1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 3539 3540 3541 3542 3543 3544 3545 3546 3547 3548 3549 3550 3551 3552 3553 3554 3555 3556 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 3569 3570 3571 3572 3573 3574 3575 3576 3577 3578 3579 3580 3581 3582 3583 3584 3585 3586 3587 3588 3589 3590 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 3662 3663 3664 3665 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 3681 3682 3683 3684 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717 3718 3719 3720 3721 3722 3723 3724 3725 3726 3727 3728 3729 3730 3731 3732 3733 3734 3735 3736 3737 3738 3739 3740 3741 3742 3743 3744 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 3761 3762 3763 3764 3765 3766 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818 3819 3820 3821 3822 3823 3824 3825 3826 3827 3828 3829 3830 3831 3832 3833 3834 3835 3836 3837 3838 3839 3840 3841 3842 3843 3844 3845 3846 3847 3848 3849 3850 3851 3852 3853 3854 3855 3856 3857 3858 3859 3860 3861 3862 3863 3864 3865 3866 3867 3868 3869 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915 3916 3917 3918 3919 3920 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221 4222 4223 4224 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 4241 4242 4243 4244 4245 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 4257 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 4305 4306 4307 4308 4309 4310 4311 4312 4313 4314 4315 4316 4317 4318 4319 4320 4321 4322 4323 4324 4325 4326 4327 4328 4329 4330 4331 4332 4333 4334 4335 4336 4337 4338 4339 4340 4341 4342 4343 4344 4345 4346 4347 4348 4349 4350 4351 4352 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414 4415 4416 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 4431 4432 4433 4434 4435 4436 4437 4438 4439 4440 4441 4442 4443 4444 4445 4446 4447 4448 4449 4450 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 4465 4466 4467 4468 4469 4470 4471 4472 4473 4474 4475 4476 4477 4478 4479 4480 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 4541 4542 4543 4544 4545 4546 4547 4548 4549 4550 4551 4552 4553 4554 4555 4556 4557 4558 4559 4560 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 4593 4594 4595 4596 4597 4598 4599 4600 4601 4602 4603 4604 4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 4617 4618 4619 4620 4621 4622 4623 4624 4625 4626 4627 4628 4629 4630 4631 4632 4633 4634 4635 4636 4637 4638 4639 4640 4641 4642 4643 4644 4645 4646 4647 4648 4649 4650 4651 4652 4653 4654 4655 4656 4657 4658 4659 4660 4661 4662 4663 4664 4665 4666 4667 4668 4669 4670 4671 4672 4673 4674 4675 4676 4677 4678 4679 4680 4681 4682 4683 4684 4685 4686 4687 4688 4689 4690 4691 4692 4693 4694 4695 4696 4697 4698 4699 4700 4701 4702 4703 4704 4705 4706 4707 4708 4709 4710 4711 4712 4713 4714 4715 4716 4717 4718 4719 4720 4721 4722 4723 4724 4725 4726 4727 4728 4729 4730 4731 4732 4733 4734 4735 4736 4737 4738 4739 4740 4741 4742 4743 4744 4745 4746 4747 4748 4749 4750 4751 4752 4753 4754 4755 4756 4757 4758 4759 4760 4761 4762 4763 4764 4765 4766 4767 4768 4769 4770 4771 4772 4773 4774 4775 4776 4777 4778 4779 4780 4781 4782 4783 4784 4785 4786 4787 4788 4789 4790 4791 4792 4793 4794 4795 4796 4797 4798 4799 4800 4801 4802 4803 4804 4805 4806 4807 4808 4809 4810 4811 4812 4813 4814 4815 4816 4817 4818 4819 4820 4821 4822 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4833 4834 4835 4836 4837 4838 4839 4840 4841 4842 4843 4844 4845 4846 4847 4848 4849 4850 4851 4852 4853 4854 4855 4856 4857 4858 4859 4860 4861 4862 4863 4864 4865 4866 4867 4868 4869 4870 4871 4872 4873 4874 4875 4876 4877 4878 4879 4880 4881 4882 4883 4884 4885 4886 4887 4888 4889 4890 4891 4892 4893 4894 4895 4896 4897 4898 4899 4900 4901 4902 4903 4904 4905 4906 4907 4908 4909 4910 4911 4912 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 4927 4928 4929 4930 4931 4932 4933 4934 4935 4936 4937 4938 4939 4940 4941 4942 4943 4944 4945 4946 4947 4948 4949 4950 4951 4952 4953 4954 4955 4956 4957 4958 4959 4960 4961 4962 4963 4964 4965 4966 4967 4968 4969 4970 4971 4972 4973 4974 4975 4976 4977 4978 4979 4980 4981 4982 4983 4984 4985 4986 4987 4988 4989 4990 4991 4992 4993 4994 4995 4996 4997 4998 4999 5000 5001 5002 5003 5004 5005 5006 5007 5008 5009 5010 5011 5012 5013 5014 5015 5016 5017 5018 5019 5020 5021 5022 5023 5024 5025 5026 5027 5028 5029 5030 5031 5032 5033 5034 5035 5036 5037 5038 5039 5040 5041 5042 5043 5044 5045 5046 5047 5048 5049 5050 5051 5052 5053 5054 5055 5056 5057 5058 5059 5060 5061 5062 5063 5064 5065 5066 5067 5068 5069 5070 5071 5072 5073 5074 5075 5076 5077 5078 5079 5080 5081 5082 5083 5084 5085 5086 5087 5088 5089 5090 5091 5092 5093 5094 5095 5096 5097 5098 5099 5100 5101 5102 5103 5104 5105 5106 5107 5108 5109 5110 5111 5112 5113 5114 5115 5116 5117 5118 5119 5120 5121 5122 5123 5124 5125 5126 5127 5128 5129 5130 5131 5132 5133 5134 5135 5136 5137 5138 5139 5140 5141 5142 5143 5144 5145 5146 5147 5148 5149 5150 5151 5152 5153 5154 5155 5156 5157 5158 5159 5160 5161 5162 5163 5164 5165 5166 5167 5168 5169 5170 5171 5172 5173 5174 5175 5176 5177 5178 5179 5180 5181 5182 5183 5184 5185 5186 5187 5188 5189 5190 5191 5192 5193 5194 5195 5196 5197 5198 5199 5200 5201 5202 5203 5204 5205 5206 5207 5208 5209 5210 5211 5212 5213 5214 5215 5216 5217 5218 5219 5220 5221 5222 5223 5224 5225 5226 5227 5228 5229 5230 5231 5232 5233 5234 5235 5236 5237 5238 5239 5240 5241 5242 5243 5244 5245 5246 5247 5248 5249 5250 5251 5252 5253 5254 5255 5256 5257 5258 5259 5260 5261 5262 5263 5264 5265 5266 5267 5268 5269 5270 5271 5272 5273 5274 5275 5276 5277 5278 5279 5280 5281 5282 5283 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293 5294 5295 5296 5297 5298 5299 5300 5301 5302 5303 5304 5305 5306 5307 5308 5309 5310 5311 5312 5313 5314 5315 5316 5317 5318 5319 5320 5321 5322 5323 5324 5325 5326 5327 5328 5329 5330 5331 5332 5333 5334 5335 5336 5337 5338 5339 5340 5341 5342 5343 5344 5345 5346 5347 5348 5349 5350 5351 5352 5353 5354 5355 5356 5357 5358 5359 5360 5361 5362 5363 5364 5365 5366 5367 5368 5369 5370 5371 5372 5373 5374 5375 5376 5377 5378 5379 5380 5381 5382 5383 5384 5385 5386 5387 5388 5389 5390 5391 5392 5393 5394 5395 5396 5397 5398 5399 5400 5401 5402 5403 5404 5405 5406 5407 5408 5409 5410 5411 5412 5413 5414 5415 5416 5417 5418 5419 5420 5421 5422 5423 5424 5425 5426 5427 5428 5429 5430 5431 5432 5433 5434 5435 5436 5437 5438 5439 5440 5441 5442 5443 5444 5445 5446 5447 5448 5449 5450 5451 5452 5453 5454 5455 5456 5457 5458 5459 5460 5461 5462 5463 5464 5465 5466 5467 5468 5469 5470 5471 5472 5473 5474 5475 5476 5477 5478 5479 5480 5481 5482 5483 5484 5485 5486 5487 5488 5489 5490 5491 5492 5493 5494 5495 5496 5497 5498 5499 5500 5501 5502 5503 5504 5505 5506 5507 5508 5509 5510 5511 5512 5513 5514 5515 5516 5517 5518 5519 5520 5521 5522 5523 5524 5525 5526 5527 5528 5529 5530 5531 5532 5533 5534 5535 5536 5537 5538 5539 5540 5541 5542 5543 5544 5545 5546 5547 5548 5549 5550 5551 5552 5553 5554 5555 5556 5557 5558 5559 5560 5561 5562 5563 5564 5565 5566 5567 5568 5569 5570 5571 5572 5573 5574 5575 5576 5577 5578 5579 5580 5581 5582 5583 5584 5585 5586 5587 5588 5589 5590 5591 5592 5593 5594 5595 5596 5597 5598 5599 5600 5601 5602 5603 5604 5605 5606 5607 5608 5609 5610 5611 5612 5613 5614 5615 5616 5617 5618 5619 5620 5621 5622 5623 5624 5625 5626 5627 5628 5629 5630 5631 5632 5633 5634 5635 5636 5637 5638 5639 5640 5641 5642 5643 5644 5645 5646 5647 5648 5649 5650 5651 5652 5653 5654 5655 5656 5657 5658 5659 5660 5661 5662 5663 5664 5665 5666 5667 5668 5669 5670 5671 5672 5673 5674 5675 5676 5677 5678 5679 5680 5681 5682 5683 5684 5685 5686 5687 5688 5689 5690 5691 5692 5693 5694 5695 5696 5697 5698 5699 5700 5701 5702 5703 5704 5705 5706 5707 5708 5709 5710 5711 5712 5713 5714 5715 5716 5717 5718 5719 5720 5721 5722 5723 5724 5725 5726 5727 5728 5729 5730 5731 5732 5733 5734 5735 5736 5737 5738 5739 5740 5741 5742 5743 5744 5745 5746 5747 5748 5749 5750 5751 5752 5753 5754 5755 5756 5757 5758 5759 5760 5761 5762 5763 5764 5765 5766 5767 5768 5769 5770 5771 5772 5773 5774 5775 5776 5777 5778 5779 5780 5781 5782 5783 5784 5785 5786 5787 5788 5789 5790 5791 5792 5793 5794 5795 5796 5797 5798 5799 5800 5801 5802 5803 5804 5805 5806 5807 5808 5809 5810 5811 5812 5813 5814 5815 5816 5817 5818 5819 5820 5821 5822 5823 5824 5825 5826 5827 5828 5829 5830 5831 5832 5833 5834 5835 5836 5837 5838 5839 5840 5841 5842 5843 5844 5845 5846 5847 5848 5849 5850 5851 5852 5853 5854 5855 5856 5857 5858 5859 5860 5861 5862 5863 5864 5865 5866 5867 5868 5869 5870 5871 5872 5873 5874 5875 5876 5877 5878 5879 5880 5881 5882 5883 5884 5885 5886 5887 5888 5889 5890 5891 5892 5893 5894 5895 5896 5897 5898 5899 5900 5901 5902 5903 5904 5905 5906 5907 5908 5909 5910 5911 5912 5913 5914 5915 5916 5917 5918 5919 5920 5921 5922 5923 5924 5925 5926 5927 5928 5929 5930 5931 5932 5933 5934 5935 5936 5937 5938 5939 5940 5941 5942 5943 5944 5945 5946 5947 5948 5949 5950 5951 5952 5953 5954 5955 5956 5957 5958 5959 5960 5961 5962 5963 5964 5965 5966 5967 5968
|
// Copyright 2016 The gemmlowp Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// This is a standalone testbed and benchmark for gemmlowp-style GEMM kernels,
// either doing integer or float arithmetic.
// It verifies that a kernel produces correct results, then benchmarks it.
//
// Some benchmark results are recorded in this spreadsheet:
//
// https://docs.google.com/spreadsheets/d/1UPbzbp9rdsD6RXxOr5q6AZ0n1omgEknLYO2ogiw6Kqk/edit?usp=sharing
//
// This program is entirely self-contained, and can be compiled manually
// such as suggested in the command lines below.
// It currently supports only Android/ARM but would trivially generalize to
// other OSes (it's mostly standard POSIX) or architectures (each kernel
// targets a specific architecture, one may simply add more).
/*
Build and run this benchmark on Android/ARM/32bit:
~/android/toolchains/arm-linux-androideabi/bin/arm-linux-androideabi-clang++ \
-fPIE -pie -O3 --std=c++11 standalone/neon-gemm-kernel-benchmark.cc -o \
/tmp/benchmark -mfloat-abi=softfp -mfpu=neon-vfpv4 && adb push /tmp/benchmark \
/data/local/tmp && adb shell /data/local/tmp/benchmark
Build and run this benchmark on Android/ARM/64bit:
~/android/toolchains/aarch64-linux-android/bin/aarch64-linux-android-clang++ \
-fPIE -static -O3 --std=c++11 standalone/neon-gemm-kernel-benchmark.cc -o \
/tmp/benchmark && adb push /tmp/benchmark /data/local/tmp && adb shell \
/data/local/tmp/benchmark
*/
// For big.LITTLE devices, use 'taskset' to select which cores to benchmark.
//
// The syntax is: taskset <mask> <commandline>
// where mask is a binary mask where each bit corresponds to a core,
// and low bits are little cores.
//
// Examples:
// Nexus 5X big cores: taskset 30
// Nexus 5X little cores: taskset 0f
// Pixel XL big cores: taskset 0c
// Pixel XL little cores: taskset 03
//
// Full example:
// adb shell taskset 0c /data/local/tmp/benchmark
#include <sched.h>
#include <unistd.h>
#include <algorithm>
#include <cassert>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <random>
#include <type_traits>
#if !defined(__arm__) && !defined(__aarch64__) && \
!(defined(__mips) && (__mips_isa_rev >= 5) && defined(__mips_msa))
#error This benchmark assumes ARM or MIPS (for intrinsics and inline assembly sections).
#endif
#if defined(__arm__) || defined(__aarch64__)
#include <arm_neon.h>
#endif
#if defined(__mips)
#include <msa.h>
// Some convenience macros to hide differences between MIPS32 and MIPS64.
#ifdef __LP64__
#define GEMMLOWP_MIPS_XADDIU "daddiu"
#else
#define GEMMLOWP_MIPS_XADDIU "addiu"
#endif
#endif
// Typically one wants to fit in L1 cache, and GEMM implementations
// are carefully optimized to tune their access patterns to that effect.
// Most devices have at least 16k of L1 cache. The Kraits have exactly 16k.
const int kDefaultCacheSizeK = 16;
const int kCacheLineSize = 64;
// These definitions are used for labels within assembly code. Required for
// iOS toolchain compatibility.
#define GEMMLOWP_LABEL_AFTER_LOOP "1"
#define GEMMLOWP_LABEL_LOOP "2"
#define GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES "3"
#define GEMMLOWP_LABEL_STORE "4"
// BEGIN code copied from gemmlowp/internal/kernel.h
// Explanation of general gemmlowp terminology
// ===========================================
//
// We use the following abbreviations:
// LHS = "left-hand side"
// RHS = "right-hand side"
// Sometimes when referring to either LHS or RHS, we just say a "Side".
//
// In a matrix product of a MxK matrix times a KxN matrix,
// we call K the 'depth'. Note that M is the number of rows
// of the result (and of the LHS), and N is the number of columns
// of the result (and of the RHS).
//
// In each of the LHS and RHS matrices, we call 'width' the
// other dimension, besides the depth. So in the LHS, 'width'
// is the number of rows, while in the RHS, 'width' is the number
// of columns.
//
// So in the LHS MxK matrix, the depth is K and the width in M.
// And in the RHS KxN matrix, the depth is K and the width in N.
//
// This is illustrated in this picture:
//
// RHS width
// <----------------->
// +-----------------+ ^
// | RHS | | Depth
// +-----------------+ v
// ^ +--+ +-----------------+
// | |L | | |
// LHS width | |H | | Result |
// | |S | | |
// v +--+ +-----------------+
// <-->
// Depth
// Explanation of gemmlowp kernel formats and "cells"
// ==================================================
//
// Kernels operate on small LHS and RHS blocks that fit in registers.
// These blocks are stored contiguously in memory, but not always
// in a traditional column-major or row-major order; instead,
// they consist of a number of sub-blocks, which we call "cells",
// that are stored in column-major or row-major order. However,
// what really matters to us is not so much rows vs columns, but
// rather width vs depth. So we refer to "width-major" and "depth-major"
// storage orders. In the LHS, width-major means row-major,
// while in the RHS, width-major means column-major.
// There is also a third possibility, "diagonal order",
// which is unused at the moment.
//
// We aim to treat both sides, LHS and RHS, on an equal footing,
// so we call them both 'sides'. A KernelFormat thus is just a pair
// of KernelSideFormat's, one for LHS and one for RHS; each KernelSideFormat
// contains a CellFormat and a number of cells; cells are only ever
// stacked in the width dimension, which means stacked vertically in the
// LHS and stacked horizondally in the RHS.
//
// Example
// =======
//
// Let's work out the data layout expected by a kernel having the
// following format (the struct names here are defined below in this file):
//
// KernelFormat<
// KernelSideFormat<CellFormat<3, 4>, 3>,
// KernelSideFormat<CellFormat<5, 4>, 2>
// >
//
// The LHS format, KernelSideFormat<CellFormat<3, 4>, 3>, means:
// 3 cells, each cell having dimensions (width=3, depth=4), laid out in
// DepthMajor order (the default value, see CellFormat). In the LHS,
// DepthMajor means column-major, so the LHS cells are of size 3x4 in
// column-major order, so the LHS layout is:
//
// 0 3 6 9
// 1 4 7 10
// 2 5 8 11
// 12 15 18 21
// 13 16 19 22
// 14 17 20 23
// 24 27 30 33
// 25 28 31 34
// 26 29 32 35
//
// The RHS format, KernelSideFormat<CellFormat<5, 4>, 2>, means:
// 2 cells each having dimensions (width=5, depth=4), laid out in
// DepthMajor order (the default value, see CellFormat). In the RHS,
// DepthMajor means row-major, so the RHS cells are of size 4x5 in
// row-major order, so the RHS layout is:
//
// 0 1 2 3 4 20 21 22 23 24
// 5 6 7 8 9 25 26 27 28 29
// 10 11 12 13 14 30 31 32 33 34
// 15 16 17 18 19 35 36 37 38 39
// CellOrder enumerates the possible storage orders (=layouts) for
// a cell (see explanation above).
enum class CellOrder { DepthMajor, WidthMajor, Diagonal };
// CellFormat describes how data is laid
// out in a cell. That is, a CellOrder together with actual dimensions.
template <int tWidth, int tDepth, CellOrder tOrder>
struct CellFormat {
static const int kWidth = tWidth;
static const int kDepth = tDepth;
static const CellOrder kOrder = tOrder;
static const int kSize = kWidth * kDepth;
};
// KernelSideFormat describes how data is laid out in a kernel side
// (i.e. LHS or RHS). That is, a CellFormat together with a number of
// cells. These cells are always stacked in the Width dimension.
// For example, in the LHS case, the Width dimension is the rows dimension,
// se we're saying that in the LHS, cells are stacked vertically.
// We never stack cells in the Depth dimension.
template <typename tCellFormat, int tCells>
struct KernelSideFormat {
typedef tCellFormat Cell;
static const int kCells = tCells;
static const int kWidth = kCells * Cell::kWidth;
static const int kDepth = Cell::kDepth;
};
// KernelFormat describes fully the input data layout that a kernel expects.
// It consists of two KernelSideFormat's, one for LHS and one for RHS.
template <typename tLhs, typename tRhs>
struct KernelFormat {
typedef tLhs Lhs;
typedef tRhs Rhs;
static_assert(Lhs::Cell::kDepth == Rhs::Cell::kDepth, "");
static const int kDepth = Lhs::Cell::kDepth;
static const int kRows = Lhs::Cell::kWidth * Lhs::kCells;
static const int kCols = Rhs::Cell::kWidth * Rhs::kCells;
};
// KernelOperandRanges specifies the minimum and maximum values an operand can
// take. It consists of two ranges: one for the LHS and one for the RHS. The
// default values are the minimum and maximum values of the operand data type.
template <typename Kernel, typename OperandType = typename Kernel::OperandType>
struct KernelOperandRanges {
static OperandType LhsMin() {
return std::numeric_limits<OperandType>::lowest();
}
static OperandType LhsMax() {
return std::numeric_limits<OperandType>::max();
}
static OperandType RhsMin() {
return std::numeric_limits<OperandType>::lowest();
}
static OperandType RhsMax() {
return std::numeric_limits<OperandType>::max();
}
};
template <typename Kernel>
struct KernelOperandRanges<Kernel, float> {
static float LhsMin() { return -100.f; }
static float LhsMax() { return 100.f; }
static float RhsMin() { return -100.f; }
static float RhsMax() { return 100.f; }
};
#define SET_7BIT_RANGES(kernel) \
template <> \
struct KernelOperandRanges<kernel, std::int8_t> { \
static std::int8_t LhsMin() { return -63; } \
static std::int8_t LhsMax() { return 63; } \
static std::int8_t RhsMin() { return -64; } \
static std::int8_t RhsMax() { return 63; } \
};
#define SET_425BIT_RANGES(kernel) \
template <> \
struct KernelOperandRanges<kernel, std::int8_t> { \
static std::int8_t LhsMin() { return -7; } \
static std::int8_t LhsMax() { return 7; } \
static std::int8_t RhsMin() { return -9; } \
static std::int8_t RhsMax() { return 9; } \
};
inline const char* CellOrderName(CellOrder o) {
switch (o) {
case CellOrder::DepthMajor:
return "DepthMajor";
case CellOrder::WidthMajor:
return "WidthMajor";
case CellOrder::Diagonal:
return "Diagonal";
default:
assert(false);
return nullptr;
}
}
// Returns the offset into a cell, at which a given coefficient is stored.
template <typename CellFormat>
inline int OffsetIntoCell(int w, int d) {
switch (CellFormat::kOrder) {
case CellOrder::DepthMajor:
return w + d * CellFormat::kWidth;
case CellOrder::WidthMajor:
return d + w * CellFormat::kDepth;
case CellOrder::Diagonal:
assert(CellFormat::kWidth == CellFormat::kDepth);
static const int size = CellFormat::kWidth;
return ((size + w - d) * size + d) % (size * size);
default:
assert(false);
return 0;
}
}
// END code copied from gemmlowp/internal/kernel.h
#ifdef __arm__
// This is the current standard kernel in gemmlowp, see:
// https://github.com/google/gemmlowp/blob/b1e2a29ff866680028f3080efc244e10e8dd7f46/internal/kernel_neon.h#L33
struct NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load 1 Rhs cell of size 2x4
"vld1.8 {d0}, [%[rhs_ptr]]!\n"
// Load 3 Lhs cells of size 4x2 each
"vld1.8 {d2}, [%[lhs_ptr]]!\n"
"vld1.8 {d4}, [%[lhs_ptr]]!\n"
"vld1.8 {d6}, [%[lhs_ptr]]!\n"
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
"subs %[depth], #2\n"
"beq " GEMMLOWP_LABEL_AFTER_LOOP "f\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Overview of register layout:
//
// A 2x4 cell of Rhs is stored in 16bit in d0--d1 (q0).
// A 12x2 block of 3 4x2 cells Lhs is stored in 16bit in d2--d7
// (q1--q3).
// A 12x4 block of accumulators is stored in 32bit in q4--q15.
//
// +-----+-----+-----+-----+
// |d0[0]|d0[1]|d0[2]|d0[3]|
// Rhs +-----+-----+-----+-----+
// |d1[0]|d1[1]|d1[2]|d1[3]|
// +-----+-----+-----+-----+
//
// | | | | |
//
// Lhs | | | | |
//
// +--+--+ - - - - +-----+-----+-----+-----+
// |d2|d3| | q4 | q5 | q6 | q7 |
// |d2|d3| | q4 | q5 | q6 | q7 |
// |d2|d3| | q4 | q5 | q6 | q7 |
// |d2|d3| | q4 | q5 | q6 | q7 |
// +--+--+ - - - - +-----+-----+-----+-----+
// |d4|d5| | q8 | q9 | q10 | q11 |
// |d4|d5| | q8 | q9 | q10 | q11 |
// |d4|d5| | q8 | q9 | q10 | q11 |
// |d4|d5| | q8 | q9 | q10 | q11 |
// +--+--+ - - - - +-----+-----+-----+-----+
// |d6|d7| | q12 | q13 | q14 | q15 |
// |d6|d7| | q12 | q13 | q14 | q15 |
// |d6|d7| | q12 | q13 | q14 | q15 |
// |d6|d7| | q12 | q13 | q14 | q15 |
// +--+--+ - - - - +-----+-----+-----+-----+
//
// Accumulator
// Expand Lhs/Rhs cells to 16 bit.
// Note: moving theses vmovls further down to allow for
// longer data pipelining helps a little on A57 but is
// harmful on A53 --- It looks as if A53 doesn't like
// interleaving vmovl's into the vmlal's.
"vmovl.u8 q0, d0\n"
"vmovl.u8 q1, d2\n"
"vmovl.u8 q2, d4\n"
"vmovl.u8 q3, d6\n"
// Multiply-accumulate, level of depth 0
"vmlal.u16 q4, d2, d0[0]\n"
"vmlal.u16 q5, d2, d0[1]\n"
"vmlal.u16 q6, d2, d0[2]\n"
"vmlal.u16 q7, d2, d0[3]\n"
"vldr d2, [%[lhs_ptr]]\n"
"vmlal.u16 q8, d4, d0[0]\n"
"vmlal.u16 q9, d4, d0[1]\n"
"vmlal.u16 q10, d4, d0[2]\n"
"vmlal.u16 q11, d4, d0[3]\n"
"vldr d4, [%[lhs_ptr], #8]\n"
"vmlal.u16 q12, d6, d0[0]\n"
"vmlal.u16 q13, d6, d0[1]\n"
"vmlal.u16 q14, d6, d0[2]\n"
"vmlal.u16 q15, d6, d0[3]\n"
"vldr d6, [%[lhs_ptr], #16]\n"
"vldr d0, [%[rhs_ptr]]\n"
// Multiply-accumulate, level of depth 1
"vmlal.u16 q4, d3, d1[0]\n"
"vmlal.u16 q5, d3, d1[1]\n"
"add %[lhs_ptr], #24\n"
"vmlal.u16 q6, d3, d1[2]\n"
"vmlal.u16 q7, d3, d1[3]\n"
"add %[rhs_ptr], #8\n"
"vmlal.u16 q8, d5, d1[0]\n"
"vmlal.u16 q9, d5, d1[1]\n"
"subs %[depth], #2\n"
"vmlal.u16 q10, d5, d1[2]\n"
"vmlal.u16 q11, d5, d1[3]\n"
"vmlal.u16 q12, d7, d1[0]\n"
"vmlal.u16 q13, d7, d1[1]\n"
"vmlal.u16 q14, d7, d1[2]\n"
"vmlal.u16 q15, d7, d1[3]\n"
"bne " GEMMLOWP_LABEL_LOOP "b\n"
GEMMLOWP_LABEL_AFTER_LOOP
":\n"
// Expand Lhs/Rhs cells to 16 bit.
"vmovl.u8 q0, d0\n"
"vmovl.u8 q1, d2\n"
"vmovl.u8 q2, d4\n"
"vmovl.u8 q3, d6\n"
// Multiply-accumulate, level of depth 0
"vmlal.u16 q4, d2, d0[0]\n"
"vmlal.u16 q5, d2, d0[1]\n"
"vmlal.u16 q6, d2, d0[2]\n"
"vmlal.u16 q7, d2, d0[3]\n"
"vmlal.u16 q8, d4, d0[0]\n"
"vmlal.u16 q9, d4, d0[1]\n"
"vmlal.u16 q10, d4, d0[2]\n"
"vmlal.u16 q11, d4, d0[3]\n"
"vmlal.u16 q12, d6, d0[0]\n"
"vmlal.u16 q13, d6, d0[1]\n"
"vmlal.u16 q14, d6, d0[2]\n"
"vmlal.u16 q15, d6, d0[3]\n"
// Multiply-accumulate, level of depth 1
"vmlal.u16 q4, d3, d1[0]\n"
"vmlal.u16 q5, d3, d1[1]\n"
"vmlal.u16 q6, d3, d1[2]\n"
"vmlal.u16 q7, d3, d1[3]\n"
"vmlal.u16 q8, d5, d1[0]\n"
"vmlal.u16 q9, d5, d1[1]\n"
"vmlal.u16 q10, d5, d1[2]\n"
"vmlal.u16 q11, d5, d1[3]\n"
"vmlal.u16 q12, d7, d1[0]\n"
"vmlal.u16 q13, d7, d1[1]\n"
"vmlal.u16 q14, d7, d1[2]\n"
"vmlal.u16 q15, d7, d1[3]\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// This is Maciek Chociej's fast kernel not expanding operands,
// from gemmlowp/meta/. Search for
// mul_3x8_3x8_int32_lhsadd_rhsadd
// in this file:
// https://raw.githubusercontent.com/google/gemmlowp/e4b9d858b6637d5d0058bfa3d869d2b95864251b/meta/single_thread_gemm.h
struct NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators_noexpand {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<3, 8, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<3, 8, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Clear aggregators.
