Tony Firshman wrote:
On Tue, 10 Jun 2003 at 00:43:13, Lau wrote: (ref: <[EMAIL PROTECTED]>)
Marcel Kilgus wrote:
The history is documented here http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html
Can someone please define "Gradual Underflow". That was the core issue being addressed. (don't if I have simply missed it in this thread) Pity Lau wasn't involved.
I have to admit that I don't know the answer.
"Gradual underflow", per se, is not suddenly going from a nice, 32 (or whatever) bit precision value near the minimum value (10E-617 for the QL) to zero. Instead, you convert over to representing values as denormals, with progressively less precision.
It's not so big a problem with the QL FP format, as the tweaked extra 30-odd bits of "keeping it non-zero" are in comparison with the 4096 exponent values.
With IEEE single precision format, yoyu have the sign bit and 23 bits of mantissa but only 8 bits of exponent to start with. The 23 bits of "gradual underflow" from the mantissa are a significant proportion of the overall +/-128 range for the exponent.
The benefits of using denormal values does become rather less significant as the exponent range becomes significantly greater that the bit count of the mantissa. For the QL format, 32 versus +/-2048 is pretty marginal.
--
Lau
http://www.bergbland.info
Get a domain from http://oneandone.co.uk/xml/init?k_id=5165217 and I'll get the commission!
