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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 ...
UCHAR_MAX, USHRT_MAX, UINT_MAX, ULONG_MAX, ULLONG_MAX(C99) – maximum possible value of unsigned integer types: unsigned char, unsigned short, unsigned int, unsigned long, unsigned long long; CHAR_MIN – minimum possible value of char; CHAR_MAX – maximum possible value of char; MB_LEN_MAX – maximum number of bytes in a multibyte character
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. Double precision may be chosen when the range or precision of single precision would be insufficient.
The minimum strictly positive (subnormal) value is 2 −16494 ≈ 10 −4965 and has a precision of only one bit. The minimum positive normal value is 2 −16382 ≈ 3.3621 × 10 −4932 and has a precision of 113 bits, i.e. ±2 −16494 as well. The maximum representable value is 2 16384 − 2 16271 ≈ 1.1897 × 10 4932.
On some PowerPC systems, [11] long double is implemented as a double-double arithmetic, where a long double value is regarded as the exact sum of two double-precision values, giving at least a 106-bit precision; with such a format, the long double type does not conform to the IEEE floating-point standard.
NOTE C does not specify a radix for float, double, and long double. An implementation can choose the representation of float, double, and long double to be the same as the decimal floating types. [2] Despite that, the radix has historically been binary (base 2), meaning numbers like 1/2 or 1/4 are exact, but not 1/10, 1/100 or 1/3.
It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks. Almost all modern uses follow the IEEE 754-2008 standard, where the 16-bit base-2 format is referred to as binary16, and the exponent uses 5 bits. This can express values in the range ...
If approximate values of factorial numbers are desired, Stirling's approximation gives good results using floating-point arithmetic. The largest representable value for a fixed-size integer variable may be exceeded even for relatively small arguments as shown in the table below.