[Cfp-interest 2047] Re: Underflow

[Jim Thomas]

> On Jul 1, 2021, at 9:41 PM, Fred J. Tydeman <tydeman at tybor.com> wrote:
> 
> On Thu, 1 Jul 2021 21:01:44 -0700 Jim Thomas wrote:
>> 
>>> I would prefer:
>>> 
>>> [6] The result underflows if a nonzero result value, before rounding,
>>> would have magnitude (absolute value) less than the minimum normalized
>>> number in the type.249
>> 
>> This seems to assume a model where a wider precision result is computed and then rounded to the result format. C
>> doesn't have that model for math functions.
> 
> Both
>  Float from Float * Float, eg (MinFloat*(1.f+FLT_EPSILON))  *  ( 1.f - FLT_EPSILON)  is MinFloat after rounding
>  Float from Float / Float
> Are not wider precision (everything done as Float), but have a rounding.

I don’t understand this response.

For example, sin(x) might just return x after comparing x with an underflow threshold. What was rounded?

- Jim Thomas

> 
>>> Also, I believe that "inexact" should be added to the footnote as:
>>> 
>>> 249)The term underflow here is intended to encompass both "gradual
>>> underflow" as in IEC 60559 and also "flush-to-zero" underflow. IEC
>>> 60559 underflow can occur in cases where the magnitude of the inexact
>>> rounded result equals the minimum normalized number in the format.
>> 
>> Change "the inexact" to "an inexact".
> 
> OK
> 
> 
> ---
> Fred J. Tydeman        Tydeman Consulting
> tydeman at tybor.com      Testing, numerics, programming
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