What range of numbers can be represented in a 16-, 32- and 64-bit IEEE-754 systems?

For a given IEEE-754 floating point number X, if 2^E <= abs(X) < 2^(E+1) then the distance from X to the next largest representable floating point number (epsilon) is: epsilon = 2^(E-52) % For a 64-bit float (double precision) epsilon = 2^(E-23) % For a 32-bit float (single precision) epsilon = 2^(E-10) % For a … Read more

PHP – Floating Number Precision [duplicate]

Because floating point arithmetic != real number arithmetic. An illustration of the difference due to imprecision is, for some floats a and b, (a+b)-b != a. This applies to any language using floats. Since floating point are binary numbers with finite precision, there’s a finite amount of representable numbers, which leads accuracy problems and surprises … Read more

How do I print a double value with full precision using cout?

You can set the precision directly on std::cout and use the std::fixed format specifier. double d = 3.14159265358979; cout.precision(17); cout << “Pi: ” << fixed << d << endl; You can #include <limits> to get the maximum precision of a float or double. #include <limits> typedef std::numeric_limits< double > dbl; double d = 3.14159265358979; cout.precision(dbl::max_digits10); … Read more