Function acosh_simd 

pub fn acosh_simd<F>(x: &ArrayView1<'_, F>) -> Array1<F>
where
    F: Float + SimdUnifiedOps,

Apply inverse hyperbolic cosine (acosh) using SIMD operations

The inverse hyperbolic cosine is defined as: acosh(x) = ln(x + √(x² - 1))

Domain: [1, +∞), Range: [0, +∞) Returns NaN for x < 1. This is the inverse function of cosh.

Mathematical Properties

• acosh(1) = 0
• acosh(x) is monotonically increasing for x ≥ 1
• acosh’(x) = 1/√(x² - 1)
• For large x: acosh(x) ≈ ln(2x)

Arguments

• x - Input array (values should be ≥ 1 for valid results)

Returns

• Array with acosh applied elementwise (NaN for values < 1)

Example

use scirs2_core::ndarray_ext::elementwise::acosh_simd;
use ndarray::{array, ArrayView1};

let x = array![1.0_f64, 2.0, 10.0];
let result = acosh_simd(&x.view());
assert!((result[0] - 0.0).abs() < 1e-10);         // acosh(1) = 0
assert!((result[1] - 1.316957897).abs() < 1e-6);  // acosh(2)

// Out of domain returns NaN
let x_invalid = array![0.5_f64];
let result_invalid = acosh_simd(&x_invalid.view());
assert!(result_invalid[0].is_nan());

Applications

• Hyperbolic Geometry: Distance in Poincaré disk model
• Physics: Catenary curves, suspension bridges
• Electronics: Transmission line analysis
• Computer Graphics: Hyperbolic tessellations