Re: [PATCH v2 4/9] math: Use an improved algorithm for hypot (dbl-64)

[Joseph Myers <joseph@codesourcery.com>]

On Fri, 29 Oct 2021, Wilco Dijkstra via Libc-alpha wrote:

> Hi Joseph,
> 
> > Scaling down doesn't set the underflow flag if the scaling down was exact 
> > (even though the actual hypot operation is inexact and so should raise 
> > underflow).
> 
> That's true, but doesn't that apply to the float version too? The convert from
> double to float might also be precise (and denormal) even if earlier calculations
> were inexact.

The only case where hypotf can have a mathematical result that is tiny and 
inexact is when both arguments are in the subnormal range for float and 
the implementation in terms of double then involves computing the (double) 
square root of a number M * 2^-298, for some (exact) M in the range [2, 
2^46), and then converting that (double) square root to float.

The square root of an integer in the range [2, 2^46) cannot be close 
enough to an integer for the result of rounding it in either direction to 
53 bits (so at least 30 fractional bits) to be an integer, so it is not 
possible for the conversion from double to float to be exact when the 
mathematical result of hypotf is tiny and inexact.

-- 
Joseph S. Myers
joseph@codesourcery.com