C-XSC - A C++ Class Library for Extended Scientific Computing
2.5.4
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The Data Type idotprecision. More...
#include <idot.hpp>
Public Member Functions | |
int | get_dotprec () const |
Get currently set precision for computation of dot products. | |
int | get_k () const |
Get currently set precision for computation of dot products. | |
idotprecision () | |
Constructor of class idotprecision. | |
idotprecision (const dotprecision &, const dotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) | |
Constructor of class idotprecision. | |
idotprecision (const idotprecision &) | |
Constructor of class idotprecision. | |
idotprecision (const real &a) | |
Constructor of class idotprecision. | |
idotprecision (const real &a, const real &b) | |
Constructor of class idotprecision. | |
idotprecision (const interval &a) | |
Constructor of class idotprecision. | |
idotprecision (const dotprecision &r) | |
Constructor of class idotprecision. | |
idotprecision (const l_real &) throw () | |
Constructor of class idotprecision. | |
idotprecision (const l_real &, const l_real &) | |
Constructor of class idotprecision. | |
idotprecision (const l_interval &) throw () | |
Constructor of class idotprecision. | |
idotprecision & | operator= (const real &a) |
Implementation of standard assigning operator. | |
idotprecision & | operator= (const interval &a) |
Implementation of standard assigning operator. | |
idotprecision & | operator= (const dotprecision &a) |
Implementation of standard assigning operator. | |
idotprecision & | operator= (const idotprecision &a) |
Implementation of standard assigning operator. | |
idotprecision & | operator= (const l_real &a) |
Implementation of standard assigning operator. | |
idotprecision & | operator= (const l_interval &) throw () |
Implementation of standard assigning operator. | |
void | set_dotprec (unsigned int i) |
Set precision for computation of dot products. | |
void | set_k (unsigned int i) |
Set precision for computation of dot products. | |
Friends | |
idotprecision | _idotprecision (const real &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _idotprecision (const real &, const real &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _idotprecision (const dotprecision &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _idotprecision (const dotprecision &, const dotprecision &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _idotprecision (const l_real &a) throw () |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _idotprecision (const l_real &a, const l_real &b) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _unchecked_idotprecision (const real &, const real &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | _unchecked_idotprecision (const dotprecision &, const dotprecision &) |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC. | |
idotprecision | abs (const idotprecision &a) throw () |
Returns the absolute value of a dotprecision interval. | |
void | accumulate (idotprecision &, const 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 real &) throw () |
The accurate scalar product of the last two arguments added to the value of the first argument. | |
void | accumulate (idotprecision &, const 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 real &, const real &) throw () |
The accurate scalar product of the last two arguments added to the value of the first argument. | |
dotprecision | diam (const idotprecision &a) throw () |
Returns the rounded diameter of the dotprecision interval. | |
dotprecision & | Inf (idotprecision &a) throw () |
Returns the infimum of a dotprecison interval. | |
const dotprecision & | Inf (const idotprecision &a) throw () |
Returns the infimum of a dotprecison interval. | |
bool | IsEmpty (const idotprecision &a) throw () |
Returns if the dotprecision interval is empty. | |
dotprecision | mid (const idotprecision &a) throw () |
Returns the middle of the dotprecision interval. | |
bool | operator! (const idotprecision &) throw () |
Implementation of standard negation operation. | |
bool | operator!= (const idotprecision &, const idotprecision &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const dotprecision &, const idotprecision &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const idotprecision &, const dotprecision &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const real &, const idotprecision &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const idotprecision &, const real &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const interval &, const idotprecision &) throw () |
Implementation of standard negated equality operation. | |
bool | operator!= (const idotprecision &, const interval &) throw () |
Implementation of standard negated equality operation. | |
idotprecision | operator& (const idotprecision &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const dotprecision &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const idotprecision &, const dotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const long &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const idotprecision &, const long &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const real &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const idotprecision &, const real &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const l_real &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const idotprecision &, const l_real &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const interval &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision | operator& (const idotprecision &, const interval &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Returns the intersection of the arguments. | |
idotprecision & | operator&= (idotprecision &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Allocates the intersection of the arguments to the first argument. | |
idotprecision & | operator&= (idotprecision &, const dotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Allocates the intersection of the arguments to the first argument. | |
idotprecision & | operator&= (idotprecision &i, const real &l) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Allocates the intersection of the arguments to the first argument. | |
idotprecision & | operator&= (idotprecision &i, const l_real &l) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Allocates the intersection of the arguments to the first argument. | |
idotprecision & | operator&= (idotprecision &i, const l_interval &l) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL) |