"vmov.i32 q0, #0\n"
"vmov.i32 q1, #0\n"
"vmov.i32 q2, #0\n"
"vmov.i32 q3, q0\n"
"vmov.i32 q4, q1\n"
"vmov.i32 q5, q2\n"
"vmov.i32 q6, q3\n"
"vmov.i32 q7, q4\n"
"vmov.i32 q8, q5\n"
// Loop head
GEMMLOWP_LABEL_LOOP
":\n"
// Subtract counter.
"subs %[depth], %[depth], #8\n"
"vld1.8 {d18, d19, d20}, [%[rhs_ptr]]!\n"
"vld1.8 {d21, d22, d23}, [%[lhs_ptr]]!\n"
"vmull.u8 q12, d18, d21\n"
"vmull.u8 q13, d18, d22\n"
"vmull.u8 q14, d18, d23\n"
"vmull.u8 q15, d19, d21\n"
"vpadal.u16 q0, q12\n"
"vpadal.u16 q1, q13\n"
"vpadal.u16 q2, q14\n"
"vpadal.u16 q3, q15\n"
"vmull.u8 q12, d19, d22\n"
"vmull.u8 q13, d19, d23\n"
"vmull.u8 q14, d20, d21\n"
"vmull.u8 q15, d20, d22\n"
"vmull.u8 q9, d20, d23\n"
"vpadal.u16 q4, q12\n"
"vpadal.u16 q5, q13\n"
"vpadal.u16 q6, q14\n"
"vpadal.u16 q7, q15\n"
"vpadal.u16 q8, q9\n"
// Loop branch
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Horizontal reduce aggregators, step 1
"vpadd.u32 d0, d0, d1\n"
"vpadd.u32 d2, d2, d3\n"
"vpadd.u32 d4, d4, d5\n"
"vpadd.u32 d6, d6, d7\n"
"vpadd.u32 d8, d8, d9\n"
"vpadd.u32 d10, d10, d11\n"
"vpadd.u32 d12, d12, d13\n"
"vpadd.u32 d14, d14, d15\n"
"vpadd.u32 d16, d16, d17\n"
// Horizontal reduce aggregators, step 2
"vpadd.u32 d0, d0, d2\n"
"vpadd.u32 d1, d4, d4\n"
"vpadd.u32 d6, d6, d8\n"
"vpadd.u32 d7, d10, d10\n"
"vpadd.u32 d12, d12, d14\n"
"vpadd.u32 d13, d16, d16\n"
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d2}, [r0]!\n"
"vld1.32 {d3[0]}, [r0]!\n"
"vld1.32 {d8}, [r0]!\n"
"vld1.32 {d9[0]}, [r0]!\n"
"vld1.32 {d14}, [r0]!\n"
"vld1.32 {d15[0]}, [r0]!\n"
// Accumulate
"vadd.s32 q0, q0, q1\n"
"vadd.s32 q3, q3, q4\n"
"vadd.s32 q6, q6, q7\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d0}, [r0]!\n"
"vst1.32 {d1[0]}, [r0]!\n"
"vst1.32 {d6}, [r0]!\n"
"vst1.32 {d7[0]}, [r0]!\n"
"vst1.32 {d12}, [r0]!\n"
"vst1.32 {d13[0]}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// Fast kernel operating on int8 operands.
// It is assumed that one of the two int8 operands only takes values
// in [-127, 127], while the other may freely range in [-128, 127].
// The issue with both operands taking the value -128 is that:
// -128*-128 + -128*-128 == -32768 overflows int16.
// Every other expression a*b + c*d, for any int8 a,b,c,d, fits in int16
// range. That is the basic idea of this kernel.
struct NEON_32bit_GEMM_Int8Operands_AccumTwoWithin16Bits {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<2, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
std::size_t start_depth = 123;
std::size_t run_depth = depth;
AccumulatorType* dst_ptr = accum_ptr;
asm volatile(
// Overview of register layout:
//
// A 2x16 block of Rhs is stored in 8 bit in d0--d3.
// A 4x16 block of Lhs is stored in 8 bit in d4--d7. That is only
// half of the register space required, so we loop over these registers
// twice. Only half of it, a 2x16 block, is stored in d4--d7 at
// any given time.
//
// A 4x2 block of accumulators is stored in q8--q15 (as 4x32 bit
// components which need to be horizontally-added at the end)
//
// The Lhs vectors are multiplied by the Rhs vectors with a widening
// multiply over the 8 first levels of depth, producing int16x8
// vectors of products for each position in the accumulator matrix.
// Here comes the special trick: since the operands are signed int8,
// their range being [ -2^7 , 2^7 ), their products are in range
// [ -2^14 , 2^14 - 1 ), meaning that we can add two such values
// without any risk of overflowing int16.
// We thus proceed with the 8 next levels of depth, multiplying
// again Lhs by Rhs, accumulating into this existing int16x8 vector.
//
// Only then, having processed 16 levels of depth, do we need to
// horizontally add these int16x8 accumulators into the final
// int32x4 accumulators.
//
// As we do not have enough registers to store all 16 int16x8
// temporary-16bit-accumulators, we have them cycle through q4--q7.
//
//
// Register layout (ignoring the q4--q7 temporary 16bit accumulators):
//
// +----+----+
// | d0 | d2 |
// | . | . |
// | . | . |
// | . | . |
// Rhs +----+----+
// | d1 | d3 |
// | . | . |
// | . | . |
// | . | . |
// +----+----+
//
// | | |
//
// Lhs | | |
//
// +--------+--------+ - - - - +----+----+
// | d4 ... | d5 ... | | q8 | q9 |
// | d6 ... | d7 ... | | q10| q11|
// | d4 ... | d5 ... | | q12| q13|
// | d6 ... | d7 ... | | q14| q15|
// +--------+--------+ - - - - +----+----+
//
// Accumulator
//
// Clear accumulators, and, interleaved with it,
// initial loads of the first loop iteration,
// taken out of the loop so that in the loop itself we have
// optimal streaming of data from memory.
"vldr d0, [%[rhs_ptr], #0]\n"
"vmov.i32 q8, #0\n"
"vldr d4, [%[lhs_ptr], #0]\n"
"vmov.i32 q9, #0\n"
"vldr d2, [%[rhs_ptr], #16]\n"
"vmov.i32 q10, q8\n"
"vldr d6, [%[lhs_ptr], #16]\n"
"vmov.i32 q11, q8\n"
"vldr d1, [%[rhs_ptr], #8]\n"
"vmov.i32 q12, q8\n"
"vldr d5, [%[lhs_ptr], #8]\n"
"vmov.i32 q13, q8\n"
"vldr d3, [%[rhs_ptr], #24]\n"
"vmov.i32 q14, q8\n"
"vldr d7, [%[lhs_ptr], #24]\n"
"vmov.i32 q15, q8\n"
// General loop.
GEMMLOWP_LABEL_LOOP
":\n"
// Multiply 8 first levels of depth.
"vmull.s8 q4, d0, d4\n"
"add %[rhs_ptr], %[rhs_ptr], #32\n"
"vmull.s8 q5, d2, d4\n"
"vldr d4, [%[lhs_ptr], #32]\n"
"vmull.s8 q6, d0, d6\n"
"vmull.s8 q7, d2, d6\n"
"vldr d6, [%[lhs_ptr], #48]\n"
// Multiply-accumulate second-half, again into the same
// 16bit local accumulator registers. This is where we
// take advantage of having int8 instead of uint8 and therefore
// being able to accumulate two products into int16.
"vmlal.s8 q4, d1, d5\n"
"vmlal.s8 q5, d3, d5\n"
"vldr d5, [%[lhs_ptr], #40]\n"
"vmlal.s8 q6, d1, d7\n"
"vmlal.s8 q7, d3, d7\n"
"vldr d7, [%[lhs_ptr], #56]\n"
// Add pairwise, accumulate into 32-bit accumulators.
"vpadal.s16 q8, q4\n"
"add %[lhs_ptr], %[lhs_ptr], #64\n"
"vpadal.s16 q9, q5\n"
"subs %[run_depth], %[run_depth], #16\n"
"vpadal.s16 q10, q6\n"
"vpadal.s16 q11, q7\n"
"beq " GEMMLOWP_LABEL_AFTER_LOOP
"f\n"
// Multiply first half.
"vmull.s8 q4, d0, d4\n"
"vmull.s8 q5, d2, d4\n"
"vldr d4, [%[lhs_ptr], #0]\n"
"vmull.s8 q6, d0, d6\n"
"vldr d0, [%[rhs_ptr], #0]\n"
"vmull.s8 q7, d2, d6\n"
"vldr d2, [%[rhs_ptr], #16]\n"
// Multiply-accumulate second-half, again into the same
// 16bit local accumulator registers. This is where we
// take advantage of having int8 instead of uint8 and therefore
// being able to accumulate two products into int16.
"vmlal.s8 q4, d1, d5\n"
"vldr d6, [%[lhs_ptr], #16]\n"
"vmlal.s8 q5, d3, d5\n"
"vldr d5, [%[lhs_ptr], #8]\n"
"vmlal.s8 q6, d1, d7\n"
"vldr d1, [%[rhs_ptr], #8]\n"
"vmlal.s8 q7, d3, d7\n"
"vldr d3, [%[rhs_ptr], #24]\n"
// Add pairwise, accumulate into 32-bit accumulators.
"vpadal.s16 q12, q4\n"
"vldr d7, [%[lhs_ptr], #24]\n"
"vpadal.s16 q13, q5\n"
"vpadal.s16 q14, q6\n"
"vpadal.s16 q15, q7\n"
"b " GEMMLOWP_LABEL_LOOP "b\n"
GEMMLOWP_LABEL_AFTER_LOOP
":\n"
// Multiply first half.
"vmull.s8 q4, d0, d4\n"
"vmull.s8 q5, d2, d4\n"
"vmull.s8 q6, d0, d6\n"
"vmull.s8 q7, d2, d6\n"
// Multiply-accumulate second-half, again into the same
// 16bit local accumulator registers. This is where we
// take advantage of having int8 instead of uint8 and therefore
// being able to accumulate two products into int16.
"vmlal.s8 q4, d1, d5\n"
"vmlal.s8 q5, d3, d5\n"
"vmlal.s8 q6, d1, d7\n"
"vmlal.s8 q7, d3, d7\n"
// Add pairwise, accumulate into 32-bit accumulators.
"vpadal.s16 q12, q4\n"
"vpadal.s16 q13, q5\n"
"vpadal.s16 q14, q6\n"
"vpadal.s16 q15, q7\n"
"cmp %[start_depth], #0\n"
// Reduce 32bit accumulators horizontally.
"vpadd.s32 d0, d16, d17\n"
"vpadd.s32 d1, d18, d19\n"
"vpadd.s32 d2, d20, d21\n"
"vpadd.s32 d3, d22, d23\n"
"vpadd.s32 d4, d24, d25\n"
"vpadd.s32 d5, d26, d27\n"
"vpadd.s32 d6, d28, d29\n"
"vpadd.s32 d7, d30, d31\n"
"bne " GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES
"f\n"
// Reduce 32bit accumulators horizontally, second pass
// (each pass adds pairwise. we need to add 4-wise).
"vpadd.s32 d8, d0, d2\n"
"vpadd.s32 d9, d4, d6\n"
"vpadd.s32 d10, d1, d3\n"
"vpadd.s32 d11, d5, d7\n"
"b " GEMMLOWP_LABEL_STORE "f\n"
GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES
":\n"
// Reduce 32bit accumulators horizontally, second pass
// (each pass adds pairwise. we need to add 4-wise),
// and load destination values from memory.
"mov r0, %[dst_ptr]\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vpadd.s32 d8, d0, d2\n"
"vpadd.s32 d9, d4, d6\n"
"vld1.32 {d18, d19}, [r0]\n"
"vpadd.s32 d10, d1, d3\n"
"vpadd.s32 d11, d5, d7\n"
// Add horizontally-reduced accumulators into
// the values loaded from memory
"vadd.s32 q4, q8, q4\n"
"vadd.s32 q5, q9, q5\n"
GEMMLOWP_LABEL_STORE
":\n"
// Store back into memory
"mov r0, %[dst_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[dst_ptr] "+r"(dst_ptr), [run_depth] "+r"(run_depth)
: // inputs
[start_depth] "r"(start_depth)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// We don't actually use int32*int32 in production. This is just an
// experiment to help dissociate the effect of integer-vs-float, from the
// effect of operands width.
struct NEON_32bit_GEMM_Int32_WithScalar {
typedef std::int32_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 1 Rhs cell of size 1x4
"vld1.32 {d0, d1}, [%[rhs_ptr]]!\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vmla.s32 q4, q1, d0[0]\n"
"vmla.s32 q5, q1, d0[1]\n"
"vmla.s32 q6, q1, d1[0]\n"
"vmla.s32 q7, q1, d1[1]\n"
"vmla.s32 q8, q2, d0[0]\n"
"vmla.s32 q9, q2, d0[1]\n"
"vmla.s32 q10, q2, d1[0]\n"
"vmla.s32 q11, q2, d1[1]\n"
"vmla.s32 q12, q3, d0[0]\n"
"vmla.s32 q13, q3, d0[1]\n"
"vmla.s32 q14, q3, d1[0]\n"
"vmla.s32 q15, q3, d1[1]\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// Not very efficient kernel, just an experiment to see what we can do
// without using NEON multiply-with-scalar instructions.
struct NEON_32bit_GEMM_Float32_MLA_WithVectorDuplicatingScalar {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vmla.f32 q4, q1, q0\n"
"vmla.f32 q8, q2, q0\n"
"vmla.f32 q12, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vmla.f32 q5, q1, q0\n"
"vmla.f32 q9, q2, q0\n"
"vmla.f32 q13, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vmla.f32 q6, q1, q0\n"
"vmla.f32 q10, q2, q0\n"
"vmla.f32 q14, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vmla.f32 q7, q1, q0\n"
"vmla.f32 q11, q2, q0\n"
"vmla.f32 q15, q3, q0\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// Not very efficient kernel, just an experiment to see what we can do
// without using NEON multiply-with-scalar instructions.
// This variant is relevant as on ARMv7 FMA does not have a with-scalar variant.
struct NEON_32bit_GEMM_Float32_FMA_WithVectorDuplicatingScalar {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vfma.f32 q4, q1, q0\n"
"vfma.f32 q8, q2, q0\n"
"vfma.f32 q12, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vfma.f32 q5, q1, q0\n"
"vfma.f32 q9, q2, q0\n"
"vfma.f32 q13, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vfma.f32 q6, q1, q0\n"
"vfma.f32 q10, q2, q0\n"
"vfma.f32 q14, q3, q0\n"
"vld1.32 {d0[], d1[]}, [%[rhs_ptr]]!\n"
"vfma.f32 q7, q1, q0\n"
"vfma.f32 q11, q2, q0\n"
"vfma.f32 q15, q3, q0\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// This is the "most natural" kernel, using NEON multiply-with-scalar
// instructions.
struct NEON_32bit_GEMM_Float32_MLA_WithScalar {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 1 Rhs cell of size 1x4
"vld1.32 {d0, d1}, [%[rhs_ptr]]!\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vmla.f32 q4, q1, d0[0]\n"
"vmla.f32 q5, q1, d0[1]\n"
"vmla.f32 q6, q1, d1[0]\n"
"vmla.f32 q7, q1, d1[1]\n"
"vmla.f32 q8, q2, d0[0]\n"
"vmla.f32 q9, q2, d0[1]\n"
"vmla.f32 q10, q2, d1[0]\n"
"vmla.f32 q11, q2, d1[1]\n"
"vmla.f32 q12, q3, d0[0]\n"
"vmla.f32 q13, q3, d0[1]\n"
"vmla.f32 q14, q3, d1[0]\n"
"vmla.f32 q15, q3, d1[1]\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// Faster kernel contributed by ARM in 64bit form
// (see NEON_64bit_GEMM_Float32_WithScalar_A53) then ported to 32bit code.
// Tuned for A53.
struct NEON_32bit_GEMM_Float32_WithScalar_A53 {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
// Overview of register layout:
//
// A 1x4 cell of Rhs is stored in d0--d1 (q0).
// A 12x1 block of 3 4x1 cells Lhs is stored in d2--d7
// (q1--q3).
// A 12x4 block of accumulators is stored in q4--q15.
//
// +-----+-----+-----+-----+
// Rhs |d0[0]|d0[1]|d1[0]|d1[1]|
// +-----+-----+-----+-----+
//
// | | | | |
//
// Lhs | | | | |
//
// +--+- - - - - - +-----+-----+-----+-----+
// |d2| | q4 | q5 | q6 | q7 |
// |d2| | q4 | q5 | q6 | q7 |
// |d3| | q4 | q5 | q6 | q7 |
// |d3| | q4 | q5 | q6 | q7 |
// +--+- - - - - - +-----+-----+-----+-----+
// |d4| | q8 | q9 | q10 | q11 |
// |d4| | q8 | q9 | q10 | q11 |
// |d5| | q8 | q9 | q10 | q11 |
// |d5| | q8 | q9 | q10 | q11 |
// +--+ - - - - - - +-----+-----+-----+-----+
// |d6| | q12 | q13 | q14 | q15 |
// |d6| | q12 | q13 | q14 | q15 |
// |d7| | q12 | q13 | q14 | q15 |
// |d7| | q12 | q13 | q14 | q15 |
// +--+- - - - - - +-----+-----+-----+-----+
//
// Accumulator
// Load Rhs cell
"vldr d0, [%[rhs_ptr]]\n"
"ldr r2, [%[rhs_ptr], #8]\n"
"ldr r3, [%[rhs_ptr], #12]\n"
// Load 1st Lhs Cell
"vld1.32 {d2, d3}, [%[lhs_ptr]]\n"
GEMMLOWP_LABEL_LOOP
":\n"
"vldr d4, [%[lhs_ptr], #16]\n" // Load 1st half of 2nd Lhs cell
"vmov d1, r2, r3\n" // Prepare 2nd half of Rhs cell
"vmla.f32 q4, q1, d0[0]\n" // Multiply 1st Lhs cell with column 0
"ldr r2, [%[lhs_ptr], #24]\n" // Load 2nd half of 2nd Lhs cell, part 1
"vmla.f32 q5, q1, d0[1]\n" // Multiply 1st Lhs cell with column 1
"ldr r3, [%[lhs_ptr], #28]\n" // Load 2nd half of 2nd Lhs cell, part 2
"vmla.f32 q6, q1, d1[0]\n" // Multiply 1st Lhs cell with column 2
"subs %[depth], #1\n"
"vldr d6, [%[lhs_ptr], #32]\n" // Load 1st half of 3rd Lhs cell
"vmov d5, r2, r3\n" // Prepare 2nd half of 2nd Lhs cell
"vmla.f32 q7, q1, d1[1]\n" // Multiply 1st Lhs cell with column 3
"ldr r2, [%[lhs_ptr], #40]\n" // Load 2nd half of 3rd Lhs cell, part 1
"vmla.f32 q8, q2, d0[0]\n" // Multiply 2nd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #44]\n" // Load 2nd half of 3rd Lhs cell, part 2
"vmla.f32 q9, q2, d0[1]\n" // Multiply 2nd Lhs cell with column 1
"add %[rhs_ptr], %[rhs_ptr], #16\n" // Move forward by 1 Rhs cell
"vldr d2, [%[lhs_ptr], #48]\n" // Load 1st half of 1st Lhs cell of next
// iteration
"vmov d7, r2, r3\n" // Prepare 2nd half of 3rd Lhs cell
"vmla.f32 q10, q2, d1[0]\n" // Multiply 2nd Lhs cell with column 2
"ldr r2, [%[lhs_ptr], #56]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 1
"vmla.f32 q12, q3, d0[0]\n" // Multiply 3rd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #60]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 2
"vmla.f32 q13, q3, d0[1]\n" // Multiply 3rd Lhs cell with column 1
"add %[lhs_ptr], %[lhs_ptr], #48\n" // Move forward by 3 Lhs cells
"vldr d0, [%[rhs_ptr]]\n" // Load 1st half of Rhs cell of next
// iteration
"vmov d3, r2, r3\n" // Prepare 2nd half of 1st Lhs cell of next
// iteration
"vmla.f32 q11, q2, d1[1]\n" // Multiply 2nd Lhs cell with column 3
"ldr r2, [%[rhs_ptr], #8]\n" // Load 2nd half of Rhs cell of next
// iteration, part 1
"vmla.f32 q14, q3, d1[0]\n" // Multiply 3rd Lhs cell with column 2
"ldr r3, [%[rhs_ptr], #12]\n" // Load 2nd half of Rhs cell of next
// iteration, part 2
"vmla.f32 q15, q3, d1[1]\n" // Multiply 3rd Lhs cell with column 3
// Loop branch. This will dual issue in fmla cycle 3 of the 4th block.
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "r2", "r3", "d0", "d1", "d2", "d3", "d4", "d5",
"d6", "d7", "d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16",
"d17", "d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26",
"d27", "d28", "d29", "d30", "d31");
}
};
struct NEON_32bit_GEMM_Float32_WithScalar_A53_depth2 {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
// Overview of register layout:
//
// A 1x4 cell of Rhs is stored in d0--d1 (q0).
// A 12x1 block of 3 4x1 cells Lhs is stored in d2--d7
// (q1--q3).
// A 12x4 block of accumulators is stored in q4--q15.
//
// +-----+-----+-----+-----+
// Rhs |d0[0]|d0[1]|d1[0]|d1[1]|
// +-----+-----+-----+-----+
//
// | | | | |
//
// Lhs | | | | |
//
// +--+- - - - - - +-----+-----+-----+-----+
// |d2| | q4 | q5 | q6 | q7 |
// |d2| | q4 | q5 | q6 | q7 |
// |d3| | q4 | q5 | q6 | q7 |
// |d3| | q4 | q5 | q6 | q7 |
// +--+- - - - - - +-----+-----+-----+-----+
// |d4| | q8 | q9 | q10 | q11 |
// |d4| | q8 | q9 | q10 | q11 |
// |d5| | q8 | q9 | q10 | q11 |
// |d5| | q8 | q9 | q10 | q11 |
// +--+ - - - - - - +-----+-----+-----+-----+
// |d6| | q12 | q13 | q14 | q15 |
// |d6| | q12 | q13 | q14 | q15 |
// |d7| | q12 | q13 | q14 | q15 |
// |d7| | q12 | q13 | q14 | q15 |
// +--+- - - - - - +-----+-----+-----+-----+
//
// Accumulator
// Load Rhs cell
"vldr d0, [%[rhs_ptr]]\n"
"ldr r2, [%[rhs_ptr], #8]\n"
"ldr r3, [%[rhs_ptr], #12]\n"
// Load 1st Lhs Cell
"vld1.32 {d2, d3}, [%[lhs_ptr]]\n"
// Loop head - handling 2 levels of depth at once
GEMMLOWP_LABEL_LOOP
":\n"
// Level of depth 1
"vldr d4, [%[lhs_ptr], #32]\n" // Load 1st half of 2nd Lhs cell
"vmov d1, r2, r3\n" // Prepare 2nd half of Rhs cell
"vmla.f32 q4, q1, d0[0]\n" // Multiply 1st Lhs cell with column 0
"ldr r2, [%[lhs_ptr], #40]\n" // Load 2nd half of 2nd Lhs cell, part 1
"vmla.f32 q5, q1, d0[1]\n" // Multiply 1st Lhs cell with column 1
"ldr r3, [%[lhs_ptr], #44]\n" // Load 2nd half of 2nd Lhs cell, part 2
"vmla.f32 q6, q1, d1[0]\n" // Multiply 1st Lhs cell with column 2
"vldr d6, [%[lhs_ptr], #64]\n" // Load 1st half of 3rd Lhs cell
"vmov d5, r2, r3\n" // Prepare 2nd half of 2nd Lhs cell
"vmla.f32 q7, q1, d1[1]\n" // Multiply 1st Lhs cell with column 3
"ldr r2, [%[lhs_ptr], #72]\n" // Load 2nd half of 3rd Lhs cell, part 1
"vmla.f32 q8, q2, d0[0]\n" // Multiply 2nd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #76]\n" // Load 2nd half of 3rd Lhs cell, part 2
"vmla.f32 q9, q2, d0[1]\n" // Multiply 2nd Lhs cell with column 1
"vldr d2, [%[lhs_ptr], #16]\n" // Load 1st half of 1st Lhs cell of next
// iteration
"vmov d7, r2, r3\n" // Prepare 2nd half of 3rd Lhs cell
"vmla.f32 q10, q2, d1[0]\n" // Multiply 2nd Lhs cell with column 2
"ldr r2, [%[lhs_ptr], #24]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 1
"vmla.f32 q12, q3, d0[0]\n" // Multiply 3rd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #28]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 2
"vmla.f32 q13, q3, d0[1]\n" // Multiply 3rd Lhs cell with column 1
"vldr d0, [%[rhs_ptr], #16]\n" // Load 1st half of Rhs cell of next
// iteration
"vmov d3, r2, r3\n" // Prepare 2nd half of 1st Lhs cell of next
// iteration
"vmla.f32 q11, q2, d1[1]\n" // Multiply 2nd Lhs cell with column 3
"ldr r2, [%[rhs_ptr], #24]\n" // Load 2nd half of Rhs cell of next
// iteration, part 1
"vmla.f32 q14, q3, d1[0]\n" // Multiply 3rd Lhs cell with column 2
"ldr r3, [%[rhs_ptr], #28]\n" // Load 2nd half of Rhs cell of next
// iteration, part 2
"vmla.f32 q15, q3, d1[1]\n" // Multiply 3rd Lhs cell with column 3
// Level of depth 2
"vldr d4, [%[lhs_ptr], #48]\n" // Load 1st half of 2nd Lhs cell
"vmov d1, r2, r3\n" // Prepare 2nd half of Rhs cell
"vmla.f32 q4, q1, d0[0]\n" // Multiply 1st Lhs cell with column 0
"ldr r2, [%[lhs_ptr], #56]\n" // Load 2nd half of 2nd Lhs cell, part 1
"vmla.f32 q5, q1, d0[1]\n" // Multiply 1st Lhs cell with column 1
"ldr r3, [%[lhs_ptr], #60]\n" // Load 2nd half of 2nd Lhs cell, part 2
"vmla.f32 q6, q1, d1[0]\n" // Multiply 1st Lhs cell with column 2
"subs %[depth], #2\n" // Decrement depth counter
"vldr d6, [%[lhs_ptr], #80]\n" // Load 1st half of 3rd Lhs cell
"vmov d5, r2, r3\n" // Prepare 2nd half of 2nd Lhs cell
"vmla.f32 q7, q1, d1[1]\n" // Multiply 1st Lhs cell with column 3
"ldr r2, [%[lhs_ptr], #88]\n" // Load 2nd half of 3rd Lhs cell, part 1
"vmla.f32 q8, q2, d0[0]\n" // Multiply 2nd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #92]\n" // Load 2nd half of 3rd Lhs cell, part 2
"vmla.f32 q9, q2, d0[1]\n" // Multiply 2nd Lhs cell with column 1
"add %[rhs_ptr], %[rhs_ptr], #32\n" // Move forward by 1 Rhs cell
"vldr d2, [%[lhs_ptr], #96]\n" // Load 1st half of 1st Lhs cell of next
// iteration
"vmov d7, r2, r3\n" // Prepare 2nd half of 3rd Lhs cell
"vmla.f32 q10, q2, d1[0]\n" // Multiply 2nd Lhs cell with column 2
"ldr r2, [%[lhs_ptr], #104]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 1
"vmla.f32 q12, q3, d0[0]\n" // Multiply 3rd Lhs cell with column 0
"ldr r3, [%[lhs_ptr], #108]\n" // Load 2nd half of 1st Lhs cell of next
// iter, part 2
"vmla.f32 q13, q3, d0[1]\n" // Multiply 3rd Lhs cell with column 1
"add %[lhs_ptr], %[lhs_ptr], #96\n" // Move forward by 3 Lhs cells
"vldr d0, [%[rhs_ptr]]\n" // Load 1st half of Rhs cell of next
// iteration
"vmov d3, r2, r3\n" // Prepare 2nd half of 1st Lhs cell of next
// iteration
"vmla.f32 q11, q2, d1[1]\n" // Multiply 2nd Lhs cell with column 3
"ldr r2, [%[rhs_ptr], #8]\n" // Load 2nd half of Rhs cell of next
// iteration, part 1
"vmla.f32 q14, q3, d1[0]\n" // Multiply 3rd Lhs cell with column 2
"ldr r3, [%[rhs_ptr], #12]\n" // Load 2nd half of Rhs cell of next
// iteration, part 2
"vmla.f32 q15, q3, d1[1]\n" // Multiply 3rd Lhs cell with column 3
// Loop branch. This will dual issue in fmla cycle 3 of the 4th block.
