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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.
However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers. ... FF H = 11111111 2: ±infinity: NaN ...
E min = 00001 2 − 01111 2 = −14; E max = 11110 2 − 01111 2 = 15; Exponent bias = 01111 2 = 15; Thus, as defined by the offset binary representation, in order to get the true exponent the offset of 15 has to be subtracted from the stored exponent. The stored exponents 00000 2 and 11111 2 are interpreted specially.
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.
An exceptional result is represented by a special code called a NaN, for "Not a Number". All NaNs in IEEE 754-1985 have this format: sign = either 0 or 1. biased exponent = all 1 bits. fraction = anything except all 0 bits (since all 0 bits represents infinity).
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.
These also may return NaN or raise an exception when given a NaN argument. In the Intel x86 Architecture assembler code, atan2 is known as the FPATAN (floating-point partial arctangent) instruction. [13] It can deal with infinities and results lie in the closed interval [−π, π], e.g. atan2(∞, x) = + π /2 for finite x.
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.