Allocates the intersection of the arguments to the first argument. | |
idotprecision | operator+ (const idotprecision &) throw () |
Implementation of standard algebraic positive sign operation. | |
idotprecision | operator+ (const idotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const idotprecision &, const dotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const dotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const idotprecision &, const long &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const long &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const idotprecision &, const real &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const real &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const idotprecision &, const l_real &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const l_real &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const idotprecision &, const interval &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision | operator+ (const interval &, const idotprecision &) throw () |
Implementation of standard algebraic addition operation. | |
idotprecision & | operator+= (idotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision & | operator+= (idotprecision &, const interval &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision & | operator+= (idotprecision &, const real &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision & | operator+= (idotprecision &, const l_real &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision & | operator+= (idotprecision &, const l_interval &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision & | operator+= (idotprecision &, const dotprecision &) throw () |
Implementation of standard algebraic addition and allocation operation. | |
idotprecision | operator- (const idotprecision &) throw () |
Implementation of standard algebraic negative sign operation. | |
idotprecision | operator- (const idotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const idotprecision &, const dotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const dotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const idotprecision &, const long &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const long &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const idotprecision &, const real &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const real &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const idotprecision &, const l_real &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const l_real &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const idotprecision &, const interval &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision | operator- (const interval &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction operation. | |
idotprecision & | operator-= (idotprecision &, const idotprecision &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
idotprecision & | operator-= (idotprecision &, const interval &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
idotprecision & | operator-= (idotprecision &, const real &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
idotprecision & | operator-= (idotprecision &, const l_real &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
idotprecision & | operator-= (idotprecision &, const l_interval &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
idotprecision & | operator-= (idotprecision &, const dotprecision &) throw () |
Implementation of standard algebraic subtraction and allocation operation. | |
bool | operator< (const idotprecision &, const idotprecision &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const dotprecision &, const idotprecision &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const idotprecision &, const dotprecision &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const real &, const idotprecision &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const idotprecision &, const real &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const interval &, const idotprecision &) throw () |
Implementation of standard less-than operation. | |
bool | operator< (const idotprecision &, const interval &) throw () |
Implementation of standard less-than operation. | |
std::ostream & | operator<< (std::ostream &s, const idotprecision &a) throw () |
Implementation of standard output method. | |
std::string & | operator<< (std::string &s, const idotprecision &a) throw () |
Implementation of standard output method. | |
bool | operator<= (const idotprecision &, const idotprecision &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const dotprecision &, const idotprecision &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const idotprecision &, const dotprecision &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const real &, const idotprecision &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const idotprecision &, const real &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const interval &, const idotprecision &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator<= (const idotprecision &, const interval &) throw () |
Implementation of standard less-or-equal-than operation. | |
bool | operator== (const idotprecision &, const idotprecision &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const dotprecision &, const idotprecision &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const idotprecision &, const dotprecision &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const real &, const idotprecision &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const idotprecision &, const real &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const interval &, const idotprecision &) throw () |
Implementation of standard equality operation. | |
bool | operator== (const idotprecision &, const interval &) throw () |
Implementation of standard equality operation. | |
bool | operator> (const idotprecision &, const idotprecision &) throw () |
Implementation of standard greater-than operation. | |
bool | operator> (const dotprecision &, const idotprecision &) throw () |
Implementation of standard more-than operation. | |
bool | operator> (const idotprecision &, const dotprecision &) throw () |
Implementation of standard more-than operation. | |
bool | operator> (const real &, const idotprecision &) throw () |
Implementation of standard more-than operation. | |
bool | operator> (const idotprecision &, const real &) throw () |
Implementation of standard more-than operation. | |
bool | operator> (const interval &, const idotprecision &) throw () |
