numpy.nan在存储器中是怎样表示的？

Question

print(type(np.nan)) #<class 'float'>
print(np.nan) #nan
看到np.nan是个float型，float应该是32和64个bits组成的，好奇np.nan的32或者64个bits在存储器中是什么呢？

Answer 1

简单来说是有特别的标志位。Wiki上是这么说的：

In IEEE 754 standard-conforming floating-point storage formats, NaNs are identified by specific, pre-defined bit patterns unique to NaNs. The sign bit does not matter. Binary format NaNs are represented with the exponential field filled with ones (like infinity values), and some non-zero number in the significand field (to make them distinct from infinity values). The original IEEE 754 standard from 1985 (IEEE 754-1985) only described binary floating-point formats, and did not specify how the signaling/quiet state was to be tagged. In practice, the most significant bit of the significand field determined whether a NaN is signaling or quiet. Two different implementations, with reversed meanings, resulted:
most processors (including those of the Intel and AMD's x86 family, the Motorola 68000 family, the AIM PowerPC family, the ARM family, the Sun SPARC family, and optionally new MIPS processors) set the signaling/quiet bit to non-zero if the NaN is quiet, and to zero if the NaN is signaling. Thus, on these processors, the bit represents an 'is_quiet' flag;
in NaNs generated by the PA-RISC and old MIPS processors, the signaling/quiet bit is zero if the NaN is quiet, and non-zero if the NaN is signaling. Thus, on these processors, the bit represents an 'is_signaling' flag.
The former choice has been preferred as it allows the implementation to quiet a signaling NaN by just setting the signaling/quiet bit to 1. The reverse is not possible with the latter choice because setting the signaling/quiet bit to 0 could yield an infinity.
The 2008 revision of the IEEE 754 standard (IEEE 754-2008) makes formal recommendations for the encoding of the signaling/quiet state.
For binary formats, the most significant bit of the significand field should be an 'is_quiet' flag. I.e. this bit is non-zero if the NaN is quiet, and zero if the NaN is signaling.
For decimal formats, whether binary or decimal encoded, a NaN is identified by having the top five bits of the combination field after the sign bit set to ones. The sixth bit of the field is the 'is_quiet' flag. The standard follows the interpretation as an 'is_signaling' flag. I.e. the signaling/quiet bit is zero if the NaN is quiet, and non-zero if the NaN is signaling. A signaling NaN is quieted by clearing this sixth bit.
For IEEE 754-2008 conformance, the meaning of the signaling/quiet bit in recent MIPS processors is now configurable via the NAN2008 field of the FCSR register. This support is optional in MIPS Release 3 and required in Release 5.[10]
The state/value of the remaining bits of the significand field are not defined by the standard. This value is called the 'payload' of the NaN. If an operation has a single NaN input and propagates it to the output, the result NaN's payload should be that of the input NaN (this is not always possible for binary formats when the signaling/quiet state is encoded by an 'is_signaling' flag, as explained above). If there are multiple NaN inputs, the result NaN's payload should be from one of the input NaNs; the standard does not specify which.