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
|
/*
** 2001 September 15
**
** The author disclaims copyright to this source code. In place of
** a legal notice, here is a blessing:
**
** May you do good and not evil.
** May you find forgiveness for yourself and forgive others.
** May you share freely, never taking more than you give.
**
*************************************************************************
** This file contains code for implementations of the r-tree and r*-tree
** algorithms packaged as an SQLite virtual table module.
*/
/*
** Database Format of R-Tree Tables
** --------------------------------
**
** The data structure for a single virtual r-tree table is stored in three
** native SQLite tables declared as follows. In each case, the '%' character
** in the table name is replaced with the user-supplied name of the r-tree
** table.
**
** CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)
** CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
** CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
**
** The data for each node of the r-tree structure is stored in the %_node
** table. For each node that is not the root node of the r-tree, there is
** an entry in the %_parent table associating the node with its parent.
** And for each row of data in the table, there is an entry in the %_rowid
** table that maps from the entries rowid to the id of the node that it
** is stored on. If the r-tree contains auxiliary columns, those are stored
** on the end of the %_rowid table.
**
** The root node of an r-tree always exists, even if the r-tree table is
** empty. The nodeno of the root node is always 1. All other nodes in the
** table must be the same size as the root node. The content of each node
** is formatted as follows:
**
** 1. If the node is the root node (node 1), then the first 2 bytes
** of the node contain the tree depth as a big-endian integer.
** For non-root nodes, the first 2 bytes are left unused.
**
** 2. The next 2 bytes contain the number of entries currently
** stored in the node.
**
** 3. The remainder of the node contains the node entries. Each entry
** consists of a single 8-byte integer followed by an even number
** of 4-byte coordinates. For leaf nodes the integer is the rowid
** of a record. For internal nodes it is the node number of a
** child page.
*/
#if !defined(SQLITE_CORE) \
|| (defined(SQLITE_ENABLE_RTREE) && !defined(SQLITE_OMIT_VIRTUALTABLE))
#ifndef SQLITE_CORE
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#else
#include "sqlite3.h"
#endif
int sqlite3GetToken(const unsigned char*,int*); /* In the SQLite core */
/*
** If building separately, we will need some setup that is normally
** found in sqliteInt.h
*/
#if !defined(SQLITE_AMALGAMATION)
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef sqlite3_uint64 u64;
typedef unsigned char u8;
typedef unsigned short u16;
typedef unsigned int u32;
#if !defined(NDEBUG) && !defined(SQLITE_DEBUG)
# define NDEBUG 1
#endif
#if defined(NDEBUG) && defined(SQLITE_DEBUG)
# undef NDEBUG
#endif
#if defined(SQLITE_COVERAGE_TEST) || defined(SQLITE_MUTATION_TEST)
# define SQLITE_OMIT_AUXILIARY_SAFETY_CHECKS 1
#endif
#if defined(SQLITE_OMIT_AUXILIARY_SAFETY_CHECKS)
# define ALWAYS(X) (1)
# define NEVER(X) (0)
#elif !defined(NDEBUG)
# define ALWAYS(X) ((X)?1:(assert(0),0))
# define NEVER(X) ((X)?(assert(0),1):0)
#else
# define ALWAYS(X) (X)
# define NEVER(X) (X)
#endif
#endif /* !defined(SQLITE_AMALGAMATION) */
/* Macro to check for 4-byte alignment. Only used inside of assert() */
#ifdef SQLITE_DEBUG
# define FOUR_BYTE_ALIGNED(X) ((((char*)(X) - (char*)0) & 3)==0)
#endif
#include <string.h>
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
/* The following macro is used to suppress compiler warnings.
*/
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(x) (void)(x)
#endif
typedef struct Rtree Rtree;
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;
typedef struct RtreeSearchPoint RtreeSearchPoint;
/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5
/* Maximum number of auxiliary columns */
#define RTREE_MAX_AUX_COLUMN 100
/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is
** used.
*/
#define HASHSIZE 97
/* The xBestIndex method of this virtual table requires an estimate of
** the number of rows in the virtual table to calculate the costs of
** various strategies. If possible, this estimate is loaded from the
** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).
** Otherwise, if no sqlite_stat1 entry is available, use
** RTREE_DEFAULT_ROWEST.
*/
#define RTREE_DEFAULT_ROWEST 1048576
#define RTREE_MIN_ROWEST 100
/*
** An rtree virtual-table object.
*/
struct Rtree {
sqlite3_vtab base; /* Base class. Must be first */
sqlite3 *db; /* Host database connection */
int iNodeSize; /* Size in bytes of each node in the node table */
u8 nDim; /* Number of dimensions */
u8 nDim2; /* Twice the number of dimensions */
u8 eCoordType; /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */
u8 nBytesPerCell; /* Bytes consumed per cell */
u8 inWrTrans; /* True if inside write transaction */
u8 nAux; /* # of auxiliary columns in %_rowid */
#ifdef SQLITE_ENABLE_GEOPOLY
u8 nAuxNotNull; /* Number of initial not-null aux columns */
#endif
#ifdef SQLITE_DEBUG
u8 bCorrupt; /* Shadow table corruption detected */
#endif
int iDepth; /* Current depth of the r-tree structure */
char *zDb; /* Name of database containing r-tree table */
char *zName; /* Name of r-tree table */
char *zNodeName; /* Name of the %_node table */
u32 nBusy; /* Current number of users of this structure */
i64 nRowEst; /* Estimated number of rows in this table */
u32 nCursor; /* Number of open cursors */
u32 nNodeRef; /* Number RtreeNodes with positive nRef */
char *zReadAuxSql; /* SQL for statement to read aux data */
/* List of nodes removed during a CondenseTree operation. List is
** linked together via the pointer normally used for hash chains -
** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree
** headed by the node (leaf nodes have RtreeNode.iNode==0).
*/
RtreeNode *pDeleted;
/* Blob I/O on xxx_node */
sqlite3_blob *pNodeBlob;
/* Statements to read/write/delete a record from xxx_node */
sqlite3_stmt *pWriteNode;
sqlite3_stmt *pDeleteNode;
/* Statements to read/write/delete a record from xxx_rowid */
sqlite3_stmt *pReadRowid;
sqlite3_stmt *pWriteRowid;
sqlite3_stmt *pDeleteRowid;
/* Statements to read/write/delete a record from xxx_parent */
sqlite3_stmt *pReadParent;
sqlite3_stmt *pWriteParent;
sqlite3_stmt *pDeleteParent;
/* Statement for writing to the "aux:" fields, if there are any */
sqlite3_stmt *pWriteAux;
RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */
};
/* Possible values for Rtree.eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32 1
/*
** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will
** only deal with integer coordinates. No floating point operations
** will be done.
*/
#ifdef SQLITE_RTREE_INT_ONLY
typedef sqlite3_int64 RtreeDValue; /* High accuracy coordinate */
typedef int RtreeValue; /* Low accuracy coordinate */
# define RTREE_ZERO 0
#else
typedef double RtreeDValue; /* High accuracy coordinate */
typedef float RtreeValue; /* Low accuracy coordinate */
# define RTREE_ZERO 0.0
#endif
/*
** Set the Rtree.bCorrupt flag
*/
#ifdef SQLITE_DEBUG
# define RTREE_IS_CORRUPT(X) ((X)->bCorrupt = 1)
#else
# define RTREE_IS_CORRUPT(X)
#endif
/*
** When doing a search of an r-tree, instances of the following structure
** record intermediate results from the tree walk.
**
** The id is always a node-id. For iLevel>=1 the id is the node-id of
** the node that the RtreeSearchPoint represents. When iLevel==0, however,
** the id is of the parent node and the cell that RtreeSearchPoint
** represents is the iCell-th entry in the parent node.
*/
struct RtreeSearchPoint {
RtreeDValue rScore; /* The score for this node. Smallest goes first. */
sqlite3_int64 id; /* Node ID */
u8 iLevel; /* 0=entries. 1=leaf node. 2+ for higher */
u8 eWithin; /* PARTLY_WITHIN or FULLY_WITHIN */
u8 iCell; /* Cell index within the node */
};
/*
** The minimum number of cells allowed for a node is a third of the
** maximum. In Gutman's notation:
**
** m = M/3
**
** If an R*-tree "Reinsert" operation is required, the same number of
** cells are removed from the overfull node and reinserted into the tree.
*/
#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
#define RTREE_MAXCELLS 51
/*
** The smallest possible node-size is (512-64)==448 bytes. And the largest
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since
** 3^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40
/*
** Number of entries in the cursor RtreeNode cache. The first entry is
** used to cache the RtreeNode for RtreeCursor.sPoint. The remaining
** entries cache the RtreeNode for the first elements of the priority queue.
*/
#define RTREE_CACHE_SZ 5
/*
** An rtree cursor object.
*/
struct RtreeCursor {
sqlite3_vtab_cursor base; /* Base class. Must be first */
u8 atEOF; /* True if at end of search */
u8 bPoint; /* True if sPoint is valid */
u8 bAuxValid; /* True if pReadAux is valid */
int iStrategy; /* Copy of idxNum search parameter */
int nConstraint; /* Number of entries in aConstraint */
RtreeConstraint *aConstraint; /* Search constraints. */
int nPointAlloc; /* Number of slots allocated for aPoint[] */
int nPoint; /* Number of slots used in aPoint[] */
int mxLevel; /* iLevel value for root of the tree */
RtreeSearchPoint *aPoint; /* Priority queue for search points */
sqlite3_stmt *pReadAux; /* Statement to read aux-data */
RtreeSearchPoint sPoint; /* Cached next search point */
RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */
u32 anQueue[RTREE_MAX_DEPTH+1]; /* Number of queued entries by iLevel */
};
/* Return the Rtree of a RtreeCursor */
#define RTREE_OF_CURSOR(X) ((Rtree*)((X)->base.pVtab))
/*
** A coordinate can be either a floating point number or a integer. All
** coordinates within a single R-Tree are always of the same time.
*/
union RtreeCoord {
RtreeValue f; /* Floating point value */
int i; /* Integer value */
u32 u; /* Unsigned for byte-order conversions */
};
/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a RtreeDValue (double or int64). This macro assumes that local
** variable pRtree points to the Rtree structure associated with the
** RtreeCoord.
*/
#ifdef SQLITE_RTREE_INT_ONLY
# define DCOORD(coord) ((RtreeDValue)coord.i)
#else
# define DCOORD(coord) ( \
(pRtree->eCoordType==RTREE_COORD_REAL32) ? \
((double)coord.f) : \
((double)coord.i) \
)
#endif
/*
** A search constraint.
*/
struct RtreeConstraint {
int iCoord; /* Index of constrained coordinate */
int op; /* Constraining operation */
union {
RtreeDValue rValue; /* Constraint value. */
int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);
int (*xQueryFunc)(sqlite3_rtree_query_info*);
} u;
sqlite3_rtree_query_info *pInfo; /* xGeom and xQueryFunc argument */
};
/* Possible values for RtreeConstraint.op */
#define RTREE_EQ 0x41 /* A */
#define RTREE_LE 0x42 /* B */
#define RTREE_LT 0x43 /* C */
#define RTREE_GE 0x44 /* D */
#define RTREE_GT 0x45 /* E */
#define RTREE_MATCH 0x46 /* F: Old-style sqlite3_rtree_geometry_callback() */
#define RTREE_QUERY 0x47 /* G: New-style sqlite3_rtree_query_callback() */
/* Special operators available only on cursors. Needs to be consecutive
** with the normal values above, but must be less than RTREE_MATCH. These
** are used in the cursor for contraints such as x=NULL (RTREE_FALSE) or
** x<'xyz' (RTREE_TRUE) */
#define RTREE_TRUE 0x3f /* ? */
#define RTREE_FALSE 0x40 /* @ */
/*
** An rtree structure node.
*/
struct RtreeNode {
RtreeNode *pParent; /* Parent node */
i64 iNode; /* The node number */
int nRef; /* Number of references to this node */
int isDirty; /* True if the node needs to be written to disk */
u8 *zData; /* Content of the node, as should be on disk */
RtreeNode *pNext; /* Next node in this hash collision chain */
};
/* Return the number of cells in a node */
#define NCELL(pNode) readInt16(&(pNode)->zData[2])
/*
** A single cell from a node, deserialized
*/
struct RtreeCell {
i64 iRowid; /* Node or entry ID */
RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2]; /* Bounding box coordinates */
};
/*
** This object becomes the sqlite3_user_data() for the SQL functions
** that are created by sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() and which appear on the right of MATCH
** operators in order to constrain a search.
**
** xGeom and xQueryFunc are the callback functions. Exactly one of
** xGeom and xQueryFunc fields is non-NULL, depending on whether the
** SQL function was created using sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback().
**
** This object is deleted automatically by the destructor mechanism in
** sqlite3_create_function_v2().
*/
struct RtreeGeomCallback {
int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);
int (*xQueryFunc)(sqlite3_rtree_query_info*);
void (*xDestructor)(void*);
void *pContext;
};
/*
** An instance of this structure (in the form of a BLOB) is returned by
** the SQL functions that sqlite3_rtree_geometry_callback() and
** sqlite3_rtree_query_callback() create, and is read as the right-hand
** operand to the MATCH operator of an R-Tree.
*/
struct RtreeMatchArg {
u32 iSize; /* Size of this object */
RtreeGeomCallback cb; /* Info about the callback functions */
int nParam; /* Number of parameters to the SQL function */
sqlite3_value **apSqlParam; /* Original SQL parameter values */
RtreeDValue aParam[1]; /* Values for parameters to the SQL function */
};
#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
#endif
/* What version of GCC is being used. 0 means GCC is not being used .
** Note that the GCC_VERSION macro will also be set correctly when using
** clang, since clang works hard to be gcc compatible. So the gcc
** optimizations will also work when compiling with clang.
*/
#ifndef GCC_VERSION
#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)
# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)
#else
# define GCC_VERSION 0
#endif
#endif
/* The testcase() macro should already be defined in the amalgamation. If
** it is not, make it a no-op.
*/
#ifndef SQLITE_AMALGAMATION
# if defined(SQLITE_COVERAGE_TEST) || defined(SQLITE_DEBUG)
unsigned int sqlite3RtreeTestcase = 0;
# define testcase(X) if( X ){ sqlite3RtreeTestcase += __LINE__; }
# else
# define testcase(X)
# endif
#endif
/*
** Make sure that the compiler intrinsics we desire are enabled when
** compiling with an appropriate version of MSVC unless prevented by
** the SQLITE_DISABLE_INTRINSIC define.
*/
#if !defined(SQLITE_DISABLE_INTRINSIC)
# if defined(_MSC_VER) && _MSC_VER>=1400
# if !defined(_WIN32_WCE)
# include <intrin.h>
# pragma intrinsic(_byteswap_ulong)
# pragma intrinsic(_byteswap_uint64)
# else
# include <cmnintrin.h>
# endif
# endif
#endif
/*
** Macros to determine whether the machine is big or little endian,
** and whether or not that determination is run-time or compile-time.
**
** For best performance, an attempt is made to guess at the byte-order
** using C-preprocessor macros. If that is unsuccessful, or if
** -DSQLITE_RUNTIME_BYTEORDER=1 is set, then byte-order is determined
** at run-time.
*/
#ifndef SQLITE_BYTEORDER /* Replicate changes at tag-20230904a */
# if defined(__BYTE_ORDER__) && __BYTE_ORDER__==__ORDER_BIG_ENDIAN__
# define SQLITE_BYTEORDER 4321
# elif defined(__BYTE_ORDER__) && __BYTE_ORDER__==__ORDER_LITTLE_ENDIAN__
# define SQLITE_BYTEORDER 1234
# elif defined(__BIG_ENDIAN__) && __BIG_ENDIAN__==1
# define SQLITE_BYTEORDER 4321
# elif defined(i386) || defined(__i386__) || defined(_M_IX86) || \
defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) || \
defined(_M_AMD64) || defined(_M_ARM) || defined(__x86) || \
defined(__ARMEL__) || defined(__AARCH64EL__) || defined(_M_ARM64)
# define SQLITE_BYTEORDER 1234
# elif defined(sparc) || defined(__ARMEB__) || defined(__AARCH64EB__)
# define SQLITE_BYTEORDER 4321
# else
# define SQLITE_BYTEORDER 0
# endif
#endif
/* What version of MSVC is being used. 0 means MSVC is not being used */
#ifndef MSVC_VERSION
#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)
