GeographicLib::Accumulator< T > Class Template Reference

An accumulator for sums. More...

#include <Accumulator.hpp>

Public Member Functions
	Accumulator (T y=T(0))
bool	operator!= (T y) const
T	operator() () const
T	operator() (T y) const
Accumulator &	operator*= (int n)
Accumulator &	operator*= (T y)
Accumulator &	operator+= (T y)
Accumulator &	operator-= (T y)
bool	operator< (T y) const
bool	operator<= (T y) const
Accumulator &	operator= (T y)
bool	operator== (T y) const
bool	operator> (T y) const
bool	operator>= (T y) const

Private Member Functions
void	Add (T y)
T	Sum (T y) const

Static Private Member Functions
static T	fastsum (T u, T v, T &t)

Private Attributes
T	_s
T	_t

Detailed Description

template<typename T = Math::real>
class GeographicLib::Accumulator< T >

An accumulator for sums.

This allows many numbers of floating point type T to be added together with twice the normal precision. Thus if T is double, the effective precision of the sum is 106 bits or about 32 decimal places.

The implementation follows J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, Discrete & Computational Geometry 18(3) 305–363 (1997).

Approximate timings (summing a vector<double>)

• double: 2ns
• Accumulator<double>: 23ns

In the documentation of the member functions, sum stands for the value currently held in the accumulator.

Example of use:

// Example of using the GeographicLib::Accumulator class
 
#include <iostream>
#include <exception>
#include <GeographicLib/Accumulator.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    // Compare using Accumulator and ordinary summation for a sum of large and
    // small terms.
    double sum = 0;
    Accumulator<> acc = 0;
    sum += 1e20; sum += 1; sum += 2; sum += 100; sum += 5000; sum += -1e20;
    acc += 1e20; acc += 1; acc += 2; acc += 100; acc += 5000; acc += -1e20;
    cout << sum << " " << acc() << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

Definition at line 40 of file Accumulator.hpp.

Constructor & Destructor Documentation

Accumulator()

template<typename T = Math::real>

GeographicLib::Accumulator< T >::Accumulator ( T  y = T(0) )

inline

Construct from a T. This is not declared explicit, so that you can write Accumulator<double> a = 5;.

Parameters

[in]

y

set sum = y.

Definition at line 102 of file Accumulator.hpp.

Member Function Documentation

Add()

template<typename T = Math::real>

void GeographicLib::Accumulator< T >::Add ( T  y )

inlineprivate

Definition at line 52 of file Accumulator.hpp.

fastsum()

template<typename T = Math::real>

static T GeographicLib::Accumulator< T >::fastsum ( T  u, T  v, T &  t  )

inlinestaticprivate

Definition at line 46 of file Accumulator.hpp.

operator!=()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator!= ( T  y ) const

inline

Test inequality of an Accumulator with a number.

Definition at line 165 of file Accumulator.hpp.

operator()() [1/2]

template<typename T = Math::real>

T GeographicLib::Accumulator< T >::operator() ( ) const

inline

Return the value held in the accumulator.

Returns

sum.

Definition at line 117 of file Accumulator.hpp.

operator()() [2/2]

template<typename T = Math::real>

T GeographicLib::Accumulator< T >::operator() ( T  y ) const

inline

Return the result of adding a number to sum (but don't change sum).

Parameters

[in]

y

the number to be added to the sum.

Returns

sum + y.

Definition at line 125 of file Accumulator.hpp.

operator*=() [1/2]

template<typename T = Math::real>

Accumulator& GeographicLib::Accumulator< T >::operator*= ( int  n )

inline

Multiply accumulator by an integer. To avoid loss of accuracy, use only integers such that n × T is exactly representable as a T (i.e., ± powers of two). Use n = −1 to negate sum.

Parameters

[in]

n

set sum *= n.

Definition at line 145 of file Accumulator.hpp.

operator*=() [2/2]

template<typename T = Math::real>

Accumulator& GeographicLib::Accumulator< T >::operator*= ( T  y )

inline

Multiply accumulator by a number. The fma (fused multiply and add) instruction is used (if available) in order to maintain accuracy.

Parameters

[in]

y

set sum *= y.

Definition at line 152 of file Accumulator.hpp.

operator+=()

template<typename T = Math::real>

Accumulator& GeographicLib::Accumulator< T >::operator+= ( T  y )

inline

Add a number to the accumulator.

Parameters

[in]

y

set sum += y.

Definition at line 131 of file Accumulator.hpp.

operator-=()

template<typename T = Math::real>

Accumulator& GeographicLib::Accumulator< T >::operator-= ( T  y )

inline

Subtract a number from the accumulator.

Parameters

[in]

y

set sum -= y.

Definition at line 137 of file Accumulator.hpp.

operator<()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator< ( T  y ) const

inline

Less operator on an Accumulator and a number.

Definition at line 169 of file Accumulator.hpp.

operator<=()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator<= ( T  y ) const

inline

Less or equal operator on an Accumulator and a number.

Definition at line 173 of file Accumulator.hpp.

operator=()

template<typename T = Math::real>

Accumulator& GeographicLib::Accumulator< T >::operator= ( T  y )

inline

Set the accumulator to a number.

Parameters

[in]

y

set sum = y.

Definition at line 111 of file Accumulator.hpp.

operator==()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator== ( T  y ) const

inline

Test equality of an Accumulator with a number.

Definition at line 161 of file Accumulator.hpp.

operator>()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator> ( T  y ) const

inline

Greater operator on an Accumulator and a number.

Definition at line 177 of file Accumulator.hpp.

operator>=()

template<typename T = Math::real>

bool GeographicLib::Accumulator< T >::operator>= ( T  y ) const

inline

Greater or equal operator on an Accumulator and a number.

Definition at line 181 of file Accumulator.hpp.

Sum()

template<typename T = Math::real>

T GeographicLib::Accumulator< T >::Sum ( T  y ) const

inlineprivate

Definition at line 90 of file Accumulator.hpp.

Member Data Documentation

_s

template<typename T = Math::real>

T GeographicLib::Accumulator< T >::_s

private

Definition at line 43 of file Accumulator.hpp.

_t

template<typename T = Math::real>

T GeographicLib::Accumulator< T >::_t

private

Definition at line 43 of file Accumulator.hpp.

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

• Accumulator.hpp