16x16 integer matrix transpose using SSE2 intrinsics in C

Question

I was inspired by this and this to make a C function that would take an array of 16 __m128i, treat it as a matrix of 16x16 uint8_t, and transpose it using SSE2 intrinsics.

File simd-transpose.h

#include <immintrin.h>
/// Transpose \a x (treating it as a 16x16 array of \c uint8_t) using SSE2 intrinsics
static void
transpose_m128ix16(__m128i x[static restrict 16])
{
 const __m128i A07_B07 = _mm_unpacklo_epi8(x[0x0], x[0x1]);
 const __m128i A8f_B8f = _mm_unpackhi_epi8(x[0x0], x[0x1]);
 const __m128i C07_D07 = _mm_unpacklo_epi8(x[0x2], x[0x3]);
 const __m128i C8f_D8f = _mm_unpackhi_epi8(x[0x2], x[0x3]);
 const __m128i E07_F07 = _mm_unpacklo_epi8(x[0x4], x[0x5]);
 const __m128i E8f_F8f = _mm_unpackhi_epi8(x[0x4], x[0x5]);
 const __m128i G07_H07 = _mm_unpacklo_epi8(x[0x6], x[0x7]);
 const __m128i G8f_H8f = _mm_unpackhi_epi8(x[0x6], x[0x7]);
 const __m128i I07_J07 = _mm_unpacklo_epi8(x[0x8], x[0x9]);
 const __m128i I8f_J8f = _mm_unpackhi_epi8(x[0x8], x[0x9]);
 const __m128i K07_L07 = _mm_unpacklo_epi8(x[0xa], x[0xb]);
 const __m128i K8f_L8f = _mm_unpackhi_epi8(x[0xa], x[0xb]);
 const __m128i M07_N07 = _mm_unpacklo_epi8(x[0xc], x[0xd]);
 const __m128i M8f_N8f = _mm_unpackhi_epi8(x[0xc], x[0xd]);
 const __m128i O07_P07 = _mm_unpacklo_epi8(x[0xe], x[0xf]);
 const __m128i O8f_P8f = _mm_unpackhi_epi8(x[0xe], x[0xf]);
 const __m128i A03_B03_C03_D03 = _mm_unpacklo_epi16(A07_B07, C07_D07);
 const __m128i A47_B47_C47_D47 = _mm_unpackhi_epi16(A07_B07, C07_D07);
 const __m128i A8b_B8b_C8b_D8b = _mm_unpacklo_epi16(A8f_B8f, C8f_D8f);
 const __m128i Acf_Bcf_Ccf_Dcf = _mm_unpackhi_epi16(A8f_B8f, C8f_D8f);
 const __m128i E03_F03_G03_H03 = _mm_unpacklo_epi16(E07_F07, G07_H07);
 const __m128i E47_F47_G47_H47 = _mm_unpackhi_epi16(E07_F07, G07_H07);
 const __m128i E8b_F8b_G8b_H8b = _mm_unpacklo_epi16(E8f_F8f, G8f_H8f);
 const __m128i Ecf_Fcf_Gcf_Hcf = _mm_unpackhi_epi16(E8f_F8f, G8f_H8f);
 const __m128i I03_J03_K03_L03 = _mm_unpacklo_epi16(I07_J07, K07_L07);
 const __m128i I47_J47_K47_L47 = _mm_unpackhi_epi16(I07_J07, K07_L07);
 const __m128i I8b_J8b_K8b_L8b = _mm_unpacklo_epi16(I8f_J8f, K8f_L8f);