# define MSVC_VERSION _MSC_VER
#else
# define MSVC_VERSION 0
#endif
#endif
/*
** Functions to deserialize a 16 bit integer, 32 bit real number and
** 64 bit integer. The deserialized value is returned.
*/
static int readInt16(u8 *p){
return (p[0]<<8) + p[1];
}
static void readCoord(u8 *p, RtreeCoord *pCoord){
assert( FOUR_BYTE_ALIGNED(p) );
#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
pCoord->u = _byteswap_ulong(*(u32*)p);
#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
pCoord->u = __builtin_bswap32(*(u32*)p);
#elif SQLITE_BYTEORDER==4321
pCoord->u = *(u32*)p;
#else
pCoord->u = (
(((u32)p[0]) << 24) +
(((u32)p[1]) << 16) +
(((u32)p[2]) << 8) +
(((u32)p[3]) << 0)
);
#endif
}
static i64 readInt64(u8 *p){
#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
u64 x;
memcpy(&x, p, 8);
return (i64)_byteswap_uint64(x);
#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
u64 x;
memcpy(&x, p, 8);
return (i64)__builtin_bswap64(x);
#elif SQLITE_BYTEORDER==4321
i64 x;
memcpy(&x, p, 8);
return x;
#else
return (i64)(
(((u64)p[0]) << 56) +
(((u64)p[1]) << 48) +
(((u64)p[2]) << 40) +
(((u64)p[3]) << 32) +
(((u64)p[4]) << 24) +
(((u64)p[5]) << 16) +
(((u64)p[6]) << 8) +
(((u64)p[7]) << 0)
);
#endif
}
/*
** Functions to serialize a 16 bit integer, 32 bit real number and
** 64 bit integer. The value returned is the number of bytes written
** to the argument buffer (always 2, 4 and 8 respectively).
*/
static void writeInt16(u8 *p, int i){
p[0] = (i>> 8)&0xFF;
p[1] = (i>> 0)&0xFF;
}
static int writeCoord(u8 *p, RtreeCoord *pCoord){
u32 i;
assert( FOUR_BYTE_ALIGNED(p) );
assert( sizeof(RtreeCoord)==4 );
assert( sizeof(u32)==4 );
#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
i = __builtin_bswap32(pCoord->u);
memcpy(p, &i, 4);
#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
i = _byteswap_ulong(pCoord->u);
memcpy(p, &i, 4);
#elif SQLITE_BYTEORDER==4321
i = pCoord->u;
memcpy(p, &i, 4);
#else
i = pCoord->u;
p[0] = (i>>24)&0xFF;
p[1] = (i>>16)&0xFF;
p[2] = (i>> 8)&0xFF;
p[3] = (i>> 0)&0xFF;
#endif
return 4;
}
static int writeInt64(u8 *p, i64 i){
#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
i = (i64)__builtin_bswap64((u64)i);
memcpy(p, &i, 8);
#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
i = (i64)_byteswap_uint64((u64)i);
memcpy(p, &i, 8);
#elif SQLITE_BYTEORDER==4321
memcpy(p, &i, 8);
#else
p[0] = (i>>56)&0xFF;
p[1] = (i>>48)&0xFF;
p[2] = (i>>40)&0xFF;
p[3] = (i>>32)&0xFF;
p[4] = (i>>24)&0xFF;
p[5] = (i>>16)&0xFF;
p[6] = (i>> 8)&0xFF;
p[7] = (i>> 0)&0xFF;
#endif
return 8;
}
/*
** Increment the reference count of node p.
*/
static void nodeReference(RtreeNode *p){
if( p ){
assert( p->nRef>0 );
p->nRef++;
}
}
/*
** Clear the content of node p (set all bytes to 0x00).
*/
static void nodeZero(Rtree *pRtree, RtreeNode *p){
memset(&p->zData[2], 0, pRtree->iNodeSize-2);
p->isDirty = 1;
}
/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static unsigned int nodeHash(i64 iNode){
return ((unsigned)iNode) % HASHSIZE;
}
/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
RtreeNode *p;
for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
return p;
}
/*
** Add node pNode to the node hash table.
*/
static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
int iHash;
assert( pNode->pNext==0 );
iHash = nodeHash(pNode->iNode);
pNode->pNext = pRtree->aHash[iHash];
pRtree->aHash[iHash] = pNode;
}
/*
** Remove node pNode from the node hash table.
*/
static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
RtreeNode **pp;
if( pNode->iNode!=0 ){
pp = &pRtree->aHash[nodeHash(pNode->iNode)];
for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }
*pp = pNode->pNext;
pNode->pNext = 0;
}
}
/*
** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
** indicating that node has not yet been assigned a node number. It is
** assigned a node number when nodeWrite() is called to write the
** node contents out to the database.
*/
static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent){
RtreeNode *pNode;
pNode = (RtreeNode *)sqlite3_malloc64(sizeof(RtreeNode) + pRtree->iNodeSize);
if( pNode ){
memset(pNode, 0, sizeof(RtreeNode) + pRtree->iNodeSize);
pNode->zData = (u8 *)&pNode[1];
pNode->nRef = 1;
pRtree->nNodeRef++;
pNode->pParent = pParent;
pNode->isDirty = 1;
nodeReference(pParent);
}
return pNode;
}
/*
** Clear the Rtree.pNodeBlob object
*/
static void nodeBlobReset(Rtree *pRtree){
sqlite3_blob *pBlob = pRtree->pNodeBlob;
pRtree->pNodeBlob = 0;
sqlite3_blob_close(pBlob);
}
/*
** Obtain a reference to an r-tree node.
*/
static int nodeAcquire(
Rtree *pRtree, /* R-tree structure */
i64 iNode, /* Node number to load */
RtreeNode *pParent, /* Either the parent node or NULL */
RtreeNode **ppNode /* OUT: Acquired node */
){
int rc = SQLITE_OK;
RtreeNode *pNode = 0;
/* Check if the requested node is already in the hash table. If so,
** increase its reference count and return it.
*/
if( (pNode = nodeHashLookup(pRtree, iNode))!=0 ){
if( pParent && ALWAYS(pParent!=pNode->pParent) ){
RTREE_IS_CORRUPT(pRtree);
return SQLITE_CORRUPT_VTAB;
}
pNode->nRef++;
*ppNode = pNode;
return SQLITE_OK;
}
if( pRtree->pNodeBlob ){
sqlite3_blob *pBlob = pRtree->pNodeBlob;
pRtree->pNodeBlob = 0;
rc = sqlite3_blob_reopen(pBlob, iNode);
pRtree->pNodeBlob = pBlob;
if( rc ){
nodeBlobReset(pRtree);
if( rc==SQLITE_NOMEM ) return SQLITE_NOMEM;
}
}
if( pRtree->pNodeBlob==0 ){
rc = sqlite3_blob_open(pRtree->db, pRtree->zDb, pRtree->zNodeName,
"data", iNode, 0,
&pRtree->pNodeBlob);
}
if( rc ){
*ppNode = 0;
/* If unable to open an sqlite3_blob on the desired row, that can only
** be because the shadow tables hold erroneous data. */
if( rc==SQLITE_ERROR ){
rc = SQLITE_CORRUPT_VTAB;
RTREE_IS_CORRUPT(pRtree);
}
}else if( pRtree->iNodeSize==sqlite3_blob_bytes(pRtree->pNodeBlob) ){
pNode = (RtreeNode *)sqlite3_malloc64(sizeof(RtreeNode)+pRtree->iNodeSize);
if( !pNode ){
rc = SQLITE_NOMEM;
}else{
pNode->pParent = pParent;
pNode->zData = (u8 *)&pNode[1];
pNode->nRef = 1;
pRtree->nNodeRef++;
pNode->iNode = iNode;
pNode->isDirty = 0;
pNode->pNext = 0;
rc = sqlite3_blob_read(pRtree->pNodeBlob, pNode->zData,
pRtree->iNodeSize, 0);
}
}
/* If the root node was just loaded, set pRtree->iDepth to the height
** of the r-tree structure. A height of zero means all data is stored on
** the root node. A height of one means the children of the root node
** are the leaves, and so on. If the depth as specified on the root node
** is greater than RTREE_MAX_DEPTH, the r-tree structure must be corrupt.
*/
if( rc==SQLITE_OK && pNode && iNode==1 ){
pRtree->iDepth = readInt16(pNode->zData);
if( pRtree->iDepth>RTREE_MAX_DEPTH ){
rc = SQLITE_CORRUPT_VTAB;
RTREE_IS_CORRUPT(pRtree);
}
}
/* If no error has occurred so far, check if the "number of entries"
** field on the node is too large. If so, set the return code to
** SQLITE_CORRUPT_VTAB.
*/
if( pNode && rc==SQLITE_OK ){
if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){
rc = SQLITE_CORRUPT_VTAB;
RTREE_IS_CORRUPT(pRtree);
}
}
if( rc==SQLITE_OK ){
if( pNode!=0 ){
nodeReference(pParent);
nodeHashInsert(pRtree, pNode);
}else{
rc = SQLITE_CORRUPT_VTAB;
RTREE_IS_CORRUPT(pRtree);
}
*ppNode = pNode;
}else{
nodeBlobReset(pRtree);
if( pNode ){
pRtree->nNodeRef--;
sqlite3_free(pNode);
}
*ppNode = 0;
}
return rc;
}
/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
Rtree *pRtree, /* The overall R-Tree */
RtreeNode *pNode, /* The node into which the cell is to be written */
RtreeCell *pCell, /* The cell to write */
int iCell /* Index into pNode into which pCell is written */
){
int ii;
u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
p += writeInt64(p, pCell->iRowid);
for(ii=0; ii<pRtree->nDim2; ii++){
p += writeCoord(p, &pCell->aCoord[ii]);
}
pNode->isDirty = 1;
}
/*
** Remove the cell with index iCell from node pNode.
*/
static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
u8 *pSrc = &pDst[pRtree->nBytesPerCell];
int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
memmove(pDst, pSrc, nByte);
writeInt16(&pNode->zData[2], NCELL(pNode)-1);
pNode->isDirty = 1;
}
/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/
static int nodeInsertCell(
Rtree *pRtree, /* The overall R-Tree */
RtreeNode *pNode, /* Write new cell into this node */
RtreeCell *pCell /* The cell to be inserted */
){
int nCell; /* Current number of cells in pNode */
int nMaxCell; /* Maximum number of cells for pNode */
nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
nCell = NCELL(pNode);
assert( nCell<=nMaxCell );
if( nCell<nMaxCell ){
nodeOverwriteCell(pRtree, pNode, pCell, nCell);
writeInt16(&pNode->zData[2], nCell+1);
pNode->isDirty = 1;
}
return (nCell==nMaxCell);
}
/*
** If the node is dirty, write it out to the database.
*/
static int nodeWrite(Rtree *pRtree, RtreeNode *pNode){
int rc = SQLITE_OK;
if( pNode->isDirty ){
sqlite3_stmt *p = pRtree->pWriteNode;
if( pNode->iNode ){
sqlite3_bind_int64(p, 1, pNode->iNode);
}else{
sqlite3_bind_null(p, 1);
}
sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);
sqlite3_step(p);
pNode->isDirty = 0;
rc = sqlite3_reset(p);
sqlite3_bind_null(p, 2);
if( pNode->iNode==0 && rc==SQLITE_OK ){
pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);
nodeHashInsert(pRtree, pNode);
}
}
return rc;
}
/*
** Release a reference to a node. If the node is dirty and the reference
** count drops to zero, the node data is written to the database.
*/
static int nodeRelease(Rtree *pRtree, RtreeNode *pNode){
int rc = SQLITE_OK;
if( pNode ){
assert( pNode->nRef>0 );
assert( pRtree->nNodeRef>0 );
pNode->nRef--;
if( pNode->nRef==0 ){
pRtree->nNodeRef--;
if( pNode->iNode==1 ){
pRtree->iDepth = -1;
}
if( pNode->pParent ){
rc = nodeRelease(pRtree, pNode->pParent);
}
if( rc==SQLITE_OK ){
rc = nodeWrite(pRtree, pNode);
}
nodeHashDelete(pRtree, pNode);
sqlite3_free(pNode);
}
}
return rc;
}
/*
** Return the 64-bit integer value associated with cell iCell of
** node pNode. If pNode is a leaf node, this is a rowid. If it is
** an internal node, then the 64-bit integer is a child page number.
*/
static i64 nodeGetRowid(
Rtree *pRtree, /* The overall R-Tree */
RtreeNode *pNode, /* The node from which to extract the ID */
int iCell /* The cell index from which to extract the ID */
){
assert( iCell<NCELL(pNode) );
return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
}
/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
Rtree *pRtree, /* The overall R-Tree */
RtreeNode *pNode, /* The node from which to extract a coordinate */
int iCell, /* The index of the cell within the node */
int iCoord, /* Which coordinate to extract */
RtreeCoord *pCoord /* OUT: Space to write result to */
){
assert( iCell<NCELL(pNode) );
readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}
/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
Rtree *pRtree, /* The overall R-Tree */
RtreeNode *pNode, /* The node containing the cell to be read */
int iCell, /* Index of the cell within the node */
RtreeCell *pCell /* OUT: Write the cell contents here */
){
u8 *pData;
RtreeCoord *pCoord;
int ii = 0;
pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);
pCoord = pCell->aCoord;
do{
readCoord(pData, &pCoord[ii]);
readCoord(pData+4, &pCoord[ii+1]);
pData += 8;
ii += 2;
}while( ii<pRtree->nDim2 );
}
/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
static int rtreeInit(
sqlite3 *, void *, int, const char *const*, sqlite3_vtab **, char **, int
);
/*
** Rtree virtual table module xCreate method.
*/
static int rtreeCreate(
sqlite3 *db,
void *pAux,
int argc, const char *const*argv,
sqlite3_vtab **ppVtab,
char **pzErr
){
return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 1);
}
/*
** Rtree virtual table module xConnect method.
*/
static int rtreeConnect(
sqlite3 *db,
void *pAux,
int argc, const char *const*argv,
sqlite3_vtab **ppVtab,
char **pzErr
){
return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 0);
}
/*
** Increment the r-tree reference count.
*/
static void rtreeReference(Rtree *pRtree){
pRtree->nBusy++;
}
/*
** Decrement the r-tree reference count. When the reference count reaches
** zero the structure is deleted.
*/
static void rtreeRelease(Rtree *pRtree){
pRtree->nBusy--;
if( pRtree->nBusy==0 ){
pRtree->inWrTrans = 0;
assert( pRtree->nCursor==0 );
nodeBlobReset(pRtree);
assert( pRtree->nNodeRef==0 || pRtree->bCorrupt );
sqlite3_finalize(pRtree->pWriteNode);
sqlite3_finalize(pRtree->pDeleteNode);
sqlite3_finalize(pRtree->pReadRowid);
sqlite3_finalize(pRtree->pWriteRowid);
sqlite3_finalize(pRtree->pDeleteRowid);
sqlite3_finalize(pRtree->pReadParent);
sqlite3_finalize(pRtree->pWriteParent);
sqlite3_finalize(pRtree->pDeleteParent);
sqlite3_finalize(pRtree->pWriteAux);
sqlite3_free(pRtree->zReadAuxSql);
sqlite3_free(pRtree);
}
}
/*
** Rtree virtual table module xDisconnect method.
*/
static int rtreeDisconnect(sqlite3_vtab *pVtab){
rtreeRelease((Rtree *)pVtab);
return SQLITE_OK;
}
/*
** Rtree virtual table module xDestroy method.
*/
static int rtreeDestroy(sqlite3_vtab *pVtab){
Rtree *pRtree = (Rtree *)pVtab;
int rc;
char *zCreate = sqlite3_mprintf(
"DROP TABLE '%q'.'%q_node';"
"DROP TABLE '%q'.'%q_rowid';"
"DROP TABLE '%q'.'%q_parent';",
pRtree->zDb, pRtree->zName,
pRtree->zDb, pRtree->zName,
pRtree->zDb, pRtree->zName
);
if( !zCreate ){
rc = SQLITE_NOMEM;
}else{
nodeBlobReset(pRtree);
rc = sqlite3_exec(pRtree->db, zCreate, 0, 0, 0);
sqlite3_free(zCreate);
}
if( rc==SQLITE_OK ){
rtreeRelease(pRtree);
}
return rc;
}
/*
** Rtree virtual table module xOpen method.
*/
static int rtreeOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){
int rc = SQLITE_NOMEM;
Rtree *pRtree = (Rtree *)pVTab;
RtreeCursor *pCsr;
pCsr = (RtreeCursor *)sqlite3_malloc64(sizeof(RtreeCursor));
if( pCsr ){
memset(pCsr, 0, sizeof(RtreeCursor));
pCsr->base.pVtab = pVTab;
rc = SQLITE_OK;
pRtree->nCursor++;
}
*ppCursor = (sqlite3_vtab_cursor *)pCsr;
return rc;
}
/*
** Reset a cursor back to its initial state.
*/
static void resetCursor(RtreeCursor *pCsr){
Rtree *pRtree = (Rtree *)(pCsr->base.pVtab);
int ii;
sqlite3_stmt *pStmt;
if( pCsr->aConstraint ){
int i; /* Used to iterate through constraint array */
for(i=0; i<pCsr->nConstraint; i++){
sqlite3_rtree_query_info *pInfo = pCsr->aConstraint[i].pInfo;
if( pInfo ){
if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);
sqlite3_free(pInfo);
}
}
sqlite3_free(pCsr->aConstraint);
pCsr->aConstraint = 0;
}
for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);
sqlite3_free(pCsr->aPoint);
pStmt = pCsr->pReadAux;
memset(pCsr, 0, sizeof(RtreeCursor));
pCsr->base.pVtab = (sqlite3_vtab*)pRtree;
pCsr->pReadAux = pStmt;
}
/*
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
Rtree *pRtree = (Rtree *)(cur->pVtab);
RtreeCursor *pCsr = (RtreeCursor *)cur;
assert( pRtree->nCursor>0 );
resetCursor(pCsr);
sqlite3_finalize(pCsr->pReadAux);
sqlite3_free(pCsr);
pRtree->nCursor--;
if( pRtree->nCursor==0 && pRtree->inWrTrans==0 ){
nodeBlobReset(pRtree);
}
return SQLITE_OK;
