interval &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_interval &, const interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const real &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_interval &, const real &) throw ()
 Implementation of standard less-than operation.
bool operator< (const idotprecision &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_interval &, const idotprecision &) throw ()
 Implementation of standard less-than operation.
bool operator< (const dotprecision &, const l_interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const l_interval &, const dotprecision &) throw ()
 Implementation of standard less-than operation.
std::ostream & operator<< (std::ostream &s, const l_interval &a) throw ()
 Implementation of standard output method.
std::string & operator<< (std::string &s, const l_interval &a) throw ()
 Implementation of standard output method.
bool operator<= (const l_interval &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_real &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_interval &, const l_real &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const interval &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_interval &, const interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const real &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_interval &, const real &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const idotprecision &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_interval &, const idotprecision &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const dotprecision &, const l_interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const l_interval &, const dotprecision &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator== (const l_interval &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_real &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_interval &, const l_real &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_interval &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const real &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_interval &, const real &) throw ()
 Implementation of standard equality operation.
bool operator== (const idotprecision &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_interval &, const idotprecision &) throw ()
 Implementation of standard equality operation.
bool operator== (const dotprecision &, const l_interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const l_interval &, const dotprecision &) throw ()
 Implementation of standard equality operation.
bool operator> (const l_interval &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_real &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_interval &, const l_real &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const interval &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_interval &, const interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const real &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_interval &, const real &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const idotprecision &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_interval &, const idotprecision &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const dotprecision &, const l_interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const l_interval &, const dotprecision &) throw ()
 Implementation of standard greater-than operation.
bool operator>= (const l_interval &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_real &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_interval &, const l_real &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const interval &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_interval &, const interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const real &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_interval &, const real &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const idotprecision &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_interval &, const idotprecision &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const dotprecision &, const l_interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const l_interval &, const dotprecision &) throw ()
 Implementation of standard greater-or-equal-than operation.
std::istream & operator>> (std::istream &s, l_interval &a) throw ()
 Implementation of standard input method.
std::string & operator>> (std::string &s, l_interval &a) throw ()
 Implementation of standard input method.
void operator>> (const std::string &s, l_interval &a) throw ()
 Implementation of standard input method.
void operator>> (const char *s, l_interval &a) throw ()
 Implementation of standard input method.
l_interval operator| (const l_interval &, const l_interval &) throw (ERROR_LINTERVAL_IN_EXACT_CH_OR_IS)
 Returns the convex hull of the arguments.
idotprecision operator| (const idotprecision &, const l_interval &) throw ()
 Returns the convex hull of the arguments.
idotprecision operator| (const l_interval &, const idotprecision &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_real &, const l_interval &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_interval &, const l_real &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_real &, const l_real &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const interval &, const l_interval &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_interval &, const interval &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const real &, const l_interval &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_interval &, const real &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const interval &, const l_real &) throw ()
 Returns the convex hull of the arguments.
l_interval operator| (const l_real &, const interval &) throw ()
 Returns the convex hull of the arguments.
l_interval & operator|= (l_interval &, const l_interval &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval & operator|= (l_interval &, const idotprecision &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval & operator|= (l_interval &, const l_real &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval & operator|= (l_interval &, const interval &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval & operator|= (l_interval &, const real &) throw ()
 Allocates the convex hull of the arguments to the first argument.
l_interval Pi2_l_interval () throw ()
 Enclosure-Interval for $ 2\pi $.
l_interval Pi2r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{2\pi} $.
l_interval Pi_l_interval () throw ()
 Enclosure-Interval for $ \pi $.
l_interval Pid2_l_interval () throw ()
 Enclosure-Interval for $ \frac{\pi}{2} $.
l_interval Pid3_l_interval () throw ()
 Enclosure-Interval for $ \frac{\pi}{3} $.
l_interval Pid4_l_interval () throw ()
 Enclosure-Interval for $ \frac{\pi}{4} $.
l_interval Pip2_l_interval () throw ()
 Enclosure-Interval for $ 2^\pi $.
l_interval Pir_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\pi} $.
bool point_intv (const l_interval &)
 Checks if the argument is a point interval.
l_interval pow (const l_interval &, const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ [x]^{[y]} $.
l_interval power (const l_interval &, int)
 Calculates $ [x]^n $.
l_interval & SetInf (l_interval &a, const l_real &b) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the interval with the new given infimum value.
l_interval & SetInf (l_interval &a, const real &b) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the interval with the new given infimum value.
l_interval & SetSup (l_interval &a, const l_real &b) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the interval with the new given supremum value.
l_interval & SetSup (l_interval &a, const real &b) throw (ERROR_LINTERVAL_EMPTY_INTERVAL)
 Returns the interval with the new given supremum value.
l_interval sin (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \sin([x]) $.
l_interval sinh (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW)
 Calculates $ \sinh([x]) $.
l_interval sqr (const l_interval &)
 Calculates $ [x]^2 $.
l_interval sqrt (const l_interval &) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \sqrt{[x]} $.
l_interval sqrt (const l_interval &, int) throw (ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \sqrt[n]{[x]} $.
l_interval Sqrt2_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{2} $.
l_interval Sqrt2Pi_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{2\pi} $.
l_interval Sqrt2Pir_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\sqrt{2\pi}} $.
l_interval Sqrt2r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\sqrt{2}} $.
l_interval Sqrt3_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{3} $.
l_interval Sqrt3d2_l_interval () throw ()
 Enclosure-Interval for $ \frac{\sqrt{3}}{2} $.
l_interval Sqrt3r_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\sqrt{3}} $.
l_interval Sqrt5_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{5} $.
l_interval Sqrt7_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{7} $.
l_interval SqrtPi_l_interval () throw ()
 Enclosure-Interval for $ \sqrt{\pi} $.
l_interval SqrtPir_l_interval () throw ()
 Enclosure-Interval for $ \frac{1}{\sqrt{\pi}} $.
int StagPrec (const l_interval &) throw ()
 Returns the precision of the long datatype value.
l_real Sup (const l_interval &) throw ()
 Returns the supremum of an interval.
l_interval tan (const l_interval &) throw (ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF)
 Calculates $ \tan([x]) $.
l_interval tanh (const l_interval &) throw ()
 Calculates $ \tanh([x]) $.
void times2pown (l_interval &, int) throw ()
 Multiplication of interval with $ 2^n $.
void Times2pown (l_interval &, const real &) throw ()
 Multiplication of interval with $ 2^n $.
l_interval & UncheckedSetInf (l_interval &a, const l_real &b) throw ()
 Returns the interval with the unchecked new given infimum value.
l_interval & UncheckedSetInf (l_interval &a, const real &b) throw ()
 Returns the interval with the unchecked new given infimum value.
l_interval & UncheckedSetSup (l_interval &a, const l_real &b) throw ()
 Returns the interval with the unchecked new given supremum value.
l_interval & UncheckedSetSup (l_interval &a, const real &b) throw ()
 Returns the interval with the unchecked new given supremum value.
bool zero_ (const l_interval &) throw ()
 Checks if the argument is zero.