//"bne loop_%=\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "r2", "r3", "d0", "d1", "d2", "d3", "d4", "d5",
"d6", "d7", "d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16",
"d17", "d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26",
"d27", "d28", "d29", "d30", "d31");
}
};
// This rotating variant performs well when permutations (vext) can be
// dual-issued with arithmetic instructions.
struct NEON_32bit_GEMM_Float32_MLA_Rotating {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
#define NEON_32BIT_ROTATING_FLOAT_KERNEL_TRANSPOSE_ACCUMULATOR_CELLS \
"vtrn.32 q4, q5\n" \
"vtrn.32 q6, q7\n" \
"vswp d9, d12\n" \
"vswp d11, d14\n" \
"vtrn.32 q8, q9\n" \
"vtrn.32 q10, q11\n" \
"vswp d17, d20\n" \
"vswp d19, d22\n" \
"vtrn.32 q12, q13\n" \
"vtrn.32 q14, q15\n" \
"vswp d25, d28\n" \
"vswp d27, d30\n"
#define NEON_32BIT_ROTATING_FLOAT_KERNEL_ROTATE_ACCUMULATOR_CELLS(a, b, c) \
NEON_32BIT_ROTATING_FLOAT_KERNEL_TRANSPOSE_ACCUMULATOR_CELLS \
"vext.32 q5, q5, q5, #" #a \
"\n" \
"vext.32 q6, q6, q6, #" #b \
"\n" \
"vext.32 q7, q7, q7, #" #c \
"\n" \
"vext.32 q9, q9, q9, #" #a \
"\n" \
"vext.32 q10, q10, q10, #" #b \
"\n" \
"vext.32 q11, q11, q11, #" #c \
"\n" \
"vext.32 q13, q13, q13, #" #a \
"\n" \
"vext.32 q14, q14, q14, #" #b \
"\n" \
"vext.32 q15, q15, q15, #" #c \
"\n" NEON_32BIT_ROTATING_FLOAT_KERNEL_TRANSPOSE_ACCUMULATOR_CELLS
NEON_32BIT_ROTATING_FLOAT_KERNEL_ROTATE_ACCUMULATOR_CELLS(1, 2, 3)
//"loop_%=:\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 1 Rhs cell of size 1x4
"vld1.32 {d0, d1}, [%[rhs_ptr]]!\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vmla.f32 q4, q1, q0\n"
"vmla.f32 q8, q2, q0\n"
"vmla.f32 q12, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vmla.f32 q5, q1, q0\n"
"vmla.f32 q9, q2, q0\n"
"vmla.f32 q13, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vmla.f32 q6, q1, q0\n"
"vmla.f32 q10, q2, q0\n"
"vmla.f32 q14, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vmla.f32 q7, q1, q0\n"
"vmla.f32 q11, q2, q0\n"
"vmla.f32 q15, q3, q0\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
//"bne loop_%=\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov r0, %[accum_ptr]\n"
NEON_32BIT_ROTATING_FLOAT_KERNEL_ROTATE_ACCUMULATOR_CELLS(3, 2, 1)
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
// This rotating variant performs well when permutations (vext) can be
// dual-issued with arithmetic instructions. It is relevant as the rotating
// approach removes the need for multiply-with-scalar instructions, and ARMv7
// FMA does not have a with-scalar variant.
struct NEON_32bit_GEMM_Float32_FMA_Rotating {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov r0, %[accum_ptr]\n"
"vld1.32 {d8, d9}, [r0]!\n"
"vld1.32 {d16, d17}, [r0]!\n"
"vld1.32 {d24, d25}, [r0]!\n"
"vld1.32 {d10, d11}, [r0]!\n"
"vld1.32 {d18, d19}, [r0]!\n"
"vld1.32 {d26, d27}, [r0]!\n"
"vld1.32 {d12, d13}, [r0]!\n"
"vld1.32 {d20, d21}, [r0]!\n"
"vld1.32 {d28, d29}, [r0]!\n"
"vld1.32 {d14, d15}, [r0]!\n"
"vld1.32 {d22, d23}, [r0]!\n"
"vld1.32 {d30, d31}, [r0]!\n"
NEON_32BIT_ROTATING_FLOAT_KERNEL_ROTATE_ACCUMULATOR_CELLS(1, 2, 3)
//"loop_%=:\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 1 Rhs cell of size 1x4
"vld1.32 {d0, d1}, [%[rhs_ptr]]!\n"
// Load 3 Lhs cells of size 4x1 each
"vld1.32 {d2, d3}, [%[lhs_ptr]]!\n"
"vld1.32 {d4, d5}, [%[lhs_ptr]]!\n"
"vld1.32 {d6, d7}, [%[lhs_ptr]]!\n"
// Multiply-accumulate
"vfma.f32 q4, q1, q0\n"
"vfma.f32 q8, q2, q0\n"
"vfma.f32 q12, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vfma.f32 q5, q1, q0\n"
"vfma.f32 q9, q2, q0\n"
"vfma.f32 q13, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vfma.f32 q6, q1, q0\n"
"vfma.f32 q10, q2, q0\n"
"vfma.f32 q14, q3, q0\n"
"vext.f32 q0, q0, q0, #1\n"
"vfma.f32 q7, q1, q0\n"
"vfma.f32 q11, q2, q0\n"
"vfma.f32 q15, q3, q0\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %[depth], #1\n"
//"bne loop_%=\n"
"bne " GEMMLOWP_LABEL_LOOP "b\n"
NEON_32BIT_ROTATING_FLOAT_KERNEL_ROTATE_ACCUMULATOR_CELLS(3, 2, 1)
// Store accumulators
"mov r0, %[accum_ptr]\n"
"vst1.32 {d8, d9}, [r0]!\n"
"vst1.32 {d16, d17}, [r0]!\n"
"vst1.32 {d24, d25}, [r0]!\n"
"vst1.32 {d10, d11}, [r0]!\n"
"vst1.32 {d18, d19}, [r0]!\n"
"vst1.32 {d26, d27}, [r0]!\n"
"vst1.32 {d12, d13}, [r0]!\n"
"vst1.32 {d20, d21}, [r0]!\n"
"vst1.32 {d28, d29}, [r0]!\n"
"vst1.32 {d14, d15}, [r0]!\n"
"vst1.32 {d22, d23}, [r0]!\n"
"vst1.32 {d30, d31}, [r0]!\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "r0", "d0", "d1", "d2", "d3", "d4", "d5", "d6", "d7",
"d8", "d9", "d10", "d11", "d12", "d13", "d14", "d15", "d16", "d17",
"d18", "d19", "d20", "d21", "d22", "d23", "d24", "d25", "d26", "d27",
"d28", "d29", "d30", "d31");
}
};
#endif // __arm__
#ifdef __aarch64__
// This is the current standard kernel in gemmlowp, see:
// https://github.com/google/gemmlowp/blob/b1e2a29ff866680028f3080efc244e10e8dd7f46/internal/kernel_neon.h#L646
struct NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load 1 Rhs cell of size 2x8
"ld1 {v5.8b}, [%[rhs_ptr]], #8\n"
"ld1 {v6.8b}, [%[rhs_ptr]], #8\n"
// Load 3 Lhs cells of size 4x2 each
"ld1 {v2.8b}, [%[lhs_ptr]], #8\n"
"ld1 {v3.8b}, [%[lhs_ptr]], #8\n"
"ld1 {v4.8b}, [%[lhs_ptr]], #8\n"
"subs %w[depth], %w[depth], #2\n"
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
"beq " GEMMLOWP_LABEL_AFTER_LOOP "f\n"
//"loop_%=:\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Overview of register layout:
//
// A 2x8 block of 2 2x4 cells of Rhs is stored in 16bit in v0--v1.
// A 12x2 block of 3 4x2 cells Lhs is stored in 16bit in v2--v4.
// A 12x8 block of accumulators is stored in 32bit in v8--v31.
//
// +--------+--------+-----+--------+--------+
// |v0.h[0] |v0.h[1] | ... |v1.h[2] |v1.h[3] |
// Rhs +--------+--------+-----+--------+--------+
// |v0.h[4] |v0.h[5] | ... |v1.h[6] |v1.h[7] |
// +--------+--------+-----+--------+--------+
//
// | | | | | |
//
// Lhs | | | | | |
//
// +-------+-------+ - - +--------+--------+-----+--------+--------+
// |v2.h[0]|v2.h[4]| |v8.s[0] |v9.s[0] | ... |v14.s[0]|v15.s[0]|
// |v2.h[1]|v2.h[5]| |v8.s[1] |v9.s[1] | ... |v14.s[1]|v15.s[1]|
// |v2.h[2]|v2.h[6]| |v8.s[2] |v9.s[2] | ... |v14.s[2]|v15.s[2]|
// |v2.h[3]|v2.h[7]| |v8.s[3] |v9.s[3] | ... |v14.s[3]|v15.s[3]|
// +-------+-------+ - - +--------+--------+-----+--------+--------+
// |v3.h[0]|v3.h[4]| |v16.s[0]|v17.s[0]| ... |v22.s[0]|v23.s[0]|
// |v3.h[1]|v3.h[5]| |v16.s[1]|v17.s[1]| ... |v22.s[1]|v23.s[1]|
// |v3.h[2]|v3.h[6]| |v16.s[2]|v17.s[2]| ... |v22.s[2]|v23.s[2]|
// |v3.h[3]|v3.h[7]| |v16.s[3]|v17.s[3]| ... |v22.s[3]|v23.s[3]|
// +-------+-------+ - - +--------+--------+-----+--------+--------+
// |v4.h[0]|v4.h[4]| |v24.s[0]|v25.s[0]| ... |v30.s[0]|v31.s[0]|
// |v4.h[1]|v4.h[5]| |v24.s[1]|v25.s[1]| ... |v30.s[1]|v31.s[1]|
// |v4.h[2]|v4.h[6]| |v24.s[2]|v25.s[2]| ... |v30.s[2]|v31.s[2]|
// |v4.h[3]|v4.h[7]| |v24.s[3]|v25.s[3]| ... |v30.s[3]|v31.s[3]|
// +-------+-------+ - - +--------+--------+-----+--------+--------+
//
// Accumulator
// Expand Lhs/Rhs cells to 16 bit.
"uxtl v0.8h, v5.8b\n"
"ld1 {v5.8b}, [%[rhs_ptr]], #8\n"
"uxtl v1.8h, v6.8b\n"
"ld1 {v6.8b}, [%[rhs_ptr]], #8\n"
"uxtl v2.8h, v2.8b\n"
"uxtl v3.8h, v3.8b\n"
"uxtl v4.8h, v4.8b\n"
// Multiply-accumulate, top third
"umlal v8.4s, v2.4h, v0.h[0]\n"
"umlal v9.4s, v2.4h, v0.h[1]\n"
"umlal v10.4s, v2.4h, v0.h[2]\n"
"umlal v11.4s, v2.4h, v0.h[3]\n"
"umlal v12.4s, v2.4h, v1.h[0]\n"
"umlal v13.4s, v2.4h, v1.h[1]\n"
"umlal v14.4s, v2.4h, v1.h[2]\n"
"umlal v15.4s, v2.4h, v1.h[3]\n"
"umlal2 v8.4s, v2.8h, v0.h[4]\n"
"umlal2 v9.4s, v2.8h, v0.h[5]\n"
"umlal2 v10.4s, v2.8h, v0.h[6]\n"
"umlal2 v11.4s, v2.8h, v0.h[7]\n"
"umlal2 v12.4s, v2.8h, v1.h[4]\n"
"umlal2 v13.4s, v2.8h, v1.h[5]\n"
"umlal2 v14.4s, v2.8h, v1.h[6]\n"
"umlal2 v15.4s, v2.8h, v1.h[7]\n"
"ld1 {v2.8b}, [%[lhs_ptr]], #8\n"
// Multiply-accumulate, middle third
"umlal v16.4s, v3.4h, v0.h[0]\n"
"umlal v17.4s, v3.4h, v0.h[1]\n"
"umlal v18.4s, v3.4h, v0.h[2]\n"
"umlal v19.4s, v3.4h, v0.h[3]\n"
"umlal v20.4s, v3.4h, v1.h[0]\n"
"umlal v21.4s, v3.4h, v1.h[1]\n"
"umlal v22.4s, v3.4h, v1.h[2]\n"
"umlal v23.4s, v3.4h, v1.h[3]\n"
"umlal2 v16.4s, v3.8h, v0.h[4]\n"
"umlal2 v17.4s, v3.8h, v0.h[5]\n"
"umlal2 v18.4s, v3.8h, v0.h[6]\n"
"umlal2 v19.4s, v3.8h, v0.h[7]\n"
"umlal2 v20.4s, v3.8h, v1.h[4]\n"
"umlal2 v21.4s, v3.8h, v1.h[5]\n"
"umlal2 v22.4s, v3.8h, v1.h[6]\n"
"umlal2 v23.4s, v3.8h, v1.h[7]\n"
"ld1 {v3.8b}, [%[lhs_ptr]], #8\n"
"subs %w[depth], %w[depth], #2\n"
// Multiply-accumulate, bottom third
"umlal v24.4s, v4.4h, v0.h[0]\n"
"umlal v25.4s, v4.4h, v0.h[1]\n"
"umlal v26.4s, v4.4h, v0.h[2]\n"
"umlal v27.4s, v4.4h, v0.h[3]\n"
"umlal v28.4s, v4.4h, v1.h[0]\n"
"umlal v29.4s, v4.4h, v1.h[1]\n"
"umlal v30.4s, v4.4h, v1.h[2]\n"
"umlal v31.4s, v4.4h, v1.h[3]\n"
"umlal2 v24.4s, v4.8h, v0.h[4]\n"
"umlal2 v25.4s, v4.8h, v0.h[5]\n"
"umlal2 v26.4s, v4.8h, v0.h[6]\n"
"umlal2 v27.4s, v4.8h, v0.h[7]\n"
"umlal2 v28.4s, v4.8h, v1.h[4]\n"
"umlal2 v29.4s, v4.8h, v1.h[5]\n"
"umlal2 v30.4s, v4.8h, v1.h[6]\n"
"umlal2 v31.4s, v4.8h, v1.h[7]\n"
"ld1 {v4.8b}, [%[lhs_ptr]], #8\n"
"bne " GEMMLOWP_LABEL_LOOP "b\n"
GEMMLOWP_LABEL_AFTER_LOOP
":\n"
// Expand Lhs/Rhs cells to 16 bit.
"uxtl v0.8h, v5.8b\n"
"uxtl v1.8h, v6.8b\n"
"uxtl v2.8h, v2.8b\n"
"uxtl v3.8h, v3.8b\n"
"uxtl v4.8h, v4.8b\n"
// Multiply-accumulate, level of depth 0
"umlal v8.4s, v2.4h, v0.h[0]\n"
"umlal v9.4s, v2.4h, v0.h[1]\n"
"umlal v10.4s, v2.4h, v0.h[2]\n"
"umlal v11.4s, v2.4h, v0.h[3]\n"
"umlal v12.4s, v2.4h, v1.h[0]\n"
"umlal v13.4s, v2.4h, v1.h[1]\n"
"umlal v14.4s, v2.4h, v1.h[2]\n"
"umlal v15.4s, v2.4h, v1.h[3]\n"
"umlal v16.4s, v3.4h, v0.h[0]\n"
"umlal v17.4s, v3.4h, v0.h[1]\n"
"umlal v18.4s, v3.4h, v0.h[2]\n"
"umlal v19.4s, v3.4h, v0.h[3]\n"
"umlal v20.4s, v3.4h, v1.h[0]\n"
"umlal v21.4s, v3.4h, v1.h[1]\n"
"umlal v22.4s, v3.4h, v1.h[2]\n"
"umlal v23.4s, v3.4h, v1.h[3]\n"
"umlal v24.4s, v4.4h, v0.h[0]\n"
"umlal v25.4s, v4.4h, v0.h[1]\n"
"umlal v26.4s, v4.4h, v0.h[2]\n"
"umlal v27.4s, v4.4h, v0.h[3]\n"
"umlal v28.4s, v4.4h, v1.h[0]\n"
"umlal v29.4s, v4.4h, v1.h[1]\n"
"umlal v30.4s, v4.4h, v1.h[2]\n"
"umlal v31.4s, v4.4h, v1.h[3]\n"
// Multiply-accumulate, level of depth 1
"umlal2 v8.4s, v2.8h, v0.h[4]\n"
"umlal2 v9.4s, v2.8h, v0.h[5]\n"
"umlal2 v10.4s, v2.8h, v0.h[6]\n"
"umlal2 v11.4s, v2.8h, v0.h[7]\n"
"umlal2 v12.4s, v2.8h, v1.h[4]\n"
"umlal2 v13.4s, v2.8h, v1.h[5]\n"
"umlal2 v14.4s, v2.8h, v1.h[6]\n"
"umlal2 v15.4s, v2.8h, v1.h[7]\n"
"umlal2 v16.4s, v3.8h, v0.h[4]\n"
"umlal2 v17.4s, v3.8h, v0.h[5]\n"
"umlal2 v18.4s, v3.8h, v0.h[6]\n"
"umlal2 v19.4s, v3.8h, v0.h[7]\n"
"umlal2 v20.4s, v3.8h, v1.h[4]\n"
"umlal2 v21.4s, v3.8h, v1.h[5]\n"
"umlal2 v22.4s, v3.8h, v1.h[6]\n"
"umlal2 v23.4s, v3.8h, v1.h[7]\n"
"umlal2 v24.4s, v4.8h, v0.h[4]\n"
"umlal2 v25.4s, v4.8h, v0.h[5]\n"
"umlal2 v26.4s, v4.8h, v0.h[6]\n"
"umlal2 v27.4s, v4.8h, v0.h[7]\n"
"umlal2 v28.4s, v4.8h, v1.h[4]\n"
"umlal2 v29.4s, v4.8h, v1.h[5]\n"
"umlal2 v30.4s, v4.8h, v1.h[6]\n"
"umlal2 v31.4s, v4.8h, v1.h[7]\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// Faster kernel by ARM. Not expanding operands before multiplication.
// Tuned for A57. Compare to
// NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators_noexpand
struct NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_noexpand_A57 {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<5, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
static const int kLhsWidth = Format::Lhs::kWidth;
static const int kRhsWidth = Format::Rhs::kWidth;
AccumulatorType rowmajor_accumulator_buffer[kLhsWidth * kRhsWidth];
asm volatile(
// Clear aggregators
"dup v12.4s, wzr\n"
"dup v13.4s, wzr\n"
"dup v14.4s, wzr\n"
"dup v15.4s, wzr\n"
"dup v16.4s, wzr\n"
"dup v17.4s, wzr\n"
"dup v18.4s, wzr\n"
"dup v19.4s, wzr\n"
"dup v20.4s, wzr\n"
"dup v21.4s, wzr\n"
"dup v22.4s, wzr\n"
"dup v23.4s, wzr\n"
"dup v24.4s, wzr\n"
"dup v25.4s, wzr\n"
"dup v26.4s, wzr\n"
"dup v27.4s, wzr\n"
"dup v28.4s, wzr\n"
"dup v29.4s, wzr\n"
"dup v30.4s, wzr\n"
"dup v31.4s, wzr\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Overview of register layout:
//
// A 4x16 block of Rhs is stored in 8 bit in v0--v3.
// A 5x16 block of Lhs is cycled through v4 and v5 in 8 bit.
//
// A 4x5 block of aggregators is stored in v12-v31 (as 4x32 bit
// components which would need to be added at the end)
//
// The Lhs vectors are multiplied by the Rhs vectors with a widening
// multiply to produce an intermediate result which is stored in
// v6-v11. Each intermediate result is 8x16 bits so this happens
// twice for each Lhs/Rhs combination (once with UMULL for elements
// 0-7 and once with UMULL2 for elements 8-15).
//
// UADALP is used to accumulate these intermediate results into the
// result aggregators.
//
//
//
// +--------+--------+--------+--------+
// |v0.b[0] |v1.b[0] |v2.b[0] |v3.b[0] |
// Rhs +--------+--------+--------+--------+
// | ... | ... | ... | ... |
// +--------+--------+--------+--------|
// |v0.b[15]|v1.b[15]|v2.b[15]|v3.b[15]|
// +--------+--------+--------+--------+
//
// | | | | |
//
// Lhs | | | | |
//
// +-------+-----+--------+ - - +--------+--------+--------+--------+
// |v4.b[0]| ... |v4.b[15]| | v12.4s | v13.4s | v14.4s | v15.4s |
// |v5.b[0]| ... |v5.b[15]| | v16.4s | v17.4s | v18.4s | v19.4s |
// |v4.b[0]| ... |v4.b[15]| | v20.4s | v21.4s | v22.4s | v23.4s |
// |v5.b[0]| ... |v5.b[15]| | v24.4s | v25.4s | v26.4s | v27.4s |
// |v4.b[0]| ... |v4.b[15]| | v28.4s | v29.4s | v30.4s | v31.4s |
// +-------+--------------+ - - +--------+--------+--------+--------+
//
// Accumulator
//
//
// Further possible optimisations (not tried):
// - Move early loads into previous iteration (see Float32_WithScalar
// for example). - Unroll loop 2x to alternate more smoothly between
// v4 and v5. - A different number of temporary registers might work
// better. - Pairing umull with corresponding umull2 might allow
// better
// register loading (e.g. at the start of the loop)
// - Interleaving umull{2} and uadalp even more aggressively might
// help, (not sure about latency vs. dispatch rate).
//
//
// Start loading Rhs - further loads are interleaved amongst the
// multiplies for better dispatch on A57.
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
// Load first Lhs vector - further loads are interleaved amongst the
// multiplies
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"umull v6.8h, v0.8b, v4.8b\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n" // 2nd RHS element
"umull v7.8h, v1.8b, v4.8b\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n" // 3rd RHS element
"umull v8.8h, v2.8b, v4.8b\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n" // 4th RHS element
"umull v9.8h, v3.8b, v4.8b\n"
"umull2 v10.8h, v0.16b, v4.16b\n"
"umull2 v11.8h, v1.16b, v4.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n" // 2nd LHS element
"uadalp v12.4s, v6.8h\n"
"umull2 v6.8h, v2.16b, v4.16b\n"
"uadalp v13.4s, v7.8h\n"
"umull2 v7.8h, v3.16b, v4.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n" // 1st LHS element done - Reuse v4
// for 3rd LHS element
"uadalp v14.4s, v8.8h\n"
"umull v8.8h, v0.8b, v5.8b\n"
"uadalp v15.4s, v9.8h\n"
"umull v9.8h, v1.8b, v5.8b\n"
"uadalp v12.4s, v10.8h\n"
"umull v10.8h, v2.8b, v5.8b\n"
"uadalp v13.4s, v11.8h\n"
"umull v11.8h, v3.8b, v5.8b\n"
"uadalp v14.4s, v6.8h\n"
"umull2 v6.8h, v0.16b, v5.16b\n"
"uadalp v15.4s, v7.8h\n"
"umull2 v7.8h, v1.16b, v5.16b\n"
"uadalp v16.4s, v8.8h\n"
"umull2 v8.8h, v2.16b, v5.16b\n"
"uadalp v17.4s, v9.8h\n"
"umull2 v9.8h, v3.16b, v5.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n" // 2nd LHS element done - Reuse v5
// for 4th LHS element
"uadalp v18.4s, v10.8h\n"
"umull v10.8h, v0.8b, v4.8b\n"
"uadalp v19.4s, v11.8h\n"
"umull v11.8h, v1.8b, v4.8b\n"
"uadalp v16.4s, v6.8h\n"
"umull v6.8h, v2.8b, v4.8b\n"
"uadalp v17.4s, v7.8h\n"
"umull v7.8h, v3.8b, v4.8b\n"
"uadalp v18.4s, v8.8h\n"
"umull2 v8.8h, v0.16b, v4.16b\n"
"uadalp v19.4s, v9.8h\n"
"umull2 v9.8h, v1.16b, v4.16b\n"
"uadalp v20.4s, v10.8h\n"
"umull2 v10.8h, v2.16b, v4.16b\n"
"uadalp v21.4s, v11.8h\n"
"umull2 v11.8h, v3.16b, v4.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n" // 3rd LHS element done - Reuse v4
// for 5th LHS element
"uadalp v22.4s, v6.8h\n"
"umull v6.8h, v0.8b, v5.8b\n"
"uadalp v23.4s, v7.8h\n"
"umull v7.8h, v1.8b, v5.8b\n"
"uadalp v20.4s, v8.8h\n"
"umull v8.8h, v2.8b, v5.8b\n"
"uadalp v21.4s, v9.8h\n"
"umull v9.8h, v3.8b, v5.8b\n"
"uadalp v22.4s, v10.8h\n"
"umull2 v10.8h, v0.16b, v5.16b\n"
"uadalp v23.4s, v11.8h\n"
"umull2 v11.8h, v1.16b, v5.16b\n"
"uadalp v24.4s, v6.8h\n"
"umull2 v6.8h, v2.16b, v5.16b\n"
"uadalp v25.4s, v7.8h\n"
"umull2 v7.8h, v3.16b, v5.16b\n"
"uadalp v26.4s, v8.8h\n"
"umull v8.8h, v0.8b, v4.8b\n"
"uadalp v27.4s, v9.8h\n"
"umull v9.8h, v1.8b, v4.8b\n"
"uadalp v24.4s, v10.8h\n"
"umull v10.8h, v2.8b, v4.8b\n"
"uadalp v25.4s, v11.8h\n"
"umull v11.8h, v3.8b, v4.8b\n"
"uadalp v26.4s, v6.8h\n"
"umull2 v6.8h, v0.16b, v4.16b\n"
"uadalp v27.4s, v7.8h\n"
"umull2 v7.8h, v1.16b, v4.16b\n"
"uadalp v28.4s, v8.8h\n"
"umull2 v8.8h, v2.16b, v4.16b\n"
"uadalp v29.4s, v9.8h\n"
"umull2 v9.8h, v3.16b, v4.16b\n"
"uadalp v30.4s, v10.8h\n"
"uadalp v31.4s, v11.8h\n"
"uadalp v28.4s, v6.8h\n"
"uadalp v29.4s, v7.8h\n"
// Loop. Decrement loop index (depth) by 16, since we just handled
// 16 levels of depth. Do this subs a bit before the end of the loop
// for better dispatch on A57.
"subs %w[depth], %w[depth], #16\n"
"uadalp v30.4s, v8.8h\n"
"uadalp v31.4s, v9.8h\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Reduce aggregators horizontally
"addp v0.4s, v12.4s, v13.4s\n"
"addp v1.4s, v14.4s, v15.4s\n"
"addp v2.4s, v16.4s, v17.4s\n"
"addp v3.4s, v18.4s, v19.4s\n"
"addp v4.4s, v20.4s, v21.4s\n"
"addp v5.4s, v22.4s, v23.4s\n"
"addp v6.4s, v24.4s, v25.4s\n"
"addp v7.4s, v26.4s, v27.4s\n"
"addp v8.4s, v28.4s, v29.4s\n"
"addp v9.4s, v30.4s, v31.4s\n"
"addp v10.4s, v0.4s, v1.4s\n"
"addp v11.4s, v2.4s, v3.4s\n"
"addp v12.4s, v4.4s, v5.4s\n"
"addp v13.4s, v6.4s, v7.4s\n"
"addp v14.4s, v8.4s, v9.4s\n"
"mov x0, %[rowmajor_accumulator_buffer]\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[rowmajor_accumulator_buffer] "r"(rowmajor_accumulator_buffer)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
// accumulate row-major accumulators into global (column-major) accumulators
for (int l = 0; l < kLhsWidth; l++) {
for (int r = 0; r < kRhsWidth; r++) {
accum_ptr[l + kLhsWidth * r] +=
rowmajor_accumulator_buffer[r + l * kRhsWidth];
}
}
}
};
// Fast kernel operating on int8 operands.