}
/*
** Rtree virtual table module xEof method.
**
** Return non-zero if the cursor does not currently point to a valid
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
RtreeCursor *pCsr = (RtreeCursor *)cur;
return pCsr->atEOF;
}
/*
** Convert raw bits from the on-disk RTree record into a coordinate value.
** The on-disk format is big-endian and needs to be converted for little-
** endian platforms. The on-disk record stores integer coordinates if
** eInt is true and it stores 32-bit floating point records if eInt is
** false. a[] is the four bytes of the on-disk record to be decoded.
** Store the results in "r".
**
** There are five versions of this macro. The last one is generic. The
** other four are various architectures-specific optimizations.
*/
#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
#define RTREE_DECODE_COORD(eInt, a, r) { \
RtreeCoord c; /* Coordinate decoded */ \
c.u = _byteswap_ulong(*(u32*)a); \
r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}
#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000
#define RTREE_DECODE_COORD(eInt, a, r) { \
RtreeCoord c; /* Coordinate decoded */ \
c.u = __builtin_bswap32(*(u32*)a); \
r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}
#elif SQLITE_BYTEORDER==1234
#define RTREE_DECODE_COORD(eInt, a, r) { \
RtreeCoord c; /* Coordinate decoded */ \
memcpy(&c.u,a,4); \
c.u = ((c.u>>24)&0xff)|((c.u>>8)&0xff00)| \
((c.u&0xff)<<24)|((c.u&0xff00)<<8); \
r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}
#elif SQLITE_BYTEORDER==4321
#define RTREE_DECODE_COORD(eInt, a, r) { \
RtreeCoord c; /* Coordinate decoded */ \
memcpy(&c.u,a,4); \
r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}
#else
#define RTREE_DECODE_COORD(eInt, a, r) { \
RtreeCoord c; /* Coordinate decoded */ \
c.u = ((u32)a[0]<<24) + ((u32)a[1]<<16) \
+((u32)a[2]<<8) + a[3]; \
r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \
}
#endif
/*
** Check the RTree node or entry given by pCellData and p against the MATCH
** constraint pConstraint.
*/
static int rtreeCallbackConstraint(
RtreeConstraint *pConstraint, /* The constraint to test */
int eInt, /* True if RTree holding integer coordinates */
u8 *pCellData, /* Raw cell content */
RtreeSearchPoint *pSearch, /* Container of this cell */
sqlite3_rtree_dbl *prScore, /* OUT: score for the cell */
int *peWithin /* OUT: visibility of the cell */
){
sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */
int nCoord = pInfo->nCoord; /* No. of coordinates */
int rc; /* Callback return code */
RtreeCoord c; /* Translator union */
sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2]; /* Decoded coordinates */
assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );
assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );
if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){
pInfo->iRowid = readInt64(pCellData);
}
pCellData += 8;
#ifndef SQLITE_RTREE_INT_ONLY
if( eInt==0 ){
switch( nCoord ){
case 10: readCoord(pCellData+36, &c); aCoord[9] = c.f;
readCoord(pCellData+32, &c); aCoord[8] = c.f;
case 8: readCoord(pCellData+28, &c); aCoord[7] = c.f;
readCoord(pCellData+24, &c); aCoord[6] = c.f;
case 6: readCoord(pCellData+20, &c); aCoord[5] = c.f;
readCoord(pCellData+16, &c); aCoord[4] = c.f;
case 4: readCoord(pCellData+12, &c); aCoord[3] = c.f;
readCoord(pCellData+8, &c); aCoord[2] = c.f;
default: readCoord(pCellData+4, &c); aCoord[1] = c.f;
readCoord(pCellData, &c); aCoord[0] = c.f;
}
}else
#endif
{
switch( nCoord ){
case 10: readCoord(pCellData+36, &c); aCoord[9] = c.i;
readCoord(pCellData+32, &c); aCoord[8] = c.i;
case 8: readCoord(pCellData+28, &c); aCoord[7] = c.i;
readCoord(pCellData+24, &c); aCoord[6] = c.i;
case 6: readCoord(pCellData+20, &c); aCoord[5] = c.i;
readCoord(pCellData+16, &c); aCoord[4] = c.i;
case 4: readCoord(pCellData+12, &c); aCoord[3] = c.i;
readCoord(pCellData+8, &c); aCoord[2] = c.i;
default: readCoord(pCellData+4, &c); aCoord[1] = c.i;
readCoord(pCellData, &c); aCoord[0] = c.i;
}
}
if( pConstraint->op==RTREE_MATCH ){
int eWithin = 0;
rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,
nCoord, aCoord, &eWithin);
if( eWithin==0 ) *peWithin = NOT_WITHIN;
*prScore = RTREE_ZERO;
}else{
pInfo->aCoord = aCoord;
pInfo->iLevel = pSearch->iLevel - 1;
pInfo->rScore = pInfo->rParentScore = pSearch->rScore;
pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;
rc = pConstraint->u.xQueryFunc(pInfo);
if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;
if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){
*prScore = pInfo->rScore;
}
}
return rc;
}
/*
** Check the internal RTree node given by pCellData against constraint p.
** If this constraint cannot be satisfied by any child within the node,
** set *peWithin to NOT_WITHIN.
*/
static void rtreeNonleafConstraint(
RtreeConstraint *p, /* The constraint to test */
int eInt, /* True if RTree holds integer coordinates */
u8 *pCellData, /* Raw cell content as appears on disk */
int *peWithin /* Adjust downward, as appropriate */
){
sqlite3_rtree_dbl val; /* Coordinate value convert to a double */
/* p->iCoord might point to either a lower or upper bound coordinate
** in a coordinate pair. But make pCellData point to the lower bound.
*/
pCellData += 8 + 4*(p->iCoord&0xfe);
assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE
|| p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_TRUE
|| p->op==RTREE_FALSE );
assert( FOUR_BYTE_ALIGNED(pCellData) );
switch( p->op ){
case RTREE_TRUE: return; /* Always satisfied */
case RTREE_FALSE: break; /* Never satisfied */
case RTREE_EQ:
RTREE_DECODE_COORD(eInt, pCellData, val);
/* val now holds the lower bound of the coordinate pair */
if( p->u.rValue>=val ){
pCellData += 4;
RTREE_DECODE_COORD(eInt, pCellData, val);
/* val now holds the upper bound of the coordinate pair */
if( p->u.rValue<=val ) return;
}
break;
case RTREE_LE:
case RTREE_LT:
RTREE_DECODE_COORD(eInt, pCellData, val);
/* val now holds the lower bound of the coordinate pair */
if( p->u.rValue>=val ) return;
break;
default:
pCellData += 4;
RTREE_DECODE_COORD(eInt, pCellData, val);
/* val now holds the upper bound of the coordinate pair */
if( p->u.rValue<=val ) return;
break;
}
*peWithin = NOT_WITHIN;
}
/*
** Check the leaf RTree cell given by pCellData against constraint p.
** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.
** If the constraint is satisfied, leave *peWithin unchanged.
**
** The constraint is of the form: xN op $val
**
** The op is given by p->op. The xN is p->iCoord-th coordinate in
** pCellData. $val is given by p->u.rValue.
*/
static void rtreeLeafConstraint(
RtreeConstraint *p, /* The constraint to test */
int eInt, /* True if RTree holds integer coordinates */
u8 *pCellData, /* Raw cell content as appears on disk */
int *peWithin /* Adjust downward, as appropriate */
){
RtreeDValue xN; /* Coordinate value converted to a double */
assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE
|| p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_TRUE
|| p->op==RTREE_FALSE );
pCellData += 8 + p->iCoord*4;
assert( FOUR_BYTE_ALIGNED(pCellData) );
RTREE_DECODE_COORD(eInt, pCellData, xN);
switch( p->op ){
case RTREE_TRUE: return; /* Always satisfied */
case RTREE_FALSE: break; /* Never satisfied */
case RTREE_LE: if( xN <= p->u.rValue ) return; break;
case RTREE_LT: if( xN < p->u.rValue ) return; break;
case RTREE_GE: if( xN >= p->u.rValue ) return; break;
case RTREE_GT: if( xN > p->u.rValue ) return; break;
default: if( xN == p->u.rValue ) return; break;
}
*peWithin = NOT_WITHIN;
}
/*
** One of the cells in node pNode is guaranteed to have a 64-bit
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
Rtree *pRtree,
RtreeNode *pNode,
i64 iRowid,
int *piIndex
){
int ii;
int nCell = NCELL(pNode);
assert( nCell<200 );
for(ii=0; ii<nCell; ii++){
if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){
*piIndex = ii;
return SQLITE_OK;
}
}
RTREE_IS_CORRUPT(pRtree);
return SQLITE_CORRUPT_VTAB;
}
/*
** Return the index of the cell containing a pointer to node pNode
** in its parent. If pNode is the root node, return -1.
*/
static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode, int *piIndex){
RtreeNode *pParent = pNode->pParent;
if( ALWAYS(pParent) ){
return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
}else{
*piIndex = -1;
return SQLITE_OK;
}
}
/*
** Compare two search points. Return negative, zero, or positive if the first
** is less than, equal to, or greater than the second.
**
** The rScore is the primary key. Smaller rScore values come first.
** If the rScore is a tie, then use iLevel as the tie breaker with smaller
** iLevel values coming first. In this way, if rScore is the same for all
** SearchPoints, then iLevel becomes the deciding factor and the result
** is a depth-first search, which is the desired default behavior.
*/
static int rtreeSearchPointCompare(
const RtreeSearchPoint *pA,
const RtreeSearchPoint *pB
){
if( pA->rScore<pB->rScore ) return -1;
if( pA->rScore>pB->rScore ) return +1;
if( pA->iLevel<pB->iLevel ) return -1;
if( pA->iLevel>pB->iLevel ) return +1;
return 0;
}
/*
** Interchange two search points in a cursor.
*/
static void rtreeSearchPointSwap(RtreeCursor *p, int i, int j){
RtreeSearchPoint t = p->aPoint[i];
assert( i<j );
p->aPoint[i] = p->aPoint[j];
p->aPoint[j] = t;
i++; j++;
if( i<RTREE_CACHE_SZ ){
if( j>=RTREE_CACHE_SZ ){
nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
p->aNode[i] = 0;
}else{
RtreeNode *pTemp = p->aNode[i];
p->aNode[i] = p->aNode[j];
p->aNode[j] = pTemp;
}
}
}
/*
** Return the search point with the lowest current score.
*/
static RtreeSearchPoint *rtreeSearchPointFirst(RtreeCursor *pCur){
return pCur->bPoint ? &pCur->sPoint : pCur->nPoint ? pCur->aPoint : 0;
}
/*
** Get the RtreeNode for the search point with the lowest score.
*/
static RtreeNode *rtreeNodeOfFirstSearchPoint(RtreeCursor *pCur, int *pRC){
sqlite3_int64 id;
int ii = 1 - pCur->bPoint;
assert( ii==0 || ii==1 );
assert( pCur->bPoint || pCur->nPoint );
if( pCur->aNode[ii]==0 ){
assert( pRC!=0 );
id = ii ? pCur->aPoint[0].id : pCur->sPoint.id;
*pRC = nodeAcquire(RTREE_OF_CURSOR(pCur), id, 0, &pCur->aNode[ii]);
}
return pCur->aNode[ii];
}
/*
** Push a new element onto the priority queue
*/
static RtreeSearchPoint *rtreeEnqueue(
RtreeCursor *pCur, /* The cursor */
RtreeDValue rScore, /* Score for the new search point */
u8 iLevel /* Level for the new search point */
){
int i, j;
RtreeSearchPoint *pNew;
if( pCur->nPoint>=pCur->nPointAlloc ){
int nNew = pCur->nPointAlloc*2 + 8;
pNew = sqlite3_realloc64(pCur->aPoint, nNew*sizeof(pCur->aPoint[0]));
if( pNew==0 ) return 0;
pCur->aPoint = pNew;
pCur->nPointAlloc = nNew;
}
i = pCur->nPoint++;
pNew = pCur->aPoint + i;
pNew->rScore = rScore;
pNew->iLevel = iLevel;
assert( iLevel<=RTREE_MAX_DEPTH );
while( i>0 ){
RtreeSearchPoint *pParent;
j = (i-1)/2;
pParent = pCur->aPoint + j;
if( rtreeSearchPointCompare(pNew, pParent)>=0 ) break;
rtreeSearchPointSwap(pCur, j, i);
i = j;
pNew = pParent;
}
return pNew;
}
/*
** Allocate a new RtreeSearchPoint and return a pointer to it. Return
** NULL if malloc fails.
*/
static RtreeSearchPoint *rtreeSearchPointNew(
RtreeCursor *pCur, /* The cursor */
RtreeDValue rScore, /* Score for the new search point */
u8 iLevel /* Level for the new search point */
){
RtreeSearchPoint *pNew, *pFirst;
pFirst = rtreeSearchPointFirst(pCur);
pCur->anQueue[iLevel]++;
if( pFirst==0
|| pFirst->rScore>rScore
|| (pFirst->rScore==rScore && pFirst->iLevel>iLevel)
){
if( pCur->bPoint ){
int ii;
pNew = rtreeEnqueue(pCur, rScore, iLevel);
if( pNew==0 ) return 0;
ii = (int)(pNew - pCur->aPoint) + 1;
assert( ii==1 );
if( ALWAYS(ii<RTREE_CACHE_SZ) ){
assert( pCur->aNode[ii]==0 );
pCur->aNode[ii] = pCur->aNode[0];
}else{
nodeRelease(RTREE_OF_CURSOR(pCur), pCur->aNode[0]);
}
pCur->aNode[0] = 0;
*pNew = pCur->sPoint;
}
pCur->sPoint.rScore = rScore;
pCur->sPoint.iLevel = iLevel;
pCur->bPoint = 1;
return &pCur->sPoint;
}else{
return rtreeEnqueue(pCur, rScore, iLevel);
}
}
#if 0
/* Tracing routines for the RtreeSearchPoint queue */
static void tracePoint(RtreeSearchPoint *p, int idx, RtreeCursor *pCur){
if( idx<0 ){ printf(" s"); }else{ printf("%2d", idx); }
printf(" %d.%05lld.%02d %g %d",
p->iLevel, p->id, p->iCell, p->rScore, p->eWithin
);
idx++;
if( idx<RTREE_CACHE_SZ ){
printf(" %p\n", pCur->aNode[idx]);
}else{
printf("\n");
}
}
static void traceQueue(RtreeCursor *pCur, const char *zPrefix){
int ii;
printf("=== %9s ", zPrefix);
if( pCur->bPoint ){
tracePoint(&pCur->sPoint, -1, pCur);
}
for(ii=0; ii<pCur->nPoint; ii++){
if( ii>0 || pCur->bPoint ) printf(" ");
tracePoint(&pCur->aPoint[ii], ii, pCur);
}
}
# define RTREE_QUEUE_TRACE(A,B) traceQueue(A,B)
#else
# define RTREE_QUEUE_TRACE(A,B) /* no-op */
#endif
/* Remove the search point with the lowest current score.
