3
$\begingroup$

After studying the process of Gradual Underflow, I'm left a little curious as to why machines don't implement Gradual Overflow; where numbers exceeding the overflow level would be stored as un-normalized floats.
Just as the precision of the mantissa is decreased for representation of a larger (in magnitude) exponent (and thus a smaller number in scientific notation) for subnormal numbers, so too could precision be traded for numbers above the overflow.

The only conceivable reason I can place for this is based on number format preservation during gradual underflow; the mantissa digits are 'right-shifted' (preceding zeros are adding after the decimal point) so although the representation is no longer normalized, it still consists of a single digit before the decimal point and the same storage spaces of mantissa and exponent.
The best conception of a Gradual Overflow implementation I can muster would involve either expanding the exponent storage space (at the cost of mantissa storage space and thus precision), or 'right-shifting' the decimal point down the mantissa (again, a loss of mantissa precision). This would seemingly break the mantissa format of a single digit before the decimal point (or otherwise change the mantissa / exponential allocated storage spaces).

I suppose I can understand that in a binary representation (with no delimiters between representation components (ie sign, mantissa, etc); distinction only made via the constant lengths of the components), breaking the storage pattern as Gradual Overflow would require is unsupportable. This assumes that there isn't a better implementation than the one I personally conceived that can preserve the storage pattern.

Is this line of thinking correct, or is there a more pertinent reason as for the lack of Gradual Overflow?
Thanks!

(I can't really tag this appropriately, since there is a rather small pool of existing tags and I don't have the reputation to create any)

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.