CODEWITHSUNDEEP
c++floating-pointepsilon
TestUser
TestUser

Reputation: 967

What is the maximum precision representable value for a given double value on a machine?

Couple of questions from below code:

a) What does std::numeric_limits::digits10 denote? b) If (a) represents max 10 digits double number re-presentable on a machine then we can keep getting more and more precision by just adding +1, +2 and then whats the maximum re-presentable double value on a machine? How can be display that? i.e what std::numeric_limits::digits10 + MaxN?

#include <iostream>
#include <iomanip>
#include <cmath>
#include <limits>


int main(void)
{
  double d1 = 0.1;
  double d2 = 0.2;
  double d3 = d1 + d2;
  std::cout << std::setprecision(std::numeric_limits<long double>::digits10 + 1) << "Sum 0.1 + 0.2 = " << d3 << std::endl;
  std::cout << std::setprecision(std::numeric_limits<long double>::digits10 + 2) << "Sum 0.1 + 0.2 = " << d3 << std::endl;
  std::cout << std::setprecision(std::numeric_limits<long double>::digits10 + 3) << "Sum 0.1 + 0.2 = " << d3 << std::endl;
  std::cout << std::setprecision(std::numeric_limits<long double>::digits10 + 4) << "Sum 0.1 + 0.2 = " << d3 << std::endl;
  return 0;
}

Upvotes: 0

Views: 1169

Answers (1)

chux
chux

Reputation: 153457

What does std::numeric_limits::digits10 denote?

double is typically 64-bits and can exactly represent about 264 different values.

Text like "0.1", "3.1415926535897932384626433832795", etc. has infinite possibilities.

Convert text to double and then back to text, do we get the same text (round-tripping)? This will not work for all possible text.

Take a sub-set of text possibilities, say only those with up to N leading significant decimal digits and with a limited exponent range.

numeric_limits<double>::digits10 (e.g. 15) is that N that allow for all successful round-tripping.

What is the maximum precision representable value for a given double value on a machine?

Typical double is encoded using base-2 and has a maximum precision of 53 significant binary digits.

can keep getting more and more precision by just adding ...

Select double values, written in decimal, take more than N significant digits to write exactly. I'd say up to about 754.

Writing a double to numeric_limits<double>::max_digits10 (e.g. 17) significant decimal digits is sufficient to distinguish it from all other double.

A quality double to text function will certainly and correctly write at least max_digits10 decimal digits. Beyond that it is up to the implementation. To meet IEEE 754, I am certain the minimum is max_digits10 + 3.

numeric_limits<double>::digits10 differs from numeric_limits<double>::max_digits10 because the double encoding using base 2 differs from text as base 10. The double values are not nicely distributed along base 10 values.

Upvotes: 1

Related Questions