// It is assumed that one of the two int8 operands only takes values
// in [-127, 127], while the other may freely range in [-128, 127].
// The issue with both operands taking the value -128 is that:
// -128*-128 + -128*-128 == -32768 overflows int16.
// Every other expression a*b + c*d, for any int8 a,b,c,d, fits in int16
// range. That is the basic idea of this kernel.
struct NEON_64bit_GEMM_Int8Operands_AccumTwoWithin16Bits {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
std::size_t start_depth = 123;
std::size_t run_depth = depth;
std::size_t dst_col_stride = 4;
AccumulatorType* dst_ptr = accum_ptr;
asm volatile(
// Overview of register layout:
//
// A 4x16 block of Rhs is stored in 8 bit in v0--v3.
// A 4x16 block of Lhs is stored in 8 bit in v4--v7.
//
// A 4x4 block of accumulators is stored in v16-v31 (as 4x32 bit
// components which need to be horizontally-added at the end)
//
// The Lhs vectors are multiplied by the Rhs vectors with a widening
// multiply over the 8 first levels of depth, producing int16x8
// vectors of products for each position in the accumulator matrix.
// Here comes the special trick: since the operands are signed int8,
// their range being [ -2^7 , 2^7 ), their products are in range
// [ -2^14 , 2^14 - 1 ), meaning that we can add two such values
// without any risk of overflowing int16.
// We thus proceed with the 8 next levels of depth, multiplying
// again Lhs by Rhs, accumulating into this existing int16x8 vector.
//
// Only then, having processed 16 levels of depth, do we need to
// horizontally add these int16x8 accumulators into the final
// int32x4 accumulators.
//
// As we do not have enough registers to store all 16 int16x8
// temporary-16bit-accumulators, we have them cycle through v8--v15.
//
//
// Register layout (ignoring the v8--v15 temporary 16bit accumulators):
//
// +--------+--------+--------+--------+
// |v0.b[0] |v1.b[0] |v2.b[0] |v3.b[0] |
// Rhs +--------+--------+--------+--------+
// | ... | ... | ... | ... |
// +--------+--------+--------+--------|
// |v0.b[15]|v1.b[15]|v2.b[15]|v3.b[15]|
// +--------+--------+--------+--------+
//
// | | | | |
//
// Lhs | | | | |
//
// +-------+-----+--------+ - - +--------+--------+--------+--------+
// |v4.b[0]| ... |v4.b[15]| | v16.4s | v17.4s | v18.4s | v19.4s |
// |v5.b[0]| ... |v5.b[15]| | v20.4s | v21.4s | v22.4s | v23.4s |
// |v6.b[0]| ... |v6.b[15]| | v24.4s | v25.4s | v26.4s | v27.4s |
// |v7.b[0]| ... |v7.b[15]| | v28.4s | v29.4s | v30.4s | v31.4s |
// +-------+--------------+ - - +--------+--------+--------+--------+
//
// Accumulator
//
// Clear accumulators
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
"dup v16.4s, wzr\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n"
"dup v17.4s, wzr\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"dup v18.4s, wzr\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"dup v19.4s, wzr\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"dup v20.4s, wzr\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"dup v21.4s, wzr\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n"
"dup v22.4s, wzr\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n"
"dup v23.4s, wzr\n"
"subs %[run_depth], %[run_depth], #16\n"
"dup v24.4s, wzr\n"
"mov x0, %[dst_ptr]\n"
"dup v25.4s, wzr\n"
"dup v26.4s, wzr\n"
"dup v27.4s, wzr\n"
"dup v28.4s, wzr\n"
"dup v29.4s, wzr\n"
"dup v30.4s, wzr\n"
"dup v31.4s, wzr\n"
"smull v12.8h, v0.8b, v4.8b\n"
"smull v13.8h, v1.8b, v4.8b\n"
"smull v14.8h, v0.8b, v5.8b\n"
"smull v15.8h, v1.8b, v5.8b\n"
"smlal2 v12.8h, v0.16b, v4.16b\n"
"smlal2 v13.8h, v1.16b, v4.16b\n"
"smlal2 v14.8h, v0.16b, v5.16b\n"
"smlal2 v15.8h, v1.16b, v5.16b\n"
"beq " GEMMLOWP_LABEL_AFTER_LOOP "f\n"
GEMMLOWP_LABEL_LOOP
":\n"
"subs %[run_depth], %[run_depth], #16\n"
"sadalp v16.4s, v12.8h\n"
"smull v12.8h, v0.8b, v6.8b\n"
"sadalp v17.4s, v13.8h\n"
"smull v13.8h, v0.8b, v7.8b\n"
"sadalp v20.4s, v14.8h\n"
"smull v14.8h, v1.8b, v6.8b\n"
"sadalp v21.4s, v15.8h\n"
"smull v15.8h, v1.8b, v7.8b\n"
"smlal2 v12.8h, v0.16b, v6.16b\n"
"smlal2 v13.8h, v0.16b, v7.16b\n"
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v14.8h, v1.16b, v6.16b\n"
"smlal2 v15.8h, v1.16b, v7.16b\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n"
"sadalp v24.4s, v12.8h\n"
"smull v12.8h, v2.8b, v4.8b\n"
"sadalp v28.4s, v13.8h\n"
"smull v13.8h, v3.8b, v4.8b\n"
"sadalp v25.4s, v14.8h\n"
"smull v14.8h, v2.8b, v5.8b\n"
"sadalp v29.4s, v15.8h\n"
"smull v15.8h, v3.8b, v5.8b\n"
"smlal2 v12.8h, v2.16b, v4.16b\n"
"smlal2 v13.8h, v3.16b, v4.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v14.8h, v2.16b, v5.16b\n"
"smlal2 v15.8h, v3.16b, v5.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"sadalp v18.4s, v12.8h\n"
"smull v12.8h, v2.8b, v6.8b\n"
"sadalp v19.4s, v13.8h\n"
"smull v13.8h, v2.8b, v7.8b\n"
"sadalp v22.4s, v14.8h\n"
"smull v14.8h, v3.8b, v6.8b\n"
"sadalp v23.4s, v15.8h\n"
"smull v15.8h, v3.8b, v7.8b\n"
"smlal2 v12.8h, v2.16b, v6.16b\n"
"smlal2 v13.8h, v2.16b, v7.16b\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v14.8h, v3.16b, v6.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v15.8h, v3.16b, v7.16b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"sadalp v26.4s, v12.8h\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n"
"smull v12.8h, v0.8b, v4.8b\n"
"sadalp v30.4s, v13.8h\n"
"smull v13.8h, v1.8b, v4.8b\n"
"sadalp v27.4s, v14.8h\n"
"smull v14.8h, v0.8b, v5.8b\n"
"sadalp v31.4s, v15.8h\n"
"smull v15.8h, v1.8b, v5.8b\n"
"smlal2 v12.8h, v0.16b, v4.16b\n"
"smlal2 v13.8h, v1.16b, v4.16b\n"
"smlal2 v14.8h, v0.16b, v5.16b\n"
"smlal2 v15.8h, v1.16b, v5.16b\n"
"bne " GEMMLOWP_LABEL_LOOP "b\n"
GEMMLOWP_LABEL_AFTER_LOOP
":\n"
// Load accumulators from memory
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"mov x0, %[dst_ptr]\n"
// Do the remaining arithmetic for the 16 last levels of depths.
// All the operands are already loaded.
"sadalp v16.4s, v12.8h\n"
"smull v12.8h, v0.8b, v6.8b\n"
"sadalp v17.4s, v13.8h\n"
"smull v13.8h, v0.8b, v7.8b\n"
"sadalp v20.4s, v14.8h\n"
"smull v14.8h, v1.8b, v6.8b\n"
"sadalp v21.4s, v15.8h\n"
"smull v15.8h, v1.8b, v7.8b\n"
"smlal2 v12.8h, v0.16b, v6.16b\n"
"smlal2 v13.8h, v0.16b, v7.16b\n"
"smlal2 v14.8h, v1.16b, v6.16b\n"
"smlal2 v15.8h, v1.16b, v7.16b\n"
"sadalp v24.4s, v12.8h\n"
"smull v12.8h, v2.8b, v4.8b\n"
"sadalp v28.4s, v13.8h\n"
"smull v13.8h, v3.8b, v4.8b\n"
"sadalp v25.4s, v14.8h\n"
"smull v14.8h, v2.8b, v5.8b\n"
"sadalp v29.4s, v15.8h\n"
"smull v15.8h, v3.8b, v5.8b\n"
"smlal2 v12.8h, v2.16b, v4.16b\n"
"smlal2 v13.8h, v3.16b, v4.16b\n"
"smlal2 v14.8h, v2.16b, v5.16b\n"
"smlal2 v15.8h, v3.16b, v5.16b\n"
"sadalp v18.4s, v12.8h\n"
"smull v12.8h, v2.8b, v6.8b\n"
"sadalp v19.4s, v13.8h\n"
"smull v13.8h, v2.8b, v7.8b\n"
"sadalp v22.4s, v14.8h\n"
"smull v14.8h, v3.8b, v6.8b\n"
"sadalp v23.4s, v15.8h\n"
"smull v15.8h, v3.8b, v7.8b\n"
"smlal2 v12.8h, v2.16b, v6.16b\n"
"smlal2 v13.8h, v2.16b, v7.16b\n"
"smlal2 v14.8h, v3.16b, v6.16b\n"
"smlal2 v15.8h, v3.16b, v7.16b\n"
"sadalp v26.4s, v12.8h\n"
"sadalp v30.4s, v13.8h\n"
"sadalp v27.4s, v14.8h\n"
"sadalp v31.4s, v15.8h\n"
// Reduce aggregators horizontally
"addp v0.4s, v16.4s, v20.4s\n"
"addp v1.4s, v17.4s, v21.4s\n"
"addp v2.4s, v18.4s, v22.4s\n"
"addp v3.4s, v19.4s, v23.4s\n"
"addp v4.4s, v24.4s, v28.4s\n"
"addp v5.4s, v25.4s, v29.4s\n"
"addp v6.4s, v26.4s, v30.4s\n"
"addp v7.4s, v27.4s, v31.4s\n"
"addp v12.4s, v0.4s, v4.4s\n"
"addp v13.4s, v1.4s, v5.4s\n"
"addp v14.4s, v2.4s, v6.4s\n"
"addp v15.4s, v3.4s, v7.4s\n"
// Add to the accumulators loaded from memory
"add v8.4s, v8.4s, v12.4s\n"
"add v9.4s, v9.4s, v13.4s\n"
"add v10.4s, v10.4s, v14.4s\n"
"add v11.4s, v11.4s, v15.4s\n"
// Store accumulators back to memory
"st1 {v8.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[dst_ptr] "+r"(dst_ptr), [run_depth] "+r"(run_depth),
[dst_col_stride] "+r"(dst_col_stride)
: // inputs
[start_depth] "r"(start_depth)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
struct NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct_narrow {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
std::size_t start_depth = 123;
std::size_t run_depth = depth;
std::size_t dst_col_stride = 4;
AccumulatorType* dst_ptr = accum_ptr;
asm volatile(
// Overview of register layout:
//
// A 4x16 block of Rhs is stored in 8 bit in v0--v3.
// A 4x16 block of Lhs is stored in 8 bit in v4--v7.
//
// A 4x4 block of accumulators is stored in v16-v31 (as 4x32 bit
// components which need to be horizontally-added at the end)
//
// Register layout:
//
// +--------+--------+--------+--------+
// |v0.b[0] |v1.b[0] |v2.b[0] |v3.b[0] |
// Rhs +--------+--------+--------+--------+
// | ... | ... | ... | ... |
// +--------+--------+--------+--------|
// |v0.b[15]|v1.b[15]|v2.b[15]|v3.b[15]|
// +--------+--------+--------+--------+
//
// | | | | |
//
// Lhs | | | | |
//
// +-------+-----+--------+ - - +--------+--------+--------+--------+
// |v4.b[0]| ... |v4.b[15]| | v16.4s | v17.4s | v18.4s | v19.4s |
// |v5.b[0]| ... |v5.b[15]| | v20.4s | v21.4s | v22.4s | v23.4s |
// |v6.b[0]| ... |v6.b[15]| | v24.4s | v25.4s | v26.4s | v27.4s |
// |v7.b[0]| ... |v7.b[15]| | v28.4s | v29.4s | v30.4s | v31.4s |
// +-------+--------------+ - - +--------+--------+--------+--------+
//
// Accumulator
//
// Clear accumulators
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
"dup v16.4s, wzr\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n"
"dup v17.4s, wzr\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"dup v18.4s, wzr\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"dup v19.4s, wzr\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"dup v20.4s, wzr\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"dup v21.4s, wzr\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n"
"dup v22.4s, wzr\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n"
"dup v23.4s, wzr\n"
"subs %w[run_depth], %w[run_depth], #16\n"
"dup v24.4s, wzr\n"
"mov x0, %[dst_ptr]\n"
"dup v25.4s, wzr\n"
"dup v26.4s, wzr\n"
"dup v27.4s, wzr\n"
"dup v28.4s, wzr\n"
"dup v29.4s, wzr\n"
"dup v30.4s, wzr\n"
"dup v31.4s, wzr\n"
"beq 1f\n"
"cmp %w[run_depth], #32\n"
"blt 2f\n"
"3:\n"
"ld1 {v12.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e809490 // udot v16.4s, v4.16b, v0.16b\n"
".word 0x6e819491 // udot v17.4s, v4.16b, v1.16b\n"
"ld1 {v13.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e829492 // udot v18.4s, v4.16b, v2.16b\n"
".word 0x6e839493 // udot v19.4s, v4.16b, v3.16b\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8094b4 // udot v20.4s, v5.16b, v0.16b\n"
".word 0x6e8194b5 // udot v21.4s, v5.16b, v1.16b\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8294b6 // udot v22.4s, v5.16b, v2.16b\n"
".word 0x6e8394b7 // udot v23.4s, v5.16b, v3.16b\n"
"ld1 {v10.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8094d8 // udot v24.4s, v6.16b, v0.16b\n"
".word 0x6e8194d9 // udot v25.4s, v6.16b, v1.16b\n"
"ld1 {v11.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8294da // udot v26.4s, v6.16b, v2.16b\n"
"prfm pldl1keep, [%[rhs_ptr], #128]\n"
".word 0x6e8394db // udot v27.4s, v6.16b, v3.16b\n"
"ld1 {v14.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8094fc // udot v28.4s, v7.16b, v0.16b\n"
".word 0x6e8194fd // udot v29.4s, v7.16b, v1.16b\n"
"ld1 {v15.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8294fe // udot v30.4s, v7.16b, v2.16b\n"
"prfm pldl1keep, [%[lhs_ptr], #128]\n"
".word 0x6e8394ff // udot v31.4s, v7.16b, v3.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e889590 // udot v16.4s, v12.16b, v8.16b\n"
".word 0x6e899591 // udot v17.4s, v12.16b, v9.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8a9592 // udot v18.4s, v12.16b, v10.16b\n"
".word 0x6e8b9593 // udot v19.4s, v12.16b, v11.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8895b4 // udot v20.4s, v13.16b, v8.16b\n"
".word 0x6e8995b5 // udot v21.4s, v13.16b, v9.16b\n"
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
"sub %[run_depth], %[run_depth], #32\n"
".word 0x6e8a95b6 // udot v22.4s, v13.16b, v10.16b\n"
".word 0x6e8b95b7 // udot v23.4s, v13.16b, v11.16b\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8895d8 // udot v24.4s, v14.16b, v8.16b\n"
".word 0x6e8995d9 // udot v25.4s, v14.16b, v9.16b\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8a95da // udot v26.4s, v14.16b, v10.16b\n"
".word 0x6e8b95db // udot v27.4s, v14.16b, v11.16b\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8895fc // udot v28.4s, v15.16b, v8.16b\n"
"prfm pldl1keep, [%[rhs_ptr], #128]\n"
".word 0x6e8995fd // udot v29.4s, v15.16b, v9.16b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"cmp %w[run_depth], #32\n"
".word 0x6e8a95fe // udot v30.4s, v15.16b, v10.16b\n"
"prfm pldl1keep, [%[lhs_ptr], #128]\n"
".word 0x6e8b95ff // udot v31.4s, v15.16b, v11.16b\n"
"bge 3b\n"
"cmp %w[run_depth], #0\n"
"beq 1f\n"
"2:\n"
"subs %w[run_depth], %w[run_depth], #16\n"
".word 0x6e809490 // udot v16.4s, v4.16b, v0.16b\n"
".word 0x6e819491 // udot v17.4s, v4.16b, v1.16b\n"
".word 0x6e829492 // udot v18.4s, v4.16b, v2.16b\n"
".word 0x6e839493 // udot v19.4s, v4.16b, v3.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8094b4 // udot v20.4s, v5.16b, v0.16b\n"
".word 0x6e8194b5 // udot v21.4s, v5.16b, v1.16b\n"
".word 0x6e8294b6 // udot v22.4s, v5.16b, v2.16b\n"
".word 0x6e8394b7 // udot v23.4s, v5.16b, v3.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8094d8 // udot v24.4s, v6.16b, v0.16b\n"
".word 0x6e8194d9 // udot v25.4s, v6.16b, v1.16b\n"
".word 0x6e8294da // udot v26.4s, v6.16b, v2.16b\n"
".word 0x6e8394db // udot v27.4s, v6.16b, v3.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
".word 0x6e8094fc // udot v28.4s, v7.16b, v0.16b\n"
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8194fd // udot v29.4s, v7.16b, v1.16b\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8294fe // udot v30.4s, v7.16b, v2.16b\n"
"ld1 {v2.16b}, [%[rhs_ptr]], #16\n"
".word 0x6e8394ff // udot v31.4s, v7.16b, v3.16b\n"
"ld1 {v3.16b}, [%[rhs_ptr]], #16\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"bne 2b\n"
"1:\n"
".word 0x6e809490 // udot v16.4s, v4.16b, v0.16b\n"
".word 0x6e819491 // udot v17.4s, v4.16b, v1.16b\n"
".word 0x6e829492 // udot v18.4s, v4.16b, v2.16b\n"
".word 0x6e839493 // udot v19.4s, v4.16b, v3.16b\n"
".word 0x6e8094b4 // udot v20.4s, v5.16b, v0.16b\n"
".word 0x6e8194b5 // udot v21.4s, v5.16b, v1.16b\n"
".word 0x6e8294b6 // udot v22.4s, v5.16b, v2.16b\n"
".word 0x6e8394b7 // udot v23.4s, v5.16b, v3.16b\n"
".word 0x6e8094d8 // udot v24.4s, v6.16b, v0.16b\n"
".word 0x6e8194d9 // udot v25.4s, v6.16b, v1.16b\n"
".word 0x6e8294da // udot v26.4s, v6.16b, v2.16b\n"
".word 0x6e8394db // udot v27.4s, v6.16b, v3.16b\n"
".word 0x6e8094fc // udot v28.4s, v7.16b, v0.16b\n"
".word 0x6e8194fd // udot v29.4s, v7.16b, v1.16b\n"
".word 0x6e8294fe // udot v30.4s, v7.16b, v2.16b\n"
".word 0x6e8394ff // udot v31.4s, v7.16b, v3.16b\n"
// Load accumulators from memory
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"mov x0, %[dst_ptr]\n"
// Reduce aggregators horizontally
"addp v0.4s, v16.4s, v20.4s\n"
"addp v1.4s, v17.4s, v21.4s\n"
"addp v2.4s, v18.4s, v22.4s\n"
"addp v3.4s, v19.4s, v23.4s\n"
"addp v4.4s, v24.4s, v28.4s\n"
"addp v5.4s, v25.4s, v29.4s\n"
"addp v6.4s, v26.4s, v30.4s\n"
"addp v7.4s, v27.4s, v31.4s\n"
"addp v12.4s, v0.4s, v4.4s\n"
"addp v13.4s, v1.4s, v5.4s\n"
"addp v14.4s, v2.4s, v6.4s\n"
"addp v15.4s, v3.4s, v7.4s\n"
// Add to the accumulators loaded from memory
"add v8.4s, v8.4s, v12.4s\n"
"add v9.4s, v9.4s, v13.4s\n"
"add v10.4s, v10.4s, v14.4s\n"
"add v11.4s, v11.4s, v15.4s\n"
// Store accumulators back to memory
"st1 {v8.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[dst_ptr] "+r"(dst_ptr), [run_depth] "+r"(run_depth),
[dst_col_stride] "+r"(dst_col_stride)
: // inputs
[start_depth] "r"(start_depth)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// Fast kernel operating on int8 operands with 7-bit range.
// It is assumed that one of the two operands only takes values in [-63, 63],
// while the other take values in [-64, 63].
// With this restriction, it is possible to multiply-accumulate operands into
// a 16-bit integer eight times without overflow.
struct NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<2, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
#define GEMMLOWP_LABEL_64_DEPTH_LOOP "1"
#define GEMMLOWP_LABEL_64_DEPTH_AFTER_LOOP "2"
#define GEMMLOWP_LABEL_16_DEPTH_LOOP "3"
#define GEMMLOWP_LABEL_16_DEPTH_AFTER_LOOP "4"
AccumulatorType* dst_ptr = accum_ptr;
asm volatile(
// Overview of register layout:
//
// A 4x16 block of Lhs is stored in 8 bit in v0--v7.
// A 2x16 block of Rhs is stored in 8 bit in v8--v15.
//
// A 4x2 block of global accumulators is stored in v24-v31 (as 4x32 bit
// components which need to be horizontally-added at the end).
//
// A 4x2 block of local accumulators is stored in v16-v23 (as 8x16 bit
// components which are added to global accumulators every 64 depth
// iteration.
//
// The Lhs vectors are multiplied by the Rhs vectors with a widening
// multiply over the 8 first levels of depth, producing int16x8
// vectors of products for each position in the accumulator matrix.
//
// Like the trick used in the fast 8-bit kernel, the operands are
// restricted to 7-bit range [-2^6, 2^6) so their products are in range
// [-2^12, 2^12 -1). This enables adding eight such products without any
// risk of overflowing int16, equating to 64 levels of depth before
// horizontally adding these int16x8 accumulators into the final int32x4
// accumulators.
//
// Register layout including both local and global accumulators.
// Since we do not have enough registers to store all Lhs values, we
// reuse the same registers v0--v7 to load the rest of the Lhs values.
//
// +-----+-----+
// | v8 | v9 |
// Rhs +-----+-----+
// | v10 | v11 |
// +-----+-----+
// | v12 | v13 |
// +-----+-----+
// | v14 | v15 |
// Lhs +-----+-----+
// +----+----+----+----+ - - +-----+-----+ +--------+--------+
// | v0 | v4 | v0 | v4 | | v16 | v20 | | v24.4s | v28.4s |
// | v1 | v5 | v1 | v5 | | v17 | v21 | -> | v25.4s | v29.4s |
// | v2 | v6 | v2 | v6 | | v18 | v22 | | v26.4s | v30.4s |
// | v3 | v7 | v3 | v7 | | v19 | v23 | | v27.4s | v31.4s |
// +----+----+----+----+ - - +-----+-----+ +--------+--------+
//
// Local Accumulator Global Accumulator
//
// Clear accumulators.
"dup v16.4s, wzr\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"dup v24.4s, wzr\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"dup v17.4s, wzr\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"dup v25.4s, wzr\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"dup v18.4s, wzr\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"dup v26.4s, wzr\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"dup v19.4s, wzr\n"
"dup v27.4s, wzr\n"
"dup v20.4s, wzr\n"
"dup v28.4s, wzr\n"
"dup v21.4s, wzr\n"
"dup v29.4s, wzr\n"
"dup v22.4s, wzr\n"
"dup v30.4s, wzr\n"
"dup v23.4s, wzr\n"
"dup v31.4s, wzr\n"
"cmp %w[depth], #64\n"
"blt " GEMMLOWP_LABEL_64_DEPTH_AFTER_LOOP "f\n"
//"loop_%=:\n"
GEMMLOWP_LABEL_64_DEPTH_LOOP
":\n"
"subs %w[depth], %w[depth], #64\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"sadalp v24.4s, v16.8h\n"
"smull v16.8h, v0.8b, v8.8b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"sadalp v25.4s, v17.8h\n"
"smull v17.8h, v1.8b, v8.8b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"sadalp v26.4s, v18.8h\n"
"smull v18.8h, v2.8b, v8.8b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"sadalp v27.4s, v19.8h\n"
"smull v19.8h, v3.8b, v8.8b\n"
"ld1 {v10.16b}, [%[rhs_ptr]], #16\n"
"sadalp v28.4s, v20.8h\n"
"smull v20.8h, v0.8b, v9.8b\n"
"ld1 {v11.16b}, [%[rhs_ptr]], #16\n"
"sadalp v29.4s, v21.8h\n"
"smull v21.8h, v1.8b, v9.8b\n"
"ld1 {v12.16b}, [%[rhs_ptr]], #16\n"
"sadalp v30.4s, v22.8h\n"
"smull v22.8h, v2.8b, v9.8b\n"
"ld1 {v13.16b}, [%[rhs_ptr]], #16\n"
"sadalp v31.4s, v23.8h\n"
"smull v23.8h, v3.8b, v9.8b\n"
"cmp %w[depth], #64\n"
"smlal2 v16.8h, v0.16b, v8.16b\n"
"ld1 {v14.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v17.8h, v1.16b, v8.16b\n"
"ld1 {v15.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v18.8h, v2.16b, v8.16b\n"
"smlal2 v19.8h, v3.16b, v8.16b\n"
"smlal2 v20.8h, v0.16b, v9.16b\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v21.8h, v1.16b, v9.16b\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v22.8h, v2.16b, v9.16b\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v23.8h, v3.16b, v9.16b\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"smlal v16.8h, v4.8b, v10.8b\n"
"smlal v17.8h, v5.8b, v10.8b\n"
"smlal v18.8h, v6.8b, v10.8b\n"
"smlal v19.8h, v7.8b, v10.8b\n"
"smlal v20.8h, v4.8b, v11.8b\n"
"smlal v21.8h, v5.8b, v11.8b\n"
"smlal v22.8h, v6.8b, v11.8b\n"
"smlal v23.8h, v7.8b, v11.8b\n"
"smlal2 v16.8h, v4.16b, v10.16b\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v17.8h, v5.16b, v10.16b\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v18.8h, v6.16b, v10.16b\n"
"smlal2 v19.8h, v7.16b, v10.16b\n"
"smlal2 v20.8h, v4.16b, v11.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v21.8h, v5.16b, v11.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v22.8h, v6.16b, v11.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v23.8h, v7.16b, v11.16b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"smlal v16.8h, v0.8b, v12.8b\n"
"smlal v17.8h, v1.8b, v12.8b\n"
"smlal v18.8h, v2.8b, v12.8b\n"
"smlal v19.8h, v3.8b, v12.8b\n"
"smlal v20.8h, v0.8b, v13.8b\n"
"smlal v21.8h, v1.8b, v13.8b\n"
"smlal v22.8h, v2.8b, v13.8b\n"
"smlal v23.8h, v3.8b, v13.8b\n"
"smlal2 v16.8h, v0.16b, v12.16b\n"
"smlal2 v17.8h, v1.16b, v12.16b\n"
"smlal2 v18.8h, v2.16b, v12.16b\n"
"smlal2 v19.8h, v3.16b, v12.16b\n"
"smlal2 v20.8h, v0.16b, v13.16b\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v21.8h, v1.16b, v13.16b\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v22.8h, v2.16b, v13.16b\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v23.8h, v3.16b, v13.16b\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"smlal v16.8h, v4.8b, v14.8b\n"
"smlal v17.8h, v5.8b, v14.8b\n"
"smlal v18.8h, v6.8b, v14.8b\n"
"smlal v19.8h, v7.8b, v14.8b\n"
"smlal v20.8h, v4.8b, v15.8b\n"
"smlal v21.8h, v5.8b, v15.8b\n"
"smlal v22.8h, v6.8b, v15.8b\n"
"smlal v23.8h, v7.8b, v15.8b\n"
"smlal2 v16.8h, v4.16b, v14.16b\n"
"smlal2 v17.8h, v5.16b, v14.16b\n"
"smlal2 v18.8h, v6.16b, v14.16b\n"
"smlal2 v19.8h, v7.16b, v14.16b\n"
"smlal2 v20.8h, v4.16b, v15.16b\n"
"smlal2 v21.8h, v5.16b, v15.16b\n"
"smlal2 v22.8h, v6.16b, v15.16b\n"
"smlal2 v23.8h, v7.16b, v15.16b\n"
"bge " GEMMLOWP_LABEL_64_DEPTH_LOOP "b\n"
GEMMLOWP_LABEL_64_DEPTH_AFTER_LOOP
":\n"
"cmp %w[depth], #16\n"
"blt " GEMMLOWP_LABEL_16_DEPTH_AFTER_LOOP "f\n"
//"loop_%=:\n"
GEMMLOWP_LABEL_16_DEPTH_LOOP
":\n"
"sadalp v24.4s, v16.8h\n"
"smull v16.8h, v0.8b, v8.8b\n"
"subs %w[depth], %w[depth], #16\n"
"sadalp v25.4s, v17.8h\n"
"smull v17.8h, v1.8b, v8.8b\n"
"sadalp v26.4s, v18.8h\n"
"smull v18.8h, v2.8b, v8.8b\n"
"sadalp v27.4s, v19.8h\n"
"smull v19.8h, v3.8b, v8.8b\n"
"sadalp v28.4s, v20.8h\n"
"smull v20.8h, v0.8b, v9.8b\n"
"sadalp v29.4s, v21.8h\n"
"smull v21.8h, v1.8b, v9.8b\n"
"sadalp v30.4s, v22.8h\n"
"smull v22.8h, v2.8b, v9.8b\n"
"sadalp v31.4s, v23.8h\n"
"smull v23.8h, v3.8b, v9.8b\n"
"cmp %w[depth], #16\n"
"smlal2 v16.8h, v0.16b, v8.16b\n"
"smlal2 v17.8h, v1.16b, v8.16b\n"
"smlal2 v18.8h, v2.16b, v8.16b\n"
"smlal2 v19.8h, v3.16b, v8.16b\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"smlal2 v20.8h, v0.16b, v9.16b\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v21.8h, v1.16b, v9.16b\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v22.8h, v2.16b, v9.16b\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"smlal2 v23.8h, v3.16b, v9.16b\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"bge " GEMMLOWP_LABEL_16_DEPTH_LOOP "b\n"
GEMMLOWP_LABEL_16_DEPTH_AFTER_LOOP
":\n"
"sadalp v24.4s, v16.8h\n"
"sadalp v25.4s, v17.8h\n"
"sadalp v26.4s, v18.8h\n"
"sadalp v27.4s, v19.8h\n"
"sadalp v28.4s, v20.8h\n"
"sadalp v29.4s, v21.8h\n"
"sadalp v30.4s, v22.8h\n"
"sadalp v31.4s, v23.8h\n"
// Reduce aggregators horizontally.
