### hard 1

##### Inlets

frac32buffer input

##### Outlets

frac32buffer output, bound to normal range

##### Parameters

frac32.s.map Amount of distortion.. It's some sort of gain, actually.

Declaration
typedef struct {
float x_old = 0;
float Y_old = 0;
float a = 0;
} waveshaper_state;

/*
* The function i'm trying to map is: f(x) = sgn(x)*(ax^2)*(ax^2+3)/(ax^2+1)^2
* Its integral is equal to F(x) = |x|*(ax^2)/(ax^2+1)
* The function peaks at x = (+/-) sqrt(3/a), and the peak value is (+/-) 9/8
* I implemented the function in floating point, it's cheaper than fixed point
*
* You easily can hack the code. If you do it, please give credit.
*/

float waveshaper_update(float x, waveshaper_state *wss) {
float x_abs;
float x_sgn;

if (x > 0) {
x_abs = x;
x_sgn = 1;
} else {
x_abs = -x;
x_sgn = -1;
}

float ax2 = (wss->a) * x * x;    // ax^2
float g_x = 1.0f / (1.0f + ax2); // 1/(b+ax^2)
float y = x_sgn * ax2 * g_x * g_x * (ax2 + 3.0f);
float Y = x_abs * ax2 * g_x;

float dY = Y - (wss->Y_old);
float dx = x - (wss->x_old);
float dx_abs = dx > 0 ? dx : -dx;

float mean = dY / dx;
(wss->x_old) = x;
(wss->Y_old) = Y;
return dx_abs > 0.0001f ? mean : y;
}

void waveshaper_coefs(int32_t squeeze, waveshaper_state *wss) {
float xmax = 1.05f - (squeeze / 134217728.0f);
(wss->a) = 3.0f / (xmax * xmax);
}

waveshaper_state satu;
Control Rate
waveshaper_coefs(param_amt, &satu);
Audio Rate
outlet_out =
119304647.0f * waveshaper_update(((float)inlet_in) / 134217728.0f, &satu);
// that 119304647 corresponds (in Q27) to 8/9
// This is because this function peaks at 9/8 before asymptotically going to 1,
// so in order to keep the output in normal range