| /* | |
| * Pochhammer symbol (a)_m = gamma(a + m) / gamma(a) | |
| */ | |
| namespace xsf { | |
| namespace cephes { | |
| namespace detail { | |
| XSF_HOST_DEVICE inline double is_nonpos_int(double x) { | |
| return x <= 0 && x == std::ceil(x) && std::abs(x) < 1e13; | |
| } | |
| } // namespace detail | |
| XSF_HOST_DEVICE inline double poch(double a, double m) { | |
| double r = 1.0; | |
| /* | |
| * 1. Reduce magnitude of `m` to |m| < 1 by using recurrence relations. | |
| * | |
| * This may end up in over/underflow, but then the function itself either | |
| * diverges or goes to zero. In case the remainder goes to the opposite | |
| * direction, we end up returning 0*INF = NAN, which is OK. | |
| */ | |
| /* Recurse down */ | |
| while (m >= 1.0) { | |
| if (a + m == 1) { | |
| break; | |
| } | |
| m -= 1.0; | |
| r *= (a + m); | |
| if (!std::isfinite(r) || r == 0) { | |
| break; | |
| } | |
| } | |
| /* Recurse up */ | |
| while (m <= -1.0) { | |
| if (a + m == 0) { | |
| break; | |
| } | |
| r /= (a + m); | |
| m += 1.0; | |
| if (!std::isfinite(r) || r == 0) { | |
| break; | |
| } | |
| } | |
| /* | |
| * 2. Evaluate function with reduced `m` | |
| * | |
| * Now either `m` is not big, or the `r` product has over/underflown. | |
| * If so, the function itself does similarly. | |
| */ | |
| if (m == 0) { | |
| /* Easy case */ | |
| return r; | |
| } else if (a > 1e4 && std::abs(m) <= 1) { | |
| /* Avoid loss of precision */ | |
| return r * std::pow(a, m) * | |
| (1 + m * (m - 1) / (2 * a) + m * (m - 1) * (m - 2) * (3 * m - 1) / (24 * a * a) + | |
| m * m * (m - 1) * (m - 1) * (m - 2) * (m - 3) / (48 * a * a * a)); | |
| } | |
| /* Check for infinity */ | |
| if (detail::is_nonpos_int(a + m) && !detail::is_nonpos_int(a) && a + m != m) { | |
| return std::numeric_limits<double>::infinity(); | |
| } | |
| /* Check for zero */ | |
| if (!detail::is_nonpos_int(a + m) && detail::is_nonpos_int(a)) { | |
| return 0; | |
| } | |
| return r * std::exp(lgam(a + m) - lgam(a)) * gammasgn(a + m) * gammasgn(a); | |
| } | |
| } // namespace cephes | |
| } // namespace xsf | |