"addp v0.4s, v24.4s, v25.4s\n"
"addp v1.4s, v26.4s, v27.4s\n"
"addp v2.4s, v28.4s, v29.4s\n"
"addp v3.4s, v30.4s, v31.4s\n"
"addp v4.4s, v0.4s, v1.4s\n"
"addp v5.4s, v2.4s, v3.4s\n"
// Load accumulators from memory.
"mov x0, %[dst_ptr]\n"
"ld1 {v6.16b}, [x0], #16\n"
"ld1 {v7.16b}, [x0], #16\n"
// Add to the accumulators loaded from memory.
"add v6.4s, v6.4s, v4.4s\n"
"add v7.4s, v7.4s, v5.4s\n"
// Store accumulators back to memory.
"mov x0, %[dst_ptr]\n"
"st1 {v6.16b}, [x0], #16\n"
"st1 {v7.16b}, [x0], #16\n"
:
// Outputs.
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[dst_ptr] "+r"(dst_ptr), [depth] "+r"(depth)
:
// Inputs.
:
// Clobbers.
"cc", "memory",
// We use these NEON registers
"v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7", "v8", "v9", "v10",
"v11", "v12", "v13", "v14", "v15", "v16", "v17", "v18", "v19", "v20",
"v21", "v22", "v23", "v24", "v25", "v26", "v27", "v28", "v29", "v30",
"v31", "x0");
}
};
SET_7BIT_RANGES(NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits);
// Kernel operating on int8 operands with 4.25-bit range.
// It is assumed that one of the two operands only takes values in [-7, 7],
// while the other take values in [-9, 9].
// With this restriction, it is possible to multiply-accumulate operands into
// a 16-bit integer thirty-two times without overflow.
struct NEON_64bit_GEMM_Int425Operands {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 32, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<2, 32, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
#define GEMMLOWP_LABEL_512_DEPTH_LOOP "1"
#define GEMMLOWP_LABEL_32_DEPTH_LOOP "2"
#define GEMMLOWP_LABEL_32_DEPTH_AFTER_LOOP "3"
AccumulatorType* dst_ptr = accum_ptr;
int outer_depth = depth / 512 + 1;
asm volatile(
// Overview of register layout:
//
// A 4x32 block of Lhs is stored in 8 bit in v0--v7.
// A 2x32 block of Rhs is stored in 8 bit in v8--v11.
//
// A 4x2 block of global accumulators is stored in v24-v31 (as 4x32 bit
// components which need to be horizontally-added at the end).
//
// A 4x2 block of local accumulators is stored in v16-v23 (as 8x16 bit
// components which are horizontally-added to global accumulators every
// 512 depth iteration.
//
// The Lhs vectors are multiplied by the Rhs vectors with a multiply
// over the 16 first levels of depth, producing int8x16 vectors of
// products for each position in the accumulator matrix.
//
// Like the trick used in the fast 8-bit and 7-bit kernels, the operands
// are restricted to 4.25-bit range, [-7, 7] for one operand and [-9, 9]
// for the other operand. This enables adding two such products without
// any risk of overflowing int8, and thiry-two such products without
// overflowing int16. This equates to 512 levels of depth before
// horizontally adding these int16x8 accumulators into the final int32x4
// accumulators.
//
// Register layout (ignoring the v12--v15 temporary 8-bit accumulators).
// Since we do not have enough registers to store all Lhs values and Rhs
// values, we reuse the same registers v0--v7 to load subsequent Lhs
// values and v8-v11 to subsequent Rhs values.
//
// +-----+-----+
// | v8 | v9 |
// Rhs +-----+-----+
// | v10 | v11 |
// +-----+-----+
// | v8 | v9 |
// +-----+-----+
// | v10 | v11 |
// Lhs +-----+-----+
// +----+----+----+----+ - - +-----+-----+ +--------+--------+
// | v0 | v4 | v0 | v4 | | v16 | v17 | | v24.4s | v25.4s |
// | v1 | v5 | v1 | v5 | | v18 | v19 | -> | v26.4s | v27.4s |
// | v2 | v6 | v2 | v6 | | v20 | v21 | | v28.4s | v29.4s |
// | v3 | v7 | v3 | v7 | | v22 | v23 | | v30.4s | v31.4s |
// +----+----+----+----+ - - +-----+-----+ +--------+--------+
//
// Local Accumulator Global Accumulator
//
// Clear global accumulators.
"dup v24.4s, wzr\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"dup v25.4s, wzr\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"dup v26.4s, wzr\n"
"ld1 {v10.16b}, [%[rhs_ptr]], #16\n"
"dup v27.4s, wzr\n"
"ld1 {v11.16b}, [%[rhs_ptr]], #16\n"
"dup v28.4s, wzr\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"dup v29.4s, wzr\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"dup v30.4s, wzr\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"dup v31.4s, wzr\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
//"loop_%=:\n"
GEMMLOWP_LABEL_512_DEPTH_LOOP
":\n"
// Clear local accumulators.
"dup v16.8h, wzr\n"
"dup v17.8h, wzr\n"
"dup v18.8h, wzr\n"
"mov x1, #512\n"
"dup v19.8h, wzr\n"
"dup v20.8h, wzr\n"
"dup v21.8h, wzr\n"
"dup v22.8h, wzr\n"
"dup v23.8h, wzr\n"
//"loop_%=:\n"
GEMMLOWP_LABEL_32_DEPTH_LOOP
":\n"
"mul v12.16b, v0.16b, v8.16b\n"
"mul v13.16b, v0.16b, v10.16b\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"mul v14.16b, v2.16b, v8.16b\n"
"mul v15.16b, v2.16b, v10.16b\n"
"mla v12.16b, v1.16b, v9.16b\n"
"mla v13.16b, v1.16b, v11.16b\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"mla v14.16b, v3.16b, v9.16b\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"mla v15.16b, v3.16b, v11.16b\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"sadalp v16.8h, v12.16b\n"
"sadalp v17.8h, v13.16b\n"
"subs %w[depth], %w[depth], #32\n"
"sadalp v18.8h, v14.16b\n"
"sadalp v19.8h, v15.16b\n"
"subs x1, x1, #32\n"
"mul v12.16b, v4.16b, v8.16b\n"
"mul v13.16b, v4.16b, v10.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"mul v14.16b, v6.16b, v8.16b\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"mul v15.16b, v6.16b, v10.16b\n"
"mla v12.16b, v5.16b, v9.16b\n"
"mla v13.16b, v5.16b, v11.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"mla v14.16b, v7.16b, v9.16b\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"mla v15.16b, v7.16b, v11.16b\n"
"ld1 {v10.16b}, [%[rhs_ptr]], #16\n"
"sadalp v20.8h, v12.16b\n"
"ld1 {v11.16b}, [%[rhs_ptr]], #16\n"
"sadalp v21.8h, v13.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"sadalp v22.8h, v14.16b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"sadalp v23.8h, v15.16b\n"
"mul v12.16b, v0.16b, v8.16b\n"
"mul v13.16b, v0.16b, v10.16b\n"
"ld1 {v0.16b}, [%[lhs_ptr]], #16\n"
"mul v14.16b, v2.16b, v8.16b\n"
"mul v15.16b, v2.16b, v10.16b\n"
"mla v12.16b, v1.16b, v9.16b\n"
"mla v13.16b, v1.16b, v11.16b\n"
"ld1 {v1.16b}, [%[lhs_ptr]], #16\n"
"mla v14.16b, v3.16b, v9.16b\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
"mla v15.16b, v3.16b, v11.16b\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n"
"sadalp v16.8h, v12.16b\n"
"sadalp v17.8h, v13.16b\n"
"sadalp v18.8h, v14.16b\n"
"sadalp v19.8h, v15.16b\n"
"mul v12.16b, v4.16b, v8.16b\n"
"mul v13.16b, v4.16b, v10.16b\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n"
"mul v14.16b, v6.16b, v8.16b\n"
"ld1 {v8.16b}, [%[rhs_ptr]], #16\n"
"mul v15.16b, v6.16b, v10.16b\n"
"mla v12.16b, v5.16b, v9.16b\n"
"mla v13.16b, v5.16b, v11.16b\n"
"ld1 {v5.16b}, [%[lhs_ptr]], #16\n"
"mla v14.16b, v7.16b, v9.16b\n"
"ld1 {v9.16b}, [%[rhs_ptr]], #16\n"
"mla v15.16b, v7.16b, v11.16b\n"
"ld1 {v10.16b}, [%[rhs_ptr]], #16\n"
"sadalp v20.8h, v12.16b\n"
"ld1 {v11.16b}, [%[rhs_ptr]], #16\n"
"sadalp v21.8h, v13.16b\n"
"ld1 {v6.16b}, [%[lhs_ptr]], #16\n"
"sadalp v22.8h, v14.16b\n"
"ld1 {v7.16b}, [%[lhs_ptr]], #16\n"
"sadalp v23.8h, v15.16b\n"
"beq " GEMMLOWP_LABEL_32_DEPTH_AFTER_LOOP
"f\n"
"cmp %w[depth], #0\n"
"bne " GEMMLOWP_LABEL_32_DEPTH_LOOP "b\n"
GEMMLOWP_LABEL_32_DEPTH_AFTER_LOOP
":\n"
// Pairwise add 16-bit local accums to 32-bit global accums.
"sadalp v24.4s, v16.8h\n"
"sadalp v25.4s, v17.8h\n"
"sadalp v26.4s, v18.8h\n"
"sadalp v27.4s, v19.8h\n"
"sadalp v28.4s, v20.8h\n"
"sadalp v29.4s, v21.8h\n"
"sadalp v30.4s, v22.8h\n"
"sadalp v31.4s, v23.8h\n"
"bne " GEMMLOWP_LABEL_512_DEPTH_LOOP
"b\n"
// Reduce aggregators horizontally.
"addp v0.4s, v24.4s, v26.4s\n"
"addp v1.4s, v28.4s, v30.4s\n"
"addp v2.4s, v25.4s, v27.4s\n"
"addp v3.4s, v29.4s, v31.4s\n"
"addp v4.4s, v0.4s, v1.4s\n"
"addp v5.4s, v2.4s, v3.4s\n"
// Load accumulators from memory.
"mov x0, %[dst_ptr]\n"
"ld1 {v6.16b}, [x0], #16\n"
"ld1 {v7.16b}, [x0], #16\n"
// Add to the accumulators loaded from memory.
"add v6.4s, v6.4s, v4.4s\n"
"add v7.4s, v7.4s, v5.4s\n"
// Store accumulators back to memory.
"mov x0, %[dst_ptr]\n"
"st1 {v6.16b}, [x0], #16\n"
"st1 {v7.16b}, [x0], #16\n"
:
// Outputs.
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[dst_ptr] "+r"(dst_ptr), [depth] "+r"(depth),
[outer_depth] "+r"(outer_depth)
:
// Inputs.
:
// Clobbers.
"cc", "memory",
// We use these NEON registers
"v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7", "v8", "v9", "v10",
"v11", "v12", "v13", "v14", "v15", "v16", "v17", "v18", "v19", "v20",
"v21", "v22", "v23", "v24", "v25", "v26", "v27", "v28", "v29", "v30",
"v31", "x0", "x1");
}
};
SET_425BIT_RANGES(NEON_64bit_GEMM_Int425Operands);
#ifdef __ARM_FEATURE_DOTPROD
// Kernels utilizing the Armv8.2 Dot Product extension.
//
// The dot product instructions work by taking 4 consecutive 8-bit depth
// values from each operand, multiplying the 4 pairs together and
// accumulating all the results into the corresponding 32-bit accumulator
// lane. As such, the operation is identical to a 32-bit instruction (like
// FMLA used in SGEMM), except that 4 depth values are processed at a time
// instead of 1.
// Thus, this first kernel is a carbon copy of
// "NEON_64bit_GEMM_Float32_WithScalar_A57" (which should provide good
// performance for most processors) below with the opcode (fmla -> udot) and
// types (float32 -> uint8/uint32) changed.
//
// A signed version of this kernel could be produced by replacing "udot"
// with "sdot" - performance should be identical to this udot kernel.
struct NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 4, CellOrder::WidthMajor>, 3>,
KernelSideFormat<CellFormat<4, 4, CellOrder::WidthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.4s}, [x0], #16\n"
"ld1 {v16.4s}, [x0], #16\n"
"ld1 {v24.4s}, [x0], #16\n"
"ld1 {v9.4s}, [x0], #16\n"
"ld1 {v17.4s}, [x0], #16\n"
"ld1 {v25.4s}, [x0], #16\n"
"ld1 {v10.4s}, [x0], #16\n"
"ld1 {v18.4s}, [x0], #16\n"
"ld1 {v26.4s}, [x0], #16\n"
"ld1 {v11.4s}, [x0], #16\n"
"ld1 {v19.4s}, [x0], #16\n"
"ld1 {v27.4s}, [x0], #16\n"
"ld1 {v12.4s}, [x0], #16\n"
"ld1 {v20.4s}, [x0], #16\n"
"ld1 {v28.4s}, [x0], #16\n"
"ld1 {v13.4s}, [x0], #16\n"
"ld1 {v21.4s}, [x0], #16\n"
"ld1 {v29.4s}, [x0], #16\n"
"ld1 {v14.4s}, [x0], #16\n"
"ld1 {v22.4s}, [x0], #16\n"
"ld1 {v30.4s}, [x0], #16\n"
"ld1 {v15.4s}, [x0], #16\n"
"ld1 {v23.4s}, [x0], #16\n"
"ld1 {v31.4s}, [x0], #16\n"
// The start of the loop assumes first Rhs cell is already loaded, so
// do it here for first iteration.
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n"
// And the same for the first Lhs cell.
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Start the MACs at the head of the loop - 1st cell from each side
// already loaded.
".word 0x6f80e048 // udot v8.4s, v2.16b, v0.4b[0]\n"
".word 0x6fa0e049 // udot v9.4s, v2.16b, v0.4b[1]\n"
"ld1 {v1.16b}, [%[rhs_ptr]], #16\n" // Load second Rhs cell.
".word 0x6f80e84a // udot v10.4s, v2.16b, v0.4b[2]\n"
".word 0x6fa0e84b // udot v11.4s, v2.16b, v0.4b[3]\n"
"ld1 {v3.16b}, [%[lhs_ptr]], #16\n" // Load second Lhs cell.
".word 0x6f81e04c // udot v12.4s, v2.16b, v1.4b[0]\n"
".word 0x6fa1e04d // udot v13.4s, v2.16b, v1.4b[1]\n"
"ld1 {v4.16b}, [%[lhs_ptr]], #16\n" // Load third Lhs cell.
".word 0x6f81e84e // udot v14.4s, v2.16b, v1.4b[2]\n"
".word 0x6fa1e84f // udot v15.4s, v2.16b, v1.4b[3]\n"
"ld1 {v2.16b}, [%[lhs_ptr]], #16\n" // Done with first Lhs cell - load
// for the next iteration early.
".word 0x6f80e070 // udot v16.4s, v3.16b, v0.4b[0]\n"
".word 0x6fa0e071 // udot v17.4s, v3.16b, v0.4b[1]\n"
".word 0x6f80e872 // udot v18.4s, v3.16b, v0.4b[2]\n"
".word 0x6fa0e873 // udot v19.4s, v3.16b, v0.4b[3]\n"
".word 0x6f81e074 // udot v20.4s, v3.16b, v1.4b[0]\n"
".word 0x6fa1e075 // udot v21.4s, v3.16b, v1.4b[1]\n"
".word 0x6f81e876 // udot v22.4s, v3.16b, v1.4b[2]\n"
".word 0x6fa1e877 // udot v23.4s, v3.16b, v1.4b[3]\n"
".word 0x6f80e098 // udot v24.4s, v4.16b, v0.4b[0]\n"
".word 0x6fa0e099 // udot v25.4s, v4.16b, v0.4b[1]\n"
".word 0x6f80e89a // udot v26.4s, v4.16b, v0.4b[2]\n"
".word 0x6fa0e89b // udot v27.4s, v4.16b, v0.4b[3]\n"
"ld1 {v0.16b}, [%[rhs_ptr]], #16\n" // Done with the first Rhs cell -
// load for the next iteration early.
".word 0x6f81e09c // udot v28.4s, v4.16b, v1.4b[0]\n"
".word 0x6fa1e09d // udot v29.4s, v4.16b, v1.4b[1]\n"
// Loop. Decrement loop index (depth) by 4 as udot processes 4
// depth values.
"subs %w[depth], %w[depth], #4\n"
".word 0x6f81e89e // udot v30.4s, v4.16b, v1.4b[2]\n"
".word 0x6fa1e89f // udot v31.4s, v4.16b, v1.4b[3]\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// As above, except tuned for Cortex-A55r1.
//
// Similarly, this is a clone of NEON_64bit_GEMM_Float32_WithScalar_A55r1
// with the names changed.
struct NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct_A55r1 {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 4, CellOrder::WidthMajor>, 3>,
KernelSideFormat<CellFormat<4, 4, CellOrder::WidthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.4s}, [x0], #16\n"
"ld1 {v16.4s}, [x0], #16\n"
"ld1 {v24.4s}, [x0], #16\n"
"ld1 {v9.4s}, [x0], #16\n"
"ld1 {v17.4s}, [x0], #16\n"
"ld1 {v25.4s}, [x0], #16\n"
"ld1 {v10.4s}, [x0], #16\n"
"ld1 {v18.4s}, [x0], #16\n"
"ld1 {v26.4s}, [x0], #16\n"
"ld1 {v11.4s}, [x0], #16\n"
"ld1 {v19.4s}, [x0], #16\n"
"ld1 {v27.4s}, [x0], #16\n"
"ld1 {v12.4s}, [x0], #16\n"
"ld1 {v20.4s}, [x0], #16\n"
"ld1 {v28.4s}, [x0], #16\n"
"ld1 {v13.4s}, [x0], #16\n"
"ld1 {v21.4s}, [x0], #16\n"
"ld1 {v29.4s}, [x0], #16\n"
"ld1 {v14.4s}, [x0], #16\n"
"ld1 {v22.4s}, [x0], #16\n"
"ld1 {v30.4s}, [x0], #16\n"
"ld1 {v15.4s}, [x0], #16\n"
"ld1 {v23.4s}, [x0], #16\n"
"ld1 {v31.4s}, [x0], #16\n"
// For details on how this kernel works, see the Float32 kernel below.
"ldr d0, [%[rhs_ptr]]\n"
"ldr x18, [%[rhs_ptr], #8]\n"
"ldr q2, [%[lhs_ptr]]\n"
"ldr q3, [%[lhs_ptr], #16]\n"
GEMMLOWP_LABEL_LOOP
":\n"
".word 0x6f80e048 // udot v8.4s, v2.16b, v0.4b[0]\n"
"ldr d1, [%[rhs_ptr], #16]\n" // Bottom half of v1
".word 0x6fa0e049 // udot v9.4s, v2.16b, v0.4b[1]\n"
"ins v0.d[1], x18\n" // Finish loading v0
".word 0x6f80e070 // udot v16.4s, v3.16b, v0.4b[0]\n" // out of
// sequence -
// used to
// reduce
// load/use
// pressure.
"ldr x18, [%[rhs_ptr], #24]\n" // Top half of v1 to X register
".word 0x6fa0e071 // udot v17.4s, v3.16b, v0.4b[1]\n" // out of
// sequence -
// used to
// reduce
// load/use
// pressure.
"add %[rhs_ptr], %[rhs_ptr], #32\n" // RHS loads complete - increment
// pointer.
".word 0x6f80e84a // udot v10.4s, v2.16b, v0.4b[2]\n"
"ldr d4, [%[lhs_ptr], #32]\n" // Bottom half of v4
".word 0x6fa0e84b // udot v11.4s, v2.16b, v0.4b[3]\n"
"ins v1.d[1], x18\n" // Finish loading v1
".word 0x6f81e04c // udot v12.4s, v2.16b, v1.4b[0]\n"
"ldr x18, [%[lhs_ptr], #40]\n" // Top half of v4 to X register
".word 0x6fa1e04d // udot v13.4s, v2.16b, v1.4b[1]\n"
"add %[lhs_ptr], %[lhs_ptr], #48\n" // LHS loads complete - increment
// pointer.
".word 0x6f81e84e // udot v14.4s, v2.16b, v1.4b[2]\n"
".word 0x6fa1e84f // udot v15.4s, v2.16b, v1.4b[3]\n"
"ldr d2, [%[lhs_ptr]]\n" // Bottom half of v2 (for next time)
".word 0x6f80e872 // udot v18.4s, v3.16b, v0.4b[2]\n"
"ins v4.d[1], x18\n" // Finish loading v4
".word 0x6fa0e873 // udot v19.4s, v3.16b, v0.4b[3]\n"
"ldr x18, [%[lhs_ptr], #8]\n" // Top half of next v2 to X register
".word 0x6f81e074 // udot v20.4s, v3.16b, v1.4b[0]\n"
"subs %w[depth], %w[depth], #4\n"
".word 0x6fa1e075 // udot v21.4s, v3.16b, v1.4b[1]\n"
".word 0x6f81e876 // udot v22.4s, v3.16b, v1.4b[2]\n"
".word 0x6fa1e877 // udot v23.4s, v3.16b, v1.4b[3]\n"
"ldr d3, [%[lhs_ptr], #16]\n" // Bottom half of v3 (for next time)
".word 0x6f80e098 // udot v24.4s, v4.16b, v0.4b[0]\n"
"ins v2.d[1], x18\n" // Finish loading next v2
".word 0x6fa0e099 // udot v25.4s, v4.16b, v0.4b[1]\n"
"ldr x18, [%[lhs_ptr], #24]\n" // Top half of next v3 to X register
".word 0x6f80e89a // udot v26.4s, v4.16b, v0.4b[2]\n"
".word 0x6fa0e89b // udot v27.4s, v4.16b, v0.4b[3]\n"
"ldr d0, [%[rhs_ptr]]\n" // Bottom half of v0 (for next time)
".word 0x6f81e09c // udot v28.4s, v4.16b, v1.4b[0]\n"
"ins v3.d[1], x18\n" // Finish loading next v3
".word 0x6fa1e09d // udot v29.4s, v4.16b, v1.4b[1]\n"
"ldr x18, [%[rhs_ptr], #8]\n" // Top half of next v0 to X register
".word 0x6f81e89e // udot v30.4s, v4.16b, v1.4b[2]\n"
".word 0x6fa1e89f // udot v31.4s, v4.16b, v1.4b[3]\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.4s}, [x0], #16\n"
"st1 {v16.4s}, [x0], #16\n"
"st1 {v24.4s}, [x0], #16\n"
"st1 {v9.4s}, [x0], #16\n"
"st1 {v17.4s}, [x0], #16\n"
"st1 {v25.4s}, [x0], #16\n"
"st1 {v10.4s}, [x0], #16\n"
"st1 {v18.4s}, [x0], #16\n"
"st1 {v26.4s}, [x0], #16\n"
"st1 {v11.4s}, [x0], #16\n"
"st1 {v19.4s}, [x0], #16\n"
"st1 {v27.4s}, [x0], #16\n"
"st1 {v12.4s}, [x0], #16\n"
"st1 {v20.4s}, [x0], #16\n"
"st1 {v28.4s}, [x0], #16\n"
"st1 {v13.4s}, [x0], #16\n"
"st1 {v21.4s}, [x0], #16\n"
"st1 {v29.4s}, [x0], #16\n"
"st1 {v14.4s}, [x0], #16\n"
"st1 {v22.4s}, [x0], #16\n"
"st1 {v30.4s}, [x0], #16\n"
"st1 {v15.4s}, [x0], #16\n"
"st1 {v23.4s}, [x0], #16\n"
"st1 {v31.4s}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "x18", "v0", "v1", "v2", "v3", "v4", "v5", "v6",
"v7", "v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16",
"v17", "v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26",
"v27", "v28", "v29", "v30", "v31");
}
};
#endif // __ARM_FEATURE_DOTPROD
// We don't actually use int32*int32 in production. This is just an
// experiment to help dissociate the effect of integer-vs-float, from the
// effect of operands width.
struct NEON_64bit_GEMM_Int32_WithScalar {
typedef std::int32_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 2 Rhs cell of size 1x4 each
"ld1 {v0.4s}, [%[rhs_ptr]], #16\n"
"ld1 {v1.4s}, [%[rhs_ptr]], #16\n"
// Load 3 Lhs cells of size 4x1 each
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v3.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v4.4s}, [%[lhs_ptr]], #16\n"
// Multiply-accumulate
"mla v8.4s, v2.4s, v0.s[0]\n"
"mla v9.4s, v2.4s, v0.s[1]\n"
"mla v10.4s, v2.4s, v0.s[2]\n"
"mla v11.4s, v2.4s, v0.s[3]\n"
"mla v12.4s, v2.4s, v1.s[0]\n"
"mla v13.4s, v2.4s, v1.s[1]\n"
"mla v14.4s, v2.4s, v1.s[2]\n"
"mla v15.4s, v2.4s, v1.s[3]\n"
"mla v16.4s, v3.4s, v0.s[0]\n"
"mla v17.4s, v3.4s, v0.s[1]\n"
"mla v18.4s, v3.4s, v0.s[2]\n"
"mla v19.4s, v3.4s, v0.s[3]\n"
"mla v20.4s, v3.4s, v1.s[0]\n"
"mla v21.4s, v3.4s, v1.s[1]\n"
"mla v22.4s, v3.4s, v1.s[2]\n"
"mla v23.4s, v3.4s, v1.s[3]\n"
"mla v24.4s, v4.4s, v0.s[0]\n"
"mla v25.4s, v4.4s, v0.s[1]\n"
"mla v26.4s, v4.4s, v0.s[2]\n"
"mla v27.4s, v4.4s, v0.s[3]\n"
"mla v28.4s, v4.4s, v1.s[0]\n"
"mla v29.4s, v4.4s, v1.s[1]\n"
"mla v30.4s, v4.4s, v1.s[2]\n"
"mla v31.4s, v4.4s, v1.s[3]\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %w[depth], %w[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// Not very efficient kernel, just an experiment to see what we can do
// without using NEON multiply-with-scalar instructions.
