Exact math. More...

#include <stdlib.h>
#include <cmath>
#include <vector>
#include <boost/array.hpp>

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Functions
void	fastTwoSum (double a, double b, double &res, double &err)
	Calculates the sum of two numbers. More...

void	fastTwoDiff (double a, double b, double &res, double &err)
	Subtracts two numbers. More...

void	twoSum (double a, double b, double &res, double &err)
	Calculates the sum of a and b. More...

void	twoDiff (double a, double b, double &res, double &err)
	Difference between two numbers. More...

void	split (double num, double &high, double &low)
	Splits a given number into two, Used for multiplication. More...

void	twoProduct (double a, double b, double &res, double &err)
	Product of two number. More...

void	square (double num, double &res, double &err)
	Calculates the square of a number. More...

boost::array< double, 3 >	twoOneSum (boost::array< double, 2 > const &a, double b)
	Calculates the sum of a two-expansion and a double. More...

boost::array< double, 3 >	twoOneDiff (boost::array< double, 2 > const &a, double b)
	Calculates the difference between a two-expansion and a double. More...

vector< double >	twoTwoSum (boost::array< double, 2 > const &a, boost::array< double, 2 > const &b)
	Calculates the sum of two two-expansions. More...

vector< double >	twoTwoDiff (boost::array< double, 2 > const &a, boost::array< double, 2 > const &b)
	Calculates the difference between two two-expansions. More...

vector< double >	growExpansionZeroElim (vector< double > const &e, double b)
	Adds a scalar to an existing expansion. More...

vector< double >	expansionSumZeroElim (vector< double > const &e, vector< double > const &f)
	Adds up two expansions. More...

vector< double >	fastExpansionSumZeroElim (vector< double > const &e, vector< double > const &f)
	Adds up two expansions. More...

vector< double >	linearExpansionSumZeroElim (vector< double > const &e, vector< double > const &f)
	Adds up two expansions. More...

void	scaleExpansionZeroElim (vector< double > const &e, double b, vector< double > &result)
	Multiplies a scalar by an expansion. More...

vector< double >	compress (vector< double > const &e)
	Compresses an expansion. More...

double	estimate (vector< double > const &e)
	Calculate a double precision approximation of the expansion. More...

Detailed Description

Exact math.

Author: Elad Steinberg

Definition in file exactmath.hpp.

Function Documentation

◆ compress()

vector<double> compress ( vector< double > const & e )

Compresses an expansion.

Parameters

e Expansion

Returns: Expansion

Definition at line 450 of file exactmath.cpp.

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◆ estimate()

double estimate ( vector< double > const & e )

Calculate a double precision approximation of the expansion.

Parameters

e Expansion

Returns: A number

Definition at line 488 of file exactmath.cpp.

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◆ expansionSumZeroElim()

vector<double> expansionSumZeroElim	(	vector< double > const &	e,
		vector< double > const &	f
	)

Adds up two expansions.

Parameters

e	First expansion
f	Second expansion

Returns: Sum

Definition at line 173 of file exactmath.cpp.

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◆ fastExpansionSumZeroElim()

vector<double> fastExpansionSumZeroElim	(	vector< double > const &	e,
		vector< double > const &	f
	)

Adds up two expansions.

Parameters

e	First expansion
f	Second expansion

Returns: Sum

Definition at line 213 of file exactmath.cpp.

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◆ fastTwoDiff()

void fastTwoDiff	(	double	a,
		double	b,
		double &	res,
		double &	err
	)

Subtracts two numbers.

Parameters

a	First number
b	Second number
res	Output
err	Roundoff error

Definition at line 26 of file exactmath.cpp.

◆ fastTwoSum()

void fastTwoSum	(	double	a,
		double	b,
		double &	res,
		double &	err
	)

Calculates the sum of two numbers.

Parameters

a	First number
b	Second number
res	Output
err	Roundoff error

Definition at line 12 of file exactmath.cpp.