*/
static void rtreeSearchPointPop(RtreeCursor *p){
int i, j, k, n;
i = 1 - p->bPoint;
assert( i==0 || i==1 );
if( p->aNode[i] ){
nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);
p->aNode[i] = 0;
}
if( p->bPoint ){
p->anQueue[p->sPoint.iLevel]--;
p->bPoint = 0;
}else if( ALWAYS(p->nPoint) ){
p->anQueue[p->aPoint[0].iLevel]--;
n = --p->nPoint;
p->aPoint[0] = p->aPoint[n];
if( n<RTREE_CACHE_SZ-1 ){
p->aNode[1] = p->aNode[n+1];
p->aNode[n+1] = 0;
}
i = 0;
while( (j = i*2+1)<n ){
k = j+1;
if( k<n && rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[j])<0 ){
if( rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[i])<0 ){
rtreeSearchPointSwap(p, i, k);
i = k;
}else{
break;
}
}else{
if( rtreeSearchPointCompare(&p->aPoint[j], &p->aPoint[i])<0 ){
rtreeSearchPointSwap(p, i, j);
i = j;
}else{
break;
}
}
}
}
}
/*
** Continue the search on cursor pCur until the front of the queue
** contains an entry suitable for returning as a result-set row,
** or until the RtreeSearchPoint queue is empty, indicating that the
** query has completed.
*/
static int rtreeStepToLeaf(RtreeCursor *pCur){
RtreeSearchPoint *p;
Rtree *pRtree = RTREE_OF_CURSOR(pCur);
RtreeNode *pNode;
int eWithin;
int rc = SQLITE_OK;
int nCell;
int nConstraint = pCur->nConstraint;
int ii;
int eInt;
RtreeSearchPoint x;
eInt = pRtree->eCoordType==RTREE_COORD_INT32;
while( (p = rtreeSearchPointFirst(pCur))!=0 && p->iLevel>0 ){
u8 *pCellData;
pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);
if( rc ) return rc;
nCell = NCELL(pNode);
assert( nCell<200 );
pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);
while( p->iCell<nCell ){
sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;
eWithin = FULLY_WITHIN;
for(ii=0; ii<nConstraint; ii++){
RtreeConstraint *pConstraint = pCur->aConstraint + ii;
if( pConstraint->op>=RTREE_MATCH ){
rc = rtreeCallbackConstraint(pConstraint, eInt, pCellData, p,
&rScore, &eWithin);
if( rc ) return rc;
}else if( p->iLevel==1 ){
rtreeLeafConstraint(pConstraint, eInt, pCellData, &eWithin);
}else{
rtreeNonleafConstraint(pConstraint, eInt, pCellData, &eWithin);
}
if( eWithin==NOT_WITHIN ){
p->iCell++;
pCellData += pRtree->nBytesPerCell;
break;
}
}
if( eWithin==NOT_WITHIN ) continue;
p->iCell++;
x.iLevel = p->iLevel - 1;
if( x.iLevel ){
x.id = readInt64(pCellData);
for(ii=0; ii<pCur->nPoint; ii++){
if( pCur->aPoint[ii].id==x.id ){
RTREE_IS_CORRUPT(pRtree);
return SQLITE_CORRUPT_VTAB;
}
}
x.iCell = 0;
}else{
x.id = p->id;
x.iCell = p->iCell - 1;
}
if( p->iCell>=nCell ){
RTREE_QUEUE_TRACE(pCur, "POP-S:");
rtreeSearchPointPop(pCur);
}
if( rScore<RTREE_ZERO ) rScore = RTREE_ZERO;
p = rtreeSearchPointNew(pCur, rScore, x.iLevel);
if( p==0 ) return SQLITE_NOMEM;
p->eWithin = (u8)eWithin;
p->id = x.id;
p->iCell = x.iCell;
RTREE_QUEUE_TRACE(pCur, "PUSH-S:");
break;
}
if( p->iCell>=nCell ){
RTREE_QUEUE_TRACE(pCur, "POP-Se:");
rtreeSearchPointPop(pCur);
}
}
pCur->atEOF = p==0;
return SQLITE_OK;
}
/*
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
int rc = SQLITE_OK;
/* Move to the next entry that matches the configured constraints. */
RTREE_QUEUE_TRACE(pCsr, "POP-Nx:");
if( pCsr->bAuxValid ){
pCsr->bAuxValid = 0;
sqlite3_reset(pCsr->pReadAux);
}
rtreeSearchPointPop(pCsr);
rc = rtreeStepToLeaf(pCsr);
return rc;
}
/*
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
int rc = SQLITE_OK;
RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
if( rc==SQLITE_OK && ALWAYS(p) ){
if( p->iCell>=NCELL(pNode) ){
rc = SQLITE_ABORT;
}else{
*pRowid = nodeGetRowid(RTREE_OF_CURSOR(pCsr), pNode, p->iCell);
}
}
return rc;
}
/*
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
Rtree *pRtree = (Rtree *)cur->pVtab;
RtreeCursor *pCsr = (RtreeCursor *)cur;
RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
RtreeCoord c;
int rc = SQLITE_OK;
RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
if( rc ) return rc;
if( NEVER(p==0) ) return SQLITE_OK;
if( p->iCell>=NCELL(pNode) ) return SQLITE_ABORT;
if( i==0 ){
sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));
}else if( i<=pRtree->nDim2 ){
nodeGetCoord(pRtree, pNode, p->iCell, i-1, &c);
#ifndef SQLITE_RTREE_INT_ONLY
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
sqlite3_result_double(ctx, c.f);
}else
#endif
{
assert( pRtree->eCoordType==RTREE_COORD_INT32 );
sqlite3_result_int(ctx, c.i);
}
}else{
if( !pCsr->bAuxValid ){
if( pCsr->pReadAux==0 ){
rc = sqlite3_prepare_v3(pRtree->db, pRtree->zReadAuxSql, -1, 0,
&pCsr->pReadAux, 0);
if( rc ) return rc;
}
sqlite3_bind_int64(pCsr->pReadAux, 1,
nodeGetRowid(pRtree, pNode, p->iCell));
rc = sqlite3_step(pCsr->pReadAux);
if( rc==SQLITE_ROW ){
pCsr->bAuxValid = 1;
}else{
sqlite3_reset(pCsr->pReadAux);
if( rc==SQLITE_DONE ) rc = SQLITE_OK;
return rc;
}
}
sqlite3_result_value(ctx,
sqlite3_column_value(pCsr->pReadAux, i - pRtree->nDim2 + 1));
}
return SQLITE_OK;
}
/*
** Use nodeAcquire() to obtain the leaf node containing the record with
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(
Rtree *pRtree, /* RTree to search */
i64 iRowid, /* The rowid searching for */
RtreeNode **ppLeaf, /* Write the node here */
sqlite3_int64 *piNode /* Write the node-id here */
){
int rc;
*ppLeaf = 0;
sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
if( piNode ) *piNode = iNode;
rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
sqlite3_reset(pRtree->pReadRowid);
}else{
rc = sqlite3_reset(pRtree->pReadRowid);
}
return rc;
}
/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
RtreeMatchArg *pBlob, *pSrc; /* BLOB returned by geometry function */
sqlite3_rtree_query_info *pInfo; /* Callback information */
pSrc = sqlite3_value_pointer(pValue, "RtreeMatchArg");
if( pSrc==0 ) return SQLITE_ERROR;
pInfo = (sqlite3_rtree_query_info*)
sqlite3_malloc64( sizeof(*pInfo)+pSrc->iSize );
if( !pInfo ) return SQLITE_NOMEM;
memset(pInfo, 0, sizeof(*pInfo));
pBlob = (RtreeMatchArg*)&pInfo[1];
memcpy(pBlob, pSrc, pSrc->iSize);
pInfo->pContext = pBlob->cb.pContext;
pInfo->nParam = pBlob->nParam;
pInfo->aParam = pBlob->aParam;
pInfo->apSqlParam = pBlob->apSqlParam;
if( pBlob->cb.xGeom ){
pCons->u.xGeom = pBlob->cb.xGeom;
}else{
pCons->op = RTREE_QUERY;
pCons->u.xQueryFunc = pBlob->cb.xQueryFunc;
}
pCons->pInfo = pInfo;
return SQLITE_OK;
}
int sqlite3IntFloatCompare(i64,double);
/*
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
sqlite3_vtab_cursor *pVtabCursor,
int idxNum, const char *idxStr,
int argc, sqlite3_value **argv
){
Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
RtreeNode *pRoot = 0;
int ii;
int rc = SQLITE_OK;
int iCell = 0;
rtreeReference(pRtree);
/* Reset the cursor to the same state as rtreeOpen() leaves it in. */
resetCursor(pCsr);
pCsr->iStrategy = idxNum;
if( idxNum==1 ){
/* Special case - lookup by rowid. */
RtreeNode *pLeaf; /* Leaf on which the required cell resides */
RtreeSearchPoint *p; /* Search point for the leaf */
i64 iRowid = sqlite3_value_int64(argv[0]);
i64 iNode = 0;
int eType = sqlite3_value_numeric_type(argv[0]);
if( eType==SQLITE_INTEGER
|| (eType==SQLITE_FLOAT
&& 0==sqlite3IntFloatCompare(iRowid,sqlite3_value_double(argv[0])))
){
rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);
}else{
rc = SQLITE_OK;
pLeaf = 0;
}
if( rc==SQLITE_OK && pLeaf!=0 ){
p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
assert( p!=0 ); /* Always returns pCsr->sPoint */
pCsr->aNode[0] = pLeaf;
p->id = iNode;
p->eWithin = PARTLY_WITHIN;
rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
p->iCell = (u8)iCell;
RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
}else{
pCsr->atEOF = 1;
}
}else{
/* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array
** with the configured constraints.
*/
rc = nodeAcquire(pRtree, 1, 0, &pRoot);
if( rc==SQLITE_OK && argc>0 ){
pCsr->aConstraint = sqlite3_malloc64(sizeof(RtreeConstraint)*argc);
pCsr->nConstraint = argc;
if( !pCsr->aConstraint ){
rc = SQLITE_NOMEM;
}else{
memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
assert( (idxStr==0 && argc==0)
|| (idxStr && (int)strlen(idxStr)==argc*2) );
for(ii=0; ii<argc; ii++){
RtreeConstraint *p = &pCsr->aConstraint[ii];
int eType = sqlite3_value_numeric_type(argv[ii]);
p->op = idxStr[ii*2];
p->iCoord = idxStr[ii*2+1]-'0';
if( p->op>=RTREE_MATCH ){
/* A MATCH operator. The right-hand-side must be a blob that
** can be cast into an RtreeMatchArg object. One created using
** an sqlite3_rtree_geometry_callback() SQL user function.
*/
rc = deserializeGeometry(argv[ii], p);
if( rc!=SQLITE_OK ){
break;
}
p->pInfo->nCoord = pRtree->nDim2;
p->pInfo->anQueue = pCsr->anQueue;
p->pInfo->mxLevel = pRtree->iDepth + 1;
}else if( eType==SQLITE_INTEGER ){
sqlite3_int64 iVal = sqlite3_value_int64(argv[ii]);
#ifdef SQLITE_RTREE_INT_ONLY
p->u.rValue = iVal;
#else
p->u.rValue = (double)iVal;
if( iVal>=((sqlite3_int64)1)<<48
|| iVal<=-(((sqlite3_int64)1)<<48)
){
if( p->op==RTREE_LT ) p->op = RTREE_LE;
if( p->op==RTREE_GT ) p->op = RTREE_GE;
}
#endif
}else if( eType==SQLITE_FLOAT ){
#ifdef SQLITE_RTREE_INT_ONLY
p->u.rValue = sqlite3_value_int64(argv[ii]);
#else
p->u.rValue = sqlite3_value_double(argv[ii]);
#endif
}else{
p->u.rValue = RTREE_ZERO;
if( eType==SQLITE_NULL ){
p->op = RTREE_FALSE;
}else if( p->op==RTREE_LT || p->op==RTREE_LE ){
p->op = RTREE_TRUE;
}else{
p->op = RTREE_FALSE;
}
}
}
}
}
if( rc==SQLITE_OK ){
RtreeSearchPoint *pNew;
assert( pCsr->bPoint==0 ); /* Due to the resetCursor() call above */
pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, (u8)(pRtree->iDepth+1));
if( NEVER(pNew==0) ){ /* Because pCsr->bPoint was FALSE */
return SQLITE_NOMEM;
}
pNew->id = 1;
pNew->iCell = 0;
pNew->eWithin = PARTLY_WITHIN;
assert( pCsr->bPoint==1 );
pCsr->aNode[0] = pRoot;
pRoot = 0;
RTREE_QUEUE_TRACE(pCsr, "PUSH-Fm:");
rc = rtreeStepToLeaf(pCsr);
}
}
nodeRelease(pRtree, pRoot);
rtreeRelease(pRtree);
return rc;
}
/*
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to
** least desirable):
**
** idxNum idxStr Strategy
** ------------------------------------------------
** 1 Unused Direct lookup by rowid.
** 2 See below R-tree query or full-table scan.
** ------------------------------------------------
**
** If strategy 1 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each
** constraint used. The first two bytes of idxStr correspond to
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
**
** Operator Byte Value
** ----------------------
** = 0x41 ('A')
** <= 0x42 ('B')
** < 0x43 ('C')
** >= 0x44 ('D')
** > 0x45 ('E')
** MATCH 0x46 ('F')
** ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
Rtree *pRtree = (Rtree*)tab;
int rc = SQLITE_OK;
int ii;
int bMatch = 0; /* True if there exists a MATCH constraint */
i64 nRow; /* Estimated rows returned by this scan */
int iIdx = 0;
char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
memset(zIdxStr, 0, sizeof(zIdxStr));
/* Check if there exists a MATCH constraint - even an unusable one. If there
** is, do not consider the lookup-by-rowid plan as using such a plan would
** require the VDBE to evaluate the MATCH constraint, which is not currently
** possible. */
for(ii=0; ii<pIdxInfo->nConstraint; ii++){
if( pIdxInfo->aConstraint[ii].op==SQLITE_INDEX_CONSTRAINT_MATCH ){
bMatch = 1;
}
}
assert( pIdxInfo->idxStr==0 );
for(ii=0; ii<pIdxInfo->nConstraint && iIdx<(int)(sizeof(zIdxStr)-1); ii++){
struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];
if( bMatch==0 && p->usable
&& p->iColumn<=0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ
){
/* We have an equality constraint on the rowid. Use strategy 1. */
int jj;
for(jj=0; jj<ii; jj++){
pIdxInfo->aConstraintUsage[jj].argvIndex = 0;
pIdxInfo->aConstraintUsage[jj].omit = 0;
}
pIdxInfo->idxNum = 1;
pIdxInfo->aConstraintUsage[ii].argvIndex = 1;
pIdxInfo->aConstraintUsage[jj].omit = 1;
/* This strategy involves a two rowid lookups on an B-Tree structures
** and then a linear search of an R-Tree node. This should be
** considered almost as quick as a direct rowid lookup (for which
** sqlite uses an internal cost of 0.0). It is expected to return
** a single row.
*/
pIdxInfo->estimatedCost = 30.0;
pIdxInfo->estimatedRows = 1;
pIdxInfo->idxFlags = SQLITE_INDEX_SCAN_UNIQUE;
return SQLITE_OK;
}
if( p->usable
&& ((p->iColumn>0 && p->iColumn<=pRtree->nDim2)
|| p->op==SQLITE_INDEX_CONSTRAINT_MATCH)
){
u8 op;
u8 doOmit = 1;
switch( p->op ){
case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; doOmit = 0; break;
case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; doOmit = 0; break;
case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; doOmit = 0; break;
case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
case SQLITE_INDEX_CONSTRAINT_MATCH: op = RTREE_MATCH; break;
default: op = 0; break;
}
if( op ){
zIdxStr[iIdx++] = op;
zIdxStr[iIdx++] = (char)(p->iColumn - 1 + '0');
pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
pIdxInfo->aConstraintUsage[ii].omit = doOmit;
}
}
}
pIdxInfo->idxNum = 2;
pIdxInfo->needToFreeIdxStr = 1;
if( iIdx>0 ){
pIdxInfo->idxStr = sqlite3_malloc( iIdx+1 );
if( pIdxInfo->idxStr==0 ){
return SQLITE_NOMEM;
}
memcpy(pIdxInfo->idxStr, zIdxStr, iIdx+1);
}
nRow = pRtree->nRowEst >> (iIdx/2);
pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;
pIdxInfo->estimatedRows = nRow;
return rc;
}
/*
** Return the N-dimensional volumn of the cell stored in *p.
*/
static RtreeDValue cellArea(Rtree *pRtree, RtreeCell *p){
RtreeDValue area = (RtreeDValue)1;
assert( pRtree->nDim>=1 && pRtree->nDim<=5 );
#ifndef SQLITE_RTREE_INT_ONLY
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
switch( pRtree->nDim ){
case 5: area = p->aCoord[9].f - p->aCoord[8].f;
case 4: area *= p->aCoord[7].f - p->aCoord[6].f;
case 3: area *= p->aCoord[5].f - p->aCoord[4].f;
case 2: area *= p->aCoord[3].f - p->aCoord[2].f;
default: area *= p->aCoord[1].f - p->aCoord[0].f;
}
}else
#endif
{
switch( pRtree->nDim ){
case 5: area = (i64)p->aCoord[9].i - (i64)p->aCoord[8].i;
case 4: area *= (i64)p->aCoord[7].i - (i64)p->aCoord[6].i;
case 3: area *= (i64)p->aCoord[5].i - (i64)p->aCoord[4].i;
case 2: area *= (i64)p->aCoord[3].i - (i64)p->aCoord[2].i;
default: area *= (i64)p->aCoord[1].i - (i64)p->aCoord[0].i;
}
}
return area;
}
/*
** Return the margin length of cell p. The margin length is the sum
** of the objects size in each dimension.
*/
static RtreeDValue cellMargin(Rtree *pRtree, RtreeCell *p){
RtreeDValue margin = 0;
int ii = pRtree->nDim2 - 2;
do{
margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
ii -= 2;
}while( ii>=0 );
return margin;
}
/*
** Store the union of cells p1 and p2 in p1.
*/
static void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
int ii = 0;
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
do{
p1->aCoord[ii].f = MIN(p1->aCoord[ii].f, p2->aCoord[ii].f);
p1->aCoord[ii+1].f = MAX(p1->aCoord[ii+1].f, p2->aCoord[ii+1].f);
ii += 2;
}while( ii<pRtree->nDim2 );
}else{
do{
p1->aCoord[ii].i = MIN(p1->aCoord[ii].i, p2->aCoord[ii].i);
p1->aCoord[ii+1].i = MAX(p1->aCoord[ii+1].i, p2->aCoord[ii+1].i);
ii += 2;
}while( ii<pRtree->nDim2 );
