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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.
For the binary interchange formats whose encoding follows the IEEE 754-2008 recommendation on placement of the NaN signaling bit, the comparison is identical to one that type puns the floating-point numbers to a sign–magnitude integer (assuming a payload ordering consistent with this comparison), an old trick for FP comparison without an FPU.
Shown here is another possible encoding; XML schema does not define an encoding for this datatype. ^ The RFC CSV specification only deals with delimiters, newlines, and quote characters; it does not directly deal with serializing programming data structures.
Here we can show how to convert a base-10 real number into an IEEE 754 binary32 format using the following outline: Consider a real number with an integer and a fraction part such as 12.375; Convert and normalize the integer part into binary; Convert the fraction part using the following technique as shown here
C source code to convert between IEEE double, single, and half precision can be found here; Java source code for half-precision floating-point conversion; Half precision floating point for one of the extended GCC features
The remaining combinations encode infinities and NaNs. BID and DPD use different bits of the combination field for that. In the cases of Infinity and NaN, all other bits of the encoding are ignored. Thus, it is possible to initialize an array to Infinities or NaNs by filling it with a single byte value.
The format is written with the significand having an implicit integer bit of value 1 (except for special data, see the exponent encoding below). With the 52 bits of the fraction (F) significand appearing in the memory format, the total precision is therefore 53 bits (approximately 16 decimal digits, 53 log 10 (2) ≈ 15.955).
Infinity, quiet NaN and signaling NaN use encodings beginning with s 1111: s 11110 xxxxxxxxxxxxxxxxxxxxxxxxxx s 111110 xxxxxxxxxxxxxxxxxxxxxxxxx s 111111 xxxxxxxxxxxxxxxxxxxxxxxxx The bits shown in parentheses are implicit: they are not included in the 32 bits of the Decimal32 encoding, but are implied by the two bits after the sign bit.