26#ifndef _CXSC_INTERVAL_H_INCLUDED
27#define _CXSC_INTERVAL_H_INCLUDED
73 explicit inline interval(
const real &r) noexcept :inf(r),sup(r) { }
433extern int in (
const real&,
const interval& );
435extern int in (
const interval&,
const interval& );
438extern interval
Blow (
const interval&,
const real& );
440extern int Disjoint (
const interval&,
const interval& );
442extern real
AbsMin (
const interval& );
444extern real
AbsMax (
const interval& );
446extern real
RelDiam (
const interval& );
448extern int UlpAcc (
const interval&,
int );
451real
mid (
const interval& a)
noexcept;
526#include "interval.inl"
The Data Type dotprecision.
The Data Type idotprecision.
The Data Type imatrix_slice.
The Scalar Type interval.
friend std::ostream & operator<<(std::ostream &, const interval &) noexcept
Implementation of standard output method.
interval & operator=(const real &a)
Implementation of standard assigning operator.
friend interval operator|(const interval &, const interval &) noexcept
Returns the convex hull of the arguments.
friend std::istream & operator>>(std::istream &, interval &) noexcept
Implementation of standard input method.
friend bool operator<=(const interval &, const interval &) noexcept
Implementation of standard less-or-equal-than operation.
interval(const imatrix_slice &m) noexcept
Constructor of class interval.
friend real & Sup(interval &) noexcept
Returns the supremum of an interval.
interval()
Constructor of class interval.
friend interval & UncheckedSetInf(interval &, const real &) noexcept
Returns the interval with the unchecked new given infimum value.
friend void times2pown(interval &, const int &) noexcept
Multiplication of interval with .
friend interval operator+(const interval &) noexcept
Implementation of standard algebraic positive sign operation.
friend interval _interval(const ivector_slice &) noexcept
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend interval & operator-=(interval &, const interval &) noexcept
Implementation of standard algebraic subtraction and allocation operation.
friend bool operator==(const interval &, const interval &) noexcept
Implementation of standard equality operation.
friend interval _interval(const ivector &) noexcept
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend interval & SetInf(interval &, const real &) noexcept
Returns the interval with the new given infimum value.
friend interval & UncheckedSetSup(interval &, const real &) noexcept
Returns the interval with the unchecked new given supremum value.
friend real mid(const interval &) noexcept
Returns the rounded middle of the interval.
friend interval operator*(const interval &, const interval &) noexcept
Implementation of standard algebraic multiplication operation.
friend bool operator>(const interval &, const interval &) noexcept
Implementation of standard greater-than operation.
friend interval & operator|=(interval &, const interval &) noexcept
Allocates the convex hull of the arguments to the first argument.
friend interval _interval(const imatrix &m) noexcept
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend interval operator/(const interval &, const interval &)
Implementation of standard algebraic division operation.
friend bool operator!(const interval &) noexcept
Implementation of standard negation operation.
friend interval _unchecked_interval(const real &, const real &)
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend interval operator-(const interval &) noexcept
Implementation of standard algebraic negative sign operation.
friend bool operator>=(const interval &, const interval &) noexcept
Implementation of standard greater-or-equal-than operation.
friend interval abs(const interval &) noexcept
Returns the absolute value of the interval.
friend interval & operator*=(interval &, const interval &) noexcept
Implementation of standard algebraic multiplication and allocation operation.
friend real diam(const interval &) noexcept
Returns the rounded diameter of the interval.
friend interval & operator&=(interval &, const interval &)
Allocates the intersection of the arguments to the first argument.
friend interval _interval(const l_real &a, const l_real &b)
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend interval & SetSup(interval &, const real &) noexcept
Returns the interval with the new given supremum value.
interval(const real &r) noexcept
Typecast for converting a real value in an interval.
friend interval _interval(const imatrix_slice &m) noexcept
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
friend bool operator<(const interval &, const interval &) noexcept
Implementation of standard less-than operation.
friend bool IsEmpty(const interval &) noexcept
Returns true if the interval is empty.
friend interval & operator+=(interval &, const interval &) noexcept
Implementation of standard algebraic addition and allocation operation.
friend interval & operator/=(interval &, const interval &) noexcept
Implementation of standard algebraic division and allocation operation.
friend real & Inf(interval &) noexcept
Returns the infimum of an interval.
friend bool operator!=(const interval &, const interval &) noexcept
Implementation of standard negated equality operation.
friend interval operator&(const interval &, const interval &)
Returns the intersection of the arguments.
The Data Type ivector_slice.
The Multiple-Precision Data Type l_interval.
The Multiple-Precision Data Type l_real.
The namespace cxsc, providing all functionality of the class library C-XSC.
const interval Sqrt2Pi_interval
Enclosure-Interval for .
const interval EpPi_interval
Enclosure-Interval for .
const interval Sqrt5_interval
Enclosure-Interval for .
const interval Er_interval
Enclosure-Interval for .
const interval Sqrt3d2_interval
Enclosure-Interval for .
const interval Pid4_interval
Enclosure-Interval for .
const interval Pi2r_interval
Enclosure-Interval for .
const interval Sqrt2_interval
Enclosure-Interval for .
const interval Ln2Pi_interval
Enclosure-Interval for .
const interval Sqrt3r_interval
Enclosure-Interval for .
const interval Ln2r_interval
Enclosure-Interval for .
const interval EpPid4_interval
Enclosure-Interval for .
int Disjoint(const interval &a, const interval &b)
Checks arguments for disjointness.
const interval E_interval
Enclosure-Interval for .
const interval LnPi_interval
Enclosure-Interval for .
const interval Pid2_interval
Enclosure-Interval for .
int UlpAcc(const interval &x, int n)
Checks if the diameter of the interval is ulps.
const interval Ep2_interval
Enclosure-Interval for .
real RelDiam(const interval &x)
Computes the relative diameter .
const interval Sqrt7_interval
Enclosure-Interval for .
int in(const cinterval &x, const cinterval &y)
Checks if first argument is part of second argument.
const interval Pir_interval
Enclosure-Interval for .
const interval Pip2_interval
Enclosure-Interval for .
const interval Ln2_interval
Enclosure-Interval for .
const interval Pid3_interval
Enclosure-Interval for .
const interval SqrtPir_interval
Enclosure-Interval for .
const interval Sqrt2r_interval
Enclosure-Interval for .
const interval Pi2_interval
Enclosure-Interval for .
const interval Ep2Pi_interval
Enclosure-Interval for .
const interval Ln10_interval
Enclosure-Interval for .
const interval Ep2r_interval
Enclosure-Interval for .
real AbsMax(const interval &x)
Computes the greatest absolute value .
const interval Ln10r_interval
Enclosure-Interval for .
cvector mid(const cimatrix_subv &mv) noexcept
Returns the middle of the matrix.
const interval EpPid2_interval
Enclosure-Interval for .
const interval Sqrt3_interval
Enclosure-Interval for .
const interval Sqrt2Pir_interval
Enclosure-Interval for .
const interval Pi3_interval
Enclosure-Interval for .
const interval SqrtPi_interval
Enclosure-Interval for .
cinterval Blow(cinterval x, const real &eps)
Performs an epsilon inflation.
const interval Pi_interval
Enclosure-Interval for .
real AbsMin(const interval &x)
Computes the smallest absolute value .