 const __m128i Icf_Jcf_Kcf_Lcf = _mm_unpackhi_epi16(I8f_J8f, K8f_L8f);
 const __m128i M03_N03_O03_P03 = _mm_unpacklo_epi16(M07_N07, O07_P07);
 const __m128i M47_N47_O47_P47 = _mm_unpackhi_epi16(M07_N07, O07_P07);
 const __m128i M8b_N8b_O8b_P8b = _mm_unpacklo_epi16(M8f_N8f, O8f_P8f);
 const __m128i Mcf_Ncf_Ocf_Pcf = _mm_unpackhi_epi16(M8f_N8f, O8f_P8f);
 const __m128i A01_B01_C01_D01_E01_F01_G01_H01 = _mm_unpacklo_epi32(A03_B03_C03_D03, E03_F03_G03_H03);
 const __m128i A23_B23_C23_D23_E23_F23_G23_H23 = _mm_unpackhi_epi32(A03_B03_C03_D03, E03_F03_G03_H03);
 const __m128i I01_J01_K01_L01_M01_N01_O01_P01 = _mm_unpacklo_epi32(I03_J03_K03_L03, M03_N03_O03_P03);
 const __m128i I23_J23_K23_L23_M23_N23_O23_P23 = _mm_unpackhi_epi32(I03_J03_K03_L03, M03_N03_O03_P03);
 const __m128i A45_B45_C45_D45_E45_F45_G45_H45 = _mm_unpacklo_epi32(A47_B47_C47_D47, E47_F47_G47_H47);
 const __m128i A67_B67_C67_D67_E67_F67_G67_H67 = _mm_unpackhi_epi32(A47_B47_C47_D47, E47_F47_G47_H47);
 const __m128i I45_J45_K45_L45_M45_N45_O45_P45 = _mm_unpacklo_epi32(I47_J47_K47_L47, M47_N47_O47_P47);
 const __m128i I67_J67_K67_L67_M67_N67_O67_P67 = _mm_unpackhi_epi32(I47_J47_K47_L47, M47_N47_O47_P47);
 const __m128i A89_B89_C89_D89_E89_F89_G89_H89 = _mm_unpacklo_epi32(A8b_B8b_C8b_D8b, E8b_F8b_G8b_H8b);
 const __m128i Aab_Bab_Cab_Dab_Eab_Fab_Gab_Hab = _mm_unpackhi_epi32(A8b_B8b_C8b_D8b, E8b_F8b_G8b_H8b);
 const __m128i I89_J89_K89_L89_M89_N89_O89_P89 = _mm_unpacklo_epi32(I8b_J8b_K8b_L8b, M8b_N8b_O8b_P8b);
 const __m128i Iab_Jab_Kab_Lab_Mab_Nab_Oab_Pab = _mm_unpackhi_epi32(I8b_J8b_K8b_L8b, M8b_N8b_O8b_P8b);
 const __m128i Acd_Bcd_Ccd_Dcd_Ecd_Fcd_Gcd_Hcd = _mm_unpacklo_epi32(Acf_Bcf_Ccf_Dcf, Ecf_Fcf_Gcf_Hcf);
 const __m128i Aef_Bef_Cef_Def_Eef_Fef_Gef_Hef = _mm_unpackhi_epi32(Acf_Bcf_Ccf_Dcf, Ecf_Fcf_Gcf_Hcf);
 const __m128i Icd_Jcd_Kcd_Lcd_Mcd_Ncd_Ocd_Pcd = _mm_unpacklo_epi32(Icf_Jcf_Kcf_Lcf, Mcf_Ncf_Ocf_Pcf);
 const __m128i Ief_Jef_Kef_Lef_Mef_Nef_Oef_Pef = _mm_unpackhi_epi32(Icf_Jcf_Kcf_Lcf, Mcf_Ncf_Ocf_Pcf);
 x[0x0] = _mm_unpacklo_epi64(A01_B01_C01_D01_E01_F01_G01_H01, I01_J01_K01_L01_M01_N01_O01_P01); // A0_B0_C0_D0_E0_F0_G0_H0_I0_J0_K0_L0_M0_N0_O0_P0
