## Questions on Function Approximation (using FPGAs)

### Questions on Function Approximation (using FPGAs)

Dear all,

I am working on (compound) function approximation with one input
variable using piecewise polynomial approximation with non-linear
joints. These approximations are implemented in hardware using Xilinx FPGAs.

Example of such functions include: f(x)=sqrt(-ln(x)) or
f(x)=x*ln(x) where x = [0,1), which are used for Gaussian noise
generation (Box-Muller method) and Entropy calculation
respectively.

Does anyone know any other real-life applications where compound
functions need to be approximated?

My second question is on the function f(x)=sqrt(-ln(x)) over x =
[0,1). This function is highly non-linear and approaches infinity
as x gets close to zero. This requires floating point
implementation (due to the large polynomial coefficients, which I
want to avoid). Are there any transformations I am apply to the
function to decompose it 2 or more functions that are more linear?
(Note that ln(x) is also highly non-linear over x = [0,1))

Regards,

Dong-U Lee

### Questions on Function Approximation (using FPGAs)

Dear all,

I am working on (compound) function approximation with one input
variable using piecewise polynomial approximation with non-linear
joints. These approximations are implemented in hardware using Xilinx FPGAs.

Example of such functions include: f(x)=sqrt(-ln(x)) or
f(x)=x*ln(x) where x = [0,1), which are used for Gaussian noise
generation (Box-Muller method) and Entropy calculation
respectively.

Does anyone know any other real-life applications where compound
functions need to be approximated?

My second question is on the function f(x)=sqrt(-ln(x)) over x =
[0,1). This function is highly non-linear and approaches infinity
as x gets close to zero. This requires floating point
implementation (due to the large polynomial coefficients, which I
want to avoid). Are there any transformations I am apply to the
function to decompose it 2 or more functions that are more linear?
(Note that ln(x) is also highly non-linear over x = [0,1))

Regards,

Dong-U Lee

### Questions on Function Approximation (using FPGAs)

> Dear all,

> I am working on (compound) function approximation with one input
> variable using piecewise polynomial approximation with non-linear
> joints. These approximations are implemented in hardware using Xilinx FPGAs.

> Example of such functions include: f(x)=sqrt(-ln(x)) or
> f(x)=x*ln(x) where x = [0,1), which are used for Gaussian noise
> generation (Box-Muller method) and Entropy calculation
> respectively.

> Does anyone know any other real-life applications where compound
> functions need to be approximated?

sqrt(1/x) is used so often that more than one modern cpu contains
built-in lookup tables to generate a good starting point for a NR iteration.

Quote:> My second question is on the function f(x)=sqrt(-ln(x)) over x =
> [0,1). This function is highly non-linear and approaches infinity
> as x gets close to zero. This requires floating point
> implementation (due to the large polynomial coefficients, which I
> want to avoid). Are there any transformations I am apply to the
> function to decompose it 2 or more functions that are more linear?
> (Note that ln(x) is also highly non-linear over x = [0,1))

My first guess would be to look for some kind of rational approximation,
even if this does require a final division.

Terje

--

"almost all programming can be viewed as an exercise in caching"

Hi folks!

i was wondering..if one emulates the x86 architecture using
multiple FPGAs, and thus makes use of many more execution units
than are available in a single chip Pentium, how much performance
improvement is possible?

of course this system will be bulky, and will consume much more power etc..,
but assuming those issues dont matter and are taken care of, is it
worth trying..?

Thanks....Ravindra.