Dot Product

Given two arrays of 32-bit signed integers, compute and return their dot product using AVX2 intrinsics.

The dot product is the sum of element-wise products: a[0]*b[0] + a[1]*b[1] + ... + a[n-1]*b[n-1].

Function Signature

#include <immintrin.h>
#include <cstdint>

int32_t dot_product(const int32_t* a, const int32_t* b, int n);

Parameters:

• a — pointer to the first array of n signed 32-bit integers, guaranteed 32-byte aligned
• b — pointer to the second array of n signed 32-bit integers, guaranteed 32-byte aligned
• n — number of elements, guaranteed to be a multiple of 8 and at least 8

Returns: the dot product of the two arrays (guaranteed to fit in int32_t)

Example

Input:  a = [1, 2, 3, 4, 5, 6, 7, 8]
        b = [2, 2, 2, 2, 2, 2, 2, 2]
Output: 72

Constraints

• 8 ≤ n ≤ 1,000,000
• n is always a multiple of 8
• All elements are in range [-1000, 1000]
• The dot product fits in a 32-bit signed integer
• Both arrays are 32-byte aligned

Notes

Your solution should use AVX2 intrinsics to process 8 integer pairs at a time. Multiply corresponding elements, accumulate the products, and reduce to a scalar at the end.

Useful Intrinsics