Table of Contents

Machine Epsilon

Routine Name: maceps

Author: Philip Nelson

Language: C++

Description

maceps returns the machine epsilon and precision of any primitive type. A make file is included with a driver program that compares maceps to std::numeric_limits<T>::epsilon().

$ make
$ ./maceps.out

This will compile and run the driver program.

Input

maceps<T>( ) requires a template argument T with the type of machine epsilon you want ( float, double, long double, etc… ). Otherwise, maceps takes no input.

Output

maceps returns an eps struct with members int prec which holds the precision and T maceps which holds the machine epsilon for the specified type.

Code

template <typename T>
eps<T> maceps()
{
  T e = 1;
  T one = 1;
  T half = 0.5;
  int prec = 1;
  while (one + e * half > one)
  {
    e *= half;
    ++prec;
  }

  return eps(prec, e);
}

Example

int main()
{
  auto doubleeps = maceps<double>();
  std::cout << "double\n";
  std::cout << "precision:\t"    << doubleeps.prec << std::endl;
  std::cout << "maceps:\t\t"     << doubleeps.maceps << std::endl;
  std::cout << "std::numeric:\t" << std::numeric_limits<double>::epsilon() << std::endl << std::endl;
}

Result

double
precision:	53
maceps:		2.22045e-16
std::numeric:	2.22045e-16

Last Modification date: 11 January 2018