NaN - Encoding

Encoding

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 (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 signaled/quiet state was to be tagged. In practice, the most significant bit of the significand determined whether a NaN is signalling or quiet. Two different implementations, with reversed meanings, resulted.

• most processors (including those of the Intel/AMD x86-32/x86-64 family, the Motorola 68000 family, the AIM PowerPC family, the ARM family, and the Sun SPARC family) set the signaled/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 MIPS processors, the signaled/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 2008 revision of the IEEE 754 standard (IEEE 754-2008) makes formal recommendations for the encoding of the signaled/quiet bit.

• For binary formats, the standard follows the interpretation as an 'is_quiet' flag. I.e. the signaled/quiet bit is non-zero if the NaN is quiet, and zero if the NaN is signaling. The 'is-quiet' bit should be the most significant bit of the significand.
• 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 signaled/quiet bit is zero if the NaN is quiet, and non-zero if the N is identified by having the aN is signaling.

The state/value of the remaining bits (i.e. other than the ones used to identify a NaN as NaN, including the quiet/signaled bits) are not defined by the standard except that they must not be all zero. This value is called the 'payload' of the NaN and the recommendation is to pass the value of the first qNaN operand through operations when generating an output qNaN to assist with debugging.