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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 system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times.
Some operations of floating-point arithmetic are invalid, such as taking the square root of a negative number. The act of reaching an invalid result is called a floating-point exception. An exceptional result is represented by a special code called a NaN, for "Not a Number". All NaNs in IEEE 754-1985 have this format: sign = either 0 or 1.
Usually, the 32-bit and 64-bit IEEE 754 binary floating-point formats are used for float and double respectively. The C99 standard includes new real floating-point types float_t and double_t, defined in <math.h>. They correspond to the types used for the intermediate results of floating-point expressions when FLT_EVAL_METHOD is 0, 1, or 2.
In C, they lead to undefined behavior, but if annex F is supported, the operation yields an "invalid" floating-point exception (as required by the IEEE standard) and an unspecified value. Perl 's Math::BigInt package uses "NaN" for the result of strings that do not represent valid integers.
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit ...
Lastly we have the problem wherein the storage of the floating point data may be in big endian or little endian memory order and thus the sign bit could be in the least significant byte or the most significant byte. Therefore the use of type punning with floating point data is a questionable method with unpredictable results.
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point.