Module elementwise

Expand description

Element-wise mathematical operations with SIMD acceleration (abs, sqrt, etc.) SIMD-accelerated element-wise mathematical operations

This module provides high-performance implementations of common element-wise mathematical functions that are fundamental for scientific computing, numerical analysis, and data processing.

§Operations

§Basic Operations

Absolute Value (abs_simd): Computes |x| for each element
Sign (sign_simd): Computes sign(x) = +1, 0, or -1 for each element
Square Root (sqrt_simd): Computes √x for each element

§Exponential and Logarithmic

Exponential (exp_simd): Computes e^x for each element
Natural Logarithm (ln_simd): Computes ln(x) for each element

§Trigonometric Functions

Sine (sin_simd): Computes sin(x) for each element
Cosine (cos_simd): Computes cos(x) for each element
Tangent (tan_simd): Computes tan(x) for each element

§Hyperbolic Functions

Hyperbolic Sine (sinh_simd): Computes sinh(x) for each element
Hyperbolic Cosine (cosh_simd): Computes cosh(x) for each element
Hyperbolic Tangent (tanh_simd): Computes tanh(x) for each element

§Power Functions

Power (scalar) (powf_simd): Computes base^exp with scalar exponent
Power (array) (pow_simd): Computes base[i]^exp[i] element-wise

§Rounding Functions

Floor (floor_simd): Rounds down to largest integer <= x
Ceiling (ceil_simd): Rounds up to smallest integer >= x
Round (round_simd): Rounds to nearest integer (ties to even)
Fractional Part (fract_simd): Returns fractional part (x - floor(x))

§Inverse Trigonometric Functions

Arctangent (atan_simd): Computes atan(x) for each element
Arcsine (asin_simd): Computes asin(x) for each element
Arccosine (acos_simd): Computes acos(x) for each element
Two-argument arctangent (atan2_simd): Computes atan2(y, x) element-wise

§Logarithm Variants

Base-10 Logarithm (log10_simd): Computes log₁₀(x) for each element
Base-2 Logarithm (log2_simd): Computes log₂(x) for each element

§Clamping Operations

Clamp (clamp_simd): Constrains each element to [min, max] range

§Performance

All operations automatically use SIMD acceleration when:

Platform supports AVX2 (x86_64) or NEON (ARM)
Array size is large enough to benefit from vectorization
Array memory layout is contiguous

Falls back to scalar implementations for small arrays or unsupported platforms.

§Examples

use scirs2_core::ndarray::array;
use scirs2_core::ndarray_ext::elementwise::{abs_simd, sign_simd, sqrt_simd, sinh_simd, tanh_simd, floor_simd, atan2_simd, log10_simd, clamp_simd};

// Absolute value
let x = array![-3.0, -1.0, 0.0, 1.0, 3.0];
let abs_x = abs_simd(&x.view());
// Result: [3.0, 1.0, 0.0, 1.0, 3.0]

// Sign function (signum)
let signs = sign_simd(&x.view());
// Result: [-1.0, -1.0, 0.0, 1.0, 1.0]

// Square root
let y = array![1.0, 4.0, 9.0, 16.0, 25.0];
let sqrt_y = sqrt_simd(&y.view());
// Result: [1.0, 2.0, 3.0, 4.0, 5.0]

// Hyperbolic tangent (neural network activation)
let z = array![-1.0, 0.0, 1.0];
let tanh_z = tanh_simd(&z.view());
// Result: [-0.762, 0.0, 0.762]

// Floor (rounding down)
let w = array![1.2, 2.7, -1.3, -2.9];
let floor_w = floor_simd(&w.view());
// Result: [1.0, 2.0, -2.0, -3.0]

// Arctangent 2 (angle from coordinates)
let y_coords = array![1.0, 1.0, -1.0, -1.0];
let x_coords = array![1.0, -1.0, -1.0, 1.0];
let angles = atan2_simd(&y_coords.view(), &x_coords.view());
// Result: [π/4, 3π/4, -3π/4, -π/4]

// Base-10 logarithm (decibels, pH scale)
let powers = array![1.0, 10.0, 100.0, 1000.0];
let log10_powers = log10_simd(&powers.view());
// Result: [0.0, 1.0, 2.0, 3.0]

// Clamp values to range (pixel normalization)
let pixels = array![-0.5, 0.3, 0.7, 1.2, 1.8];
let normalized = clamp_simd(&pixels.view(), 0.0, 1.0);
// Result: [0.0, 0.3, 0.7, 1.0, 1.0]

