NaN Propagation Rules

For instructions that generate a result, special propagation rules apply when one or both source operands are NaN values, such that sNaNs can be successfully used as “tracer” values.

When both source operands are NaNs, qNaNs take priority over sNaNs. The appropriate NaN values will be selected as the operation default result as shown in Table 6-38. In the absence of any NaN source operands, any other floating-point numbers will be processed by the FPU module to generate the result.

Note: Source sNaN values will always generate an Invalid exception, but the corresponding quieted sNaN may not always be the operation result.

This magnitude comparison is based on the magnitude of the significand associated with each of these values (the sign is ignored). It is straightforward to implement because:

The MSb of a sNaN significant is 0 (with any non-zero value in the remaining bits).
The MSb of a qNaN significant is 1 (with any value in the remaining bits).

An example tracer sNaN propagation is shown in Figure 6-18. When an FPU operation (Op1) executes with a sNaN and a normal floating-point number, the sNaN will be quieted and propagate as the result. In Figure 6-18, this is sNaN1 (the initial tracer) being propagated as qNaN1. Should a subsequent operation (Op2) execute with qNaN1 and, for example, a later sNaN tracer (sNaN2), operand qNaN1 will have priority, thereby maintaining propagation of the original tracer payload. However, should that qNaN1 value then be presented to another FPU operation (Op3) together with another qNaN, the qNaN result could be either of the source qNaNs, depending upon the magnitude of their respective significands.

However, if the significand of the initial sNaN1 tracer is large enough, it will ultimately be able to continue to propagate past all subsequent NaNs and be available to view at the end of the code block, thereby allowing it to be traced back to its source.

Figure 6-18. Tracker sNaN Operand Propagation Example

Table 6-39. FMAC NaN Propagation Priority
Multiply Source Operands		Add Source Operands		FMAC Result (Fd)	Notes
Fb or Fs	Fs or Fb	Intermediate Result	Accumulator Source (Fd)	FMAC Result (Fd)
FP Multiply
		FP Add
FPN	FPN	FPN	FPN	FPN
			qNaN	qNaN
			sNaN	Quieted sNaN	INVAL signaled
		Distinguished qNaN⁽³⁾	FPN	Distinguished qNaN	INVAL signaled
			qNaN1	Distinguished qNaN or qNaN1⁽²⁾	INVAL signaled
			sNaN	Distinguished qNaN or Quieted sNaN⁽²⁾	INVAL signaled
FPN	sNaN1	Quieted sNaN1	FPN	Quieted sNaN1	INVAL signaled
			qNaN	Quieted sNaN1 or qNaN⁽²⁾	INVAL signaled
			sNaN2	Quieted sNaN1⁽²⁾	INVAL signaled
FPN	qNaN1	qNaN1	FPN	qNaN1
			qNaN2	qNaN1 or qNaN22
			sNaN	qNaN1	INVAL signaled
qNaN1	qNaN2	qNaN1 or qNaN2⁽²⁾	FPN	qNaN1 or qNaN2⁽²⁾
			qNaN3	qNaN1 or qNaN2 or qNaN3⁽²⁾
			sNaN	qNaN1 or qNaN2⁽²⁾	INVAL signaled
sNaN1	sNaN2	Quieted (sNaN1 or sNaN2)⁽²⁾	FPN	Quieted (sNaN1 or sNaN2)⁽²⁾	INVAL signaled
			qNaN	Quieted (sNaN1 or sNaN2)⁽²⁾ or qNaN	INVAL signaled
			sNaN3	Quieted (sNaN1 or sNaN2)⁽²⁾	INVAL signaled
Note: FPN is a floating-point number that is not a NaN. Using significand magnitude comparisons as defined in Table 6-38. Distinguished qNaN intermediate result will arise when operands are 0 and Inf (any sign).