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◆ growExpansionZeroElim()

vector<double> growExpansionZeroElim	(	vector< double > const &	e,
		double	b
	)

Adds a scalar to an existing expansion.

Parameters

e	Expansion
b	Scalar

Returns: Expansion

Definition at line 150 of file exactmath.cpp.

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◆ linearExpansionSumZeroElim()

vector<double> linearExpansionSumZeroElim	(	vector< double > const &	e,
		vector< double > const &	f
	)

Adds up two expansions.

Parameters

e	First expansion
f	Second expansion

Returns: Expansion

Definition at line 330 of file exactmath.cpp.

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◆ scaleExpansionZeroElim()

void scaleExpansionZeroElim	(	vector< double > const &	e,
		double	b,
		vector< double > &	result
	)

Multiplies a scalar by an expansion.

Parameters

e	Expansion
b	Scalar
result	Result

Definition at line 416 of file exactmath.cpp.

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◆ split()

void split	(	double	num,
		double &	high,
		double &	low
	)

Splits a given number into two, Used for multiplication.

Parameters

num	Number
high	Higher part
low	Lower part

Definition at line 66 of file exactmath.cpp.

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◆ square()

void square	(	double	num,
		double &	res,
		double &	err
	)

Calculates the square of a number.

Parameters

num	Number
res	Result
err	Roundoff error

Definition at line 104 of file exactmath.cpp.

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◆ twoDiff()

void twoDiff	(	double	a,
		double	b,
		double &	res,
		double &	err
	)

Difference between two numbers.

Parameters

a	First number
b	Second number
res	Result
err	Roundoff error

Definition at line 60 of file exactmath.cpp.

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◆ twoOneDiff()

boost::array<double,3> twoOneDiff	(	boost::array< double, 2 > const &	a,
		double	b
	)

Calculates the difference between a two-expansion and a double.

Parameters

a	Two expansion
b	Number

Returns: Difference

Definition at line 119 of file exactmath.cpp.

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◆ twoOneSum()

boost::array<double,3> twoOneSum	(	boost::array< double, 2 > const &	a,
		double	b
	)

Calculates the sum of a two-expansion and a double.

Parameters

a	Two expansion
b	A number

Returns: Sum

Definition at line 110 of file exactmath.cpp.

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◆ twoProduct()

void twoProduct	(	double	a,
		double	b,
		double &	res,
		double &	err
	)

Product of two number.

Parameters

a	First number
b	Second number
res	Result
err	Error

Definition at line 87 of file exactmath.cpp.

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◆ twoSum()

void twoSum	(	double	a,
		double	b,
		double &	res,
		double &	err
	)

Calculates the sum of a and b.

Parameters

a	First number
b	Second number
res	Result
err	Roundoff error

Definition at line 43 of file exactmath.cpp.

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◆ twoTwoDiff()

vector<double> twoTwoDiff	(	boost::array< double, 2 > const &	a,
		boost::array< double, 2 > const &	b
	)

Calculates the difference between two two-expansions.

Parameters

a	First two expansion
b	Second two expansion

Returns: Difference

Definition at line 139 of file exactmath.cpp.

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◆ twoTwoSum()

vector<double> twoTwoSum	(	boost::array< double, 2 > const &	a,
		boost::array< double, 2 > const &	b
	)

Calculates the sum of two two-expansions.

Parameters

a	First two expansion
b	Second two expansio

Returns: sum

Definition at line 128 of file exactmath.cpp.

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Functions

Detailed Description

Function Documentation

◆ compress()

◆ estimate()

◆ expansionSumZeroElim()

◆ fastExpansionSumZeroElim()

◆ fastTwoDiff()

◆ fastTwoSum()

◆ growExpansionZeroElim()

◆ linearExpansionSumZeroElim()

◆ scaleExpansionZeroElim()

◆ split()

◆ square()

◆ twoDiff()

◆ twoOneDiff()

◆ twoOneSum()

◆ twoProduct()

◆ twoSum()

◆ twoTwoDiff()

◆ twoTwoSum()