Matrix Transpose 8×8

Transpose an 8x8 matrix of 32-bit signed integers in place using AVX2 intrinsics.

Function Signature

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

void transpose_8x8(int32_t* matrix);

Parameters:

• matrix — pointer to 64 contiguous int32_t values representing an 8x8 matrix in row-major order, guaranteed 32-byte aligned

The matrix is stored as 64 elements: row 0 occupies indices [0..7], row 1 occupies indices [8..15], and so on.

After the function returns, matrix[r*8 + c] must equal the original matrix[c*8 + r] for all r, c in [0, 7].

Example

Input (row-major):
  Row 0: [ 0,  1,  2,  3,  4,  5,  6,  7]
  Row 1: [ 8,  9, 10, 11, 12, 13, 14, 15]
  Row 2: [16, 17, 18, 19, 20, 21, 22, 23]
  ...
  Row 7: [56, 57, 58, 59, 60, 61, 62, 63]

Output (transposed):
  Row 0: [ 0,  8, 16, 24, 32, 40, 48, 56]
  Row 1: [ 1,  9, 17, 25, 33, 41, 49, 57]
  Row 2: [ 2, 10, 18, 26, 34, 42, 50, 58]
  ...
  Row 7: [ 7, 15, 23, 31, 39, 47, 55, 63]

Constraints

• The matrix is always exactly 8x8 (64 elements)
• matrix is 32-byte aligned
• Elements are stored in row-major order
• Element values are in range [-1,000,000, 1,000,000]

Notes

This is the classic AVX2 "butterfly" transpose. The key insight is that an 8x8 transpose can be decomposed into three phases of pairwise operations on 256-bit registers, avoiding any scalar element shuffling.

Useful Intrinsics