int
gsl_sf_beta_e(const double x, const double y, gsl_sf_result * result)
{
if((x > 0 && y > 0) && x < 50.0 && y < 50.0) {
/* Handle the easy case */
gsl_sf_result gx, gy, gxy;
gsl_sf_gamma_e(x, &gx);
gsl_sf_gamma_e(y, &gy);
gsl_sf_gamma_e(x+y, &gxy);
result->val = (gx.val*gy.val)/gxy.val;
result->err = gx.err * fabs(gy.val/gxy.val);
result->err += gy.err * fabs(gx.val/gxy.val);
result->err += fabs((gx.val*gy.val)/(gxy.val*gxy.val)) * gxy.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else if (isnegint(x) || isnegint(y)) {
DOMAIN_ERROR(result);
} else if (isnegint(x+y)) { /* infinity in the denominator */
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
} else {
gsl_sf_result lb;
double sgn;
int stat_lb = gsl_sf_lnbeta_sgn_e(x, y, &lb, &sgn);
if(stat_lb == GSL_SUCCESS) {
int status = gsl_sf_exp_err_e(lb.val, lb.err, result);
result->val *= sgn;
return status;
}
else {
result->val = 0.0;
result->err = 0.0;
return stat_lb;
}
}
}
int
gsl_sf_lnbeta_sgn_e(const double x, const double y, gsl_sf_result * result, double * sgn)
{
/* CHECK_POINTER(result) */
if(x == 0.0 || y == 0.0) {
*sgn = 0.0;
DOMAIN_ERROR(result);
} else if (isnegint(x) || isnegint(y)) {
*sgn = 0.0;
DOMAIN_ERROR(result); /* not defined for negative integers */
}
/* See if we can handle the postive case with min/max < 0.2 */
if (x > 0 && y > 0) {
const double max = GSL_MAX(x,y);
const double min = GSL_MIN(x,y);
const double rat = min/max;
if(rat < 0.2) {
/* min << max, so be careful
* with the subtraction
*/
double lnpre_val;
double lnpre_err;
double lnpow_val;
double lnpow_err;
double t1, t2, t3;
gsl_sf_result lnopr;
gsl_sf_result gsx, gsy, gsxy;
gsl_sf_gammastar_e(x, &gsx);
gsl_sf_gammastar_e(y, &gsy);
gsl_sf_gammastar_e(x+y, &gsxy);
gsl_sf_log_1plusx_e(rat, &lnopr);
lnpre_val = log(gsx.val*gsy.val/gsxy.val * M_SQRT2*M_SQRTPI);
lnpre_err = gsx.err/gsx.val + gsy.err/gsy.val + gsxy.err/gsxy.val;
t1 = min*log(rat);
t2 = 0.5*log(min);
t3 = (x+y-0.5)*lnopr.val;
lnpow_val = t1 - t2 - t3;
lnpow_err = GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3));
lnpow_err += fabs(x+y-0.5) * lnopr.err;
result->val = lnpre_val + lnpow_val;
result->err = lnpre_err + lnpow_err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
*sgn = 1.0;
return GSL_SUCCESS;
}
}
/* General case - Fallback */
{
gsl_sf_result lgx, lgy, lgxy;
double sgx, sgy, sgxy, xy = x+y;
int stat_gx = gsl_sf_lngamma_sgn_e(x, &lgx, &sgx);
int stat_gy = gsl_sf_lngamma_sgn_e(y, &lgy, &sgy);
int stat_gxy = gsl_sf_lngamma_sgn_e(xy, &lgxy, &sgxy);
*sgn = sgx * sgy * sgxy;
result->val = lgx.val + lgy.val - lgxy.val;
result->err = lgx.err + lgy.err + lgxy.err;
result->err += 2.0 * GSL_DBL_EPSILON * (fabs(lgx.val) + fabs(lgy.val) + fabs(lgxy.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_3(stat_gx, stat_gy, stat_gxy);
}
}
int
gsl_sf_beta_inc_e(
const double a,
const double b,
const double x,
gsl_sf_result * result
)
{
if(x < 0.0 || x > 1.0) {
DOMAIN_ERROR(result);
} else if (isnegint(a) || isnegint(b)) {
DOMAIN_ERROR(result);
} else if (isnegint(a+b)) {
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 if (a <= 0 || b <= 0) {
gsl_sf_result f, beta;
int stat;
const int stat_f = gsl_sf_hyperg_2F1_e(a, 1-b, a+1, x, &f);
const int stat_beta = gsl_sf_beta_e(a, b, &beta);
double prefactor = (pow(x, a) / a);
result->val = prefactor * f.val / beta.val;
result->err = fabs(prefactor) * f.err/ fabs(beta.val) + fabs(result->val/beta.val) * beta.err;
stat = GSL_ERROR_SELECT_2(stat_f, stat_beta);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
} 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;
}
}
}
