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For example, the calculation x 0 may produce the result 1, even where x is NaN, so checking only the final result would obscure the fact that a calculation before the x 0 resulted in a NaN. In general, then, a later test for a set invalid flag is needed to detect all cases where NaNs are introduced [ 3 ] (see Function definition below for ...
IEEE 754-1985 [1] is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. [2]
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.) qNaN and sNaN are treated as if qNaN had a larger absolute value than sNaN. (−qNaN < −sNaN; +sNaN < +qNaN.) NaN is then sorted according to the payload.
Hardware and software for machine learning or neural networks tend to use half precision: such applications usually do a large amount of calculation, but don't require a high level of precision. Due to hardware typically not supporting 16-bit half-precision floats, neural networks often use the bfloat16 format, which is the single precision ...
Hence the production of a subnormal number is sometimes called gradual underflow because it allows a calculation to lose precision slowly when the result is small. In IEEE 754-2008, denormal numbers are renamed subnormal numbers and are supported in both binary and decimal formats.
French President Emmanuel Macron’s office announced a new government Monday, after the previous Cabinet collapsed in a historic vote prompted by fighting over the country's budget. The ...
Inf − Inf and (−Inf) + Inf results in NaN too (green area). Inf can be augmented and decremented by finite values without change. Sums with finite operands can give an infinite result (i.e. 14.0 + 3.0 = +Inf as a result is the cyan area, −Inf is the magenta area).
A NaN (not a number) value represents undefined results. In IEEE arithmetic, division of 0/0 or ∞/∞ results in NaN, but otherwise division always produces a well-defined result. Dividing any non-zero number by positive zero (+0) results in an infinity of the same sign as the dividend.