The most hardest mathematical function implemented in hardware

[psihodelia]

Following question is not directly about VHDL language, but about
mathematical operations in hardware and their limits. Most reasonable
solutions to date are to have simple ALUs in the processing cores,
building complex behavior in the software.

But the world is changing and soon we will have a FPGA coprocessor as
very usual thing in the motherboard. Physics, DSP, scheduling, 3D
graphics, pattern recognition to be faster in hardware.

Questions:
Is it possible (there is no practical limits) to build in
hardware ...

1) ALU which will support very fast operations on complex-numbers ? So
that it also will calculate args, phases, lengths.

2) cos, arccos, tan, pow(e, 1+2.4j) etc. ?

3) cubic and n-th roots from real numbers?

4) Are there examples of most complex math functions in processors
from the history?

Thank you in advance!

 

[Dwayne Dilbeck]

Everything is possible. It just depends how much money the boss decides
this feature is worth, and is it the man power required reasonable.

As far as the ALU and functions are concerned, There is already atleast one
person doing just that...search this board for topic==Complex Multiply

 

[Tony Burch]

Following question is not directly about VHDL language, but about
mathematical operations in hardware and their limits. Most reasonable
solutions to date are to have simple ALUs in the processing cores,
building complex behavior in the software.

But the world is changing and soon we will have a FPGA coprocessor as
very usual thing in the motherboard. Physics, DSP, scheduling, 3D
graphics, pattern recognition to be faster in hardware.

Questions:
Is it possible (there is no practical limits) to build in
hardware ...

1) ALU which will support very fast operations on complex-numbers ? So
that it also will calculate args, phases, lengths.

2) cos, arccos, tan, pow(e, 1+2.4j) etc. ?

3) cubic and n-th roots from real numbers?

4) Are there examples of most complex math functions in processors
from the history?

Thank you in advance!

Hi,

It's always possible to implement your computation in an FPGA but it is
often not the best way to get the job done.

For some references on implementation of algorithms in FPGAs, a couple of
good books are
"Digital Signal Processing with Field Programmable Gate Arrays", Uwe
Meyer-Baese
"Computer Arithmetic, Algorithms and Hardware Designs", Behrooz Parhami

Cheers,
Anthony Burch http://www.burched.com

 

[naliali]

cos, arccos, tan, pow(e, 1+2.4j) etc, are already beeing implemented
on FPGA indirectly, and these are not very complex arithmetic
operations. but it depends on the required speed and desired cost.
there are some sulotions to implement such operations, like cordic.
but if you mean that one single instruction can do such operands, it's
another topic!!

 

[Thomas Stanka]

Questions:
Is it possible (there is no practical limits) to build in
hardware ...

It is possible to build everything calculateable in Hardware.
The complexity arises typically from
1) precision/vector length(/datatype)
2) time constraints
3) area constraints

Addition or multiplication are simple functions in HW if we talk
about 1 bit. They are normal if we talk about 16 bit and are
impossible if you like to have 1023 bit words with a result every 500
ps.

bye Thomas

 

[psihodelia]

It is possible to build everything calculateable in Hardware.

The complexity arises typically from
1) precision/vector length(/datatype)
2) time constraints
3) area constraints

I think, it is just impossible with existed VLSI technology to build
very complex circuits. And, for most tasks it is not required to have
complex hardware arithmetics, because all complex operations are
combined simple ones.

But what kind of the most complex arithmetics is already implemented
in hardware today?

 

[MikeShepherd564]

I think, it is just impossible with existed VLSI technology to build
very complex circuits. And, for most tasks it is not required to have
complex hardware arithmetics, because all complex operations are
combined simple ones.

But what kind of the most complex arithmetics is already implemented
in hardware today?

Do you have a well-defined question to ask (I don't see it there) or
is this another of your philosophical musings?

Search on Google (and, no, we don't want to know what you find).

 

[Thomas Stanka]

I think, it is just impossible with existed VLSI technology to build
very complex circuits. And, for most tasks it is not required to have
complex hardware arithmetics, because all complex operations are
combined simple ones.

This is true for some values of complex, but totally wrong for other
values....

You ignored precision. I have no doubt that every possible function
using two inputs with width <= 4bit is allready implemented in HW.
I'm pretty sure, that this is true for even 6-8 bit inputs.

But what kind of the most complex arithmetics is already implemented
in hardware today?

Maybe you need to add more details to your question.
If you ignore the problem of time you will find very complex
functionality serialised. I did some serial 3-sat for variable
(finite) input (using external memory for input, intermediate result
and final result).

bye Thomas