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In computing, NaN (/ n æ n /), standing for Not a Number, is a particular value of a numeric data type (often a floating-point number) which is undefined as a number, such as the result of 0/0. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities ...
In the IEEE standard the base is binary, i.e. =, and normalization is used.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).
For example, the number 2469/200 is a floating-point number in base ten with five digits: / = = ⏟ ⏟ ⏞ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346.
It preserves the approximate dynamic range of 32-bit floating-point numbers by retaining 8 exponent bits, but supports only an 8-bit precision rather than the 24-bit significand of the binary32 format. More so than single-precision 32-bit floating-point numbers, bfloat16 numbers are unsuitable for integer calculations, but this is not their ...
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.
C does not provide direct support to exception handling: it is the programmer's responsibility to prevent errors in the first place and test return values from the functions.
The figure below shows the absolute precision for both formats over a range of values. This figure can be used to select an appropriate format given the expected value of a number and the required precision. Precision of binary32 and binary64 in the range 10 −12 to 10 12. An example of a layout for 32-bit floating point is
Negative numbers (s is 1) are encoded as 2's complements. The two encodings in which all non-sign bits are 0 have special interpretations: If the sign bit is 1, the posit value is NaR ("not a real") If the sign bit is 0, the posit value is 0 (which is unsigned and the only value for which the sign function returns 0)