struct NEON_64bit_GEMM_Float32_WithVectorDuplicatingScalar {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 2 Rhs cell of size 1x4 each
"ld1 {v5.4s}, [%[rhs_ptr]], #16\n"
"ld1 {v6.4s}, [%[rhs_ptr]], #16\n"
// Load 3 Lhs cells of size 4x1 each
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v3.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v4.4s}, [%[lhs_ptr]], #16\n"
// Multiply-accumulate
"dup v0.4s, v5.s[0]\n"
"dup v1.4s, v5.s[1]\n"
"fmla v8.4s, v2.4s, v0.4s\n"
"fmla v16.4s, v3.4s, v0.4s\n"
"fmla v24.4s, v4.4s, v0.4s\n"
"fmla v9.4s, v2.4s, v1.4s\n"
"fmla v17.4s, v3.4s, v1.4s\n"
"fmla v25.4s, v4.4s, v1.4s\n"
"dup v0.4s, v5.s[2]\n"
"dup v1.4s, v5.s[3]\n"
"fmla v10.4s, v2.4s, v0.4s\n"
"fmla v18.4s, v3.4s, v0.4s\n"
"fmla v26.4s, v4.4s, v0.4s\n"
"fmla v11.4s, v2.4s, v1.4s\n"
"fmla v19.4s, v3.4s, v1.4s\n"
"fmla v27.4s, v4.4s, v1.4s\n"
"dup v0.4s, v6.s[0]\n"
"dup v1.4s, v6.s[1]\n"
"fmla v12.4s, v2.4s, v0.4s\n"
"fmla v20.4s, v3.4s, v0.4s\n"
"fmla v28.4s, v4.4s, v0.4s\n"
"fmla v13.4s, v2.4s, v1.4s\n"
"fmla v21.4s, v3.4s, v1.4s\n"
"fmla v29.4s, v4.4s, v1.4s\n"
"dup v0.4s, v6.s[2]\n"
"dup v1.4s, v6.s[3]\n"
"fmla v14.4s, v2.4s, v0.4s\n"
"fmla v22.4s, v3.4s, v0.4s\n"
"fmla v30.4s, v4.4s, v0.4s\n"
"fmla v15.4s, v2.4s, v1.4s\n"
"fmla v23.4s, v3.4s, v1.4s\n"
"fmla v31.4s, v4.4s, v1.4s\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %w[depth], %w[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// This is the "most natural" kernel, using NEON multiply-with-scalar
// instructions.
struct NEON_64bit_GEMM_Float32_WithScalar {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Load 2 Rhs cell of size 1x4 each
"ld1 {v0.4s}, [%[rhs_ptr]], #16\n"
"ld1 {v1.4s}, [%[rhs_ptr]], #16\n"
// Load 3 Lhs cells of size 4x1 each
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v3.4s}, [%[lhs_ptr]], #16\n"
"ld1 {v4.4s}, [%[lhs_ptr]], #16\n"
// Multiply-accumulate
"fmla v8.4s, v2.4s, v0.s[0]\n"
"fmla v9.4s, v2.4s, v0.s[1]\n"
"fmla v10.4s, v2.4s, v0.s[2]\n"
"fmla v11.4s, v2.4s, v0.s[3]\n"
"fmla v12.4s, v2.4s, v1.s[0]\n"
"fmla v13.4s, v2.4s, v1.s[1]\n"
"fmla v14.4s, v2.4s, v1.s[2]\n"
"fmla v15.4s, v2.4s, v1.s[3]\n"
"fmla v16.4s, v3.4s, v0.s[0]\n"
"fmla v17.4s, v3.4s, v0.s[1]\n"
"fmla v18.4s, v3.4s, v0.s[2]\n"
"fmla v19.4s, v3.4s, v0.s[3]\n"
"fmla v20.4s, v3.4s, v1.s[0]\n"
"fmla v21.4s, v3.4s, v1.s[1]\n"
"fmla v22.4s, v3.4s, v1.s[2]\n"
"fmla v23.4s, v3.4s, v1.s[3]\n"
"fmla v24.4s, v4.4s, v0.s[0]\n"
"fmla v25.4s, v4.4s, v0.s[1]\n"
"fmla v26.4s, v4.4s, v0.s[2]\n"
"fmla v27.4s, v4.4s, v0.s[3]\n"
"fmla v28.4s, v4.4s, v1.s[0]\n"
"fmla v29.4s, v4.4s, v1.s[1]\n"
"fmla v30.4s, v4.4s, v1.s[2]\n"
"fmla v31.4s, v4.4s, v1.s[3]\n"
// Loop. Decrement loop index (depth) by 1, since we just handled 1
// level of depth.
"subs %w[depth], %w[depth], #1\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
// Faster kernel contributed by ARM. Tuned for A57.
struct NEON_64bit_GEMM_Float32_WithScalar_A57 {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
// The start of the loop assumes first Rhs cell is already loaded, so
// do it here for first iteration.
"ld1 {v0.4s}, [%[rhs_ptr]], #16\n"
// And the same for the first Lhs cell.
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Start the MACs at the head of the loop - 1st cell from each side
// already loaded.
"fmla v8.4s, v2.4s, v0.s[0]\n"
"fmla v9.4s, v2.4s, v0.s[1]\n"
"ld1 {v1.4s}, [%[rhs_ptr]], #16\n" // Load second Rhs cell.
"fmla v10.4s, v2.4s, v0.s[2]\n"
"fmla v11.4s, v2.4s, v0.s[3]\n"
"ld1 {v3.4s}, [%[lhs_ptr]], #16\n" // Load second Lhs cell.
"fmla v12.4s, v2.4s, v1.s[0]\n"
"fmla v13.4s, v2.4s, v1.s[1]\n"
"ld1 {v4.4s}, [%[lhs_ptr]], #16\n" // Load third Lhs cell.
"fmla v14.4s, v2.4s, v1.s[2]\n"
"fmla v15.4s, v2.4s, v1.s[3]\n"
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n" // Done with first Lhs cell - load
// for the next iteration early.
"fmla v16.4s, v3.4s, v0.s[0]\n"
"fmla v17.4s, v3.4s, v0.s[1]\n"
"fmla v18.4s, v3.4s, v0.s[2]\n"
"fmla v19.4s, v3.4s, v0.s[3]\n"
"fmla v20.4s, v3.4s, v1.s[0]\n"
"fmla v21.4s, v3.4s, v1.s[1]\n"
"fmla v22.4s, v3.4s, v1.s[2]\n"
"fmla v23.4s, v3.4s, v1.s[3]\n"
"fmla v24.4s, v4.4s, v0.s[0]\n"
"fmla v25.4s, v4.4s, v0.s[1]\n"
"fmla v26.4s, v4.4s, v0.s[2]\n"
"fmla v27.4s, v4.4s, v0.s[3]\n"
"ld1 {v0.4s}, [%[rhs_ptr]], #16\n" // Done with the first Rhs cell -
// load for the next iteration
// early.
"fmla v28.4s, v4.4s, v1.s[0]\n"
"fmla v29.4s, v4.4s, v1.s[1]\n"
// Loop. Decrement loop index (depth) by 1, since we just handled
// 1 level of depth. Do this a bit before the end of the loop for
// better dispatch on A57.
"subs %w[depth], %w[depth], #1\n"
"fmla v30.4s, v4.4s, v1.s[2]\n"
"fmla v31.4s, v4.4s, v1.s[3]\n"
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7",
"v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16", "v17",
"v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26", "v27",
"v28", "v29", "v30", "v31");
}
};
#ifndef __APPLE__
// Faster kernel contributed by ARM. Tuned for A53.
struct NEON_64bit_GEMM_Float32_WithScalar_A53 {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.16b}, [x0], #16\n"
"ld1 {v16.16b}, [x0], #16\n"
"ld1 {v24.16b}, [x0], #16\n"
"ld1 {v9.16b}, [x0], #16\n"
"ld1 {v17.16b}, [x0], #16\n"
"ld1 {v25.16b}, [x0], #16\n"
"ld1 {v10.16b}, [x0], #16\n"
"ld1 {v18.16b}, [x0], #16\n"
"ld1 {v26.16b}, [x0], #16\n"
"ld1 {v11.16b}, [x0], #16\n"
"ld1 {v19.16b}, [x0], #16\n"
"ld1 {v27.16b}, [x0], #16\n"
"ld1 {v12.16b}, [x0], #16\n"
"ld1 {v20.16b}, [x0], #16\n"
"ld1 {v28.16b}, [x0], #16\n"
"ld1 {v13.16b}, [x0], #16\n"
"ld1 {v21.16b}, [x0], #16\n"
"ld1 {v29.16b}, [x0], #16\n"
"ld1 {v14.16b}, [x0], #16\n"
"ld1 {v22.16b}, [x0], #16\n"
"ld1 {v30.16b}, [x0], #16\n"
"ld1 {v15.16b}, [x0], #16\n"
"ld1 {v23.16b}, [x0], #16\n"
"ld1 {v31.16b}, [x0], #16\n"
// For A53, a very different-looking loop is needed.
//
// The main reason for this is that on A53 128-bit loads take two
// cycles during which no dual issue can occur. Doing two separate
// 64-bit loads avoids this issue - they each take one cycle and are
// able to dual issue. Since vector register loads don't dual issue
// with FMLA, we load half the register as normal and the other half
// into an integer register. This second half can then be moved into
// place later with an INS instruction - which will dual issue with a
// later FP load.
//
// For this kernel there are approximately 3 times as many multiplies
// as loads, so it makes sense to structure the loop into blocks of 4
// cycles, with 1 dedicated "load cycle" and 3 "multiply cycles" per
// block. Strictly preserving this structure with NOPs where no load
// is needed seems to result in higher performance.
//
// Choice of x18 to store the upper halves on their way into the
// vector registers is arbitrary. Added to the clobber list so that
// the compiler will make it available.
//
//
// At the start of the loop, it is assumed that v0 is "half loaded" -
// bottom half in place in d0 and the upper half in x18 ready to
// insert. So set that up here for the first iteration:
"ldr d0, [%[rhs_ptr]]\n" // Bottom half of first Rhs cell
"ldr x18, [%[rhs_ptr], #8]\n" // Upper half
"add %[rhs_ptr], %[rhs_ptr], #16\n" // Separate increment (needed as
// there is no operation to load at
// reg + 8 but then increment reg
// by 16).
// v2 should be fully loaded - as it's outside the loop proper it's fine
// to use a 128-bit load here.
"ld1 {v2.4s}, [%[lhs_ptr]], #16\n" // first Lhs cell
GEMMLOWP_LABEL_LOOP
":\n"
// First block of four cycles. Multplies all require v2 and v0; v2 is
// loaded earlier and v0 is half loaded and completed in the load
// cycle at the start.
"ldr d1, [%[rhs_ptr]]\n" // "load" cycle - loading bottom half of v1
// (second Rhs cell).
"ins v0.d[1], x18\n" // "load" cycle - moving the upper half of v0 into
// place.
"fmla v8.4s, v2.4s, v0.s[0]\n" // "fmla" cycle 1 - first multiply.
"ldr x18, [%[rhs_ptr], #8]\n" // "fmla" cycle 1 - load upper half of v1
// into x18.
"fmla v9.4s, v2.4s, v0.s[1]\n" // "fmla" cycle 2 - second multiply
"add %[rhs_ptr], %[rhs_ptr], #16\n" // "fmla" cycle 2 - increment Rhs
// pointer (if needed)
"fmla v10.4s, v2.4s, v0.s[2]\n" // "fmla" cycle 3 - third multiply. No
// more work to dual issue.
// Second block. Start loading v3 (second Lhs cell), finish loading v1.
"ldr d3, [%[lhs_ptr]]\n"
"ins v1.d[1], x18\n" // v1 ready here.
"fmla v11.4s, v2.4s, v0.s[3]\n"
"ldr x18, [%[lhs_ptr], #8]\n"
"fmla v12.4s, v2.4s, v1.s[0]\n" // First use of v1.
"add %[lhs_ptr], %[lhs_ptr], #16\n"
"fmla v13.4s, v2.4s, v1.s[1]\n"
// Third block. Start loading v4 (third Lhs cell), finish loading v3.
"ldr d4, [%[lhs_ptr]]\n"
"ins v3.d[1], x18\n" // v3 ready here.
"fmla v14.4s, v2.4s, v1.s[2]\n"
"ldr x18, [%[lhs_ptr], #8]\n"
"fmla v15.4s, v2.4s, v1.s[3]\n"
"add %[lhs_ptr], %[lhs_ptr], #16\n"
"fmla v16.4s, v3.4s, v0.s[0]\n" // First use of v3.
// Fourth block. v2 (first Lhs cell) is now finished with, so start
// loading value for next iteration. Finish loading v4.
"ldr d2, [%[lhs_ptr]]\n"
"ins v4.d[1], x18\n" // v4 ready here.
"fmla v17.4s, v3.4s, v0.s[1]\n"
"ldr x18, [%[lhs_ptr], #8]\n"
"fmla v18.4s, v3.4s, v0.s[2]\n"
"add %[lhs_ptr], %[lhs_ptr], #16\n"
"fmla v19.4s, v3.4s, v0.s[3]\n"
// Fifth block, finish loading v2. No new load to start as the other
// registers are all still live.
"ins v2.d[1], x18\n"
"fmla v20.4s, v3.4s, v1.s[0]\n"
"fmla v21.4s, v3.4s, v1.s[1]\n"
"fmla v22.4s, v3.4s, v1.s[2]\n"
// Sixth block, nothing to load. 2 nops needed as a single nop would
// dual issue with the FMLA and break the timing.
"nop\n"
"nop\n"
"fmla v23.4s, v3.4s, v1.s[3]\n"
"fmla v24.4s, v4.4s, v0.s[0]\n" // First use of v4.
"fmla v25.4s, v4.4s, v0.s[1]\n"
// Seventh block, nothing to load. Decrement the loop counter in this
// block as the last block is very full.
"nop\n"
"nop\n"
"fmla v26.4s, v4.4s, v0.s[2]\n"
"subs %w[depth], %w[depth], #1\n"
"fmla v27.4s, v4.4s, v0.s[3]\n"
"fmla v28.4s, v4.4s, v1.s[0]\n"
// Eighth block - start loading v0 for next iteration.
"ldr d0, [%[rhs_ptr]]\n"
"fmla v29.4s, v4.4s, v1.s[1]\n"
"ldr x18, [%[rhs_ptr], #8]\n"
"fmla v30.4s, v4.4s, v1.s[2]\n"
"add %[rhs_ptr], %[rhs_ptr], #16\n"
"fmla v31.4s, v4.4s, v1.s[3]\n"
// Loop branch. This will dual issue in fmla cycle 3 of the 8th block.
"bne " GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.16b}, [x0], #16\n"
"st1 {v16.16b}, [x0], #16\n"
"st1 {v24.16b}, [x0], #16\n"
"st1 {v9.16b}, [x0], #16\n"
"st1 {v17.16b}, [x0], #16\n"
"st1 {v25.16b}, [x0], #16\n"
"st1 {v10.16b}, [x0], #16\n"
"st1 {v18.16b}, [x0], #16\n"
"st1 {v26.16b}, [x0], #16\n"
"st1 {v11.16b}, [x0], #16\n"
"st1 {v19.16b}, [x0], #16\n"
"st1 {v27.16b}, [x0], #16\n"
"st1 {v12.16b}, [x0], #16\n"
"st1 {v20.16b}, [x0], #16\n"
"st1 {v28.16b}, [x0], #16\n"
"st1 {v13.16b}, [x0], #16\n"
"st1 {v21.16b}, [x0], #16\n"
"st1 {v29.16b}, [x0], #16\n"
"st1 {v14.16b}, [x0], #16\n"
"st1 {v22.16b}, [x0], #16\n"
"st1 {v30.16b}, [x0], #16\n"
"st1 {v15.16b}, [x0], #16\n"
"st1 {v23.16b}, [x0], #16\n"
"st1 {v31.16b}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "x18", "v0", "v1", "v2", "v3", "v4", "v5", "v6",
"v7", "v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16",
"v17", "v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26",
"v27", "v28", "v29", "v30", "v31");
}
};
#endif
// Faster kernel contributed by ARM. Tuned for A55r1.
struct NEON_64bit_GEMM_Float32_WithScalar_A55r1 {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 2> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"mov x0, %[accum_ptr]\n"
"ld1 {v8.4s}, [x0], #16\n"
"ld1 {v16.4s}, [x0], #16\n"
"ld1 {v24.4s}, [x0], #16\n"
"ld1 {v9.4s}, [x0], #16\n"
"ld1 {v17.4s}, [x0], #16\n"
"ld1 {v25.4s}, [x0], #16\n"
"ld1 {v10.4s}, [x0], #16\n"
"ld1 {v18.4s}, [x0], #16\n"
"ld1 {v26.4s}, [x0], #16\n"
"ld1 {v11.4s}, [x0], #16\n"
"ld1 {v19.4s}, [x0], #16\n"
"ld1 {v27.4s}, [x0], #16\n"
"ld1 {v12.4s}, [x0], #16\n"
"ld1 {v20.4s}, [x0], #16\n"
"ld1 {v28.4s}, [x0], #16\n"
"ld1 {v13.4s}, [x0], #16\n"
"ld1 {v21.4s}, [x0], #16\n"
"ld1 {v29.4s}, [x0], #16\n"
"ld1 {v14.4s}, [x0], #16\n"
"ld1 {v22.4s}, [x0], #16\n"
"ld1 {v30.4s}, [x0], #16\n"
"ld1 {v15.4s}, [x0], #16\n"
"ld1 {v23.4s}, [x0], #16\n"
"ld1 {v31.4s}, [x0], #16\n"
// A55r1 requires a hybrid of the A53 and standard approaches.
//
// Like A53, this processor prefers 64-bit loads.
//
// Unlike A53, it is capable of dual-issuing a 64-bit vector load
// (or INS) with a FMLA instruction.
//
// Therefore we aim to issue an FMLA instruction every cycle.
// Alongside three FMLAs we can dual issue a (vector) 64-bit load, a
// scalar 64-bit load and finally an INS to replicate the effect of
// a single 128-bit load.
//
// The loop contains 24 FMLA instructions, and 5 vector registers
// need to be loaded, consuming 15 dual issue slots. This leaves 9
// dual issue slots. Four of these are used for loop housekeeping
// (2 pointer adds, 1 counter update and 1 branch), leaving 5 left
// over (marked by blank lines).
//
// Choice of x18 to store the upper halves on their way into the
// vector registers is arbitrary. Added to the clobber list so that
// the compiler will make it available.
// At the start of the loop, it is assumed that v0 is "half loaded" -
// bottom half in place in d0 and the upper half in x18 ready to
// insert. So set that up here for the first iteration:
"ldr d0, [%[rhs_ptr]]\n" // Bottom half of first Rhs cell
"ldr x18, [%[rhs_ptr], #8]\n" // Upper half
// v2-v3 should be fully loaded - as it's outside the loop proper it's fine
// to use a 128-bit load here.
"ldr q2, [%[lhs_ptr]]\n" // first Lhs cell
"ldr q3, [%[lhs_ptr], #16]\n" // second Lhs cell
GEMMLOWP_LABEL_LOOP
":\n"
"fmla v8.4s, v2.4s, v0.s[0]\n"
"ldr d1, [%[rhs_ptr], #16]\n" // Bottom half of v1
"fmla v9.4s, v2.4s, v0.s[1]\n"
"ins v0.d[1], x18\n" // Finish loading v0
"fmla v16.4s, v3.4s, v0.s[0]\n" // out of sequence - used to reduce load/use pressure.
"ldr x18, [%[rhs_ptr], #24]\n" // Top half of v1 to X register
"fmla v17.4s, v3.4s, v0.s[1]\n" // out of sequence - used to reduce load/use pressure.
"add %[rhs_ptr], %[rhs_ptr], #32\n" // RHS loads complete - increment pointer.
"fmla v10.4s, v2.4s, v0.s[2]\n"
"ldr d4, [%[lhs_ptr], #32]\n" // Bottom half of v4
"fmla v11.4s, v2.4s, v0.s[3]\n"
"ins v1.d[1], x18\n" // Finish loading v1
"fmla v12.4s, v2.4s, v1.s[0]\n"
"ldr x18, [%[lhs_ptr], #40]\n" // Top half of v4 to X register
"fmla v13.4s, v2.4s, v1.s[1]\n"
"add %[lhs_ptr], %[lhs_ptr], #48\n" // LHS loads complete - increment pointer.
"fmla v14.4s, v2.4s, v1.s[2]\n"
"fmla v15.4s, v2.4s, v1.s[3]\n"
"ldr d2, [%[lhs_ptr]]\n" // Bottom half of v2 (for next time)
"fmla v18.4s, v3.4s, v0.s[2]\n"
"ins v4.d[1], x18\n" // Finish loading v4
"fmla v19.4s, v3.4s, v0.s[3]\n"
"ldr x18, [%[lhs_ptr], #8]\n" // Top half of next v2 to X register
"fmla v20.4s, v3.4s, v1.s[0]\n"
"subs %w[depth], %w[depth], #1\n"
"fmla v21.4s, v3.4s, v1.s[1]\n"
"fmla v22.4s, v3.4s, v1.s[2]\n"
"fmla v23.4s, v3.4s, v1.s[3]\n"
"ldr d3, [%[lhs_ptr], #16]\n" // Bottom half of v3 (for next time)
"fmla v24.4s, v4.4s, v0.s[0]\n"
"ins v2.d[1], x18\n" // Finish loading next v2
"fmla v25.4s, v4.4s, v0.s[1]\n"
"ldr x18, [%[lhs_ptr], #24]\n" // Top half of next v3 to X register
"fmla v26.4s, v4.4s, v0.s[2]\n"
"fmla v27.4s, v4.4s, v0.s[3]\n"
"ldr d0, [%[rhs_ptr]]\n" // Bottom half of v0 (for next time)
"fmla v28.4s, v4.4s, v1.s[0]\n"
"ins v3.d[1], x18\n" // Finish loading next v3
"fmla v29.4s, v4.4s, v1.s[1]\n"
"ldr x18, [%[rhs_ptr], #8]\n" // Top half of next v0 to X register
"fmla v30.4s, v4.4s, v1.s[2]\n"
"fmla v31.4s, v4.4s, v1.s[3]\n"
"bne " GEMMLOWP_LABEL_LOOP "b\n"
// Store accumulators
"mov x0, %[accum_ptr]\n"
"st1 {v8.4s}, [x0], #16\n"
"st1 {v16.4s}, [x0], #16\n"
"st1 {v24.4s}, [x0], #16\n"
"st1 {v9.4s}, [x0], #16\n"
"st1 {v17.4s}, [x0], #16\n"
"st1 {v25.4s}, [x0], #16\n"
"st1 {v10.4s}, [x0], #16\n"
"st1 {v18.4s}, [x0], #16\n"
"st1 {v26.4s}, [x0], #16\n"
"st1 {v11.4s}, [x0], #16\n"
"st1 {v19.4s}, [x0], #16\n"
"st1 {v27.4s}, [x0], #16\n"
"st1 {v12.4s}, [x0], #16\n"
"st1 {v20.4s}, [x0], #16\n"
"st1 {v28.4s}, [x0], #16\n"
"st1 {v13.4s}, [x0], #16\n"
"st1 {v21.4s}, [x0], #16\n"
"st1 {v29.4s}, [x0], #16\n"
"st1 {v14.4s}, [x0], #16\n"
"st1 {v22.4s}, [x0], #16\n"
"st1 {v30.4s}, [x0], #16\n"
"st1 {v15.4s}, [x0], #16\n"
"st1 {v23.4s}, [x0], #16\n"
"st1 {v31.4s}, [x0], #16\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"cc", "memory", "x0", "x18", "v0", "v1", "v2", "v3", "v4", "v5", "v6",
"v7", "v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15", "v16",
"v17", "v18", "v19", "v20", "v21", "v22", "v23", "v24", "v25", "v26",
"v27", "v28", "v29", "v30", "v31");
}
};
#endif // __aarch64__
#if defined(__arm__) || defined(__aarch64__)
#ifndef __aarch64__
inline int32x4_t vpaddq_s32(int32x4_t a, int32x4_t b) {
const int32x2_t c = vpadd_s32(vget_low_s32(a), vget_high_s32(a));
const int32x2_t d = vpadd_s32(vget_low_s32(b), vget_high_s32(b));
return vcombine_s32(c, d);
}
#endif
// C++ intrinsics-based variant of the deep, int8, fast kernel
template <int Cols>
struct NEON_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<Cols, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
int32x4_t acc[4][Cols];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < Cols; j++) {
acc[i][j] = vdupq_n_s32(0);
}
}
for (int d = 0; d < depth; d += 16) {
int8x16_t lhs[4];
for (int i = 0; i < 4; i++) {
lhs[i] = vld1q_s8(lhs_ptr + 16 * i);
}
int8x16_t rhs[Cols];
for (int i = 0; i < Cols; i++) {
rhs[i] = vld1q_s8(rhs_ptr + 16 * i);
}
for (int i = 0; i < 4; i++) {
for (int j = 0; j < Cols; j++) {
int16x8_t local_acc =
vmull_s8(vget_low_s8(lhs[i]), vget_low_s8(rhs[j]));
local_acc =
vmlal_s8(local_acc, vget_high_s8(lhs[i]), vget_high_s8(rhs[j]));
acc[i][j] = vpadalq_s16(acc[i][j], local_acc);
}
}
lhs_ptr += 64;
rhs_ptr += 16 * Cols;
}
for (int i = 0; i < Cols; i++) {
int32x4_t acc_2x_0 = vpaddq_s32(acc[0][i], acc[1][i]);
int32x4_t acc_2x_1 = vpaddq_s32(acc[2][i], acc[3][i]);
int32x4_t acc_4x = vpaddq_s32(acc_2x_0, acc_2x_1);
int32x4_t dst_val = vld1q_s32(accum_ptr + 4 * i);
dst_val = vaddq_s32(dst_val, acc_4x);
vst1q_s32(accum_ptr + 4 * i, dst_val);
}
}
};
using NEON_64bit_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics =
NEON_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics<4>;
using NEON_32bit_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics =
NEON_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics<2>;
// C++ intrinsics-based variant of the wide, uint8, general kernel
template <int RhsCells>
struct NEON_GEMM_Uint8Operands_Uint32Accumulators_intrinsics {
typedef std::uint8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, RhsCells> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
int32x4_t acc[3][4 * RhsCells];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4 * RhsCells; j++) {
acc[i][j] = vld1q_s32(accum_ptr + 4 * (i + 3 * j));
}
}
for (int d = 0; d < depth; d += 2) {
int16x8_t lhs[3];
for (int i = 0; i < 3; i++) {
lhs[i] = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(lhs_ptr + 8 * i)));
}
int16x8_t rhs[RhsCells];
for (int i = 0; i < RhsCells; i++) {
rhs[i] = vreinterpretq_s16_u16(vmovl_u8(vld1_u8(rhs_ptr + 8 * i)));
}
for (int i = 0; i < 3; i++) {
for (int j = 0; j < RhsCells; j++) {
acc[i][4 * j + 0] = vmlal_lane_s16(
acc[i][4 * j + 0], vget_low_s16(lhs[i]), vget_low_s16(rhs[j]), 0);
acc[i][4 * j + 1] = vmlal_lane_s16(
acc[i][4 * j + 1], vget_low_s16(lhs[i]), vget_low_s16(rhs[j]), 1);
acc[i][4 * j + 2] = vmlal_lane_s16(
acc[i][4 * j + 2], vget_low_s16(lhs[i]), vget_low_s16(rhs[j]), 2);
acc[i][4 * j + 3] = vmlal_lane_s16(
acc[i][4 * j + 3], vget_low_s16(lhs[i]), vget_low_s16(rhs[j]), 3);
acc[i][4 * j + 0] =
vmlal_lane_s16(acc[i][4 * j + 0], vget_high_s16(lhs[i]),
vget_high_s16(rhs[j]), 0);
acc[i][4 * j + 1] =
vmlal_lane_s16(acc[i][4 * j + 1], vget_high_s16(lhs[i]),
vget_high_s16(rhs[j]), 1);
acc[i][4 * j + 2] =
vmlal_lane_s16(acc[i][4 * j + 2], vget_high_s16(lhs[i]),
vget_high_s16(rhs[j]), 2);
acc[i][4 * j + 3] =
vmlal_lane_s16(acc[i][4 * j + 3], vget_high_s16(lhs[i]),
vget_high_s16(rhs[j]), 3);
}
}
lhs_ptr += 24;
rhs_ptr += 8 * RhsCells;
}
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4 * RhsCells; j++) {
vst1q_s32(accum_ptr + 4 * (i + 3 * j), acc[i][j]);
}
}
}
};
using NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators_intrinsics =
NEON_GEMM_Uint8Operands_Uint32Accumulators_intrinsics<1>;
using NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_intrinsics =
NEON_GEMM_Uint8Operands_Uint32Accumulators_intrinsics<2>;
template <int RhsCells>
struct NEON_GEMM_Float32_WithScalar_intrinsics {
typedef float OperandType;
typedef float AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 1, CellOrder::DepthMajor>, RhsCells> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
float32x4_t acc[3][4 * RhsCells];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4 * RhsCells; j++) {
acc[i][j] = vld1q_f32(accum_ptr + 4 * (i + 3 * j));
}
}
for (int d = 0; d < depth; d++) {
float32x4_t lhs[3];
for (int i = 0; i < 3; i++) {
lhs[i] = vld1q_f32(lhs_ptr + 4 * i);
}
float32x4_t rhs[RhsCells];
for (int i = 0; i < RhsCells; i++) {
rhs[i] = vld1q_f32(rhs_ptr + 4 * i);
}
for (int i = 0; i < 3; i++) {
for (int j = 0; j < RhsCells; j++) {
acc[i][4 * j + 0] = vmlaq_lane_f32(acc[i][4 * j + 0], lhs[i],
vget_low_f32(rhs[j]), 0);
acc[i][4 * j + 1] = vmlaq_lane_f32(acc[i][4 * j + 1], lhs[i],
vget_low_f32(rhs[j]), 1);
acc[i][4 * j + 2] = vmlaq_lane_f32(acc[i][4 * j + 2], lhs[i],
vget_high_f32(rhs[j]), 0);
acc[i][4 * j + 3] = vmlaq_lane_f32(acc[i][4 * j + 3], lhs[i],
vget_high_f32(rhs[j]), 1);
}
}
lhs_ptr += 12;
rhs_ptr += 4 * RhsCells;
}
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4 * RhsCells; j++) {
vst1q_f32(accum_ptr + 4 * (i + 3 * j), acc[i][j]);
}
}
}
};
using NEON_32bit_GEMM_Float32_WithScalar_intrinsics =
NEON_GEMM_Float32_WithScalar_intrinsics<1>;
using NEON_64bit_GEMM_Float32_WithScalar_intrinsics =
NEON_GEMM_Float32_WithScalar_intrinsics<2>;
// C++ intrinsics-based variant of the deep, 7-bit, fast kernel
struct NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits_intrinsics {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<2, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
int32x4_t acc[4][2];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
acc[i][j] = vdupq_n_s32(0);
}
}
int d = 0;
for (; d <= depth - 64; d += 64) {
int16x8_t local_acc[4][2];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
local_acc[i][j] = vdupq_n_s16(0);
}
}
// There are not enough registers to fit all lhs and rhs values for 64
// depth. Instead, load values for 32 depth at a time.
