C++: `std::valarray`

cpp_valarray.md

C++: std::valarray

Disclaimer: Grok generated document.

std::valarray is a C++ standard library container introduced in C++98 specifically for high-performance numerical computations on arrays of numeric types (like float, double, int, etc.). It was designed with the intention of allowing aggressive optimizations for mathematical operations, especially on entire arrays at once.

Main Intended Use Cases

1. Element-wise mathematical operations with a clean syntax

   std::valarray<double> a = {1, 2, 3, 4};
   std::valarray<double> b = {5, 6, 7, 8};
   
   auto c = a + b;        // {6, 8, 10, 12}
   auto d = a * b;        // {5, 12, 21, 32}
   auto e = sin(a) + cos(b);  // applies sin/cos element-wise

2. Built-in support for mathematical functions (applied element-wise):

   • abs(), sqrt(), exp(), log(), sin(), cos(), tan(), acos(), asin(), atan(), sinh(), cosh(), tanh(), pow(), etc.

3. Slicing and indirect array access (advanced indexing)

   std::valarray<double> v(12);
   std::slice s(0, 4, 3);           // start=0, length=4, stride=3
   v[s] = 99.0;                     // v[0], v[3], v[6], v[9] = 99.0
   auto subset = v[std::gslice(...)];  // multi-dimensional-like slicing

4. Operations with scalars

   auto x = a * 2.0 + 5.0;   // every element multiplied by 2 and add 5

Why it was created

In the 1990s, people wanted something like MATLAB/NumPy in C++:

• Vectorized operations without explicit loops
• Potential for compiler optimizations (expression templates, loop fusion, SIMD)
• Clean mathematical syntax

Reality Check: Why std::valarray is rarely used today

Despite good intentions, std::valarray has major drawbacks and is widely considered a failed experiment:

Issue	Explanation
Poor performance in practice	Most compilers do not apply the expected aggressive optimizations. Often slower than hand-written loops or std::vector with SIMD.
Expression templates missing	The original design assumed expression templates (like in Blitz++ or Eigen), but the standard version uses temporary objects → many copies.
Awkward, non-intuitive API	Slicing (std::slice, std::gslice, std::mask_array, std::indirect_array) is complex and hard to use correctly.
No dynamic allocation control	Always copies on operations unless compiler optimizes heavily (which it usually doesn’t).
No iterator support pre-C++11	Made it incompatible with STL algorithms.
Very little real-world adoption	Almost no major numerical library (Eigen, Armadillo, Blaze, etc.) uses or recommends it.

Modern Alternatives (2025)

Library	Advantages over std::valarray
Eigen	Extremely fast, expression templates, lazy evaluation, excellent SIMD, MATLAB-like syntax
blaze-lib	Modern C++ design, hybrid CPU/GPU, great performance
Armadillo	MATLAB-like syntax, integrates with LAPACK/BLAS
xtensor	NumPy-like API, multi-dimensional, lazy evaluation
std::mdspan (C++23) + std::simd (upcoming)	Future standard solution for multi-dimensional arrays and explicit SIMD
Simple std::vector + loops + SIMD intrinsics/OpenMP	Often faster and much clearer

Verdict

Use std::valarray only if:

• You are maintaining very old numerical code that already uses it.
• You are doing educational experiments with the original C++98 numerical array design.

Do NOT use std::valarray for new code if performance or clarity matters.

For any serious numerical work in modern C++, use Eigen, blaze, xtensor, or wait for the emerging standard solutions based on std::mdspan and std::simd.

In short: std::valarray is an interesting historical artifact with a great idea that never quite worked out in practice.