Function ln_simd 

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

Compute the natural logarithm (ln(x)) of each element (SIMD-accelerated).

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

Arguments

• x - Input 1D array (must contain positive values)

Returns

Array1<F> with the same length as input, with natural logarithm values.

Performance

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

Mathematical Definition

ln(x) = log_e(x) = y such that e^y = x

Examples

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

let x = array![1.0_f64, 2.718281828, 7.389056099];
let result = ln_simd(&x.view());

assert!((result[0] - 0.0).abs() < 1e-10);
assert!((result[1] - 1.0).abs() < 1e-9);
assert!((result[2] - 2.0).abs() < 1e-9);

Edge Cases

• Empty array: Returns empty array
• One: ln(1) = 0
• Zero: Returns negative infinity
• Negative numbers: Returns NaN (undefined in reals)
• NaN: Returns NaN (preserves NaN)
• Positive infinity: Returns positive infinity

Applications

• Machine Learning: Log-likelihood, cross-entropy loss
• Statistics: Log-normal distribution, Shannon entropy
• Optimization: Log-barrier methods, logarithmic objectives
• Automatic Differentiation: Logarithmic derivatives
• Information Theory: Mutual information, KL divergence

Note on Negative Values

Natural logarithm of negative numbers is undefined in real arithmetic. The function will return NaN for negative inputs, following IEEE 754 standard.

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

let x = array![-1.0_f64];
let result = ln_simd(&x.view());
assert!(result[0].is_nan());