Practical C Programming, 3rd Edition

There is a simple way of determining how accurate your floating point is (for simple calculations). The method used in the following program is to add 1.0 + 0.1, 1.0 + 0.01, 1.0 + 0.001, and so on until the second number gets so small that it makes no difference in the result.

The old C language specified that all floating-point numbers were to be done in double . C++ removed that restriction, but because many C++ compilers are really front-ends to a C compiler, frequently C++ arithmetic is done in double . This means that if number1 and number2 are declared as float , the expression:

while (number1 + number2 != number1)

is equivalent to:

while (double(number1) + double(number2) != double(number1))

If you use the 1 + 0.001 trick, the automatic conversion of float to double may give a distorted picture of the accuracy of your machine. (In one case, 84 bits of accuracy were reported for a 32-bit format.) Example 19-1 computes the accuracy of both floating point as used in equations and floating point as stored in memory. Note the trick used to determine the accuracy of the floating-point numbers in storage.

Example 19-1. float/float.cpp

#include <iostream> #include <iomanip> int main( ) { // two number to work with float number1, number2; float result; // result of calculation int counter; // loop counter and accuracy check number1 = 1.0; number2 = 1.0; counter = 0; while (number1 + number2 != number1) { ++counter; number2 = number2 / 10.0; } std::cout << std::setw(2) << counter << " digits accuracy in calculations\n"; number2 = 1.0; counter = 0; while (true) { result = number1 + number2; if (result == number1) break; ++counter; number2 = number2 / 10.0; } std::cout << std::setw(2) << counter << " digits accuracy in storage\n"; return (0); }

The results are as follows :

20 digits accuracy in calculations 8 digits accuracy in storage

This program gives only an approximation of the floating-point precision arithmetic. A more accurate definition can be found in the standard include file float.h .