Trait BesselDetails 

pub trait BesselDetails<V: FloatVector + PrimalProjection> {
    const ASYM_TWO_TERMS: bool = false;

    // Provided methods
    fn near(z: V) -> V::Mask { ... }
    fn beyond(z: V, threshold: V::Primal) -> V::Mask { ... }
    fn valid(z: V) -> V::Mask { ... }
    fn exp_far(z: V, threshold: V::Primal) -> V::Mask { ... }
    fn asym_second_exponent(z: V, _nu: V::Primal) -> V { ... }
}

Per-arithmetic decisions of the real-order modified Bessel kernel, bessel_ik_real.

The kernel’s arithmetic (Temme’s series, two continued fractions, the Wronskian, the asymptotic series) is the same over R and over C. What changes is every place it compares the argument: region selects by magnitude, the domain test, the overflow corner of the exponential. On a real vector those are plain comparisons. On Complex cmp_lt is a lexicographic sort order, not a modulus, and would route far-off-axis points into the wrong arm. Same split as ExpIntDetails.

The order is always real (V::Primal), which is why every threshold here is a primal and why the kernel takes the order as a separate real vector.

The blanket impl below covers every primal type (real f32/f64 vectors, Compensated) with the real-line defaults. Complex overrides all of it.

Provided Associated Constants

const ASYM_TWO_TERMS: bool = false

Whether the large-argument expansion of I carries its second exponential.

$I_\nu(z) \sim \frac{e^{z}}{\sqrt{2\pi z}}\sum(-1)^k a_k z^{-k} + \frac{e^{-z \pm (\nu+1/2)\pi i}}{\sqrt{2\pi z}}\sum a_k z^{-k}$ (DLMF 10.40.5). On the real line the second term is $e^{-2x}$ relative and below epsilon wherever the arm runs, so the default drops it. Off the axis its modulus is $e^{-2\,\mathrm{Re}\,z}$, which on the imaginary axis is one, so Complex keeps it.

Provided Methods

fn near(z: V) -> V::Mask

Lanes in the small-argument region, |z| <= 2, where K comes from Temme’s series.

fn beyond(z: V, threshold: V::Primal) -> V::Mask

Lanes with |z| >= threshold, per lane: where I takes the asymptotic series.

fn valid(z: V) -> V::Mask

Lanes inside the kernel’s domain: the open positive axis, or the closed right half-plane less the origin. The origin itself is selected to its limits by the kernel. Everything else outside this mask is NaN.

fn exp_far(z: V, threshold: V::Primal) -> V::Mask

Lanes where a single e^z overflows before e^z * a does, so the exponential is halved and applied twice: Re z >= threshold.

fn asym_second_exponent(z: V, _nu: V::Primal) -> V

The exponent of that second term in the scaled domain, $-2z \pm (\nu+1/2)\pi i$ with the sign of Im z. Only read when ASYM_TWO_TERMS.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors

impl<E: FloatElement, V: FloatVector<Element = E> + SpecializedPrimalMath<E>> BesselDetails<V> for V