Search results
Results from the WOW.Com Content Network
Conversely, precision can be lost when converting representations from integer to floating-point, since a floating-point type may be unable to exactly represent all possible values of some integer type. For example, float might be an IEEE 754 single precision type, which cannot represent the integer 16777217 exactly, while a 32-bit integer type ...
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
The 80-bit floating-point format has a range (including subnormals) from approximately 3.65 × 10 −4951 to 1.18 × 10 +4932. Although log 10 ( 2 64 ) ≈ 19.266 , this format is usually described as giving approximately eighteen significant digits of precision (the floor of log 10 ( 2 63 ) , the minimum guaranteed precision).
This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
However, supposing that floating-point comparisons are expensive, and also supposing that float is represented according to the IEEE floating-point standard, and integers are 32 bits wide, we could engage in type punning to extract the sign bit of the floating-point number using only integer operations:
Here, attempting to use a non-class type in a qualified name (T::foo) results in a deduction failure for f<int> because int has no nested type named foo, but the program is well-formed because a valid function remains in the set of candidate functions.