Version 5 (modified by 53 years ago) (diff) | ,
---|

# Remez tutorial first example: exp(x)

This is a hands-on example of the Lol Remez toolkit.

In this section we are going to approximate the *exp(x)* function using a polynomial.

## Getting started

If you do not have the full Lol Engine source code, download and unpack the latest LolRemez tarball.

The file you should edit is `remez.cpp`

.

## Source code

#include "lol/math/real.h" #include "lol/math/remez.h" using lol::real; using lol::RemezSolver; real f(real const &x) { return exp(x); } int main(int argc, char **argv) { RemezSolver<4, real> solver; solver.Run(-1, 1, f, 30); return 0; }

What does this mean?

- we declare function
`f`

which returns the exponential of 'x'. - we create a
`RemezSolver`

object for**4th-degree polynomials**and**real numbers**. - we run the solver on the
**[-1,1] range**, approximating**function**for`f`

**30 iterations**.

## Compilation

If you are using LolRemez, just put the above source code in `remez.cpp`

and type:

make

## Execution

To launch the test, type:

./remez

After all the iterations the output should be as follows:

Final error: 5.462771976237482581009771665937582411463e-4 Polynomial estimate: x**0*1.000090756764725753887362987792025308996 +x**1*9.973086551667860566788019540269306006270e-1 +x**2*4.988332174505582284710918757571761729419e-1 +x**3*1.773462612793916519454714108029230813767e-1 +x**4*4.415666059995979611944324860870682575219e-2

## Using the results

The above results can be used in a more CPU-friendly implementation such as the following one:

double fastexp(double x) { const double a0 = 1.000090756764725753887362987792025308996; const double a1 = 9.973086551667860566788019540269306006270e-1; const double a2 = 4.988332174505582284710918757571761729419e-1; const double a3 = 1.773462612793916519454714108029230813767e-1; const double a4 = 4.415666059995979611944324860870682575219e-2; return a0 + x * (a1 + x * (a2 + x * (a3 + x * a4))); }

## Analysing the results

Plotting the real exponential function and our `fastexp`

function gives the following curves:

The curves are undistinguishable. Actually they differ by no more than 5.462772e-4, which is the value the `./remez`

output gave.

It can be verified on the following error curve:

## Conclusion

You should now be all set up for your own minimax polynomial computation!

Please report any trouble you may have had with this document to [sam@hocevar.net]. You may then carry on to the next section: switching to relative error.

### Attachments (2)

- fastexp.png (13.0 KB) - added by 11 years ago.
- fastexp-error.png (23.2 KB) - added by 11 years ago.

Download all attachments as: .zip