}
}
/*
** Return true if the area covered by p2 is a subset of the area covered
** by p1. False otherwise.
*/
static int cellContains(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
int ii;
if( pRtree->eCoordType==RTREE_COORD_INT32 ){
for(ii=0; ii<pRtree->nDim2; ii+=2){
RtreeCoord *a1 = &p1->aCoord[ii];
RtreeCoord *a2 = &p2->aCoord[ii];
if( a2[0].i<a1[0].i || a2[1].i>a1[1].i ) return 0;
}
}else{
for(ii=0; ii<pRtree->nDim2; ii+=2){
RtreeCoord *a1 = &p1->aCoord[ii];
RtreeCoord *a2 = &p2->aCoord[ii];
if( a2[0].f<a1[0].f || a2[1].f>a1[1].f ) return 0;
}
}
return 1;
}
static RtreeDValue cellOverlap(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *aCell,
int nCell
){
int ii;
RtreeDValue overlap = RTREE_ZERO;
for(ii=0; ii<nCell; ii++){
int jj;
RtreeDValue o = (RtreeDValue)1;
for(jj=0; jj<pRtree->nDim2; jj+=2){
RtreeDValue x1, x2;
x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));
if( x2<x1 ){
o = (RtreeDValue)0;
break;
}else{
o = o * (x2-x1);
}
}
overlap += o;
}
return overlap;
}
/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
Rtree *pRtree, /* Rtree table */
RtreeCell *pCell, /* Cell to insert into rtree */
int iHeight, /* Height of sub-tree rooted at pCell */
RtreeNode **ppLeaf /* OUT: Selected leaf page */
){
int rc;
int ii;
RtreeNode *pNode = 0;
rc = nodeAcquire(pRtree, 1, 0, &pNode);
for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
int iCell;
sqlite3_int64 iBest = 0;
int bFound = 0;
RtreeDValue fMinGrowth = RTREE_ZERO;
RtreeDValue fMinArea = RTREE_ZERO;
int nCell = NCELL(pNode);
RtreeNode *pChild = 0;
/* First check to see if there is are any cells in pNode that completely
** contains pCell. If two or more cells in pNode completely contain pCell
** then pick the smallest.
*/
for(iCell=0; iCell<nCell; iCell++){
RtreeCell cell;
nodeGetCell(pRtree, pNode, iCell, &cell);
if( cellContains(pRtree, &cell, pCell) ){
RtreeDValue area = cellArea(pRtree, &cell);
if( bFound==0 || area<fMinArea ){
iBest = cell.iRowid;
fMinArea = area;
bFound = 1;
}
}
}
if( !bFound ){
/* No cells of pNode will completely contain pCell. So pick the
** cell of pNode that grows by the least amount when pCell is added.
** Break ties by selecting the smaller cell.
*/
for(iCell=0; iCell<nCell; iCell++){
RtreeCell cell;
RtreeDValue growth;
RtreeDValue area;
nodeGetCell(pRtree, pNode, iCell, &cell);
area = cellArea(pRtree, &cell);
cellUnion(pRtree, &cell, pCell);
growth = cellArea(pRtree, &cell)-area;
if( iCell==0
|| growth<fMinGrowth
|| (growth==fMinGrowth && area<fMinArea)
){
fMinGrowth = growth;
fMinArea = area;
iBest = cell.iRowid;
}
}
}
rc = nodeAcquire(pRtree, iBest, pNode, &pChild);
nodeRelease(pRtree, pNode);
pNode = pChild;
}
*ppLeaf = pNode;
return rc;
}
/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in
** all ancestor elements.
*/
static int AdjustTree(
Rtree *pRtree, /* Rtree table */
RtreeNode *pNode, /* Adjust ancestry of this node. */
RtreeCell *pCell /* This cell was just inserted */
){
RtreeNode *p = pNode;
int cnt = 0;
int rc;
while( p->pParent ){
RtreeNode *pParent = p->pParent;
RtreeCell cell;
int iCell;
cnt++;
if( NEVER(cnt>100) ){
RTREE_IS_CORRUPT(pRtree);
return SQLITE_CORRUPT_VTAB;
}
rc = nodeParentIndex(pRtree, p, &iCell);
if( NEVER(rc!=SQLITE_OK) ){
RTREE_IS_CORRUPT(pRtree);
return SQLITE_CORRUPT_VTAB;
}
nodeGetCell(pRtree, pParent, iCell, &cell);
if( !cellContains(pRtree, &cell, pCell) ){
cellUnion(pRtree, &cell, pCell);
nodeOverwriteCell(pRtree, pParent, &cell, iCell);
}
p = pParent;
}
return SQLITE_OK;
}
/*
** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
*/
static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);
sqlite3_step(pRtree->pWriteRowid);
return sqlite3_reset(pRtree->pWriteRowid);
}
/*
** Write mapping (iNode->iPar) to the <rtree>_parent table.
*/
static int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){
sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);
sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
sqlite3_step(pRtree->pWriteParent);
return sqlite3_reset(pRtree->pWriteParent);
}
static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);
/*
** Arguments aIdx, aCell and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to dimension iDim of the cells in aCell. The
** minimum value of dimension iDim is considered first, the
** maximum used to break ties.
**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDimension(
Rtree *pRtree,
int *aIdx,
int nIdx,
int iDim,
RtreeCell *aCell,
int *aSpare
){
if( nIdx>1 ){
int iLeft = 0;
int iRight = 0;
int nLeft = nIdx/2;
int nRight = nIdx-nLeft;
int *aLeft = aIdx;
int *aRight = &aIdx[nLeft];
SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);
SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);
memcpy(aSpare, aLeft, sizeof(int)*nLeft);
aLeft = aSpare;
while( iLeft<nLeft || iRight<nRight ){
RtreeDValue xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
RtreeDValue xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
RtreeDValue xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
RtreeDValue xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
if( (iLeft!=nLeft) && ((iRight==nRight)
|| (xleft1<xright1)
|| (xleft1==xright1 && xleft2<xright2)
)){
aIdx[iLeft+iRight] = aLeft[iLeft];
iLeft++;
}else{
aIdx[iLeft+iRight] = aRight[iRight];
iRight++;
}
}
#if 0
/* Check that the sort worked */
{
int jj;
for(jj=1; jj<nIdx; jj++){
RtreeDValue xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
RtreeDValue xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
RtreeDValue xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
RtreeDValue xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
}
}
#endif
}
}
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeNode *pLeft,
RtreeNode *pRight,
RtreeCell *pBboxLeft,
RtreeCell *pBboxRight
){
int **aaSorted;
int *aSpare;
int ii;
int iBestDim = 0;
int iBestSplit = 0;
RtreeDValue fBestMargin = RTREE_ZERO;
sqlite3_int64 nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));
aaSorted = (int **)sqlite3_malloc64(nByte);
if( !aaSorted ){
return SQLITE_NOMEM;
}
aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];
memset(aaSorted, 0, nByte);
for(ii=0; ii<pRtree->nDim; ii++){
int jj;
aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];
for(jj=0; jj<nCell; jj++){
aaSorted[ii][jj] = jj;
}
SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
}
for(ii=0; ii<pRtree->nDim; ii++){
RtreeDValue margin = RTREE_ZERO;
RtreeDValue fBestOverlap = RTREE_ZERO;
RtreeDValue fBestArea = RTREE_ZERO;
int iBestLeft = 0;
int nLeft;
for(
nLeft=RTREE_MINCELLS(pRtree);
nLeft<=(nCell-RTREE_MINCELLS(pRtree));
nLeft++
){
RtreeCell left;
RtreeCell right;
int kk;
RtreeDValue overlap;
RtreeDValue area;
memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
for(kk=1; kk<(nCell-1); kk++){
if( kk<nLeft ){
cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
}else{
cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
}
}
margin += cellMargin(pRtree, &left);
margin += cellMargin(pRtree, &right);
overlap = cellOverlap(pRtree, &left, &right, 1);
area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
if( (nLeft==RTREE_MINCELLS(pRtree))
|| (overlap<fBestOverlap)
|| (overlap==fBestOverlap && area<fBestArea)
){
iBestLeft = nLeft;
fBestOverlap = overlap;
fBestArea = area;
}
}
if( ii==0 || margin<fBestMargin ){
iBestDim = ii;
fBestMargin = margin;
iBestSplit = iBestLeft;
}
}
memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));
memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));
for(ii=0; ii<nCell; ii++){
RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;
RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;
RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];
nodeInsertCell(pRtree, pTarget, pCell);
cellUnion(pRtree, pBbox, pCell);
}
sqlite3_free(aaSorted);
return SQLITE_OK;
}
static int updateMapping(
Rtree *pRtree,
i64 iRowid,
RtreeNode *pNode,
int iHeight
){
int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);
xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);
if( iHeight>0 ){
RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);
RtreeNode *p;
for(p=pNode; p; p=p->pParent){
if( p==pChild ) return SQLITE_CORRUPT_VTAB;
}
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
if( NEVER(pNode==0) ) return SQLITE_ERROR;
return xSetMapping(pRtree, iRowid, pNode->iNode);
}
static int SplitNode(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iHeight
){
int i;
int newCellIsRight = 0;
int rc = SQLITE_OK;
int nCell = NCELL(pNode);
RtreeCell *aCell;
int *aiUsed;
RtreeNode *pLeft = 0;
RtreeNode *pRight = 0;
RtreeCell leftbbox;
RtreeCell rightbbox;
/* Allocate an array and populate it with a copy of pCell and
** all cells from node pLeft. Then zero the original node.
*/
aCell = sqlite3_malloc64((sizeof(RtreeCell)+sizeof(int))*(nCell+1));
if( !aCell ){
rc = SQLITE_NOMEM;
goto splitnode_out;
}
aiUsed = (int *)&aCell[nCell+1];
memset(aiUsed, 0, sizeof(int)*(nCell+1));
for(i=0; i<nCell; i++){
nodeGetCell(pRtree, pNode, i, &aCell[i]);
}
nodeZero(pRtree, pNode);
memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
nCell++;
if( pNode->iNode==1 ){
pRight = nodeNew(pRtree, pNode);
pLeft = nodeNew(pRtree, pNode);
pRtree->iDepth++;
pNode->isDirty = 1;
writeInt16(pNode->zData, pRtree->iDepth);
}else{
pLeft = pNode;
pRight = nodeNew(pRtree, pLeft->pParent);
pLeft->nRef++;
}
if( !pLeft || !pRight ){
rc = SQLITE_NOMEM;
goto splitnode_out;
}
memset(pLeft->zData, 0, pRtree->iNodeSize);
memset(pRight->zData, 0, pRtree->iNodeSize);
rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,
&leftbbox, &rightbbox);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
/* Ensure both child nodes have node numbers assigned to them by calling
** nodeWrite(). Node pRight always needs a node number, as it was created
** by nodeNew() above. But node pLeft sometimes already has a node number.
** In this case avoid the all to nodeWrite().
*/
if( SQLITE_OK!=(rc = nodeWrite(pRtree, pRight))
|| (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
){
goto splitnode_out;
}
rightbbox.iRowid = pRight->iNode;
leftbbox.iRowid = pLeft->iNode;
if( pNode->iNode==1 ){
rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}else{
RtreeNode *pParent = pLeft->pParent;
int iCell;
rc = nodeParentIndex(pRtree, pLeft, &iCell);
if( ALWAYS(rc==SQLITE_OK) ){
nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
rc = AdjustTree(pRtree, pParent, &leftbbox);
assert( rc==SQLITE_OK );
}
if( NEVER(rc!=SQLITE_OK) ){
goto splitnode_out;
}
}
if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
goto splitnode_out;
}
for(i=0; i<NCELL(pRight); i++){
i64 iRowid = nodeGetRowid(pRtree, pRight, i);
rc = updateMapping(pRtree, iRowid, pRight, iHeight);
if( iRowid==pCell->iRowid ){
newCellIsRight = 1;
}
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}
if( pNode->iNode==1 ){
for(i=0; i<NCELL(pLeft); i++){
i64 iRowid = nodeGetRowid(pRtree, pLeft, i);
rc = updateMapping(pRtree, iRowid, pLeft, iHeight);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}
}else if( newCellIsRight==0 ){
rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);
}
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pRight);
pRight = 0;
}
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pLeft);
pLeft = 0;
}
splitnode_out:
nodeRelease(pRtree, pRight);
nodeRelease(pRtree, pLeft);
sqlite3_free(aCell);
return rc;
}
/*
** If node pLeaf is not the root of the r-tree and its pParent pointer is
** still NULL, load all ancestor nodes of pLeaf into memory and populate
** the pLeaf->pParent chain all the way up to the root node.
**
** This operation is required when a row is deleted (or updated - an update
** is implemented as a delete followed by an insert). SQLite provides the
** rowid of the row to delete, which can be used to find the leaf on which
** the entry resides (argument pLeaf). Once the leaf is located, this
** function is called to determine its ancestry.
*/
static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
int rc = SQLITE_OK;
RtreeNode *pChild = pLeaf;
while( rc==SQLITE_OK && pChild->iNode!=1 && pChild->pParent==0 ){
int rc2 = SQLITE_OK; /* sqlite3_reset() return code */
sqlite3_bind_int64(pRtree->pReadParent, 1, pChild->iNode);
rc = sqlite3_step(pRtree->pReadParent);
if( rc==SQLITE_ROW ){
RtreeNode *pTest; /* Used to test for reference loops */
i64 iNode; /* Node number of parent node */
/* Before setting pChild->pParent, test that we are not creating a
** loop of references (as we would if, say, pChild==pParent). We don't
** want to do this as it leads to a memory leak when trying to delete
** the referenced counted node structures.
*/
iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);
if( pTest==0 ){
rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);
}
}
rc = sqlite3_reset(pRtree->pReadParent);
if( rc==SQLITE_OK ) rc = rc2;
if( rc==SQLITE_OK && !pChild->pParent ){
RTREE_IS_CORRUPT(pRtree);
rc = SQLITE_CORRUPT_VTAB;
}
pChild = pChild->pParent;
}
return rc;
}
static int deleteCell(Rtree *, RtreeNode *, int, int);
static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
int rc;
int rc2;
RtreeNode *pParent = 0;
int iCell;
assert( pNode->nRef==1 );
/* Remove the entry in the parent cell. */
rc = nodeParentIndex(pRtree, pNode, &iCell);
if( rc==SQLITE_OK ){
pParent = pNode->pParent;
pNode->pParent = 0;
rc = deleteCell(pRtree, pParent, iCell, iHeight+1);
testcase( rc!=SQLITE_OK );
}
rc2 = nodeRelease(pRtree, pParent);
if( rc==SQLITE_OK ){
rc = rc2;
}
if( rc!=SQLITE_OK ){
return rc;
}
/* Remove the xxx_node entry. */
sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
sqlite3_step(pRtree->pDeleteNode);
if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
return rc;
}
/* Remove the xxx_parent entry. */
sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);
sqlite3_step(pRtree->pDeleteParent);
if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){
return rc;
}
/* Remove the node from the in-memory hash table and link it into
** the Rtree.pDeleted list. Its contents will be re-inserted later on.
*/
nodeHashDelete(pRtree, pNode);
pNode->iNode = iHeight;
pNode->pNext = pRtree->pDeleted;
pNode->nRef++;
pRtree->pDeleted = pNode;
return SQLITE_OK;
}
static int fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
RtreeNode *pParent = pNode->pParent;
int rc = SQLITE_OK;
if( pParent ){
int ii;
int nCell = NCELL(pNode);
RtreeCell box; /* Bounding box for pNode */
nodeGetCell(pRtree, pNode, 0, &box);
for(ii=1; ii<nCell; ii++){
RtreeCell cell;
nodeGetCell(pRtree, pNode, ii, &cell);
cellUnion(pRtree, &box, &cell);
}
box.iRowid = pNode->iNode;
rc = nodeParentIndex(pRtree, pNode, &ii);
if( rc==SQLITE_OK ){
nodeOverwriteCell(pRtree, pParent, &box, ii);
rc = fixBoundingBox(pRtree, pParent);
}
}
return rc;
}
/*
** Delete the cell at index iCell of node pNode. After removing the
** cell, adjust the r-tree data structure if required.
*/
static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
RtreeNode *pParent;
int rc;
if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
return rc;
}
/* Remove the cell from the node. This call just moves bytes around
** the in-memory node image, so it cannot fail.
*/
nodeDeleteCell(pRtree, pNode, iCell);
/* If the node is not the tree root and now has less than the minimum
** number of cells, remove it from the tree. Otherwise, update the
** cell in the parent node so that it tightly contains the updated
** node.
*/
pParent = pNode->pParent;
assert( pParent || pNode->iNode==1 );
if( pParent ){
if( NCELL(pNode)<RTREE_MINCELLS(pRtree) ){
rc = removeNode(pRtree, pNode, iHeight);
}else{
rc = fixBoundingBox(pRtree, pNode);
}
}
return rc;
}
/*
** Insert cell pCell into node pNode. Node pNode is the head of a
** subtree iHeight high (leaf nodes have iHeight==0).
*/
static int rtreeInsertCell(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iHeight
){
int rc = SQLITE_OK;
if( iHeight>0 ){
RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
if( nodeInsertCell(pRtree, pNode, pCell) ){
rc = SplitNode(pRtree, pNode, pCell, iHeight);
}else{
rc = AdjustTree(pRtree, pNode, pCell);
if( ALWAYS(rc==SQLITE_OK) ){
if( iHeight==0 ){
rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
}else{
rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
}
}
}
return rc;
}
static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
int ii;
int rc = SQLITE_OK;
int nCell = NCELL(pNode);
for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){
RtreeNode *pInsert;
RtreeCell cell;
nodeGetCell(pRtree, pNode, ii, &cell);
/* Find a node to store this cell in. pNode->iNode currently contains
** the height of the sub-tree headed by the cell.
*/
rc = ChooseLeaf(pRtree, &cell, (int)pNode->iNode, &pInsert);
if( rc==SQLITE_OK ){
int rc2;
rc = rtreeInsertCell(pRtree, pInsert, &cell, (int)pNode->iNode);
rc2 = nodeRelease(pRtree, pInsert);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
}
return rc;
