// Bollinger Bands
//
// bollinger_bands - BB
//
// Upper: SMA + mult * stddev
// Middle: SMA
// Lower: SMA - mult * stddev
//
// Inputs:    1
// Outputs:   3 (Upper, Middle, Lower)
// Constants: 2 (period, std multiplier)

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


typedef struct {
    uint_t k;
    fp_t std_mult;
} ts_bollinger_bands_params_t;

ts_parameter_t const ts_bollinger_bands_p = { .n_inputs = 1, .n_outputs = 3, .n_constants = 2, .params_size = sizeof(ts_bollinger_bands_params_t) };


uint_t ts_bollinger_bands_offset( ts_constant_t const *c )
{
	( void )c;
	return ( c ? ((ts_bollinger_bands_params_t const *)c)->k > 0 ? ((ts_bollinger_bands_params_t const *)c)->k - 1 : 0 : 0 );
}

int ts_bollinger_bands(
	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_bollinger_bands_p );
	if ( !c ) return -1;
	TS_CHECK_INPUT(x, x_n, n);
	uint_t k = ((ts_bollinger_bands_params_t const *)c)->k;
	if (k == 0 || n < k) return -1;
	fp_t std_mult = ((ts_bollinger_bands_params_t const *)c)->std_mult;
	if (std_mult < 0 || isnan(std_mult) || isinf(std_mult)) return -1;

	for( uint_t i = 0; i < k - 1; ++i )
	{
		y[0][i] = NAN;
		y[1][i] = NAN;
		y[2][i] = NAN;
	}

	// Two-pass initial window for numerical stability
	{
		fp_t mean = 0;
		for( uint_t j = 0; j < k; ++j )
			mean += x[0][j];
		mean /= (fp_t)k;
		fp_t variance = 0;
		for( uint_t j = 0; j < k; ++j )
		{
			fp_t d = x[0][j] - mean;
			variance += d * d;
		}
		variance /= (fp_t)k;
		fp_t stddev = sqrt( variance );
		y[0][k - 1] = mean + std_mult * stddev;
		y[1][k - 1] = mean;
		y[2][k - 1] = mean - std_mult * stddev;
	}

	// Sliding window: maintain running mean, two-pass variance
	fp_t sum = 0;
	for( uint_t j = 0; j < k; ++j )
		sum += x[0][j];
	fp_t rk = 1.0 / (fp_t)k;
	for( uint_t i = k; i < n; ++i )
	{
		sum = sum + x[0][i] - x[0][i - k];
		fp_t mean = sum * rk;
		// Two-pass variance for stability
		fp_t variance = 0;
		for( uint_t j = i - k + 1; j <= i; ++j )
		{
			fp_t d = x[0][j] - mean;
			variance += d * d;
		}
		variance *= rk;
		fp_t stddev = sqrt( variance );
		y[0][i] = mean + std_mult * stddev;
		y[1][i] = mean;
		y[2][i] = mean - std_mult * stddev;
	}
	return 0;
}