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In particular, IEEE 754 already uses "canonical NaN" with the meaning of "canonical encoding of a NaN" (e.g. "isCanonical(x) is true if and only if x is a finite number, infinity, or NaN that is canonical." page 38, but also for totalOrder page 42), thus a different meaning from what is used here. Please help clarify the section.
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.
The above describes an example 8-bit float with 1 sign bit, 4 exponent bits, and 3 significand bits, which is a nice balance. However, any bit allocation is possible. A format could choose to give more of the bits to the exponent if they need more dynamic range with less precision, or give more of the bits to the significand if they need more ...
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory.
However, float in Python, ... ±infinity: NaN (quiet, signalling) The minimum positive normal value is ... Example 1: Consider decimal 1.
In single precision, the bias is 127, so in this example the biased exponent is 124; in double precision, the bias is 1023, so the biased exponent in this example is 1020. fraction = .01000… 2 . IEEE 754 adds a bias to the exponent so that numbers can in many cases be compared conveniently by the same hardware that compares signed 2's ...
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.
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.