// Lambert W
//
// lambert_w
//
// Lambert W function
//
// W(x) such that W*e^W = x
//
// Inputs:    1
// Outputs:   1
// Constants: 0


#include <math.h>
#include "ts.h"


ts_parameter_t const ts_lambert_w_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };

uint_t ts_lambert_w_offset( ts_constant_t const *c )
{
	( void )c;
	return ( 0 );
}

int ts_lambert_w(
	fp_t * const *y, uint_t y_n,
	fp_t const * const *x, uint_t x_n,
	uint_t n, ts_constant_t const *c
)
{
	TS_PROLOGUE( ts_lambert_w_p );
	(void)c;
    for (uint_t i = 0; i < n; ++i)
    {
        fp_t xv = x[0][i];
        if (xv < -1.0/exp(1.0))
        {
            y[0][i] = NAN;
            continue;
        }
        if (xv == 0.0)
        {
            y[0][i] = 0.0;
            continue;
        }
        /* Halley iteration for W(x) */
        fp_t w = xv < 1.0 ? log(xv + 1.0) : log(xv);
        for (uint_t j = 0; j < 10; ++j)
        {
            fp_t ew = exp(w);
            fp_t f = w * ew - xv;
            fp_t f1 = ew * (w + 1.0);
            if (f1 == 0) break;
            fp_t f2 = f1 * (w + 2.0);
            w = w - f / f1 * (1.0 + f * f2 / (2.0 * f1 * f1));
        }
        y[0][i] = w;
    }
	return 0;
}