 x[0x1] = _mm_unpackhi_epi64(A01_B01_C01_D01_E01_F01_G01_H01, I01_J01_K01_L01_M01_N01_O01_P01); // A1_B1_C1_D1_E1_F1_G1_H1_I1_J1_K1_L1_M1_N1_O1_P1
 x[0x2] = _mm_unpacklo_epi64(A23_B23_C23_D23_E23_F23_G23_H23, I23_J23_K23_L23_M23_N23_O23_P23); // A2_B2_C2_D2_E2_F2_G2_H2_I2_J2_K2_L2_M2_N2_O2_P2
 x[0x3] = _mm_unpackhi_epi64(A23_B23_C23_D23_E23_F23_G23_H23, I23_J23_K23_L23_M23_N23_O23_P23); // A3_B3_C3_D3_E3_F3_G3_H3_I3_J3_K3_L3_M3_N3_O3_P3
 x[0x4] = _mm_unpacklo_epi64(A45_B45_C45_D45_E45_F45_G45_H45, I45_J45_K45_L45_M45_N45_O45_P45); // A4_B4_C4_D4_E4_F4_G4_H4_I4_J4_K4_L4_M4_N4_O4_P4
 x[0x5] = _mm_unpackhi_epi64(A45_B45_C45_D45_E45_F45_G45_H45, I45_J45_K45_L45_M45_N45_O45_P45); // A5_B5_C5_D5_E5_F5_G5_H5_I5_J5_K5_L5_M5_N5_O5_P5
 x[0x6] = _mm_unpacklo_epi64(A67_B67_C67_D67_E67_F67_G67_H67, I67_J67_K67_L67_M67_N67_O67_P67); // A6_B6_C6_D6_E6_F6_G6_H6_I6_J6_K6_L6_M6_N6_O6_P6
 x[0x7] = _mm_unpackhi_epi64(A67_B67_C67_D67_E67_F67_G67_H67, I67_J67_K67_L67_M67_N67_O67_P67); // A7_B7_C7_D7_E7_F7_G7_H7_I7_J7_K7_L7_M7_N7_O7_P7
 x[0x8] = _mm_unpacklo_epi64(A89_B89_C89_D89_E89_F89_G89_H89, I89_J89_K89_L89_M89_N89_O89_P89); // A8_B8_C8_D8_E8_F8_G8_H8_I8_J8_K8_L8_M8_N8_O8_P8
 x[0x9] = _mm_unpackhi_epi64(A89_B89_C89_D89_E89_F89_G89_H89, I89_J89_K89_L89_M89_N89_O89_P89); // A9_B9_C9_D9_E9_F9_G9_H9_I9_J9_K9_L9_M9_N9_O9_P9
 x[0xa] = _mm_unpacklo_epi64(Aab_Bab_Cab_Dab_Eab_Fab_Gab_Hab, Iab_Jab_Kab_Lab_Mab_Nab_Oab_Pab); // Aa_Ba_Ca_Da_Ea_Fa_Ga_Ha_Ia_Ja_Ka_La_Ma_Na_Oa_Pa
 x[0xb] = _mm_unpackhi_epi64(Aab_Bab_Cab_Dab_Eab_Fab_Gab_Hab, Iab_Jab_Kab_Lab_Mab_Nab_Oab_Pab); // Ab_Bb_Cb_Db_Eb_Fb_Gb_Hb_Ib_Jb_Kb_Lb_Mb_Nb_Ob_Pb
 x[0xc] = _mm_unpacklo_epi64(Acd_Bcd_Ccd_Dcd_Ecd_Fcd_Gcd_Hcd, Icd_Jcd_Kcd_Lcd_Mcd_Ncd_Ocd_Pcd); // Ac_Bc_Cc_Dc_Ec_Fc_Gc_Hc_Ic_Jc_Kc_Lc_Mc_Nc_Oc_Pc
 x[0xd] = _mm_unpackhi_epi64(Acd_Bcd_Ccd_Dcd_Ecd_Fcd_Gcd_Hcd, Icd_Jcd_Kcd_Lcd_Mcd_Ncd_Ocd_Pcd); // Ad_Bd_Cd_Dd_Ed_Fd_Gd_Hd_Id_Jd_Kd_Ld_Md_Nd_Od_Pd
 x[0xe] = _mm_unpacklo_epi64(Aef_Bef_Cef_Def_Eef_Fef_Gef_Hef, Ief_Jef_Kef_Lef_Mef_Nef_Oef_Pef); // Ae_Be_Ce_De_Ee_Fe_Ge_He_Ie_Je_Ke_Le_Me_Ne_Oe_Pe
 x[0xf] = _mm_unpackhi_epi64(Aef_Bef_Cef_Def_Eef_Fef_Gef_Hef, Ief_Jef_Kef_Lef_Mef_Nef_Oef_Pef); // Af_Bf_Cf_Df_Ef_Ff_Gf_Hf_If_Jf_Kf_Lf_Mf_Nf_Of_Pf
}

