> How many cycles of latency ?
For 13kLUTs about 66 1 per bit plus a little overhead, can start a new calc every clock.
For 1.5kLUTs about 66, but must wait for completion.

<
For My 66000 TMAC unit::
................float...............double
sin()..........11...................19
cos().........11...................19
tan().......11-22..............19-33
ln2()............9...................15
exp2().........9...................15
atan2().....26....................36
pow()........21...................34
{including all argument reduction, polynomial evaluation, and reconstruction}

Looks impressive to me.

Reading up on Payne and Hanek argument reduction and wondering how well it
applies to 128-bit floats.

On Wednesday, May 31, 2023 at 11:15:19 PM UTC-5, robf...@gmail.com wrote:
> > How many cycles of latency ?
> For 13kLUTs about 66 1 per bit plus a little overhead, can start a new calc every clock.
> For 1.5kLUTs about 66, but must wait for completion.
>
> <
> For My 66000 TMAC unit::
> ...............float...............double
> sin()..........11...................19
> cos().........11...................19
> tan().......11-22..............19-33
> ln2()............9...................15
> exp2().........9...................15
> atan2().....26....................36
> pow()........21...................34
> {including all argument reduction, polynomial evaluation, and reconstruction}
>
> Looks impressive to me.
>
> Reading up on Payne and Hanek argument reduction and wondering how well it
> applies to 128-bit floats.
<
Payne and Hanek argument reductions allow you to get the correct
reduced arguments for very big arguments for things like::
<
SIN( 10^22 ) = -0.8522008497671888017727
and
COS( 6381956970095103×2^797) = -4.68716592425462761112×10^-19
<
If you have 128-bit FP but only 64-bit ints P&H comes into play around 10^22.
If you have 128-bit ints P&H comes into play around 10^43.

robf...@gmail.com wrote:
>> How many cycles of latency ?
> For 13kLUTs about 66 1 per bit plus a little overhead, can start a new calc every clock.
> For 1.5kLUTs about 66, but must wait for completion.
>
> <
> For My 66000 TMAC unit::
> ...............float...............double
> sin()..........11...................19
> cos().........11...................19
> tan().......11-22..............19-33
> ln2()............9...................15
> exp2().........9...................15
> atan2().....26....................36
> pow()........21...................34
> {including all argument reduction, polynomial evaluation, and reconstruction}
>
> Looks impressive to me.
>
> Reading up on Payne and Hanek argument reduction and wondering how well it
> applies to 128-bit floats.

<Grin>

It's not that bad: fp128 use 1:15:112 afair, that is the same exponent
size as x87 80-bit extended real format.

2^15 + twice the mantissa is almost 33 kbit, so you need a little bit
more than a 4kB page to hold it if you implement this in software. I
really don't think a 33 kbit rom is going to make a big impact on the
total size of a 128-bit FPU?

Terje

--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"