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// Digamma Function
//
// digamma - ψ(z)
//
// Logarithmic derivative of the gamma function: ψ(z) = Γ'(z) / Γ(z)
//
// Inputs: 1
// Outputs: 1
// Constants: 0
#include <math.h>
#include "ts.h"
static fp_t digamma_impl( fp_t z )
{
if (z > 7.0)
{
fp_t sum = log(z) - 1.0 / (2.0 * z) - 1.0 / (12.0 * z * z);
return sum;
}
fp_t sum = 0.0;
if (z > 0.0 && z < 7.0)
{
fp_t tmp = z;
while (tmp < 7.0)
{
sum -= 1.0 / tmp;
tmp += 1.0;
}
return sum + digamma_impl(tmp);
}
else if (z == 0.0)
{
return -INFINITY;
}
else if (z < 0.0)
{
fp_t n = floor(z);
fp_t frac = z - n;
return digamma_impl(1.0 - frac) - PI / tan(PI * frac);
}
return digamma_impl(z + 1.0) - 1.0 / z;
}
ts_parameter_t const ts_digamma_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };
uint_t ts_digamma_offset( ts_constant_t const *c )
{
( void )c;
return ( 0 );
}
int ts_digamma(
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_digamma_p );
(void)c;
for( uint_t i = 0; i < n; ++i )
{
y[0][i] = digamma_impl( x[0][i] );
}
return 0;
}
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