}
/*
** Select a currently unused rowid for a new r-tree record.
*/
static int rtreeNewRowid(Rtree *pRtree, i64 *piRowid){
int rc;
sqlite3_bind_null(pRtree->pWriteRowid, 1);
sqlite3_bind_null(pRtree->pWriteRowid, 2);
sqlite3_step(pRtree->pWriteRowid);
rc = sqlite3_reset(pRtree->pWriteRowid);
*piRowid = sqlite3_last_insert_rowid(pRtree->db);
return rc;
}
/*
** Remove the entry with rowid=iDelete from the r-tree structure.
*/
static int rtreeDeleteRowid(Rtree *pRtree, sqlite3_int64 iDelete){
int rc; /* Return code */
RtreeNode *pLeaf = 0; /* Leaf node containing record iDelete */
int iCell; /* Index of iDelete cell in pLeaf */
RtreeNode *pRoot = 0; /* Root node of rtree structure */
/* Obtain a reference to the root node to initialize Rtree.iDepth */
rc = nodeAcquire(pRtree, 1, 0, &pRoot);
/* Obtain a reference to the leaf node that contains the entry
** about to be deleted.
*/
if( rc==SQLITE_OK ){
rc = findLeafNode(pRtree, iDelete, &pLeaf, 0);
}
#ifdef CORRUPT_DB
assert( pLeaf!=0 || rc!=SQLITE_OK || CORRUPT_DB );
#endif
/* Delete the cell in question from the leaf node. */
if( rc==SQLITE_OK && pLeaf ){
int rc2;
rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);
if( rc==SQLITE_OK ){
rc = deleteCell(pRtree, pLeaf, iCell, 0);
}
rc2 = nodeRelease(pRtree, pLeaf);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
/* Delete the corresponding entry in the <rtree>_rowid table. */
if( rc==SQLITE_OK ){
sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
sqlite3_step(pRtree->pDeleteRowid);
rc = sqlite3_reset(pRtree->pDeleteRowid);
}
/* Check if the root node now has exactly one child. If so, remove
** it, schedule the contents of the child for reinsertion and
** reduce the tree height by one.
**
** This is equivalent to copying the contents of the child into
** the root node (the operation that Gutman's paper says to perform
** in this scenario).
*/
if( rc==SQLITE_OK && pRtree->iDepth>0 && NCELL(pRoot)==1 ){
int rc2;
RtreeNode *pChild = 0;
i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
rc = nodeAcquire(pRtree, iChild, pRoot, &pChild); /* tag-20210916a */
if( rc==SQLITE_OK ){
rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
}
rc2 = nodeRelease(pRtree, pChild);
if( rc==SQLITE_OK ) rc = rc2;
if( rc==SQLITE_OK ){
pRtree->iDepth--;
writeInt16(pRoot->zData, pRtree->iDepth);
pRoot->isDirty = 1;
}
}
/* Re-insert the contents of any underfull nodes removed from the tree. */
for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
if( rc==SQLITE_OK ){
rc = reinsertNodeContent(pRtree, pLeaf);
}
pRtree->pDeleted = pLeaf->pNext;
pRtree->nNodeRef--;
sqlite3_free(pLeaf);
}
/* Release the reference to the root node. */
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pRoot);
}else{
nodeRelease(pRtree, pRoot);
}
return rc;
}
/*
** Rounding constants for float->double conversion.
*/
#define RNDTOWARDS (1.0 - 1.0/8388608.0) /* Round towards zero */
#define RNDAWAY (1.0 + 1.0/8388608.0) /* Round away from zero */
#if !defined(SQLITE_RTREE_INT_ONLY)
/*
** Convert an sqlite3_value into an RtreeValue (presumably a float)
** while taking care to round toward negative or positive, respectively.
*/
static RtreeValue rtreeValueDown(sqlite3_value *v){
double d = sqlite3_value_double(v);
float f = (float)d;
if( f>d ){
f = (float)(d*(d<0 ? RNDAWAY : RNDTOWARDS));
}
return f;
}
static RtreeValue rtreeValueUp(sqlite3_value *v){
double d = sqlite3_value_double(v);
float f = (float)d;
if( f<d ){
f = (float)(d*(d<0 ? RNDTOWARDS : RNDAWAY));
}
return f;
}
#endif /* !defined(SQLITE_RTREE_INT_ONLY) */
/*
** A constraint has failed while inserting a row into an rtree table.
** Assuming no OOM error occurs, this function sets the error message
** (at pRtree->base.zErrMsg) to an appropriate value and returns
** SQLITE_CONSTRAINT.
**
** Parameter iCol is the index of the leftmost column involved in the
** constraint failure. If it is 0, then the constraint that failed is
** the unique constraint on the id column. Otherwise, it is the rtree
** (c1<=c2) constraint on columns iCol and iCol+1 that has failed.
**
** If an OOM occurs, SQLITE_NOMEM is returned instead of SQLITE_CONSTRAINT.
*/
static int rtreeConstraintError(Rtree *pRtree, int iCol){
sqlite3_stmt *pStmt = 0;
char *zSql;
int rc;
assert( iCol==0 || iCol%2 );
zSql = sqlite3_mprintf("SELECT * FROM %Q.%Q", pRtree->zDb, pRtree->zName);
if( zSql ){
rc = sqlite3_prepare_v2(pRtree->db, zSql, -1, &pStmt, 0);
}else{
rc = SQLITE_NOMEM;
}
sqlite3_free(zSql);
if( rc==SQLITE_OK ){
if( iCol==0 ){
const char *zCol = sqlite3_column_name(pStmt, 0);
pRtree->base.zErrMsg = sqlite3_mprintf(
"UNIQUE constraint failed: %s.%s", pRtree->zName, zCol
);
}else{
const char *zCol1 = sqlite3_column_name(pStmt, iCol);
const char *zCol2 = sqlite3_column_name(pStmt, iCol+1);
pRtree->base.zErrMsg = sqlite3_mprintf(
"rtree constraint failed: %s.(%s<=%s)", pRtree->zName, zCol1, zCol2
);
}
}
sqlite3_finalize(pStmt);
return (rc==SQLITE_OK ? SQLITE_CONSTRAINT : rc);
}
/*
** The xUpdate method for rtree module virtual tables.
*/
static int rtreeUpdate(
sqlite3_vtab *pVtab,
int nData,
sqlite3_value **aData,
sqlite_int64 *pRowid
){
Rtree *pRtree = (Rtree *)pVtab;
int rc = SQLITE_OK;
RtreeCell cell; /* New cell to insert if nData>1 */
int bHaveRowid = 0; /* Set to 1 after new rowid is determined */
if( pRtree->nNodeRef ){
/* Unable to write to the btree while another cursor is reading from it,
** since the write might do a rebalance which would disrupt the read
** cursor. */
return SQLITE_LOCKED_VTAB;
}
rtreeReference(pRtree);
assert(nData>=1);
memset(&cell, 0, sizeof(cell));
/* Constraint handling. A write operation on an r-tree table may return
** SQLITE_CONSTRAINT for two reasons:
**
** 1. A duplicate rowid value, or
** 2. The supplied data violates the "x2>=x1" constraint.
**
** In the first case, if the conflict-handling mode is REPLACE, then
** the conflicting row can be removed before proceeding. In the second
** case, SQLITE_CONSTRAINT must be returned regardless of the
** conflict-handling mode specified by the user.
*/
if( nData>1 ){
int ii;
int nn = nData - 4;
if( nn > pRtree->nDim2 ) nn = pRtree->nDim2;
/* Populate the cell.aCoord[] array. The first coordinate is aData[3].
**
** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared
** with "column" that are interpreted as table constraints.
** Example: CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));
** This problem was discovered after years of use, so we silently ignore
** these kinds of misdeclared tables to avoid breaking any legacy.
*/
#ifndef SQLITE_RTREE_INT_ONLY
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
for(ii=0; ii<nn; ii+=2){
cell.aCoord[ii].f = rtreeValueDown(aData[ii+3]);
cell.aCoord[ii+1].f = rtreeValueUp(aData[ii+4]);
if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
rc = rtreeConstraintError(pRtree, ii+1);
goto constraint;
}
}
}else
#endif
{
for(ii=0; ii<nn; ii+=2){
cell.aCoord[ii].i = sqlite3_value_int(aData[ii+3]);
cell.aCoord[ii+1].i = sqlite3_value_int(aData[ii+4]);
if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
rc = rtreeConstraintError(pRtree, ii+1);
goto constraint;
}
}
}
/* If a rowid value was supplied, check if it is already present in
** the table. If so, the constraint has failed. */
if( sqlite3_value_type(aData[2])!=SQLITE_NULL ){
cell.iRowid = sqlite3_value_int64(aData[2]);
if( sqlite3_value_type(aData[0])==SQLITE_NULL
|| sqlite3_value_int64(aData[0])!=cell.iRowid
){
int steprc;
sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
steprc = sqlite3_step(pRtree->pReadRowid);
rc = sqlite3_reset(pRtree->pReadRowid);
if( SQLITE_ROW==steprc ){
if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
rc = rtreeDeleteRowid(pRtree, cell.iRowid);
}else{
rc = rtreeConstraintError(pRtree, 0);
goto constraint;
}
}
}
bHaveRowid = 1;
}
}
/* If aData[0] is not an SQL NULL value, it is the rowid of a
** record to delete from the r-tree table. The following block does
** just that.
*/
if( sqlite3_value_type(aData[0])!=SQLITE_NULL ){
rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(aData[0]));
}
/* If the aData[] array contains more than one element, elements
** (aData[2]..aData[argc-1]) contain a new record to insert into
** the r-tree structure.
*/
if( rc==SQLITE_OK && nData>1 ){
/* Insert the new record into the r-tree */
RtreeNode *pLeaf = 0;
/* Figure out the rowid of the new row. */
if( bHaveRowid==0 ){
rc = rtreeNewRowid(pRtree, &cell.iRowid);
}
*pRowid = cell.iRowid;
if( rc==SQLITE_OK ){
rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
}
if( rc==SQLITE_OK ){
int rc2;
rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
rc2 = nodeRelease(pRtree, pLeaf);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
if( rc==SQLITE_OK && pRtree->nAux ){
sqlite3_stmt *pUp = pRtree->pWriteAux;
int jj;
sqlite3_bind_int64(pUp, 1, *pRowid);
for(jj=0; jj<pRtree->nAux; jj++){
sqlite3_bind_value(pUp, jj+2, aData[pRtree->nDim2+3+jj]);
}
sqlite3_step(pUp);
rc = sqlite3_reset(pUp);
}
}
constraint:
rtreeRelease(pRtree);
return rc;
}
/*
** Called when a transaction starts.
*/
static int rtreeBeginTransaction(sqlite3_vtab *pVtab){
Rtree *pRtree = (Rtree *)pVtab;
assert( pRtree->inWrTrans==0 );
pRtree->inWrTrans = 1;
return SQLITE_OK;
}
/*
** Called when a transaction completes (either by COMMIT or ROLLBACK).
** The sqlite3_blob object should be released at this point.
*/
static int rtreeEndTransaction(sqlite3_vtab *pVtab){
Rtree *pRtree = (Rtree *)pVtab;
pRtree->inWrTrans = 0;
nodeBlobReset(pRtree);
return SQLITE_OK;
}
static int rtreeRollback(sqlite3_vtab *pVtab){
return rtreeEndTransaction(pVtab);
}
/*
** The xRename method for rtree module virtual tables.
*/
static int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){
Rtree *pRtree = (Rtree *)pVtab;
int rc = SQLITE_NOMEM;
char *zSql = sqlite3_mprintf(
"ALTER TABLE %Q.'%q_node' RENAME TO \"%w_node\";"
"ALTER TABLE %Q.'%q_parent' RENAME TO \"%w_parent\";"
"ALTER TABLE %Q.'%q_rowid' RENAME TO \"%w_rowid\";"
, pRtree->zDb, pRtree->zName, zNewName
, pRtree->zDb, pRtree->zName, zNewName
, pRtree->zDb, pRtree->zName, zNewName
);
if( zSql ){
nodeBlobReset(pRtree);
rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
sqlite3_free(zSql);
}
return rc;
}
/*
** The xSavepoint method.
**
** This module does not need to do anything to support savepoints. However,
** it uses this hook to close any open blob handle. This is done because a
** DROP TABLE command - which fortunately always opens a savepoint - cannot
** succeed if there are any open blob handles. i.e. if the blob handle were
** not closed here, the following would fail:
**
** BEGIN;
** INSERT INTO rtree...
** DROP TABLE <tablename>; -- Would fail with SQLITE_LOCKED
** COMMIT;
*/
static int rtreeSavepoint(sqlite3_vtab *pVtab, int iSavepoint){
Rtree *pRtree = (Rtree *)pVtab;
u8 iwt = pRtree->inWrTrans;
UNUSED_PARAMETER(iSavepoint);
pRtree->inWrTrans = 0;
nodeBlobReset(pRtree);
pRtree->inWrTrans = iwt;
return SQLITE_OK;
}
/*
** This function populates the pRtree->nRowEst variable with an estimate
** of the number of rows in the virtual table. If possible, this is based
** on sqlite_stat1 data. Otherwise, use RTREE_DEFAULT_ROWEST.
*/
static int rtreeQueryStat1(sqlite3 *db, Rtree *pRtree){
const char *zFmt = "SELECT stat FROM %Q.sqlite_stat1 WHERE tbl = '%q_rowid'";
char *zSql;
sqlite3_stmt *p;
int rc;
i64 nRow = RTREE_MIN_ROWEST;
rc = sqlite3_table_column_metadata(
db, pRtree->zDb, "sqlite_stat1",0,0,0,0,0,0
);
if( rc!=SQLITE_OK ){
pRtree->nRowEst = RTREE_DEFAULT_ROWEST;
return rc==SQLITE_ERROR ? SQLITE_OK : rc;
}
zSql = sqlite3_mprintf(zFmt, pRtree->zDb, pRtree->zName);
if( zSql==0 ){
rc = SQLITE_NOMEM;
}else{
rc = sqlite3_prepare_v2(db, zSql, -1, &p, 0);
if( rc==SQLITE_OK ){
if( sqlite3_step(p)==SQLITE_ROW ) nRow = sqlite3_column_int64(p, 0);
rc = sqlite3_finalize(p);
}
sqlite3_free(zSql);
}
pRtree->nRowEst = MAX(nRow, RTREE_MIN_ROWEST);
return rc;