for (int k = 0; k < 2; k++) {
int8x16_t lhs[4][2];
for (int i = 0; i < 4; i++) {
lhs[i][0] = vld1q_s8(lhs_ptr + 16 * i + 128 * k);
lhs[i][1] = vld1q_s8(lhs_ptr + 64 + 16 * i + 128 * k);
}
int8x16_t rhs[4];
for (int i = 0; i < 4; i++) {
rhs[i] = vld1q_s8(rhs_ptr + 16 * i + 64 * k);
}
for (int i = 0; i < 4; i++) {
if (k == 0) {
local_acc[i][0] = vmull_s8(vget_low_s8(lhs[i][0]),
vget_low_s8(rhs[0]));
local_acc[i][0] = vmlal_s8(local_acc[i][0], vget_low_s8(lhs[i][1]),
vget_low_s8(rhs[2]));
local_acc[i][1] = vmull_s8(vget_low_s8(lhs[i][0]),
vget_low_s8(rhs[1]));
local_acc[i][1] = vmlal_s8(local_acc[i][1],
vget_low_s8(lhs[i][1]),
vget_low_s8(rhs[3]));
} else {
local_acc[i][0] = vmlal_s8(local_acc[i][0], vget_low_s8(lhs[i][0]),
vget_low_s8(rhs[0]));
local_acc[i][0] = vmlal_s8(local_acc[i][0], vget_low_s8(lhs[i][1]),
vget_low_s8(rhs[2]));
local_acc[i][1] = vmlal_s8(local_acc[i][1], vget_low_s8(lhs[i][0]),
vget_low_s8(rhs[1]));
local_acc[i][1] = vmlal_s8(local_acc[i][1], vget_low_s8(lhs[i][1]),
vget_low_s8(rhs[3]));
}
local_acc[i][0] = vmlal_s8(local_acc[i][0], vget_high_s8(lhs[i][0]),
vget_high_s8(rhs[0]));
local_acc[i][0] = vmlal_s8(local_acc[i][0], vget_high_s8(lhs[i][1]),
vget_high_s8(rhs[2]));
local_acc[i][1] = vmlal_s8(local_acc[i][1], vget_high_s8(lhs[i][0]),
vget_high_s8(rhs[1]));
local_acc[i][1] = vmlal_s8(local_acc[i][1], vget_high_s8(lhs[i][1]),
vget_high_s8(rhs[3]));
}
}
for (int i = 0; i < 4; i++) {
acc[i][0] = vpadalq_s16(acc[i][0], local_acc[i][0]);
acc[i][1] = vpadalq_s16(acc[i][1], local_acc[i][1]);
}
lhs_ptr += 64 * 4;
rhs_ptr += 64 * 2;
}
for (; d <= depth - 16; d += 16) {
int8x16_t lhs[4];
for (int i = 0; i < 4; i++) {
lhs[i] = vld1q_s8(lhs_ptr + 16 * i);
}
int8x16_t rhs[2];
for (int i = 0; i < 2; i++) {
rhs[i] = vld1q_s8(rhs_ptr + 16 * i);
}
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
int16x8_t local_acc =
vmull_s8(vget_low_s8(lhs[i]), vget_low_s8(rhs[j]));
local_acc =
vmlal_s8(local_acc, vget_high_s8(lhs[i]), vget_high_s8(rhs[j]));
acc[i][j] = vpadalq_s16(acc[i][j], local_acc);
}
}
lhs_ptr += 16 * 4;
rhs_ptr += 16 * 2;
}
for (int i = 0; i < 2; i++) {
int32x4_t acc_2x_0 = vpaddq_s32(acc[0][i], acc[1][i]);
int32x4_t acc_2x_1 = vpaddq_s32(acc[2][i], acc[3][i]);
int32x4_t acc_4x = vpaddq_s32(acc_2x_0, acc_2x_1);
int32x4_t dst_val = vld1q_s32(accum_ptr + 4 * i);
dst_val = vaddq_s32(dst_val, acc_4x);
vst1q_s32(accum_ptr + 4 * i, dst_val);
}
}
};
SET_7BIT_RANGES(NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits_intrinsics);
// C++ intrinsics-based variant of the deep, 4.25-bit, fast kernel.
struct NEON_64bit_GEMM_Int425Operands_intrinsics {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 32, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<2, 32, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
int32x4_t acc[4][2];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
acc[i][j] = vdupq_n_s32(0);
}
}
const int num_outer_depth_loop = depth / 512 + 1;
int d = 0;
for (int od = 0; od < num_outer_depth_loop; od++) {
int16x8_t local_acc[4][2];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
local_acc[i][j] = vdupq_n_s16(0);
}
}
for (int k = 0; k < 16 && d <= depth - 32; k++, d += 32) {
int8x16_t lhs[8];
for (int i = 0; i < 8; i++) {
lhs[i] = vld1q_s8(lhs_ptr + 16 * i);
}
int8x16_t rhs[4];
for (int i = 0; i < 4; i++) {
rhs[i] = vld1q_s8(rhs_ptr + 16 * i);
}
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
int8x16_t temp_acc = vmulq_s8(lhs[i * 2], rhs[j * 2]);
temp_acc = vmlaq_s8(temp_acc, lhs[i * 2 + 1], rhs[j * 2 + 1]);
local_acc[i][j] = vpadalq_s8(local_acc[i][j], temp_acc);
}
}
lhs_ptr += 128;
rhs_ptr += 64;
}
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 2; j++) {
acc[i][j] = vpadalq_s16(acc[i][j], local_acc[i][j]);
}
}
}
for (int i = 0; i < 2; i++) {
int32x4_t acc_2x_0 = vpaddq_s32(acc[0][i], acc[1][i]);
int32x4_t acc_2x_1 = vpaddq_s32(acc[2][i], acc[3][i]);
int32x4_t acc_4x = vpaddq_s32(acc_2x_0, acc_2x_1);
int32x4_t dst_val = vld1q_s32(accum_ptr + 4 * i);
dst_val = vaddq_s32(dst_val, acc_4x);
vst1q_s32(accum_ptr + 4 * i, dst_val);
}
}
};
SET_425BIT_RANGES(NEON_64bit_GEMM_Int425Operands_intrinsics);
#endif // __arm__ || __aarch64__
#ifdef __mips
// 12x8 depth 2 depth-major kernel.
struct MSA_GEMM_12x8_Uint8Operands_Uint32Accumulators1 {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::DepthMajor>, 2> >
Format;
static void Run(OperandType* lhs_ptr, OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"ld.w $w0, (0*16)(%[accum_ptr])\n"
"ld.w $w4, (1*16)(%[accum_ptr])\n"
"ld.w $w8, (2*16)(%[accum_ptr])\n"
"ld.w $w1, (3*16)(%[accum_ptr])\n"
"ld.w $w5, (4*16)(%[accum_ptr])\n"
"ld.w $w9, (5*16)(%[accum_ptr])\n"
"ld.w $w2, (6*16)(%[accum_ptr])\n"
"ld.w $w6, (7*16)(%[accum_ptr])\n"
"ld.w $w10, (8*16)(%[accum_ptr])\n"
"ld.w $w3, (9*16)(%[accum_ptr])\n"
"ld.w $w7, (10*16)(%[accum_ptr])\n"
"ld.w $w11, (11*16)(%[accum_ptr])\n"
"ld.w $w12, (12*16)(%[accum_ptr])\n"
"ld.w $w16, (13*16)(%[accum_ptr])\n"
"ld.w $w20, (14*16)(%[accum_ptr])\n"
"ld.w $w13, (15*16)(%[accum_ptr])\n"
"ld.w $w17, (16*16)(%[accum_ptr])\n"
"ld.w $w21, (17*16)(%[accum_ptr])\n"
"ld.w $w14, (18*16)(%[accum_ptr])\n"
"ld.w $w18, (19*16)(%[accum_ptr])\n"
"ld.w $w22, (20*16)(%[accum_ptr])\n"
"ld.w $w15, (21*16)(%[accum_ptr])\n"
"ld.w $w19, (22*16)(%[accum_ptr])\n"
"ld.w $w23, (23*16)(%[accum_ptr])\n"
// Set a temp to all zeroes.
"ldi.b $w31, 0\n"
GEMMLOWP_LABEL_LOOP ":\n"
// Overview of register layout:
//
// A half of the 2 2x4 cells of Rhs is stored in 16bit in w27-w30
// (each register contains 4 replicas of a pair of elements).
// A 12x2 block of 3 4x2 cells Lhs is stored in 16bit in w24-w26.
// A 12x8 block of accumulators is stored in 32bit in w0-w23.
//
// +------+------+------+------+
// Rhs |w27 |w28 |w29 |w30 |
// +------+------+------+------+
//
// | | | | |
//
// Lhs | | | | |
//
// +---+ - - - - +------+------+------+------+
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// +---+ - - - - +------+------+------+------+
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// +---+ - - - - +------+------+------+------+
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// +---+ - - - - +------+------+------+------+
//
// Accumulators
// Load 3 x 8 bytes of lhs[] with 2 16-byte overlapped loads.
"ld.b $w24, 0(%[lhs_ptr])\n"
"ld.b $w25, 8(%[lhs_ptr])\n"
// Load 4 bytes of rhs[] for the first half of depth 0.
"lbu $a0, 0(%[rhs_ptr])\n"
"lbu $a1, 1(%[rhs_ptr])\n"
"lbu $a2, 2(%[rhs_ptr])\n"
"lbu $a3, 3(%[rhs_ptr])\n"
// Load 4 bytes of rhs[] for the first half of depth 1.
"lbu $v0, 4(%[rhs_ptr])\n"
"lbu $v1, 5(%[rhs_ptr])\n"
"lbu $t8, 6(%[rhs_ptr])\n"
"lbu $t9, 7(%[rhs_ptr])\n"
// Zero-extend 8-bit elements of lhs[] to 16 bits.
"ilvr.b $w24, $w31, $w24\n"
"ilvl.b $w26, $w31, $w25\n"
"ilvr.b $w25, $w31, $w25\n"
// Interleave depth 0 and depth 1 elements of lhs[] for dpadd_u.w.
"ilvl.d $w27, $w31, $w24\n"
"ilvl.d $w28, $w31, $w25\n"
"ilvl.d $w29, $w31, $w26\n"
"ilvr.h $w24, $w27, $w24\n"
"ilvr.h $w25, $w28, $w25\n"
"ilvr.h $w26, $w29, $w26\n"
// Combine and interleave depth 0 and depth 1 elements of rhs[] for dpadd_u.w
// (for the first half).
"ins $a0, $v0, 16, 8\n"
"ins $a1, $v1, 16, 8\n"
"ins $a2, $t8, 16, 8\n"
"ins $a3, $t9, 16, 8\n"
// Make 4 replicas of every pair of rhs[] elements.
"fill.w $w27, $a0\n"
"fill.w $w28, $a1\n"
"fill.w $w29, $a2\n"
"fill.w $w30, $a3\n"
// Load 4 bytes of rhs[] for the second half of depth 0.
"lbu $a0, 8(%[rhs_ptr])\n"
"lbu $a1, 9(%[rhs_ptr])\n"
"lbu $a2, 10(%[rhs_ptr])\n"
"lbu $a3, 11(%[rhs_ptr])\n"
// Load 4 bytes of rhs[] for the second half of depth 1.
"lbu $v0, 12(%[rhs_ptr])\n"
"lbu $v1, 13(%[rhs_ptr])\n"
"lbu $t8, 14(%[rhs_ptr])\n"
"lbu $t9, 15(%[rhs_ptr])\n"
// First half of depths 0 and 1.
// Dot-product-(and)-add doubles multiplicand width.
"dpadd_u.w $w0, $w24, $w27\n"
"dpadd_u.w $w4, $w25, $w27\n"
"dpadd_u.w $w8, $w26, $w27\n"
"dpadd_u.w $w1, $w24, $w28\n"
"dpadd_u.w $w5, $w25, $w28\n"
"dpadd_u.w $w9, $w26, $w28\n"
"dpadd_u.w $w2, $w24, $w29\n"
"dpadd_u.w $w6, $w25, $w29\n"
"dpadd_u.w $w10, $w26, $w29\n"
"dpadd_u.w $w3, $w24, $w30\n"
"dpadd_u.w $w7, $w25, $w30\n"
"dpadd_u.w $w11, $w26, $w30\n"
// Combine and interleave depth 0 and depth 1 elements of rhs[] for dpadd_u.w
// (for the second half).
"ins $a0, $v0, 16, 8\n"
"ins $a1, $v1, 16, 8\n"
"ins $a2, $t8, 16, 8\n"
"ins $a3, $t9, 16, 8\n"
// Make 4 replicas of every pair of rhs[] elements.
"fill.w $w27, $a0\n"
"fill.w $w28, $a1\n"
"fill.w $w29, $a2\n"
"fill.w $w30, $a3\n"
// Second half of depths 0 and 1.
// Dot-product-(and)-add doubles multiplicand width.
"dpadd_u.w $w12, $w24, $w27\n"
"dpadd_u.w $w16, $w25, $w27\n"
"dpadd_u.w $w20, $w26, $w27\n"
"dpadd_u.w $w13, $w24, $w28\n"
"dpadd_u.w $w17, $w25, $w28\n"
"dpadd_u.w $w21, $w26, $w28\n"
"dpadd_u.w $w14, $w24, $w29\n"
"dpadd_u.w $w18, $w25, $w29\n"
"dpadd_u.w $w22, $w26, $w29\n"
"dpadd_u.w $w15, $w24, $w30\n"
"dpadd_u.w $w19, $w25, $w30\n"
"dpadd_u.w $w23, $w26, $w30\n"
"addiu %[depth], -2\n"
GEMMLOWP_MIPS_XADDIU " %[lhs_ptr], 24\n"
GEMMLOWP_MIPS_XADDIU " %[rhs_ptr], 16\n"
"bnez %[depth]," GEMMLOWP_LABEL_LOOP "b\n"
// Store accumulators.
"st.w $w0, (0*16)(%[accum_ptr])\n"
"st.w $w4, (1*16)(%[accum_ptr])\n"
"st.w $w8, (2*16)(%[accum_ptr])\n"
"st.w $w1, (3*16)(%[accum_ptr])\n"
"st.w $w5, (4*16)(%[accum_ptr])\n"
"st.w $w9, (5*16)(%[accum_ptr])\n"
"st.w $w2, (6*16)(%[accum_ptr])\n"
"st.w $w6, (7*16)(%[accum_ptr])\n"
"st.w $w10, (8*16)(%[accum_ptr])\n"
"st.w $w3, (9*16)(%[accum_ptr])\n"
"st.w $w7, (10*16)(%[accum_ptr])\n"
"st.w $w11, (11*16)(%[accum_ptr])\n"
"st.w $w12, (12*16)(%[accum_ptr])\n"
"st.w $w16, (13*16)(%[accum_ptr])\n"
"st.w $w20, (14*16)(%[accum_ptr])\n"
"st.w $w13, (15*16)(%[accum_ptr])\n"
"st.w $w17, (16*16)(%[accum_ptr])\n"
"st.w $w21, (17*16)(%[accum_ptr])\n"
"st.w $w14, (18*16)(%[accum_ptr])\n"
"st.w $w18, (19*16)(%[accum_ptr])\n"
"st.w $w22, (20*16)(%[accum_ptr])\n"
"st.w $w15, (21*16)(%[accum_ptr])\n"
"st.w $w19, (22*16)(%[accum_ptr])\n"
"st.w $w23, (23*16)(%[accum_ptr])\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"memory",
"v0", "v1",
"a0", "a1", "a2", "a3",
"t8", "t9",
"$f0", "$f1", "$f2", "$f3", "$f4", "$f5", "$f6", "$f7",
"$f8", "$f9", "$f10", "$f11", "$f12", "$f13", "$f14", "$f15",
"$f16", "$f17", "$f18", "$f19", "$f20", "$f21", "$f22", "$f23",
"$f24", "$f25", "$f26", "$f27", "$f28", "$f29", "$f30", "$f31");
}
};
// 12x8 depth 2 width-major kernel.
// Does less shuffling and replication than the kernel above.
struct MSA_GEMM_12x8_Uint8Operands_Uint32Accumulators2 {
typedef std::uint8_t OperandType;
typedef std::uint32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 2, CellOrder::WidthMajor>, 3>,
KernelSideFormat<CellFormat<4, 2, CellOrder::WidthMajor>, 2> >
Format;
static void Run(OperandType* lhs_ptr, OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
asm volatile(
// Load accumulators
"ld.w $w0, (0*16)(%[accum_ptr])\n"
"ld.w $w4, (1*16)(%[accum_ptr])\n"
"ld.w $w8, (2*16)(%[accum_ptr])\n"
"ld.w $w1, (3*16)(%[accum_ptr])\n"
"ld.w $w5, (4*16)(%[accum_ptr])\n"
"ld.w $w9, (5*16)(%[accum_ptr])\n"
"ld.w $w2, (6*16)(%[accum_ptr])\n"
"ld.w $w6, (7*16)(%[accum_ptr])\n"
"ld.w $w10, (8*16)(%[accum_ptr])\n"
"ld.w $w3, (9*16)(%[accum_ptr])\n"
"ld.w $w7, (10*16)(%[accum_ptr])\n"
"ld.w $w11, (11*16)(%[accum_ptr])\n"
"ld.w $w12, (12*16)(%[accum_ptr])\n"
"ld.w $w16, (13*16)(%[accum_ptr])\n"
"ld.w $w20, (14*16)(%[accum_ptr])\n"
"ld.w $w13, (15*16)(%[accum_ptr])\n"
"ld.w $w17, (16*16)(%[accum_ptr])\n"
"ld.w $w21, (17*16)(%[accum_ptr])\n"
"ld.w $w14, (18*16)(%[accum_ptr])\n"
"ld.w $w18, (19*16)(%[accum_ptr])\n"
"ld.w $w22, (20*16)(%[accum_ptr])\n"
"ld.w $w15, (21*16)(%[accum_ptr])\n"
"ld.w $w19, (22*16)(%[accum_ptr])\n"
"ld.w $w23, (23*16)(%[accum_ptr])\n"
GEMMLOWP_LABEL_LOOP
":\n"
// Overview of register layout:
//
// A half of the 2 2x4 cells of Rhs is stored in 16bit in w28-w31
// (each register contains 4 replicas of a pair of elements).
// A 12x2 block of 3 4x2 cells Lhs is stored in 16bit in w24-w26.
// A 12x8 block of accumulators is stored in 32bit in w0-w23.
//
// +------+------+------+------+
// Rhs |w28 |w29 |w30 |w31 |
// +------+------+------+------+
//
// | | | | |
//
// Lhs | | | | |
//
// +---+ - - - - +------+------+------+------+
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// |w24| |w0/12 |w1/13 |w2/14 |w3/15 |
// +---+ - - - - +------+------+------+------+
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// |w25| |w4/16 |w5/17 |w6/18 |w7/19 |
// +---+ - - - - +------+------+------+------+
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// |w26| |w8/20 |w9/21 |w10/22|w11/23|
// +---+ - - - - +------+------+------+------+
//
// Accumulators
// Load 3 x 8 bytes of lhs[] with 2 16-byte overlapped loads.
"ld.b $w24, 0(%[lhs_ptr])\n"
"ld.b $w25, 8(%[lhs_ptr])\n"
// Load 2 x 8 bytes of rhs[].
"ld.b $w27, 0(%[rhs_ptr])\n"
// Zero-extend 8-bit elements of lhs[] to 16 bits.
"ldi.b $w31, 0\n"
"ilvr.b $w24, $w31, $w24\n"
"ilvl.b $w26, $w31, $w25\n"
"ilvr.b $w25, $w31, $w25\n"
// First half of depths 0 and 1.
// Zero-extend 8-bit elements of rhs[] to 16 bits.
"ilvr.b $w31, $w31, $w27\n"
// Make 4 replicas of every pair of rhs[] elements.
"splati.w $w28, $w31[0]\n"
"splati.w $w29, $w31[1]\n"
"splati.w $w30, $w31[2]\n"
"splati.w $w31, $w31[3]\n"
// Dot-product-(and)-add doubles multiplicand width.
"dpadd_u.w $w0, $w24, $w28\n"
"dpadd_u.w $w4, $w25, $w28\n"
"dpadd_u.w $w8, $w26, $w28\n"
"dpadd_u.w $w1, $w24, $w29\n"
"dpadd_u.w $w5, $w25, $w29\n"
"dpadd_u.w $w9, $w26, $w29\n"
"dpadd_u.w $w2, $w24, $w30\n"
"dpadd_u.w $w6, $w25, $w30\n"
"dpadd_u.w $w10, $w26, $w30\n"
"dpadd_u.w $w3, $w24, $w31\n"
"dpadd_u.w $w7, $w25, $w31\n"
"dpadd_u.w $w11, $w26, $w31\n"
// Second half of depths 0 and 1.
// Zero-extend 8-bit elements of rhs[] to 16 bits.
"ldi.b $w31, 0\n"
"ilvl.b $w31, $w31, $w27\n"
// Make 4 replicas of every pair of rhs[] elements.
"splati.w $w28, $w31[0]\n"
"splati.w $w29, $w31[1]\n"
"splati.w $w30, $w31[2]\n"
"splati.w $w31, $w31[3]\n"
// Dot-product-(and)-add doubles multiplicand width.
"dpadd_u.w $w12, $w24, $w28\n"
"dpadd_u.w $w16, $w25, $w28\n"
"dpadd_u.w $w20, $w26, $w28\n"
"dpadd_u.w $w13, $w24, $w29\n"
"dpadd_u.w $w17, $w25, $w29\n"
"dpadd_u.w $w21, $w26, $w29\n"
"dpadd_u.w $w14, $w24, $w30\n"
"dpadd_u.w $w18, $w25, $w30\n"
"dpadd_u.w $w22, $w26, $w30\n"
"dpadd_u.w $w15, $w24, $w31\n"
"dpadd_u.w $w19, $w25, $w31\n"
"dpadd_u.w $w23, $w26, $w31\n"
"addiu %[depth], -2\n" GEMMLOWP_MIPS_XADDIU
" %[lhs_ptr], 24\n" GEMMLOWP_MIPS_XADDIU
" %[rhs_ptr], 16\n"
"bnez %[depth]," GEMMLOWP_LABEL_LOOP
"b\n"
// Store accumulators.
"st.w $w0, (0*16)(%[accum_ptr])\n"
"st.w $w4, (1*16)(%[accum_ptr])\n"
"st.w $w8, (2*16)(%[accum_ptr])\n"
"st.w $w1, (3*16)(%[accum_ptr])\n"
"st.w $w5, (4*16)(%[accum_ptr])\n"
"st.w $w9, (5*16)(%[accum_ptr])\n"
"st.w $w2, (6*16)(%[accum_ptr])\n"
"st.w $w6, (7*16)(%[accum_ptr])\n"
"st.w $w10, (8*16)(%[accum_ptr])\n"
"st.w $w3, (9*16)(%[accum_ptr])\n"
"st.w $w7, (10*16)(%[accum_ptr])\n"
"st.w $w11, (11*16)(%[accum_ptr])\n"
"st.w $w12, (12*16)(%[accum_ptr])\n"
"st.w $w16, (13*16)(%[accum_ptr])\n"
"st.w $w20, (14*16)(%[accum_ptr])\n"
"st.w $w13, (15*16)(%[accum_ptr])\n"
"st.w $w17, (16*16)(%[accum_ptr])\n"
"st.w $w21, (17*16)(%[accum_ptr])\n"
"st.w $w14, (18*16)(%[accum_ptr])\n"
"st.w $w18, (19*16)(%[accum_ptr])\n"
"st.w $w22, (20*16)(%[accum_ptr])\n"
"st.w $w15, (21*16)(%[accum_ptr])\n"
"st.w $w19, (22*16)(%[accum_ptr])\n"
"st.w $w23, (23*16)(%[accum_ptr])\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[depth] "+r"(depth)
: // inputs
[accum_ptr] "r"(accum_ptr)
: // clobbers
"memory", "$f0", "$f1", "$f2", "$f3", "$f4", "$f5", "$f6", "$f7", "$f8",
"$f9", "$f10", "$f11", "$f12", "$f13", "$f14", "$f15", "$f16", "$f17",
"$f18", "$f19", "$f20", "$f21", "$f22", "$f23", "$f24", "$f25", "$f26",
"$f27", "$f28", "$f29", "$f30", "$f31");
}
};
// 4x4 depth 16 width-major kernel operating on int8 operands.
// It is assumed that one of the two int8 operands only takes values
// in [-127, 127], while the other may freely range in [-128, 127].
// The issue with both operands taking the value -128 is that:
// -128*-128 + -128*-128 == -32768 overflows int16.
