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// 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;
}
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