Functions§

abs_simd: Compute the absolute value of each element (SIMD-accelerated).
acos_simd: Compute the arccosine of each element (SIMD-accelerated).
acosh_simd: Apply inverse hyperbolic cosine (acosh) using SIMD operations
add_simd: SIMD-accelerated element-wise addition
argmax_simd: SIMD-accelerated argmax (index of maximum)
argmin_simd: SIMD-accelerated argmin (index of minimum)
asin_simd: Compute the arcsine of each element (SIMD-accelerated).
asinh_simd: Apply inverse hyperbolic sine (asinh) using SIMD operations
atan2_simd: Compute the two-argument arctangent element-wise (SIMD-accelerated).
atan_simd: Compute the arctangent of each element (SIMD-accelerated).
atanh_simd: Apply inverse hyperbolic tangent (atanh) using SIMD operations
beta_simd: Compute the Beta function B(a, b) using SIMD operations
cbrt_simd: Compute the cube root of each element (SIMD-accelerated).
ceil_simd: Compute the ceiling (round up) of each element (SIMD-accelerated).
clamp_simd: Clamp each element to a specified range [min, max] (SIMD-accelerated).
clip_simd: SIMD-accelerated element-wise clipping (clamping)
copysign_simd: SIMD-accelerated copysign operation
cos_simd: Compute the cosine of each element (SIMD-accelerated).
cosh_simd: Compute the hyperbolic cosine of each element (SIMD-accelerated).
cosine_similarity_simd: SIMD-accelerated cosine similarity
cumprod_simd: SIMD-accelerated cumulative product
cumsum_simd: SIMD-accelerated cumulative sum (prefix sum)
diff_simd: SIMD-accelerated first-order difference
digamma_simd: Computes the element-wise digamma function ψ(x) = d/dx ln(Γ(x)) using SIMD acceleration.
distance_chebyshev_simd: SIMD-accelerated Chebyshev distance
distance_cosine_simd: SIMD-accelerated cosine distance
distance_euclidean_simd: SIMD-accelerated Euclidean distance
distance_manhattan_simd: SIMD-accelerated Manhattan distance
div_simd: SIMD-accelerated element-wise division
dot_simd: SIMD-accelerated dot product
elu_simd: Apply ELU (Exponential Linear Unit) activation using SIMD operations
erf_simd: Element-wise error function erf(x) = (2/√π) ∫₀ˣ e^(-t²) dt
erfc_simd: Element-wise complementary error function erfc(x) = 1 - erf(x)
erfcinv_simd: Element-wise inverse complementary error function erfcinv(y) = x such that erfc(x) = y
erfinv_simd: Element-wise inverse error function erfinv(y) = x such that erf(x) = y
exp2_simd: Compute 2^x for each element (SIMD-accelerated).
exp_m1_simd: Compute exp(x)-1 for each element (SIMD-accelerated, numerically stable).
exp_simd: Compute the exponential (e^x) of each element (SIMD-accelerated).
expm1_simd: SIMD-accelerated numerically stable exp(x) - 1
floor_simd: Compute the floor (round down) of each element (SIMD-accelerated).
fma_simd: SIMD-accelerated fused multiply-add
fract_simd: Compute the fractional part of each element (SIMD-accelerated).
gamma_simd: Compute the gamma function Γ(x) for each element (SIMD-accelerated).
gelu_simd: Compute the element-wise GELU (Gaussian Error Linear Unit) of an array.
hardsigmoid_simd: Apply Hardsigmoid activation using SIMD operations
hardswish_simd: Apply Hardswish activation using SIMD operations
hypot_simd: SIMD-accelerated hypotenuse calculation
leaky_relu_simd: Apply Leaky ReLU / PReLU activation using SIMD operations
lerp_simd: SIMD-accelerated linear interpolation
ln_1p_simd: Compute ln(1+x) for each element (SIMD-accelerated, numerically stable).
ln_beta_simd: Compute the Log-Beta function ln(B(a, b)) using SIMD operations
ln_gamma_simd: Computes the element-wise log-gamma function ln(Γ(x)) using SIMD acceleration.
ln_simd: Compute the natural logarithm (ln(x)) of each element (SIMD-accelerated).
log1p_simd: SIMD-accelerated numerically stable ln(1 + x)
log2_simd: Compute the base-2 logarithm of each element (SIMD-accelerated).