I know some lines are long, but I wanted the variable names to be elucidative.

File test-simd-transpose.c

This test code demonstrates the correctness of the transpose function.

#include "simd-transpose.h"
#include <assert.h>
#include <stdint.h>
#include <stdio.h>
int main()
{
 typedef union
 {
 __m128i xmm[16];
 uint8_t u8[16][16];
 } data_16_t;
 const data_16_t original_data_16 = {.u8 = {
 {0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f},
 {0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f},
 {0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f},
 {0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f},
 {0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f},
 {0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f},
 {0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f},
 {0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f},
 {0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f},
 {0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f},
 {0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf},
 {0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf},
 {0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf},
 {0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf},
 {0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef},
 {0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
 }};
 data_16_t transposed_data_16 = original_data_16;
 transpose_m128ix16(transposed_data_16.xmm);
 printf("original_data_16 = {\n");
 for (int i = 0; i < 16; ++i)
 {
 for (int j = 0; j < 16; ++j)
 {
 printf(" %02x,", original_data_16.u8[i][j]);
 }
 printf("\n");
 }
 printf("}\n\n");
 printf("transposed_data_16 = {\n");
 for (int i = 0; i < 16; ++i)
 {
 for (int j = 0; j < 16; ++j)
 {
 printf(" %02x,", transposed_data_16.u8[i][j]);
 }
 printf("\n");
 }
 printf("}\n\n");
 for (int i = 0; i < 16; ++i)
 {
 for (int j = 0; j < 16; ++j)
 {
 assert(original_data_16.u8[i][j] == transposed_data_16.u8[j][i]);
 }
 }
 return 0;
}

Environment

I used GCC on Linux.

gcc -dumpversion

14.2.1

uname -srm

Linux 6.14.3-arch1-1 x86_64

Output

gcc -msse2 -Wall test-simd-transpose.c && ./a.out

original_data_16 = {
 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0a, 0b, 0c, 0d, 0e, 0f,
 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f,
 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f,
 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 3a, 3b, 3c, 3d, 3e, 3f,
 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 4a, 4b, 4c, 4d, 4e, 4f,
 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 5a, 5b, 5c, 5d, 5e, 5f,
 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 6a, 6b, 6c, 6d, 6e, 6f,
 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 7a, 7b, 7c, 7d, 7e, 7f,
 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 8a, 8b, 8c, 8d, 8e, 8f,
 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 9a, 9b, 9c, 9d, 9e, 9f,
 a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, aa, ab, ac, ad, ae, af,
 b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, ba, bb, bc, bd, be, bf,
 c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, ca, cb, cc, cd, ce, cf,
 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, da, db, dc, dd, de, df,
 e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, ea, eb, ec, ed, ee, ef,
 f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, fa, fb, fc, fd, fe, ff,
}
transposed_data_16 = {
 00, 10, 20, 30, 40, 50, 60, 70, 80, 90, a0, b0, c0, d0, e0, f0,
 01, 11, 21, 31, 41, 51, 61, 71, 81, 91, a1, b1, c1, d1, e1, f1,
 02, 12, 22, 32, 42, 52, 62, 72, 82, 92, a2, b2, c2, d2, e2, f2,
 03, 13, 23, 33, 43, 53, 63, 73, 83, 93, a3, b3, c3, d3, e3, f3,
 04, 14, 24, 34, 44, 54, 64, 74, 84, 94, a4, b4, c4, d4, e4, f4,
 05, 15, 25, 35, 45, 55, 65, 75, 85, 95, a5, b5, c5, d5, e5, f5,
 06, 16, 26, 36, 46, 56, 66, 76, 86, 96, a6, b6, c6, d6, e6, f6,
 07, 17, 27, 37, 47, 57, 67, 77, 87, 97, a7, b7, c7, d7, e7, f7,
 08, 18, 28, 38, 48, 58, 68, 78, 88, 98, a8, b8, c8, d8, e8, f8,
 09, 19, 29, 39, 49, 59, 69, 79, 89, 99, a9, b9, c9, d9, e9, f9,
 0a, 1a, 2a, 3a, 4a, 5a, 6a, 7a, 8a, 9a, aa, ba, ca, da, ea, fa,
 0b, 1b, 2b, 3b, 4b, 5b, 6b, 7b, 8b, 9b, ab, bb, cb, db, eb, fb,
 0c, 1c, 2c, 3c, 4c, 5c, 6c, 7c, 8c, 9c, ac, bc, cc, dc, ec, fc,
 0d, 1d, 2d, 3d, 4d, 5d, 6d, 7d, 8d, 9d, ad, bd, cd, dd, ed, fd,
 0e, 1e, 2e, 3e, 4e, 5e, 6e, 7e, 8e, 9e, ae, be, ce, de, ee, fe,
 0f, 1f, 2f, 3f, 4f, 5f, 6f, 7f, 8f, 9f, af, bf, cf, df, ef, ff,
}

Questions

Is there a better or faster way to do this transpose? Perhaps using AVX or AVX2 intrinsics? I don't have access to AVX-512 hardware.

• chux: Useful to provide link about uncommon word: " ... wanted the variable names to be elucidative".