static double
beta_inc_AXPY (const double A, const double Y,
const double a, const double b, const double x)
{
if (x == 0.0)
{
return A * 0 + Y;
}
else if (x == 1.0)
{
return A * 1 + Y;
}
else if (a > 1e5 && b < 10 && x > a / (a + b))
{
/* Handle asymptotic regime, large a, small b, x > peak [AS 26.5.17] */
double N = a + (b - 1.0) / 2.0;
return A * gsl_sf_gamma_inc_Q (b, -N * log (x)) + Y;
}
else if (b > 1e5 && a < 10 && x < b / (a + b))
{
/* Handle asymptotic regime, small a, large b, x < peak [AS 26.5.17] */
double N = b + (a - 1.0) / 2.0;
return A * gsl_sf_gamma_inc_P (a, -N * log1p (-x)) + Y;
}
else
{
double ln_beta = gsl_sf_lnbeta (a, b);
double ln_pre = -ln_beta + a * log (x) + b * log1p (-x);
double prefactor = exp (ln_pre);
if (x < (a + 1.0) / (a + b + 2.0))
{
/* Apply continued fraction directly. */
double epsabs = fabs (Y / (A * prefactor / a)) * GSL_DBL_EPSILON;
double cf = beta_cont_frac (a, b, x, epsabs);
return A * (prefactor * cf / a) + Y;
}
else
{
/* Apply continued fraction after hypergeometric transformation. */
double epsabs =
fabs ((A + Y) / (A * prefactor / b)) * GSL_DBL_EPSILON;
double cf = beta_cont_frac (b, a, 1.0 - x, epsabs);
double term = prefactor * cf / b;
if (A == -Y)
{
return -A * term;
}
else
{
return A * (1 - term) + Y;
}
}
}
}
static double
beta_inc_AXPY (const double A, const double Y,
const double a, const double b, const double x)
{
if (x == 0.0)
{
return A * 0 + Y;
}
else if (x == 1.0)
{
return A * 1 + Y;
}
else
{
double ln_beta = gsl_sf_lnbeta (a, b);
double ln_pre = -ln_beta + a * log (x) + b * log1p (-x);
double prefactor = exp (ln_pre);
if (x < (a + 1.0) / (a + b + 2.0))
{
/* Apply continued fraction directly. */
double epsabs = fabs (Y / (A * prefactor / a)) * GSL_DBL_EPSILON;
double cf = beta_cont_frac (a, b, x, epsabs);
return A * (prefactor * cf / a) + Y;
}
else
{
/* Apply continued fraction after hypergeometric transformation. */
double epsabs =
fabs ((A + Y) / (A * prefactor / b)) * GSL_DBL_EPSILON;
double cf = beta_cont_frac (b, a, 1.0 - x, epsabs);
double term = prefactor * cf / b;
if (A == -Y)
{
return -A * term;
}
else
{
return A * (1 - term) + Y;
}
}
}
}
int
gsl_sf_beta_inc_e(
const double a,
const double b,
const double x,
gsl_sf_result * result
)
{
if(a <= 0.0 || b <= 0.0 || x < 0.0 || x > 1.0) {
DOMAIN_ERROR(result);
}
else if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(x == 1.0) {
result->val = 1.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else {
gsl_sf_result ln_beta;
gsl_sf_result ln_x;
gsl_sf_result ln_1mx;
gsl_sf_result prefactor;
const int stat_ln_beta = gsl_sf_lnbeta_e(a, b, &ln_beta);
const int stat_ln_1mx = gsl_sf_log_1plusx_e(-x, &ln_1mx);
const int stat_ln_x = gsl_sf_log_e(x, &ln_x);
const int stat_ln = GSL_ERROR_SELECT_3(stat_ln_beta, stat_ln_1mx, stat_ln_x);
const double ln_pre_val = -ln_beta.val + a * ln_x.val + b * ln_1mx.val;
const double ln_pre_err = ln_beta.err + fabs(a*ln_x.err) + fabs(b*ln_1mx.err);
const int stat_exp = gsl_sf_exp_err_e(ln_pre_val, ln_pre_err, &prefactor);
if(stat_ln != GSL_SUCCESS) {
result->val = 0.0;
result->err = 0.0;
GSL_ERROR ("error", GSL_ESANITY);
}
if(x < (a + 1.0)/(a+b+2.0)) {
/* Apply continued fraction directly. */
gsl_sf_result cf;
const int stat_cf = beta_cont_frac(a, b, x, &cf);
int stat;
result->val = prefactor.val * cf.val / a;
result->err = (fabs(prefactor.err * cf.val) + fabs(prefactor.val * cf.err))/a;
stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
}
else {
/* Apply continued fraction after hypergeometric transformation. */
gsl_sf_result cf;
const int stat_cf = beta_cont_frac(b, a, 1.0-x, &cf);
int stat;
const double term = prefactor.val * cf.val / b;
result->val = 1.0 - term;
result->err = fabs(prefactor.err * cf.val)/b;
result->err += fabs(prefactor.val * cf.err)/b;
result->err += 2.0 * GSL_DBL_EPSILON * (1.0 + fabs(term));
stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
}
}
}