Detailed Description

The Multiple-Precision Data Type l_interval.

The multiple-precision data type l_interval is a variant of the scalar type interval, which provides support for longer numbers, thus increasing the accuracy of the data type.

The external variable stagprec(=p) defines the precision of the staggered arithmetic. An interval x of type l_interval is realized by

$ x = x_1 + x_2 + ... + x_p + x_{(p+1)}; p = 1,2,3, ...;$

$ \mbox{Inf}(x) = x_1 + x_2 + ... + x_p;$

$ \mbox{Sup}(x) = x_1 + x_2 + ... + x_{(p-1)} + x_{(p+1)};$

$ \mbox{diam}(x) = x_{(p+1)} - x_{(p-1)};$

Staggered interval computations with precision p are only sensible, if

$ RelDiam(x) < 10^{-16*(p-1)}$

is fulfilled. Interim results with $|x|-->10^{-300}$ should be avoided in order to keep a hight accuracy of the final result.

See also:
interval

Definition at line 71 of file l_interval.hpp.

Friends And Related Function Documentation

int expo_gr ( const l_interval &  x) [friend]

Returns the maximum of the expo-function.

Parameters:
xThe value for which to calculate
Returns:
The result of the calculation
See also:
expo_gr(const l_real&)

Definition at line 522 of file l_interval.inl.

int expo_sm ( const l_interval &  x) [friend]

Returns the minimum of the expo-function.

Parameters:
xThe value for which to calculate
Returns:
The result of the calculation
See also:
expo_sm(const l_real&)

Definition at line 539 of file l_interval.inl.

The documentation for this class was generated from the following files: