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The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits). The two most commonly used levels of precision for floating-point numbers are single precision and double precision.
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.
This is usually measured in bits, but sometimes in decimal digits. It is related to precision in mathematics, which describes the number of digits that are used to express a value. Some of the standardized precision formats are Half-precision floating-point format; Single-precision floating-point format; Double-precision floating-point format
Relative precision of single (binary32) and double precision (binary64) numbers, compared with decimal representations using a fixed number of significant digits. Relative precision is defined here as ulp( x )/ x , where ulp( x ) is the unit in the last place in the representation of x , i.e. the gap between x and the next representable number.
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 ...
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 IEEE standard IEEE 754 specifies a standard method for both floating-point calculations and storage of floating-point values in various formats, including single (32-bit, used in Java's float) or double (64-bit, used in Java's double) precision.
The set of basic C data types is similar to Java's. Minimally, there are four types, char, int, float, and double, but the qualifiers short, long, signed, and unsigned mean that C contains numerous target-dependent integer and floating-point primitive types. [15]