Calculate Reciprocal of Array Elements using C++ SIMD

Calculate Reciprocal of Array Elements using C++ SIMD

For many applications requiring mathematical operations over large datasets, performance is critical. Calculating the reciprocal of each element in an array is one such task. While a basic scalar implementation can handle small arrays, using SIMD can greatly accelerate the process by allowing simultaneous calculations on multiple elements.

The scalar implementation is straightforward:

#include <iostream> #include <vector> void reciprocal(float *data, const size_t n) { for (size_t i = 0; i < n; ++i) { data[i] = 1.0f / data[i]; } } int main() { std::vector<float> a = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, }; reciprocal(a.data(), a.size()); for (auto value: a) { std::cout << value << " "; } return 0; }

This version iterates through the array and computes each element’s reciprocal individually. While simple, it can be slow for large arrays. A part of the output:

1 0.5 0.333333 ... 0.0625 0.0588235 0.0555556

Here's how to perform the same operation using AVX2:

#include <immintrin.h> void reciprocal(float *data, const size_t n) { __m256 one = _mm256_set1_ps(1.0f); size_t i = 0; for (; i + 8 <= n; i += 8) { __m256 vdata = _mm256_loadu_ps(&data[i]); __m256 vresult = _mm256_div_ps(one, vdata); _mm256_storeu_ps(&data[i], vresult); } for (; i < n; ++i) { data[i] = 1.0f / data[i]; } }

Explanation of AVX2 code:

  • _mm256_set1_ps creates a vector where each element is 1.0, which will be divided by elements in the input array.
  • _mm256_loadu_ps loads 8 float values from the array.
  • _mm256_div_ps computes the reciprocal of each element simultaneously.
  • _mm256_storeu_ps stores result back into the array.

For cases where the array size isn't a multiple of 8, a scalar loop handles the remaining elements.

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