Function cosh_simd 

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

Compute the hyperbolic cosine of each element (SIMD-accelerated).

Computes cosh(x) for each element in the array.

Arguments

• x - Input 1D array

Returns

Array1<F> with the same length as input, with hyperbolic cosine values.

Performance

• Auto-vectorization: Compiler optimizations provide excellent performance
• Speedup: 2-4x on large arrays via auto-vectorization

Mathematical Definition

cosh(x) = (e^x + e^(-x)) / 2
Range: [1, ∞) (always >= 1)

Examples

use scirs2_core::ndarray::array;
use scirs2_core::ndarray_ext::elementwise::cosh_simd;

let x = array![0.0_f64, 1.0, -1.0];
let result = cosh_simd(&x.view());

// cosh(0) = 1, cosh(1) ≈ 1.543, cosh(-1) ≈ 1.543
assert!((result[0] - 1.0).abs() < 1e-10);
assert!((result[1] - 1.5430806348).abs() < 1e-9);
assert!((result[2] - 1.5430806348).abs() < 1e-9);

Edge Cases

• Empty array: Returns empty array
• Zero: cosh(0) = 1
• Symmetric: cosh(-x) = cosh(x)
• Large values: May overflow to infinity
• NaN: Returns NaN (preserves NaN)

Applications

• Neural Networks: Activation functions, normalization
• Physics: Wave propagation, special relativity
• Engineering: Cable suspension, arch design
• Mathematics: Hyperbolic identities (cosh² - sinh² = 1)
• Numerical Methods: Stability analysis