On Friday, 5 August 2016 at 06:59:21 UTC, Walter Bright wrote:
On 8/4/2016 11:05 PM, Fool wrote:
I understand your point of view. However, there are (probably
rare) situations
where one requires more control. I think that simulating
double-double precision
arithmetic using Veltkamp split was mentioned as a resonable
example, earlier.
There are cases where doing things at higher precision results
in double rounding and a less accurate result. But I am pretty
sure there are far fewer of those cases compared to routine
computations that get a more accurate result with more
precision.
If that wasn't true, we wouldn't ever need double precision.
You are wrong that there are far fewer of those cases. This is
naive point of view. A lot of netlib math functions require exact
IEEE arithmetic. Tinflex requires it. Python C backend and Mir
library require exact IEEE arithmetic. Atmosphere package
requires it, Atmosphere is used as reference code for my
publication in JMS, Springer. And the most important case: no one
top scientific laboratory will use a language without exact IEEE
arithmetic by default.