// Every other expression a*b + c*d, for any int8 a,b,c,d, fits in int16
// range. That is the basic idea of this kernel.
struct MSA_GEMM_Int8Operands_AccumTwoWithin16Bits {
typedef std::int8_t OperandType;
typedef std::int32_t AccumulatorType;
typedef KernelFormat<
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1>,
KernelSideFormat<CellFormat<4, 16, CellOrder::WidthMajor>, 1> >
Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
std::size_t start_depth = 123;
std::size_t run_depth = depth;
std::size_t dst_col_stride = 4;
AccumulatorType* dst_ptr = accum_ptr;
#define GEMMLOWP_LABEL_AFTER_LOOP_LAST16 "1"
#define GEMMLOWP_LABEL_LOOP "2"
#define GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES "3"
#define GEMMLOWP_LABEL_STORE "4"
asm volatile(
GEMMLOWP_MIPS_XADDIU " %[run_depth], -16\n"
// Load lhs[] and rhs[], zero out internal accumulators.
"ld.b $w16, 0(%[lhs_ptr])\n"
"ldi.b $w0, 0\n"
"ld.b $w20, 0(%[rhs_ptr])\n"
"ldi.b $w1, 0\n"
"ld.b $w17, 16(%[lhs_ptr])\n"
"ldi.b $w2, 0\n"
"ld.b $w21, 16(%[rhs_ptr])\n"
"ldi.b $w3, 0\n"
"ld.b $w18, 32(%[lhs_ptr])\n"
"ldi.b $w4, 0\n"
"ld.b $w19, 48(%[lhs_ptr])\n"
"ldi.b $w5, 0\n"
"ld.b $w22, 32(%[rhs_ptr])\n"
"ldi.b $w6, 0\n"
"ld.b $w23, 48(%[rhs_ptr])\n"
"ldi.b $w7, 0\n"
"ldi.b $w8, 0\n"
"ldi.b $w9, 0\n"
"ldi.b $w10, 0\n"
"ldi.b $w11, 0\n"
"ldi.b $w12, 0\n"
"ldi.b $w13, 0\n"
"ldi.b $w14, 0\n"
"ldi.b $w15, 0\n"
"ldi.h $w31, 1\n"
// If the loop depth is only 16, then we can skip the general loop
// and go straight to the final part of the code.
"beqz %[run_depth], " GEMMLOWP_LABEL_AFTER_LOOP_LAST16 "f\n"
GEMMLOWP_LABEL_LOOP ":\n"
// Overview of register layout:
//
// A 4x16 block of Rhs is stored in 8 bit in w16-w19.
// A 4x16 block of Lhs is stored in 8 bit in w20-w23.
//
// A 4x4 block of accumulators is stored in w0-w15 (as 4x32 bit
// components which need to be horizontally added at the end).
//
// Dot products of Lhs and Rhs are 16-bit values, which can't
// immediately be accumulated in 32-bit accumulators by that
// same instruction that calculates them.
// For example, "dotp_s.h $w25, $w16, $w20" produces 8 16-bit
// sums in w25 (note, the 16 sums have already been reduced to 8
// by the horizontal addition of the dotp instruction).
// They are then sign-extended to 32 bits, horizontally added
// (again) to form 4 32-bit sums and then they are finally added
// to the 32-bit accumulators, all by "dpadd_s.w $w0, $w25, $w31".
//
// +-----+-----+-----+-----+
// Rhs | w20 | w21 | w22 | w23 |
// +-----+-----+-----+-----+
//
// | | | | |
//
// Lhs | | | | |
//
// +---+ - - - - +-----+-----+-----+-----+
// |w16| | w0 | w4 | w8 | w12 |
// |w17| | w1 | w5 | w9 | w13 |
// |w18| | w2 | w6 | w10 | w14 |
// |w19| | w3 | w7 | w11 | w15 |
// +---+ - - - - +-----+-----+-----+-----+
//
// Accumulators
// Calculate the results for 16 depths and load
// lhs[] and rhs[] for the next iteration.
GEMMLOWP_MIPS_XADDIU " %[lhs_ptr], 64\n"
GEMMLOWP_MIPS_XADDIU " %[rhs_ptr], 64\n"
GEMMLOWP_MIPS_XADDIU " %[run_depth], -16\n"
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w25, $w16, $w20\n"
"dotp_s.h $w26, $w17, $w20\n"
"dotp_s.h $w27, $w16, $w21\n"
"dotp_s.h $w28, $w17, $w21\n"
"dotp_s.h $w29, $w18, $w20\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w0, $w25, $w31\n"
"dpadd_s.w $w1, $w26, $w31\n"
"dpadd_s.w $w4, $w27, $w31\n"
"dpadd_s.w $w5, $w28, $w31\n"
"dpadd_s.w $w2, $w29, $w31\n"
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w24, $w16, $w22\n"
"dotp_s.h $w25, $w19, $w20\n"
"dotp_s.h $w26, $w16, $w23\n"
"dotp_s.h $w27, $w17, $w22\n"
"ld.b $w20, 0(%[rhs_ptr])\n"
"dotp_s.h $w28, $w17, $w23\n"
"ld.b $w16, 0(%[lhs_ptr])\n"
"dotp_s.h $w29, $w18, $w21\n"
"ld.b $w17, 16(%[lhs_ptr])\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w8, $w24, $w31\n"
"dpadd_s.w $w3, $w25, $w31\n"
"dpadd_s.w $w12, $w26, $w31\n"
"dpadd_s.w $w9, $w27, $w31\n"
"dpadd_s.w $w13, $w28, $w31\n"
"dpadd_s.w $w6, $w29, $w31\n"
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w25, $w19, $w21\n"
"dotp_s.h $w26, $w18, $w22\n"
"dotp_s.h $w27, $w18, $w23\n"
"ld.b $w21, 16(%[rhs_ptr])\n"
"dotp_s.h $w28, $w19, $w22\n"
"ld.b $w18, 32(%[lhs_ptr])\n"
"dotp_s.h $w29, $w19, $w23\n"
"ld.b $w22, 32(%[rhs_ptr])\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w7, $w25, $w31\n"
"ld.b $w19, 48(%[lhs_ptr])\n"
"dpadd_s.w $w10, $w26, $w31\n"
"ld.b $w23, 48(%[rhs_ptr])\n"
"dpadd_s.w $w14, $w27, $w31\n"
"dpadd_s.w $w11, $w28, $w31\n"
"dpadd_s.w $w15, $w29, $w31\n"
"bnez %[run_depth], " GEMMLOWP_LABEL_LOOP "b\n"
GEMMLOWP_LABEL_AFTER_LOOP_LAST16 ":\n"
// Calculate the results for the last 16 depths.
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w25, $w16, $w20\n"
"dotp_s.h $w26, $w17, $w20\n"
"dotp_s.h $w27, $w16, $w21\n"
"dotp_s.h $w28, $w17, $w21\n"
"dotp_s.h $w29, $w18, $w20\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w0, $w25, $w31\n"
"dpadd_s.w $w1, $w26, $w31\n"
"dpadd_s.w $w4, $w27, $w31\n"
"dpadd_s.w $w5, $w28, $w31\n"
"dpadd_s.w $w2, $w29, $w31\n"
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w24, $w16, $w22\n"
"dotp_s.h $w25, $w19, $w20\n"
"dotp_s.h $w26, $w16, $w23\n"
"dotp_s.h $w27, $w17, $w22\n"
"dotp_s.h $w28, $w17, $w23\n"
"dotp_s.h $w29, $w18, $w21\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w8, $w24, $w31\n"
"dpadd_s.w $w3, $w25, $w31\n"
"dpadd_s.w $w12, $w26, $w31\n"
"dpadd_s.w $w9, $w27, $w31\n"
"dpadd_s.w $w13, $w28, $w31\n"
"dpadd_s.w $w6, $w29, $w31\n"
// Dot product: multiply-add pairs of adjacent int8 elements.
// Each dot product takes 16*2 int8 values in and produces 8 int16 sums.
"dotp_s.h $w25, $w19, $w21\n"
"dotp_s.h $w26, $w18, $w22\n"
"dotp_s.h $w27, $w18, $w23\n"
"dotp_s.h $w28, $w19, $w22\n"
"dotp_s.h $w29, $w19, $w23\n"
// Horizontal add of pairs of adjacent int16 sums into internal int32
// accumulators.
"dpadd_s.w $w7, $w25, $w31\n"
"dpadd_s.w $w10, $w26, $w31\n"
"dpadd_s.w $w14, $w27, $w31\n"
"dpadd_s.w $w11, $w28, $w31\n"
"dpadd_s.w $w15, $w29, $w31\n"
// Horizontal-add internal accumulators.
"hadd_s.d $w0, $w0, $w0\n"
"hadd_s.d $w1, $w1, $w1\n"
"hadd_s.d $w2, $w2, $w2\n"
"hadd_s.d $w3, $w3, $w3\n"
"hadd_s.d $w4, $w4, $w4\n"
"hadd_s.d $w5, $w5, $w5\n"
"hadd_s.d $w6, $w6, $w6\n"
"hadd_s.d $w7, $w7, $w7\n"
"hadd_s.d $w8, $w8, $w8\n"
"hadd_s.d $w9, $w9, $w9\n"
"hadd_s.d $w10, $w10, $w10\n"
"hadd_s.d $w11, $w11, $w11\n"
"hadd_s.d $w12, $w12, $w12\n"
"hadd_s.d $w13, $w13, $w13\n"
"hadd_s.d $w14, $w14, $w14\n"
"hadd_s.d $w15, $w15, $w15\n"
"pckev.w $w0, $w1, $w0\n"
"pckev.w $w2, $w3, $w2\n"
"pckev.w $w4, $w5, $w4\n"
"pckev.w $w6, $w7, $w6\n"
"pckev.w $w8, $w9, $w8\n"
"pckev.w $w10, $w11, $w10\n"
"pckev.w $w12, $w13, $w12\n"
"pckev.w $w14, $w15, $w14\n"
"hadd_s.d $w0, $w0, $w0\n"
"hadd_s.d $w2, $w2, $w2\n"
"hadd_s.d $w4, $w4, $w4\n"
"hadd_s.d $w6, $w6, $w6\n"
"hadd_s.d $w8, $w8, $w8\n"
"hadd_s.d $w10, $w10, $w10\n"
"hadd_s.d $w12, $w12, $w12\n"
"hadd_s.d $w14, $w14, $w14\n"
// 4 more pckev instructions follow in both paths below.
// Check if start_depth==0 to decide whether we will load
// existing accumulators from memory.
"bnez %[start_depth], " GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES "f\n"
"pckev.w $w0, $w2, $w0\n"
"pckev.w $w1, $w6, $w4\n"
"pckev.w $w2, $w10, $w8\n"
"pckev.w $w3, $w14, $w12\n"
"b " GEMMLOWP_LABEL_STORE "f\n"
GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES ":\n"
// Load accumulators from memory.
"ld.w $w16, 0(%[dst_ptr0])\n"
"pckev.w $w0, $w2, $w0\n"
"ld.w $w17, 0(%[dst_ptr1])\n"
"pckev.w $w1, $w6, $w4\n"
"ld.w $w18, 0(%[dst_ptr2])\n"
"pckev.w $w2, $w10, $w8\n"
"ld.w $w19, 0(%[dst_ptr3])\n"
"pckev.w $w3, $w14, $w12\n"
// Add them to internal accumulators.
"addv.w $w0, $w0, $w16\n"
"addv.w $w1, $w1, $w17\n"
"addv.w $w2, $w2, $w18\n"
"addv.w $w3, $w3, $w19\n"
GEMMLOWP_LABEL_STORE ":\n"
// Store accumulators.
"st.w $w0, 0(%[dst_ptr0])\n"
"st.w $w1, 0(%[dst_ptr1])\n"
"st.w $w2, 0(%[dst_ptr2])\n"
"st.w $w3, 0(%[dst_ptr3])\n"
: // outputs
[lhs_ptr] "+r"(lhs_ptr), [rhs_ptr] "+r"(rhs_ptr),
[run_depth] "+r"(run_depth)
: // inputs
[dst_ptr0] "r"(dst_ptr), [dst_ptr1] "r"(dst_ptr + dst_col_stride),
[dst_ptr2] "r"(dst_ptr + dst_col_stride * 2),
[dst_ptr3] "r"(dst_ptr + dst_col_stride * 3),
[start_depth] "r"(start_depth)
: // clobbers
"memory", "$f0", "$f1", "$f2", "$f3", "$f4", "$f5", "$f6", "$f7", "$f8",
"$f9", "$f10", "$f11", "$f12", "$f13", "$f14", "$f15", "$f16", "$f17",
"$f18", "$f19", "$f20", "$f21", "$f22", "$f23", "$f24", "$f25", "$f26",
"$f27", "$f28", "$f29", "$f30", "$f31");
#undef GEMMLOWP_LABEL_LOOP
#undef GEMMLOWP_LABEL_AFTER_LOOP_LAST16
#undef GEMMLOWP_LABEL_ACCUMULATE_EXISTING_DST_VALUES
#undef GEMMLOWP_LABEL_STORE
}
};
#endif // __mips
// BEGIN code copied from gemmlowp/internal/kernel_reference.h
// This kernel is templatized in an arbitrary Format template parameter,
// allowing it to have any arbitrary format.
template <typename tOperandType, typename tAccumulatorType, typename tFormat>
struct ReferenceKernel {
typedef tOperandType OperandType;
typedef tAccumulatorType AccumulatorType;
typedef tFormat Format;
static void Run(const OperandType* lhs_ptr, const OperandType* rhs_ptr,
AccumulatorType* accum_ptr, int depth) {
const int depth_cells = static_cast<int>(depth / Format::kDepth);
// The outer loop is over the depth dimension.
for (int dc = 0; dc < depth_cells; dc++) {
// The next two loops are over cells of the Lhs (stacked vertically),
// and over cells of the Rhs (stacked horizontally).
for (int rc = 0; rc < Format::Lhs::kCells; rc++) {
const OperandType* lhs_cell_ptr =
lhs_ptr + (dc * Format::Lhs::kCells + rc) *
Format::Lhs::Cell::kWidth * Format::kDepth;
for (int cc = 0; cc < Format::Rhs::kCells; cc++) {
const OperandType* rhs_cell_ptr =
rhs_ptr + (dc * Format::Rhs::kCells + cc) *
Format::Rhs::Cell::kWidth * Format::kDepth;
// Now we are inside one cell of the Lhs and inside one cell
// of the Rhs, so the remaining inner loops are just
// traditional three loops of matrix multiplication.
for (int di = 0; di < Format::kDepth; di++) {
for (int ri = 0; ri < Format::Lhs::Cell::kWidth; ri++) {
for (int ci = 0; ci < Format::Rhs::Cell::kWidth; ci++) {
const OperandType* lhs_coeff_ptr =
lhs_cell_ptr +
OffsetIntoCell<typename Format::Lhs::Cell>(ri, di);
const OperandType* rhs_coeff_ptr =
rhs_cell_ptr +
OffsetIntoCell<typename Format::Rhs::Cell>(ci, di);
AccumulatorType* accumulator_coeff_ptr =
accum_ptr + (ri + rc * Format::Lhs::Cell::kWidth) +
(ci + cc * Format::Rhs::Cell::kWidth) * Format::kRows;
*accumulator_coeff_ptr += AccumulatorType(*lhs_coeff_ptr) *
AccumulatorType(*rhs_coeff_ptr);
}
}
}
}
}
}
}
};
// END code copied from gemmlowp/internal/kernel_reference.h
template <typename DataType>
class CacheLineAlignedBuffer {
public:
CacheLineAlignedBuffer(std::size_t size) : size_(size) {
data_ = nullptr;
// Adds a few bytes of padding here, because the 64-bit 'A57' kernel
// reads one iteration past the end the buffer, causing a crash on iOS.
int res = posix_memalign(reinterpret_cast<void**>(&data_), kCacheLineSize,
size_ * sizeof(DataType) + 16);
(void)res;
}
~CacheLineAlignedBuffer() { free(data_); }
const DataType* data() const { return data_; }
DataType* data() { return data_; }
std::size_t size() const { return size_; }
private:
const std::size_t size_;
DataType* data_;
};
template <typename DataType>
void FillRandom(CacheLineAlignedBuffer<DataType>* buffer, DataType min,
DataType max) {
static std::mt19937 generator(0);
std::uniform_real_distribution<float> dist(min, max);
for (std::size_t i = 0; i < buffer->size(); i++) {
buffer->data()[i] = DataType(dist(generator));
}
}
template <typename DataType>
void FillZero(CacheLineAlignedBuffer<DataType>* buffer) {
for (std::size_t i = 0; i < buffer->size(); i++) {
buffer->data()[i] = DataType(0);
}
}
template <typename DataType>
void Copy(CacheLineAlignedBuffer<DataType>* dst,
const CacheLineAlignedBuffer<DataType>& src) {
assert(dst->size() == src.size());
memcpy(dst->data(), src.data(), src.size() * sizeof(DataType));
}
template <typename DataType>
void PrintMatrix(int rows, int cols, int rowstride, int colstride,
const DataType* data) {
for (int r = 0; r < rows; r++) {
for (int c = 0; c < cols; c++) {
std::cerr << double(data[r * rowstride + c * colstride]) << " ";
}
std::cerr << std::endl;
}
std::cerr << std::endl;
}
template <typename DataType>
bool approx_equals(DataType a, DataType b) {
return a == b;
}
template <>
bool approx_equals(float a, float b) {
if (!a && !b) {
return true;
}
// 1e-1 is very coarse accuracy, we should switch to an overall L2 metric
// and tighten the tolerance on that metric.
return std::abs(a - b) < 1e-1f * std::min(std::abs(a), std::abs(b));
}
template <typename Kernel>
void test_kernel(int depth, const char* kernel_name) {
typedef typename Kernel::OperandType OperandType;
typedef typename Kernel::AccumulatorType AccumulatorType;
typedef typename Kernel::Format Format;
static const int kLhsWidth = Format::Lhs::kWidth;
static const int kRhsWidth = Format::Rhs::kWidth;
typedef ReferenceKernel<OperandType, AccumulatorType, Format> ReferenceKernel;
CacheLineAlignedBuffer<OperandType> lhs(kLhsWidth * depth);
CacheLineAlignedBuffer<OperandType> rhs(kRhsWidth * depth);
CacheLineAlignedBuffer<AccumulatorType> accum_initial(kLhsWidth * kRhsWidth);
CacheLineAlignedBuffer<AccumulatorType> accum(kLhsWidth * kRhsWidth);
CacheLineAlignedBuffer<AccumulatorType> accum_reference(kLhsWidth *
kRhsWidth);
FillRandom(&lhs, KernelOperandRanges<Kernel>::LhsMin(),
KernelOperandRanges<Kernel>::LhsMax());
FillRandom(&rhs, KernelOperandRanges<Kernel>::RhsMin(),
KernelOperandRanges<Kernel>::RhsMax());
FillRandom(&accum_initial,
std::is_signed<AccumulatorType>::value
? AccumulatorType(-100)
: AccumulatorType(0),
AccumulatorType(100));
Copy(&accum, accum_initial);
Copy(&accum_reference, accum_initial);
ReferenceKernel::Run(lhs.data(), rhs.data(), accum_reference.data(), depth);
Kernel::Run(lhs.data(), rhs.data(), accum.data(), depth);
for (int l = 0; l < kLhsWidth; l++) {
for (int r = 0; r < kRhsWidth; r++) {
const int index = l + kLhsWidth * r;
if (!approx_equals(accum.data()[index], accum_reference.data()[index])) {
std::cerr << "Arithmetic error in kernel:" << std::endl
<< " " << kernel_name << std::endl
<< "Wrong accumulator for depth=" << depth << ", "
<< "at l = " << l << ", r = " << r << std::endl;
std::cerr << "reference value: " << accum_reference.data()[index]
<< std::endl;
std::cerr << "actual value: " << accum.data()[index] << std::endl;
if (depth <= 16) {
std::cerr << "LHS matrix:" << std::endl;
PrintMatrix(kLhsWidth, depth, 1, kLhsWidth, lhs.data());
std::cerr << "RHS matrix:" << std::endl;
PrintMatrix(depth, kRhsWidth, kRhsWidth, 1, rhs.data());
std::cerr << "Initial Accumulator matrix:" << std::endl;
PrintMatrix(kLhsWidth, kRhsWidth, 1, kLhsWidth, accum_initial.data());
std::cerr << "Reference Accumulator matrix:" << std::endl;
PrintMatrix(kLhsWidth, kRhsWidth, 1, kLhsWidth,
accum_reference.data());
std::cerr << "Actual Accumulator matrix:" << std::endl;
PrintMatrix(kLhsWidth, kRhsWidth, 1, kLhsWidth, accum.data());
}
abort();
}
}
}
}
template <typename Kernel>
int ops(int depth) {
// 2x the number of multiply-accumulate scalar ops.
return 2 * Kernel::Format::Lhs::kWidth * Kernel::Format::Rhs::kWidth * depth;
}
template <unsigned Modulus, typename Integer>
Integer RoundDown(Integer i) {
return i - (i % Modulus);
}
int CacheSizeInKB() {
static const char* cache_size_k_env = getenv("CACHE_SIZE_KB");
static const int cache_size_k =
cache_size_k_env ? atoi(cache_size_k_env) : kDefaultCacheSizeK;
return cache_size_k;
}
template <typename Kernel>
int BenchmarkDepthToFitInCache() {
const int cache_size_bytes = 1024 * CacheSizeInKB();
// Subtract the typical size of a few cache lines, so
// we don't need to worry too hard about e.g. some stack data.
const int conservative_cache_size_bytes =
cache_size_bytes - 2 * kCacheLineSize;
// We will subtract the memory occupied by accumulators.
typedef typename Kernel::AccumulatorType AccumulatorType;
const int kAccumulatorBytes = sizeof(AccumulatorType) *
Kernel::Format::Lhs::kWidth *
Kernel::Format::Rhs::kWidth;
// Compute the depth.
typedef typename Kernel::OperandType OperandType;
const int kBytesPerUnitOfDepth =
sizeof(OperandType) *
(Kernel::Format::Lhs::kWidth + Kernel::Format::Rhs::kWidth);
const int unrounded_depth =
(conservative_cache_size_bytes - kAccumulatorBytes) /
kBytesPerUnitOfDepth;
// Cap depth, to avoid unfairly favoring narrower kernels
const int kMaxDepth = 1024;
const int clamped_unrounded_depth = std::min(kMaxDepth, unrounded_depth);
// Round depth down to a multiple of cache line size, which helps because
// our kernels may crash if depth is not a multiple of the number of
// depth level that they want to
// handle at each loop iteration, and we don't want to require kernels
// to be more complex. Currently all kernels process 1, 2 or 8 levels of
// depth at a time. The main reason why that might increase in the future
// is if registers get wider, but I don't suppose that register could
// ever get wider than cache lines.
return RoundDown<kCacheLineSize>(clamped_unrounded_depth);
}
double current_time_in_seconds() {
timespec t;
clock_gettime(CLOCK_REALTIME, &t);
return t.tv_sec + 1e-9 * t.tv_nsec;
}
template <typename Kernel>
double benchmark(int depth) {
// Minimum duration for this benchmark to run. If the workload finishes
// sooner, we retry with double the number of iterations.
static const double min_benchmark_time_in_seconds = 1.0;
typedef typename Kernel::OperandType OperandType;
typedef typename Kernel::AccumulatorType AccumulatorType;
CacheLineAlignedBuffer<OperandType> lhs(Kernel::Format::Lhs::kWidth * depth);
CacheLineAlignedBuffer<OperandType> rhs(Kernel::Format::Rhs::kWidth * depth);
CacheLineAlignedBuffer<AccumulatorType> accum(Kernel::Format::Lhs::kWidth *
Kernel::Format::Rhs::kWidth);
for (std::uint64_t iters_at_a_time = 1;; iters_at_a_time *= 2) {
const double t_start = current_time_in_seconds();
for (std::uint64_t i = 0; i < iters_at_a_time; i++) {
Kernel::Run(lhs.data(), rhs.data(), accum.data(), depth);
}
const double t_end = current_time_in_seconds();
const double elapsed = t_end - t_start;
if (elapsed > min_benchmark_time_in_seconds) {
return iters_at_a_time * ops<Kernel>(depth) / elapsed;
}
}
}
template <typename Kernel>
void benchmark_and_print_results(const char* kernel_name) {
if (getenv("BENCHMARK_KERNEL")) {
if (strcmp(getenv("BENCHMARK_KERNEL"), kernel_name)) {
return;
}
}
const int kKernelDepth = Kernel::Format::kDepth;
for (int depth = kKernelDepth; depth <= 1024; depth += kKernelDepth) {
test_kernel<Kernel>(depth, kernel_name);
}
if (getenv("BENCHMARK_ALL_DEPTHS")) {
for (int depth = kKernelDepth;
depth <= BenchmarkDepthToFitInCache<Kernel>(); depth *= 2) {
std::cout << kernel_name << "," << depth << ","
<< benchmark<Kernel>(depth) * 1e-9f << std::endl;
}
} else {
const int depth = BenchmarkDepthToFitInCache<Kernel>();
std::cout << kernel_name << "," << benchmark<Kernel>(depth) * 1e-9f
<< std::endl;
}
}
#define BENCHMARK(Kernel) \
do { \
benchmark_and_print_results<Kernel>(#Kernel); \
} while (false)
int main() {
if (getenv("BENCHMARK_ALL_DEPTHS")) {
std::cout << "kernel,depth,Gop/s" << std::endl;
} else {
std::cout << "kernel,Gop/s" << std::endl;
}
#ifdef __arm__
BENCHMARK(NEON_32bit_GEMM_Int8Operands_AccumTwoWithin16Bits);
BENCHMARK(NEON_32bit_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics);
BENCHMARK(NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators);
BENCHMARK(NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators_intrinsics);
BENCHMARK(NEON_32bit_GEMM_Uint8Operands_Uint32Accumulators_noexpand);
BENCHMARK(NEON_32bit_GEMM_Int32_WithScalar);
BENCHMARK(NEON_32bit_GEMM_Float32_MLA_WithVectorDuplicatingScalar);
#ifdef __ARM_FEATURE_FMA
BENCHMARK(NEON_32bit_GEMM_Float32_FMA_WithVectorDuplicatingScalar);
#endif
BENCHMARK(NEON_32bit_GEMM_Float32_MLA_WithScalar);
BENCHMARK(NEON_32bit_GEMM_Float32_WithScalar_intrinsics);
BENCHMARK(NEON_32bit_GEMM_Float32_WithScalar_A53);
BENCHMARK(NEON_32bit_GEMM_Float32_WithScalar_A53_depth2);
BENCHMARK(NEON_32bit_GEMM_Float32_MLA_Rotating);
#ifdef __ARM_FEATURE_FMA
BENCHMARK(NEON_32bit_GEMM_Float32_FMA_Rotating);
#endif
#endif
#ifdef __aarch64__
BENCHMARK(NEON_64bit_GEMM_Int425Operands);
BENCHMARK(NEON_64bit_GEMM_Int425Operands_intrinsics);
BENCHMARK(NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits);
BENCHMARK(NEON_64bit_GEMM_Int7Operands_AccumEightWithin16Bits_intrinsics);
BENCHMARK(NEON_64bit_GEMM_Int8Operands_AccumTwoWithin16Bits);
BENCHMARK(NEON_64bit_GEMM_Int8Operands_AccumTwoWithin16Bits_intrinsics);
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators);
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_intrinsics);
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_noexpand_A57);
#ifdef __ARM_FEATURE_DOTPROD
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct);
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct_A55r1);
BENCHMARK(NEON_64bit_GEMM_Uint8Operands_Uint32Accumulators_dotproduct_narrow);
#endif
BENCHMARK(NEON_64bit_GEMM_Int32_WithScalar);
BENCHMARK(NEON_64bit_GEMM_Float32_WithVectorDuplicatingScalar);
BENCHMARK(NEON_64bit_GEMM_Float32_WithScalar);
BENCHMARK(NEON_64bit_GEMM_Float32_WithScalar_intrinsics);
BENCHMARK(NEON_64bit_GEMM_Float32_WithScalar_A57);
#ifndef __APPLE__
BENCHMARK(NEON_64bit_GEMM_Float32_WithScalar_A53);
#endif
BENCHMARK(NEON_64bit_GEMM_Float32_WithScalar_A55r1);
#endif
#ifdef __mips
BENCHMARK(MSA_GEMM_12x8_Uint8Operands_Uint32Accumulators1);
BENCHMARK(MSA_GEMM_12x8_Uint8Operands_Uint32Accumulators2);
BENCHMARK(MSA_GEMM_Int8Operands_AccumTwoWithin16Bits);
#endif
return 0;
}
|