exception:
- creation of a tiny nonzero result between xb1 2Emin which can cause some later exception because it is so tiny
- extraordinary loss of accuracy during the approximation of such tiny numbers by denormalized numbers.
IEEE Standard 754 allows a variety of ways to detect these events, but requires they be detected the same way for all operations.
Tininess can be detected by one of the following methods:
- after rounding (when a nonzero result, computed as though the exponent range were unbounded, would lie strictly between xb1 2Emin)
- before rounding (when a nonzero result, computed as though the exponent range and the precision were unbounded, would lie strictly between xb1 2Emin).
The MIPS architecture requires that tininess be detected after rounding.
Loss of accuracy can be detected by one of the following methods:
- denormalization loss (when the delivered result differs from what would have been computed if the exponent range were unbounded)
- inexact result (when the delivered result differs from what would have been computed if the exponent range and precision were both unbounded).
The MIPS architecture requires that loss of accuracy be detected as an inexact result.
Trap Enabled Results: If Underflow or Inexact traps are enabled, or if the FS bit is not set, then an Unimplemented exception (E) is generated, and the result register is not modified.
Trap Disabled Results: If Underflow and Inexact traps are not enabled and the FS bit is set, the result is determined by the rounding mode and the sign of the intermediate result (as listed in Table 7-1).
