Module generic 

The real-vector kernel bodies behind the ps/pd overrides and the trait defaults.

Public so a composite can call one directly from its own override when it wants a different lowering than the default (e.g. thermite-dual takes the Hermite functions with EXACT_FMA = true).

Modules

bessel

The Bessel family and what is built on it.

chebyshev

digamma

elliptic

Elliptic integrals.

erfcx

erfcx(x) = e^{x^2} erfc(x), the scaled complementary error function.

expint

fresnel

The Fresnel integrals C(x) = int_0^x cos(pi t^2/2) dt and S(x) = int_0^x sin(pi t^2/2) dt.

gamma

hermite

inverses

Newton inverses of shipped forwards: inv_digamma and wright_omega.

jacobi_elliptic

The Jacobi elliptic functions sn, cn and dn.

laguerre

langevin

Langevin function L(x) = coth(x) - 1/x and its inverse, shared by every real element type. The per-precision pieces (the polynomial tables, and Newton vs Halley for the inverse) come in from ps.rs/pd.rs.

legendre

lgamma1p

$\ln\Gamma(1+v)$ and $\Gamma(1+v)-1$ on $\lvert v\rvert \le 1/2$, both signs at once.

ndtr

The standard normal CDF ndtr, its logarithm log_ndtr, and logerfc = ln erfc.

phi

The phi-functions of exponential integrators, phi_N(z) = sum z^n/(n+N)!, shared by every element type. ps.rs/pd.rs supply a compile-time series length, while the element-agnostic default iterates to the element’s own epsilon.

pochhammer

The Pochhammer symbol $(z)_m = \Gamma(z+m)/\Gamma(z)$.

poisson

Loader’s saddle-point pieces for densities of the shape $x^k e^{-x}/\Gamma(k+1)$.

polygamma

polylog

The polylogarithm $\mathrm{Li}_s(z) = \sum_{k \ge 1} z^k / k^s$ of a real argument, at a scalar real order.

probit

quadrature

Gauss-Legendre nodes and weights, one root per lane.

sh

Real spherical harmonics, evaluated directly from Cartesian components.

sici

The trigonometric integrals Si(x) = int_0^x sin(t)/t dt and Ci(x) = gamma + ln x + int_0^x (cos t - 1)/t dt.

trigamma

zernike

The batch Zernike kernel: every mode through degree L at one point, in Cartesian coordinates.

zeta

The Riemann zeta function, as $\zeta(s) - 1$ with $\zeta$ built on top.