[Beowulf] Optimized math routines/transcendentals

[C Bergström]

On Wed, Jun 1, 2016 at 3:36 AM, Prentice Bisbal <pbisbal at pppl.gov> wrote:
>
> On 04/29/2016 02:23 PM, C Bergström wrote:
>>
>> Dear lazyweb,
>>
>> I'm working on optimizing for a non-x86 target processor and left no
>> choice but to start writing optimized math functions.
>>
>> So far I've compared
>> glibc
>> Sun solaris open sourced code
>> NetBSD mathlib (Which originated from Sun circa 1993)
>> netlib
>> {REDACTED-vendor-name} modified version of netlib
>>
>> Surprisingly, glibc does a pretty respectable job in terms of
>> accuracy, but alas it's certainly not the fastest.
>> ------------
>> One of the faster versions tested sometimes incorrectly
>> rounds for medium size and larger arguments, i.e. the least
>> significant bit differs from the other versions.
>> ---
>> sin(6e5) =
>> bfcb40318b8c1728 vs
>> bfcb40318b8c1727 =
>> -0.212896531236929975605676 (REDACTED-vendor-name) vs
>> -0.212896531236929947850101 (nearest) vs
>> -0.212896531236929960235352 (higher precision) ...
>> -------
>> Question: Is the above acceptable to your scientific codes in general?
>>
> Is this the sort of problem John Gustafson's Unums was meant to eliminate?
>
> http://www.johngustafson.net/unums.html
>
> Unfortunately, that seems to be the best (only?) page on the Internet about
> Unums, other than his Wikipedia entry:
>
> https://en.wikipedia.org/wiki/John_Gustafson_(scientist)#Unums

hah! I think he's visiting Singapore and if you're really curious I
might be able to go poke his brain and or get him to reply back with
more information..

:)