Implementation of standard more-than operation. | |
bool | operator> (const idotprecision &, const interval &) throw () |
Implementation of standard more-than operation. | |
bool | operator>= (const idotprecision &, const idotprecision &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const dotprecision &, const idotprecision &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const idotprecision &, const dotprecision &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const real &, const idotprecision &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const idotprecision &, const real &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const interval &, const idotprecision &) throw () |
Implementation of standard greater-or-equal-than operation. | |
bool | operator>= (const idotprecision &, const interval &) throw () |
Implementation of standard greater-or-equal-than operation. | |
std::istream & | operator>> (std::istream &s, idotprecision &a) throw () |
Implementation of standard input method. | |
std::string & | operator>> (std::string &s, idotprecision &a) throw () |
Implementation of standard input method. | |
void | operator>> (const std::string &s, idotprecision &a) throw () |
Implementation of standard input method. | |
void | operator>> (const char *s, idotprecision &a) throw () |
Implementation of standard input method. | |
idotprecision | operator| (const idotprecision &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const dotprecision &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const idotprecision &, const dotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const dotprecision &, const dotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const long &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const idotprecision &, const long &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const real &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const idotprecision &, const real &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const l_real &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const idotprecision &, const l_real &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const interval &, const idotprecision &) throw () |
Returns the convex hull of the arguments. | |
idotprecision | operator| (const idotprecision &, const interval &) throw () |
Returns the convex hull of the arguments. | |
idotprecision & | operator|= (idotprecision &, const idotprecision &) throw () |
Allocates the convex hull of the arguments to the first argument. | |
idotprecision & | operator|= (idotprecision &, const dotprecision &) throw () |
Allocates the convex hull of the arguments to the first argument. | |
idotprecision & | operator|= (idotprecision &i, const real &l) throw () |
Allocates the convex hull of the arguments to the first argument. | |
idotprecision & | operator|= (idotprecision &i, const l_real &l) throw () |
Allocates the convex hull of the arguments to the first argument. | |
idotprecision & | operator|= (idotprecision &i, const l_interval &l) throw () |
Allocates the convex hull of the arguments to the first argument. | |
idotprecision & | SetInf (idotprecision &, const dotprecision &) throw () |
Returns the dotprecison interval with the new given infimum value. | |
idotprecision & | SetInf (idotprecision &, const real &) throw () |
Returns the dotprecison interval with the new given infimum value. | |
idotprecision & | SetSup (idotprecision &, const dotprecision &) throw () |
Returns the dotprecison interval with the new given supremum value. | |
idotprecision & | SetSup (idotprecision &, const real &) throw () |
Returns the dotprecison interval with the new given supremum value. | |
dotprecision & | Sup (idotprecision &a) throw () |
Returns the supremum of a dotprecison interval. | |
const dotprecision & | Sup (const idotprecision &a) throw () |
Returns the supremum of a dotprecison interval. | |
idotprecision & | UncheckedSetInf (idotprecision &, const dotprecision &) throw () |
Returns the dotprecison interval with the unchecked new given infimum value. | |
idotprecision & | UncheckedSetInf (idotprecision &, const real &) throw () |
Returns the dotprecison interval with the unchecked new given infimum value. | |
idotprecision & | UncheckedSetSup (idotprecision &, const dotprecision &) throw () |
Returns the dotprecison interval with the unchecked new given supremum value. | |
idotprecision & | UncheckedSetSup (idotprecision &, const real &) throw () |
Returns the dotprecison interval with the unchecked new given supremum value. |
The Data Type idotprecision.
The data types dotprecision, idotprecision, cdotprecision and cidotprecision are based on the scalar data types real, interval, complex, and cinterval, respectively. Variables of these data types permit the exact representation of products of two arbitrary numbers of the corresponding scalar base type and the exact summation of an arbitrary number of such products in a dotprecision accumulator, i.e. in a fixed-point format of suitable size.
Since C-XSC Version 2.3.0, the precision for dot products computed with the dotprecision types can be choosen by the user. The default is precision k=0, which means maximum precision (the behaviour of older C-XSC Versions). For k=1, pure floating point operations are used and an error bound is computed using manipulation of the rounding mode of the processor. For k>=2, the so called DotK algorithm is used, simulating higher precision computations and also computing an error bound. When calling the rnd() function, the error bound will be added to the result interval. The resulting intervals will be wider for lower k, but computations will be significantly faster than with maximum precision (k=0).
idotprecision _idotprecision | ( | const real & | a | ) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
idotprecision _idotprecision | ( | const real & | a, |
const real & | b | ||
) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
idotprecision _idotprecision | ( | const dotprecision & | a | ) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
idotprecision _idotprecision | ( | const dotprecision & | a, |
const dotprecision & | b | ||
) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
idotprecision _unchecked_idotprecision | ( | const real & | a, |
const real & | b | ||
) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
idotprecision _unchecked_idotprecision | ( | const dotprecision & | a, |
const dotprecision & | b | ||
) | [friend] |
Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.