# Variable-hardness clipping function¶

notes
```k >= 1 is the "clipping hardness". 1 gives a smooth clipping, and a high value gives
hardclipping.

Don't set k too high, because the formula use the pow() function, which use exp() and
would overflow easily. 100 seems to be a reasonable value for "hardclipping"
```
code
 `1` ```f (x) = sign (x) * pow (atan (pow (abs (x), k)), (1 / k)); ```

```// Use this function instead of atan and see performance increase drastically :)

inline double fastatan( double x )
{
return (x / (1.0 + 0.28 * (x * x)));
}
```
```The greater k becomes the lesser is the change in the form of f(x, k). I recommend using
f2(x, k2) = sign(x) * pow(atan(pow(abs(x), 1 / k2)), k2) ,  k2 in [0.01, 1]
where k2 is the "clipping softness" (k2 = 0.01 means "hardclipping", k2 = 1 means
"softclipping"). This gives better control over the clipping effect.
```
```Don't know if i understood ok , but, how can i clip at diferent levels than -1.0/1.0 using this
func? tried several ways but none seems to work
```
```The most straightforward way to adjust the level (x) at which the signal is clipped would be to
multiply the signal by 1/x before the clipping function then multiply it again by x afterwards.
```
```Atan is a nice softclipping function, but you can do without pow().

x: input value
a: clipping factor (0 = none, infinity = hard)
ainv: 1/a

y = ainv * atan( x * a );
```
```Even better, you can normalize the output using:

shape = 1..infinity

precalc:
inv_atan_shape=1.0/atan(shape);
process:
output = inv_atan_shape * atan(input*shape);

This gives a very soft transition from no distortion to hard clipping.
```
```Scoofy,

What do you mean with 'shape'?
Is it a new parameter?
```
```sign (x) * pow (atan (pow (abs (x), k)), (1 / k));

OUCH! That's a lot of pow, atan and floating point division - probably kill most CPU's :) My
experience has been that any sigmoid function will create decent distortion if oversampled and
eq'ed properly. You can adjust the "hardness" of the clipping by simply changing a couple
coefficients, or by increasing/decreasing the input gain: like so:

y = A * tanh(B * x)

Cascading a couple/few of these will give you bone-crushing, Megadeth/Slayer style grind while
rolling back the gain gives a Fender Twin sound.

Two cascaded half-wave soft clippers gives duty-cycle modulation and a transfer curve similar to
the 3/2 power curve of tubes. I came up w/ a model based on that solution after reading reading
this: http://www.trueaudio.com/at_eetjlm.htm (orig. link at www.simulanalog.org)
```
```If anyone is interested, I have a working amp modeler and various c/c++ classes that model
distortion circuits by numerical solutions to non-linear ODE's like those described by
Yeh, Smith, Macak, Pakarinen, et al. in their PhD disertations and DAFX papers. Although
static waveshapers/filters can give decent approximations & cool sounds, they lack the dynamic
properties of the actual circuits and have poor harmonics. I also have whitepapers on my
implementations for those that think math is cool. Drop me a line for more info.
```