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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 ...
The predicate agrees with the comparison predicates (see section § Comparison predicates) when one floating-point number is less than the other. The main differences are: [34] NaN is sortable. NaN is treated as if it had a larger absolute value than Infinity (or any other floating-point numbers). (−NaN < −Infinity; +Infinity < +NaN.)
In languages such as C, relational operators return the integers 0 or 1, where 0 stands for false and any non-zero value stands for true. An expression created using a relational operator forms what is termed a relational expression or a condition. Relational operators can be seen as special cases of logical predicates.
In a subnormal number, since the exponent is the least that it can be, zero is the leading significant digit (0.m 1 m 2 m 3...m p−2 m p−1), allowing the representation of numbers closer to zero than the smallest normal number. A floating-point number may be recognized as subnormal whenever its exponent has the least possible value.
Example 3: Consider a value of 0.375. ... Integers greater than or equal to 2 128 are rounded ... (largest number less than one) 0 01111111 00000000000000000000000 2 ...
[3]: 19-- It does not require computing the topological degree; it only requires computing the signs of function values. The number of required evaluations is at least log 2 ( D / ϵ ) {\displaystyle \log _{2}(D/\epsilon )} , where D is the length of the longest edge of the characteristic polyhedron.
This function is unusual because it actually attains the limiting values of -1 and 1 within a finite range, meaning that its value is constant at -1 for all and at 1 for all . Nonetheless, it is smooth (infinitely differentiable, C ∞ {\displaystyle C^{\infty }} ) everywhere , including at x = ± 1 {\displaystyle x=\pm 1} .
The actual number of bits of precision can vary. In general, the magnitude of the low-order part of the number is no greater than half ULP of the high-order part. If the low-order part is less than half ULP of the high-order part, significant bits (either all 0s or all 1s) are implied between the significant of the high-order and low-order numbers.