Compaq ECQD2KCTE Denormal, Dirty zero, Infinity, Non-finite number, Not-a-Number, Trap shadow

For VAX floating-point, finites do not include reserved operands or dirty zeros (this differs from the usual VAX interpretation of dirty zeros as finite). For IEEE floating-point, finites do not include infinites, NaNs, or denormals, but do include minus zero.

denormal

An IEEE floating-point bit pattern that represents a number whose magnitude lies between zero and the smallest finite number.

dirty zero

A VAX floating-point bit pattern that represents a zero value, but not in true-zero form.

infinity

An IEEE floating-point bit pattern that represents plus or minus infinity.

LSB

The least significant bit. For a positive finite representable number A, A + 1 LSB is the next larger representative number, and A + ½ LSB is exactly halfway between A and the next larger representable number. For a positive representable number A whose fraction field is not all zeros, A – 1 LSB is the next smaller representable number, and A – ½ LSB is exactly halfway between A and the next smaller representable number.

non-finite number

An IEEE infinity, NaN, denormal number, or a VAX dirty zero or reserved operand.

Not-a-Number

An IEEE floating-point bit pattern that represents something other than a number. This comes in two forms: signaling NaNs (for Alpha, those with an initial fraction bit of 0) and quiet NaNs (for Alpha , those with initial fraction bit of 1).

representable result

A real number that can be represented exactly as a VAX or IEEE floating-point number, with finite precision and bounded exponent range.

reserved operand

A VAX floating-point bit pattern that represents an illegal value.

trap shadow

The set of instructions potentially executed after an instruction that signals an arithmetic trap but before the trap is actually taken.

true result

The mathematically correct result of an operation, assuming that the input operand values are exact. The true result is typically rounded to the nearest representable result.

4–64Alpha Architecture Handbook