log10_simd: Compute the base-10 logarithm of each element (SIMD-accelerated).
log_softmax_simd: Apply Log-Softmax function using SIMD operations
log_sum_exp_simd: SIMD-accelerated log-sum-exp
logaddexp_simd: SIMD-accelerated logaddexp: log(exp(a) + exp(b))
logit_simd: SIMD-accelerated logit function: log(p / (1-p))
max_element_simd: SIMD-accelerated maximum element
max_simd: SIMD-accelerated element-wise maximum
mean_simd: SIMD-accelerated array mean
min_element_simd: SIMD-accelerated minimum element
min_simd: SIMD-accelerated element-wise minimum
mish_simd: SIMD-accelerated Mish activation function
mul_simd: SIMD-accelerated element-wise multiplication
norm_l1_simd: SIMD-accelerated L1 norm (Manhattan norm)
norm_linf_simd: SIMD-accelerated L-infinity norm (Chebyshev/max norm)
norm_simd: SIMD-accelerated L2 norm (Euclidean norm)
normalize_simd: SIMD-accelerated L2 normalization
pow_simd: Compute the element-wise power with array exponents (SIMD-accelerated).
powf_simd: Compute the power of each element with a scalar exponent (SIMD-accelerated).
powi_simd: Compute integer power (base^n) for each element (SIMD-accelerated).
prelu_simd: Alias for leaky_relu_simd - PReLU (Parametric ReLU)
recip_simd: Compute the reciprocal (multiplicative inverse) of each element (SIMD-accelerated).
relu_simd: SIMD-accelerated ReLU (Rectified Linear Unit)
round_simd: Compute the rounding to nearest integer of each element (SIMD-accelerated).
rsqrt_simd: SIMD-accelerated inverse square root: 1/sqrt(x)
scalar_mul_simd: SIMD-accelerated scalar multiplication
selu_simd: Apply SELU (Scaled Exponential Linear Unit) activation using SIMD operations
sigmoid_simd: Compute the element-wise sigmoid (logistic) function of an array.
sign_simd: Compute the sign (signum) of each element (SIMD-accelerated).
sin_simd: Compute the sine of each element (SIMD-accelerated).
sinc_simd: Apply Sinc function using SIMD operations
sincos_simd: SIMD-accelerated simultaneous sin and cos computation
sinh_simd: Compute the hyperbolic sine of each element (SIMD-accelerated).
smootherstep_simd: SIMD-accelerated smootherstep interpolation (Ken Perlin’s improved version)
smoothstep_simd: SIMD-accelerated smoothstep interpolation
softmax_simd: SIMD-accelerated softmax
softplus_simd: SIMD-accelerated Softplus activation function
sqrt_simd: Compute the square root of each element (SIMD-accelerated).
square_simd: SIMD-accelerated element-wise square: x²
standardize_simd: SIMD-accelerated standardization (z-score normalization)
std_simd: SIMD-accelerated standard deviation computation
sub_simd: SIMD-accelerated element-wise subtraction
sum_cubes_simd: SIMD-accelerated sum of cubes
sum_simd: SIMD-accelerated array sum
sum_squares_simd: SIMD-accelerated sum of squares
swish_simd: SIMD-accelerated Swish (SiLU - Sigmoid Linear Unit) activation function
tan_simd: Compute the tangent of each element (SIMD-accelerated).
tanh_simd: Compute the hyperbolic tangent of each element (SIMD-accelerated).
to_degrees_simd: Convert radians to degrees for each element (SIMD-accelerated).
to_radians_simd: Convert degrees to radians for each element (SIMD-accelerated).
trigamma_simd: Computes the element-wise trigamma function ψ’(x) = d²/dx² ln(Γ(x)) using SIMD acceleration.
trunc_simd: SIMD-accelerated truncation (round towards zero)
variance_simd: SIMD-accelerated variance computation
weighted_mean_simd: SIMD-accelerated weighted mean
weighted_sum_simd: SIMD-accelerated weighted sum

Module elementwise

Module elementwise Copy item path

§Operations

§Basic Operations

§Exponential and Logarithmic

§Trigonometric Functions

§Hyperbolic Functions

§Power Functions

§Rounding Functions

§Inverse Trigonometric Functions

§Logarithm Variants

§Clamping Operations

§Performance

§Examples

Functions§

Module elementwise