}
/*
** Return true if zName is the extension on one of the shadow tables used
** by this module.
*/
static int rtreeShadowName(const char *zName){
static const char *azName[] = {
"node", "parent", "rowid"
};
unsigned int i;
for(i=0; i<sizeof(azName)/sizeof(azName[0]); i++){
if( sqlite3_stricmp(zName, azName[i])==0 ) return 1;
}
return 0;
}
/* Forward declaration */
static int rtreeIntegrity(sqlite3_vtab*, const char*, const char*, int, char**);
static sqlite3_module rtreeModule = {
4, /* iVersion */
rtreeCreate, /* xCreate - create a table */
rtreeConnect, /* xConnect - connect to an existing table */
rtreeBestIndex, /* xBestIndex - Determine search strategy */
rtreeDisconnect, /* xDisconnect - Disconnect from a table */
rtreeDestroy, /* xDestroy - Drop a table */
rtreeOpen, /* xOpen - open a cursor */
rtreeClose, /* xClose - close a cursor */
rtreeFilter, /* xFilter - configure scan constraints */
rtreeNext, /* xNext - advance a cursor */
rtreeEof, /* xEof */
rtreeColumn, /* xColumn - read data */
rtreeRowid, /* xRowid - read data */
rtreeUpdate, /* xUpdate - write data */
rtreeBeginTransaction, /* xBegin - begin transaction */
rtreeEndTransaction, /* xSync - sync transaction */
rtreeEndTransaction, /* xCommit - commit transaction */
rtreeRollback, /* xRollback - rollback transaction */
0, /* xFindFunction - function overloading */
rtreeRename, /* xRename - rename the table */
rtreeSavepoint, /* xSavepoint */
0, /* xRelease */
0, /* xRollbackTo */
rtreeShadowName, /* xShadowName */
rtreeIntegrity /* xIntegrity */
};
static int rtreeSqlInit(
Rtree *pRtree,
sqlite3 *db,
const char *zDb,
const char *zPrefix,
int isCreate
){
int rc = SQLITE_OK;
#define N_STATEMENT 8
static const char *azSql[N_STATEMENT] = {
/* Write the xxx_node table */
"INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(?1, ?2)",
"DELETE FROM '%q'.'%q_node' WHERE nodeno = ?1",
/* Read and write the xxx_rowid table */
"SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = ?1",
"INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(?1, ?2)",
"DELETE FROM '%q'.'%q_rowid' WHERE rowid = ?1",
/* Read and write the xxx_parent table */
"SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = ?1",
"INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(?1, ?2)",
"DELETE FROM '%q'.'%q_parent' WHERE nodeno = ?1"
};
sqlite3_stmt **appStmt[N_STATEMENT];
int i;
const int f = SQLITE_PREPARE_PERSISTENT|SQLITE_PREPARE_NO_VTAB;
pRtree->db = db;
if( isCreate ){
char *zCreate;
sqlite3_str *p = sqlite3_str_new(db);
int ii;
sqlite3_str_appendf(p,
"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY,nodeno",
zDb, zPrefix);
for(ii=0; ii<pRtree->nAux; ii++){
sqlite3_str_appendf(p,",a%d",ii);
}
sqlite3_str_appendf(p,
");CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY,data);",
zDb, zPrefix);
sqlite3_str_appendf(p,
"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY,parentnode);",
zDb, zPrefix);
sqlite3_str_appendf(p,
"INSERT INTO \"%w\".\"%w_node\"VALUES(1,zeroblob(%d))",
zDb, zPrefix, pRtree->iNodeSize);
zCreate = sqlite3_str_finish(p);
if( !zCreate ){
return SQLITE_NOMEM;
}
rc = sqlite3_exec(db, zCreate, 0, 0, 0);
sqlite3_free(zCreate);
if( rc!=SQLITE_OK ){
return rc;
}
}
appStmt[0] = &pRtree->pWriteNode;
appStmt[1] = &pRtree->pDeleteNode;
appStmt[2] = &pRtree->pReadRowid;
appStmt[3] = &pRtree->pWriteRowid;
appStmt[4] = &pRtree->pDeleteRowid;
appStmt[5] = &pRtree->pReadParent;
appStmt[6] = &pRtree->pWriteParent;
appStmt[7] = &pRtree->pDeleteParent;
rc = rtreeQueryStat1(db, pRtree);
for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
char *zSql;
const char *zFormat;
if( i!=3 || pRtree->nAux==0 ){
zFormat = azSql[i];
}else {
/* An UPSERT is very slightly slower than REPLACE, but it is needed
** if there are auxiliary columns */
zFormat = "INSERT INTO\"%w\".\"%w_rowid\"(rowid,nodeno)VALUES(?1,?2)"
"ON CONFLICT(rowid)DO UPDATE SET nodeno=excluded.nodeno";
}
zSql = sqlite3_mprintf(zFormat, zDb, zPrefix);
if( zSql ){
rc = sqlite3_prepare_v3(db, zSql, -1, f, appStmt[i], 0);
}else{
rc = SQLITE_NOMEM;
}
sqlite3_free(zSql);
}
if( pRtree->nAux && rc!=SQLITE_NOMEM ){
pRtree->zReadAuxSql = sqlite3_mprintf(
"SELECT * FROM \"%w\".\"%w_rowid\" WHERE rowid=?1",
zDb, zPrefix);
if( pRtree->zReadAuxSql==0 ){
rc = SQLITE_NOMEM;
}else{
sqlite3_str *p = sqlite3_str_new(db);
int ii;
char *zSql;
sqlite3_str_appendf(p, "UPDATE \"%w\".\"%w_rowid\"SET ", zDb, zPrefix);
for(ii=0; ii<pRtree->nAux; ii++){
if( ii ) sqlite3_str_append(p, ",", 1);
#ifdef SQLITE_ENABLE_GEOPOLY
if( ii<pRtree->nAuxNotNull ){
sqlite3_str_appendf(p,"a%d=coalesce(?%d,a%d)",ii,ii+2,ii);
}else
#endif
{
sqlite3_str_appendf(p,"a%d=?%d",ii,ii+2);
}
}
sqlite3_str_appendf(p, " WHERE rowid=?1");
zSql = sqlite3_str_finish(p);
if( zSql==0 ){
rc = SQLITE_NOMEM;
}else{
rc = sqlite3_prepare_v3(db, zSql, -1, f, &pRtree->pWriteAux, 0);
sqlite3_free(zSql);
}
}
}
return rc;
}
/*
** The second argument to this function contains the text of an SQL statement
** that returns a single integer value. The statement is compiled and executed
** using database connection db. If successful, the integer value returned
** is written to *piVal and SQLITE_OK returned. Otherwise, an SQLite error
** code is returned and the value of *piVal after returning is not defined.
*/
static int getIntFromStmt(sqlite3 *db, const char *zSql, int *piVal){
int rc = SQLITE_NOMEM;
if( zSql ){
sqlite3_stmt *pStmt = 0;
rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
if( rc==SQLITE_OK ){
if( SQLITE_ROW==sqlite3_step(pStmt) ){
*piVal = sqlite3_column_int(pStmt, 0);
}
rc = sqlite3_finalize(pStmt);
}
}
return rc;
}
/*
** This function is called from within the xConnect() or xCreate() method to
** determine the node-size used by the rtree table being created or connected
** to. If successful, pRtree->iNodeSize is populated and SQLITE_OK returned.
** Otherwise, an SQLite error code is returned.
**
** If this function is being called as part of an xConnect(), then the rtree
** table already exists. In this case the node-size is determined by inspecting
** the root node of the tree.
**
** Otherwise, for an xCreate(), use 64 bytes less than the database page-size.
** This ensures that each node is stored on a single database page. If the
** database page-size is so large that more than RTREE_MAXCELLS entries
** would fit in a single node, use a smaller node-size.
*/
static int getNodeSize(
sqlite3 *db, /* Database handle */
Rtree *pRtree, /* Rtree handle */
int isCreate, /* True for xCreate, false for xConnect */
char **pzErr /* OUT: Error message, if any */
){
int rc;
char *zSql;
if( isCreate ){
int iPageSize = 0;
zSql = sqlite3_mprintf("PRAGMA %Q.page_size", pRtree->zDb);
rc = getIntFromStmt(db, zSql, &iPageSize);
if( rc==SQLITE_OK ){
pRtree->iNodeSize = iPageSize-64;
if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
}
}else{
*pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
}
}else{
zSql = sqlite3_mprintf(
"SELECT length(data) FROM '%q'.'%q_node' WHERE nodeno = 1",
pRtree->zDb, pRtree->zName
);
rc = getIntFromStmt(db, zSql, &pRtree->iNodeSize);
if( rc!=SQLITE_OK ){
*pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
}else if( pRtree->iNodeSize<(512-64) ){
rc = SQLITE_CORRUPT_VTAB;
RTREE_IS_CORRUPT(pRtree);
*pzErr = sqlite3_mprintf("undersize RTree blobs in \"%q_node\"",
pRtree->zName);
}
}
sqlite3_free(zSql);
return rc;
}
/*
** Return the length of a token
*/
static int rtreeTokenLength(const char *z){
int dummy = 0;
return sqlite3GetToken((const unsigned char*)z,&dummy);
}
/*
** This function is the implementation of both the xConnect and xCreate
** methods of the r-tree virtual table.
**
** argv[0] -> module name
** argv[1] -> database name
** argv[2] -> table name
** argv[...] -> column names...
*/
static int rtreeInit(
sqlite3 *db, /* Database connection */
void *pAux, /* One of the RTREE_COORD_* constants */
int argc, const char *const*argv, /* Parameters to CREATE TABLE statement */
sqlite3_vtab **ppVtab, /* OUT: New virtual table */
char **pzErr, /* OUT: Error message, if any */
int isCreate /* True for xCreate, false for xConnect */
){
int rc = SQLITE_OK;
Rtree *pRtree;
int nDb; /* Length of string argv[1] */
int nName; /* Length of string argv[2] */
int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);
sqlite3_str *pSql;
char *zSql;
int ii = 4;
int iErr;
const char *aErrMsg[] = {
0, /* 0 */
"Wrong number of columns for an rtree table", /* 1 */
"Too few columns for an rtree table", /* 2 */
"Too many columns for an rtree table", /* 3 */
"Auxiliary rtree columns must be last" /* 4 */
};
assert( RTREE_MAX_AUX_COLUMN<256 ); /* Aux columns counted by a u8 */
if( argc<6 || argc>RTREE_MAX_AUX_COLUMN+3 ){
*pzErr = sqlite3_mprintf("%s", aErrMsg[2 + (argc>=6)]);
return SQLITE_ERROR;
}
sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
sqlite3_vtab_config(db, SQLITE_VTAB_INNOCUOUS);
/* Allocate the sqlite3_vtab structure */
nDb = (int)strlen(argv[1]);
nName = (int)strlen(argv[2]);
pRtree = (Rtree *)sqlite3_malloc64(sizeof(Rtree)+nDb+nName*2+8);
if( !pRtree ){
return SQLITE_NOMEM;
}
memset(pRtree, 0, sizeof(Rtree)+nDb+nName*2+8);
pRtree->nBusy = 1;
pRtree->base.pModule = &rtreeModule;
pRtree->zDb = (char *)&pRtree[1];
pRtree->zName = &pRtree->zDb[nDb+1];
pRtree->zNodeName = &pRtree->zName[nName+1];
pRtree->eCoordType = (u8)eCoordType;
memcpy(pRtree->zDb, argv[1], nDb);
memcpy(pRtree->zName, argv[2], nName);
memcpy(pRtree->zNodeName, argv[2], nName);
memcpy(&pRtree->zNodeName[nName], "_node", 6);
/* Create/Connect to the underlying relational database schema. If
** that is successful, call sqlite3_declare_vtab() to configure
** the r-tree table schema.
*/
pSql = sqlite3_str_new(db);
sqlite3_str_appendf(pSql, "CREATE TABLE x(%.*s INT",
rtreeTokenLength(argv[3]), argv[3]);
for(ii=4; ii<argc; ii++){
const char *zArg = argv[ii];
if( zArg[0]=='+' ){
pRtree->nAux++;
sqlite3_str_appendf(pSql, ",%.*s", rtreeTokenLength(zArg+1), zArg+1);
}else if( pRtree->nAux>0 ){
break;
}else{
static const char *azFormat[] = {",%.*s REAL", ",%.*s INT"};
pRtree->nDim2++;
sqlite3_str_appendf(pSql, azFormat[eCoordType],
rtreeTokenLength(zArg), zArg);
}
}
sqlite3_str_appendf(pSql, ");");
zSql = sqlite3_str_finish(pSql);
if( !zSql ){
rc = SQLITE_NOMEM;
}else if( ii<argc ){
*pzErr = sqlite3_mprintf("%s", aErrMsg[4]);
rc = SQLITE_ERROR;
}else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
*pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
}
sqlite3_free(zSql);
if( rc ) goto rtreeInit_fail;
pRtree->nDim = pRtree->nDim2/2;
if( pRtree->nDim<1 ){
iErr = 2;
}else if( pRtree->nDim2>RTREE_MAX_DIMENSIONS*2 ){
iErr = 3;
}else if( pRtree->nDim2 % 2 ){
iErr = 1;
}else{
iErr = 0;
}
if( iErr ){
*pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
goto rtreeInit_fail;
}
pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
/* Figure out the node size to use. */
rc = getNodeSize(db, pRtree, isCreate, pzErr);
if( rc ) goto rtreeInit_fail;
rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate);
if( rc ){
*pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
goto rtreeInit_fail;
}
*ppVtab = (sqlite3_vtab *)pRtree;
return SQLITE_OK;
rtreeInit_fail:
if( rc==SQLITE_OK ) rc = SQLITE_ERROR;
assert( *ppVtab==0 );
assert( pRtree->nBusy==1 );
rtreeRelease(pRtree);
return rc;
}
/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments: (1) the number of dimensions
** to the rtree (between 1 and 5, inclusive) and (2) a blob of data containing
** an r-tree node. For a two-dimensional r-tree structure called "rt", to
** deserialize all nodes, a statement like:
**
** SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the
** <num-dimension>*2 coordinates.
*/
static void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
RtreeNode node;
Rtree tree;
int ii;
int nData;
int errCode;
sqlite3_str *pOut;
UNUSED_PARAMETER(nArg);
memset(&node, 0, sizeof(RtreeNode));
memset(&tree, 0, sizeof(Rtree));
tree.nDim = (u8)sqlite3_value_int(apArg[0]);
if( tree.nDim<1 || tree.nDim>5 ) return;
tree.nDim2 = tree.nDim*2;
tree.nBytesPerCell = 8 + 8 * tree.nDim;
node.zData = (u8 *)sqlite3_value_blob(apArg[1]);
if( node.zData==0 ) return;
nData = sqlite3_value_bytes(apArg[1]);
if( nData<4 ) return;
if( nData<NCELL(&node)*tree.nBytesPerCell ) return;
pOut = sqlite3_str_new(0);
for(ii=0; ii<NCELL(&node); ii++){
RtreeCell cell;
int jj;
nodeGetCell(&tree, &node, ii, &cell);
if( ii>0 ) sqlite3_str_append(pOut, " ", 1);
sqlite3_str_appendf(pOut, "{%lld", cell.iRowid);
for(jj=0; jj<tree.nDim2; jj++){
#ifndef SQLITE_RTREE_INT_ONLY
sqlite3_str_appendf(pOut, " %g", (double)cell.aCoord[jj].f);
#else
sqlite3_str_appendf(pOut, " %d", cell.aCoord[jj].i);
#endif
}
sqlite3_str_append(pOut, "}", 1);
}
errCode = sqlite3_str_errcode(pOut);
sqlite3_result_text(ctx, sqlite3_str_finish(pOut), -1, sqlite3_free);
sqlite3_result_error_code(ctx, errCode);
}
/* This routine implements an SQL function that returns the "depth" parameter
** from the front of a blob that is an r-tree node. For example:
**
** SELECT rtreedepth(data) FROM rt_node WHERE nodeno=1;
**
** The depth value is 0 for all nodes other than the root node, and the root
** node always has nodeno=1, so the example above is the primary use for this
** routine. This routine is intended for testing and analysis only.
*/
static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
UNUSED_PARAMETER(nArg);
if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB
|| sqlite3_value_bytes(apArg[0])<2
){
sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1);
}else{
u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);
if( zBlob ){
sqlite3_result_int(ctx, readInt16(zBlob));
}else{
sqlite3_result_error_nomem(ctx);
}
}
}
/*
** Context object passed between the various routines that make up the
** implementation of integrity-check function rtreecheck().
*/
typedef struct RtreeCheck RtreeCheck;
struct RtreeCheck {
sqlite3 *db; /* Database handle */
const char *zDb; /* Database containing rtree table */
const char *zTab; /* Name of rtree table */
int bInt; /* True for rtree_i32 table */
int nDim; /* Number of dimensions for this rtree tbl */
sqlite3_stmt *pGetNode; /* Statement used to retrieve nodes */
sqlite3_stmt *aCheckMapping[2]; /* Statements to query %_parent/%_rowid */
int nLeaf; /* Number of leaf cells in table */
int nNonLeaf; /* Number of non-leaf cells in table */
int rc; /* Return code */
char *zReport; /* Message to report */
int nErr; /* Number of lines in zReport */
};
#define RTREE_CHECK_MAX_ERROR 100
/*
** Reset SQL statement pStmt. If the sqlite3_reset() call returns an error,
** and RtreeCheck.rc==SQLITE_OK, set RtreeCheck.rc to the error code.
*/
static void rtreeCheckReset(RtreeCheck *pCheck, sqlite3_stmt *pStmt){
int rc = sqlite3_reset(pStmt);
if( pCheck->rc==SQLITE_OK ) pCheck->rc = rc;
}
/*
** The second and subsequent arguments to this function are a format string
** and printf style arguments. This function formats the string and attempts
** to compile it as an SQL statement.
**
** If successful, a pointer to the new SQL statement is returned. Otherwise,
** NULL is returned and an error code left in RtreeCheck.rc.
*/
static sqlite3_stmt *rtreeCheckPrepare(
RtreeCheck *pCheck, /* RtreeCheck object */
const char *zFmt, ... /* Format string and trailing args */
){
va_list ap;
char *z;
sqlite3_stmt *pRet = 0;
va_start(ap, zFmt);
z = sqlite3_vmprintf(zFmt, ap);
if( pCheck->rc==SQLITE_OK ){
if( z==0 ){
pCheck->rc = SQLITE_NOMEM;
}else{
pCheck->rc = sqlite3_prepare_v2(pCheck->db, z, -1, &pRet, 0);
}
}
sqlite3_free(z);
va_end(ap);
return pRet;
}
/*
** The second and subsequent arguments to this function are a printf()
** style format string and arguments. This function formats the string and
** appends it to the report being accumuated in pCheck.
*/
static void rtreeCheckAppendMsg(RtreeCheck *pCheck, const char *zFmt, ...){
va_list ap;
va_start(ap, zFmt);
if( pCheck->rc==SQLITE_OK && pCheck->nErr<RTREE_CHECK_MAX_ERROR ){
char *z = sqlite3_vmprintf(zFmt, ap);
if( z==0 ){
pCheck->rc = SQLITE_NOMEM;
}else{
pCheck->zReport = sqlite3_mprintf("%z%s%z",
pCheck->zReport, (pCheck->zReport ? "\n" : ""), z
);
if( pCheck->zReport==0 ){
pCheck->rc = SQLITE_NOMEM;
}
}
pCheck->nErr++;
}
va_end(ap);
