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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.
A minifloat in 1 byte (8 bit) with 1 sign bit, 4 exponent bits and 3 significand bits (in short, a 1.4.3 minifloat) is demonstrated here. The exponent bias is defined as 7 to center the values around 1 to match other IEEE 754 floats [3] [4] so (for most values) the actual multiplier for exponent x is 2 x−7. All IEEE 754 principles should be ...
This does not violate trichotomy as long as a consistent total order is adopted: either −0 = +0 or −0 < +0 is valid. Common floating point types, however, have an exception to trichotomy: there is a special value "NaN" (Not a Number) such that x < NaN, x > NaN, and x = NaN are all false for all floating-point values x (including NaN itself).
The bfloat16 (brain floating point) [1] [2] floating-point format is a computer number format occupying 16 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
The numerical value of such a finite number is (−1) s × c × b q. [a] Moreover, there are two zero values, called signed zeros: the sign bit specifies whether a zero is +0 (positive zero) or −0 (negative zero). Two infinities: +∞ and −∞. Two kinds of NaN (not-a-number): a quiet NaN (qNaN) and a signaling NaN (sNaN).
Of these, the subnormal numbers represent values which if normalized would have exponents below the smallest representable exponent (the exponent having a limited range). The significand (or mantissa) of an IEEE floating-point number is the part of a floating-point number that represents the significant digits .
"Instead of using a single floating-point number as approximation for the value of a real variable in the mathematical model under investigation, interval arithmetic acknowledges limited precision by associating with the variable a set of reals as possible values. For ease of storage and computation, these sets are restricted to intervals." [7]
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false). [1] [2] Truth values are used in computing as well as various types of logic.