}
/*
** This function is a no-op if there is already an error code stored
** in the RtreeCheck object indicated by the first argument. NULL is
** returned in this case.
**
** Otherwise, the contents of rtree table node iNode are loaded from
** the database and copied into a buffer obtained from sqlite3_malloc().
** If no error occurs, a pointer to the buffer is returned and (*pnNode)
** is set to the size of the buffer in bytes.
**
** Or, if an error does occur, NULL is returned and an error code left
** in the RtreeCheck object. The final value of *pnNode is undefined in
** this case.
*/
static u8 *rtreeCheckGetNode(RtreeCheck *pCheck, i64 iNode, int *pnNode){
u8 *pRet = 0; /* Return value */
if( pCheck->rc==SQLITE_OK && pCheck->pGetNode==0 ){
pCheck->pGetNode = rtreeCheckPrepare(pCheck,
"SELECT data FROM %Q.'%q_node' WHERE nodeno=?",
pCheck->zDb, pCheck->zTab
);
}
if( pCheck->rc==SQLITE_OK ){
sqlite3_bind_int64(pCheck->pGetNode, 1, iNode);
if( sqlite3_step(pCheck->pGetNode)==SQLITE_ROW ){
int nNode = sqlite3_column_bytes(pCheck->pGetNode, 0);
const u8 *pNode = (const u8*)sqlite3_column_blob(pCheck->pGetNode, 0);
pRet = sqlite3_malloc64(nNode);
if( pRet==0 ){
pCheck->rc = SQLITE_NOMEM;
}else{
memcpy(pRet, pNode, nNode);
*pnNode = nNode;
}
}
rtreeCheckReset(pCheck, pCheck->pGetNode);
if( pCheck->rc==SQLITE_OK && pRet==0 ){
rtreeCheckAppendMsg(pCheck, "Node %lld missing from database", iNode);
}
}
return pRet;
}
/*
** This function is used to check that the %_parent (if bLeaf==0) or %_rowid
** (if bLeaf==1) table contains a specified entry. The schemas of the
** two tables are:
**
** CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
** CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER, ...)
**
** In both cases, this function checks that there exists an entry with
** IPK value iKey and the second column set to iVal.
**
*/
static void rtreeCheckMapping(
RtreeCheck *pCheck, /* RtreeCheck object */
int bLeaf, /* True for a leaf cell, false for interior */
i64 iKey, /* Key for mapping */
i64 iVal /* Expected value for mapping */
){
int rc;
sqlite3_stmt *pStmt;
const char *azSql[2] = {
"SELECT parentnode FROM %Q.'%q_parent' WHERE nodeno=?1",
"SELECT nodeno FROM %Q.'%q_rowid' WHERE rowid=?1"
};
assert( bLeaf==0 || bLeaf==1 );
if( pCheck->aCheckMapping[bLeaf]==0 ){
pCheck->aCheckMapping[bLeaf] = rtreeCheckPrepare(pCheck,
azSql[bLeaf], pCheck->zDb, pCheck->zTab
);
}
if( pCheck->rc!=SQLITE_OK ) return;
pStmt = pCheck->aCheckMapping[bLeaf];
sqlite3_bind_int64(pStmt, 1, iKey);
rc = sqlite3_step(pStmt);
if( rc==SQLITE_DONE ){
rtreeCheckAppendMsg(pCheck, "Mapping (%lld -> %lld) missing from %s table",
iKey, iVal, (bLeaf ? "%_rowid" : "%_parent")
);
}else if( rc==SQLITE_ROW ){
i64 ii = sqlite3_column_int64(pStmt, 0);
if( ii!=iVal ){
rtreeCheckAppendMsg(pCheck,
"Found (%lld -> %lld) in %s table, expected (%lld -> %lld)",
iKey, ii, (bLeaf ? "%_rowid" : "%_parent"), iKey, iVal
);
}
}
rtreeCheckReset(pCheck, pStmt);
}
/*
** Argument pCell points to an array of coordinates stored on an rtree page.
** This function checks that the coordinates are internally consistent (no
** x1>x2 conditions) and adds an error message to the RtreeCheck object
** if they are not.
**
** Additionally, if pParent is not NULL, then it is assumed to point to
** the array of coordinates on the parent page that bound the page
** containing pCell. In this case it is also verified that the two
** sets of coordinates are mutually consistent and an error message added
** to the RtreeCheck object if they are not.
*/
static void rtreeCheckCellCoord(
RtreeCheck *pCheck,
i64 iNode, /* Node id to use in error messages */
int iCell, /* Cell number to use in error messages */
u8 *pCell, /* Pointer to cell coordinates */
u8 *pParent /* Pointer to parent coordinates */
){
RtreeCoord c1, c2;
RtreeCoord p1, p2;
int i;
for(i=0; i<pCheck->nDim; i++){
readCoord(&pCell[4*2*i], &c1);
readCoord(&pCell[4*(2*i + 1)], &c2);
/* printf("%e, %e\n", c1.u.f, c2.u.f); */
if( pCheck->bInt ? c1.i>c2.i : c1.f>c2.f ){
rtreeCheckAppendMsg(pCheck,
"Dimension %d of cell %d on node %lld is corrupt", i, iCell, iNode
);
}
if( pParent ){
readCoord(&pParent[4*2*i], &p1);
readCoord(&pParent[4*(2*i + 1)], &p2);
if( (pCheck->bInt ? c1.i<p1.i : c1.f<p1.f)
|| (pCheck->bInt ? c2.i>p2.i : c2.f>p2.f)
){
rtreeCheckAppendMsg(pCheck,
"Dimension %d of cell %d on node %lld is corrupt relative to parent"
, i, iCell, iNode
);
}
}
}
}
/*
** Run rtreecheck() checks on node iNode, which is at depth iDepth within
** the r-tree structure. Argument aParent points to the array of coordinates
** that bound node iNode on the parent node.
**
** If any problems are discovered, an error message is appended to the
** report accumulated in the RtreeCheck object.
*/
static void rtreeCheckNode(
RtreeCheck *pCheck,
int iDepth, /* Depth of iNode (0==leaf) */
u8 *aParent, /* Buffer containing parent coords */
i64 iNode /* Node to check */
){
u8 *aNode = 0;
int nNode = 0;
assert( iNode==1 || aParent!=0 );
assert( pCheck->nDim>0 );
aNode = rtreeCheckGetNode(pCheck, iNode, &nNode);
if( aNode ){
if( nNode<4 ){
rtreeCheckAppendMsg(pCheck,
"Node %lld is too small (%d bytes)", iNode, nNode
);
}else{
int nCell; /* Number of cells on page */
int i; /* Used to iterate through cells */
if( aParent==0 ){
iDepth = readInt16(aNode);
if( iDepth>RTREE_MAX_DEPTH ){
rtreeCheckAppendMsg(pCheck, "Rtree depth out of range (%d)", iDepth);
sqlite3_free(aNode);
return;
}
}
nCell = readInt16(&aNode[2]);
if( (4 + nCell*(8 + pCheck->nDim*2*4))>nNode ){
rtreeCheckAppendMsg(pCheck,
"Node %lld is too small for cell count of %d (%d bytes)",
iNode, nCell, nNode
);
}else{
for(i=0; i<nCell; i++){
u8 *pCell = &aNode[4 + i*(8 + pCheck->nDim*2*4)];
i64 iVal = readInt64(pCell);
rtreeCheckCellCoord(pCheck, iNode, i, &pCell[8], aParent);
if( iDepth>0 ){
rtreeCheckMapping(pCheck, 0, iVal, iNode);
rtreeCheckNode(pCheck, iDepth-1, &pCell[8], iVal);
pCheck->nNonLeaf++;
}else{
rtreeCheckMapping(pCheck, 1, iVal, iNode);
pCheck->nLeaf++;
}
}
}
}
sqlite3_free(aNode);
}
}
/*
** The second argument to this function must be either "_rowid" or
** "_parent". This function checks that the number of entries in the
** %_rowid or %_parent table is exactly nExpect. If not, it adds
** an error message to the report in the RtreeCheck object indicated
** by the first argument.
*/
static void rtreeCheckCount(RtreeCheck *pCheck, const char *zTbl, i64 nExpect){
if( pCheck->rc==SQLITE_OK ){
sqlite3_stmt *pCount;
pCount = rtreeCheckPrepare(pCheck, "SELECT count(*) FROM %Q.'%q%s'",
pCheck->zDb, pCheck->zTab, zTbl
);
if( pCount ){
if( sqlite3_step(pCount)==SQLITE_ROW ){
i64 nActual = sqlite3_column_int64(pCount, 0);
if( nActual!=nExpect ){
rtreeCheckAppendMsg(pCheck, "Wrong number of entries in %%%s table"
" - expected %lld, actual %lld" , zTbl, nExpect, nActual
);
}
}
pCheck->rc = sqlite3_finalize(pCount);
}
}
}
/*
** This function does the bulk of the work for the rtree integrity-check.
** It is called by rtreecheck(), which is the SQL function implementation.
*/
static int rtreeCheckTable(
sqlite3 *db, /* Database handle to access db through */
const char *zDb, /* Name of db ("main", "temp" etc.) */
const char *zTab, /* Name of rtree table to check */
char **pzReport /* OUT: sqlite3_malloc'd report text */
){
RtreeCheck check; /* Common context for various routines */
sqlite3_stmt *pStmt = 0; /* Used to find column count of rtree table */
int nAux = 0; /* Number of extra columns. */
/* Initialize the context object */
memset(&check, 0, sizeof(check));
check.db = db;
check.zDb = zDb;
check.zTab = zTab;
/* Find the number of auxiliary columns */
pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.'%q_rowid'", zDb, zTab);
if( pStmt ){
nAux = sqlite3_column_count(pStmt) - 2;
sqlite3_finalize(pStmt);
}else
if( check.rc!=SQLITE_NOMEM ){
check.rc = SQLITE_OK;
}
/* Find number of dimensions in the rtree table. */
pStmt = rtreeCheckPrepare(&check, "SELECT * FROM %Q.%Q", zDb, zTab);
if( pStmt ){
int rc;
check.nDim = (sqlite3_column_count(pStmt) - 1 - nAux) / 2;
if( check.nDim<1 ){
rtreeCheckAppendMsg(&check, "Schema corrupt or not an rtree");
}else if( SQLITE_ROW==sqlite3_step(pStmt) ){
check.bInt = (sqlite3_column_type(pStmt, 1)==SQLITE_INTEGER);
}
rc = sqlite3_finalize(pStmt);
if( rc!=SQLITE_CORRUPT ) check.rc = rc;
}
/* Do the actual integrity-check */
if( check.nDim>=1 ){
if( check.rc==SQLITE_OK ){
rtreeCheckNode(&check, 0, 0, 1);
}
rtreeCheckCount(&check, "_rowid", check.nLeaf);
rtreeCheckCount(&check, "_parent", check.nNonLeaf);
}
/* Finalize SQL statements used by the integrity-check */
sqlite3_finalize(check.pGetNode);
sqlite3_finalize(check.aCheckMapping[0]);
sqlite3_finalize(check.aCheckMapping[1]);
*pzReport = check.zReport;
return check.rc;
}
/*
** Implementation of the xIntegrity method for Rtree.
*/
static int rtreeIntegrity(
sqlite3_vtab *pVtab, /* The virtual table to check */
const char *zSchema, /* Schema in which the virtual table lives */
const char *zName, /* Name of the virtual table */
int isQuick, /* True for a quick_check */
char **pzErr /* Write results here */
){
Rtree *pRtree = (Rtree*)pVtab;
int rc;
assert( pzErr!=0 && *pzErr==0 );
UNUSED_PARAMETER(zSchema);
UNUSED_PARAMETER(zName);
UNUSED_PARAMETER(isQuick);
rc = rtreeCheckTable(pRtree->db, pRtree->zDb, pRtree->zName, pzErr);
if( rc==SQLITE_OK && *pzErr ){
*pzErr = sqlite3_mprintf("In RTree %s.%s:\n%z",
pRtree->zDb, pRtree->zName, *pzErr);
if( (*pzErr)==0 ) rc = SQLITE_NOMEM;
}
return rc;
}
/*
** Usage:
**
** rtreecheck(<rtree-table>);
** rtreecheck(<database>, <rtree-table>);
**
** Invoking this SQL function runs an integrity-check on the named rtree
** table. The integrity-check verifies the following:
**
** 1. For each cell in the r-tree structure (%_node table), that:
**
** a) for each dimension, (coord1 <= coord2).
**
** b) unless the cell is on the root node, that the cell is bounded
** by the parent cell on the parent node.
**
** c) for leaf nodes, that there is an entry in the %_rowid
** table corresponding to the cell's rowid value that
** points to the correct node.
**
** d) for cells on non-leaf nodes, that there is an entry in the
** %_parent table mapping from the cell's child node to the
** node that it resides on.
**
** 2. That there are the same number of entries in the %_rowid table
** as there are leaf cells in the r-tree structure, and that there
** is a leaf cell that corresponds to each entry in the %_rowid table.
**
** 3. That there are the same number of entries in the %_parent table
** as there are non-leaf cells in the r-tree structure, and that
** there is a non-leaf cell that corresponds to each entry in the
** %_parent table.
*/
static void rtreecheck(
sqlite3_context *ctx,
int nArg,
sqlite3_value **apArg
){
if( nArg!=1 && nArg!=2 ){
sqlite3_result_error(ctx,
"wrong number of arguments to function rtreecheck()", -1
);
}else{
int rc;
char *zReport = 0;
const char *zDb = (const char*)sqlite3_value_text(apArg[0]);
const char *zTab;
if( nArg==1 ){
zTab = zDb;
zDb = "main";
}else{
zTab = (const char*)sqlite3_value_text(apArg[1]);
}
rc = rtreeCheckTable(sqlite3_context_db_handle(ctx), zDb, zTab, &zReport);
if( rc==SQLITE_OK ){
sqlite3_result_text(ctx, zReport ? zReport : "ok", -1, SQLITE_TRANSIENT);
}else{
sqlite3_result_error_code(ctx, rc);
}
sqlite3_free(zReport);
}
}
/* Conditionally include the geopoly code */
#ifdef SQLITE_ENABLE_GEOPOLY
# include "geopoly.c"
#endif
/*
** Register the r-tree module with database handle db. This creates the
** virtual table module "rtree" and the debugging/analysis scalar
** function "rtreenode".
*/
int sqlite3RtreeInit(sqlite3 *db){
const int utf8 = SQLITE_UTF8;
int rc;
rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
if( rc==SQLITE_OK ){
rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
}
if( rc==SQLITE_OK ){
rc = sqlite3_create_function(db, "rtreecheck", -1, utf8, 0,rtreecheck, 0,0);
}
if( rc==SQLITE_OK ){
#ifdef SQLITE_RTREE_INT_ONLY
void *c = (void *)RTREE_COORD_INT32;
#else
void *c = (void *)RTREE_COORD_REAL32;
#endif
rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
}
if( rc==SQLITE_OK ){
void *c = (void *)RTREE_COORD_INT32;
rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
}
#ifdef SQLITE_ENABLE_GEOPOLY
if( rc==SQLITE_OK ){
rc = sqlite3_geopoly_init(db);
}
#endif
return rc;
}
/*
** This routine deletes the RtreeGeomCallback object that was attached
** one of the SQL functions create by sqlite3_rtree_geometry_callback()
** or sqlite3_rtree_query_callback(). In other words, this routine is the
** destructor for an RtreeGeomCallback objecct. This routine is called when
** the corresponding SQL function is deleted.
*/
static void rtreeFreeCallback(void *p){
RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;
if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);
sqlite3_free(p);
}
/*
** This routine frees the BLOB that is returned by geomCallback().
*/
static void rtreeMatchArgFree(void *pArg){
int i;
RtreeMatchArg *p = (RtreeMatchArg*)pArg;
for(i=0; i<p->nParam; i++){
sqlite3_value_free(p->apSqlParam[i]);
}
sqlite3_free(p);
}
/*
** Each call to sqlite3_rtree_geometry_callback() or
** sqlite3_rtree_query_callback() creates an ordinary SQLite
** scalar function that is implemented by this routine.
**
** All this function does is construct an RtreeMatchArg object that
** contains the geometry-checking callback routines and a list of
** parameters to this function, then return that RtreeMatchArg object
** as a BLOB.
**
** The R-Tree MATCH operator will read the returned BLOB, deserialize
** the RtreeMatchArg object, and use the RtreeMatchArg object to figure
** out which elements of the R-Tree should be returned by the query.
*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
RtreeMatchArg *pBlob;
sqlite3_int64 nBlob;
int memErr = 0;
nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue)
+ nArg*sizeof(sqlite3_value*);
pBlob = (RtreeMatchArg *)sqlite3_malloc64(nBlob);
if( !pBlob ){
sqlite3_result_error_nomem(ctx);
}else{
int i;
pBlob->iSize = nBlob;
pBlob->cb = pGeomCtx[0];
pBlob->apSqlParam = (sqlite3_value**)&pBlob->aParam[nArg];
pBlob->nParam = nArg;
for(i=0; i<nArg; i++){
pBlob->apSqlParam[i] = sqlite3_value_dup(aArg[i]);
if( pBlob->apSqlParam[i]==0 ) memErr = 1;
#ifdef SQLITE_RTREE_INT_ONLY
pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);
#else
pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
#endif
}
if( memErr ){
sqlite3_result_error_nomem(ctx);
rtreeMatchArgFree(pBlob);
}else{
sqlite3_result_pointer(ctx, pBlob, "RtreeMatchArg", rtreeMatchArgFree);
}
}
}
/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
sqlite3 *db, /* Register SQL function on this connection */
const char *zGeom, /* Name of the new SQL function */
int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */
void *pContext /* Extra data associated with the callback */
){
RtreeGeomCallback *pGeomCtx; /* Context object for new user-function */
/* Allocate and populate the context object. */
pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
if( !pGeomCtx ) return SQLITE_NOMEM;
pGeomCtx->xGeom = xGeom;
pGeomCtx->xQueryFunc = 0;
pGeomCtx->xDestructor = 0;
pGeomCtx->pContext = pContext;
return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY,
(void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
);
}
/*
** Register a new 2nd-generation geometry function for use with the
** r-tree MATCH operator.
*/
int sqlite3_rtree_query_callback(
sqlite3 *db, /* Register SQL function on this connection */
const char *zQueryFunc, /* Name of new SQL function */
int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */
void *pContext, /* Extra data passed into the callback */
void (*xDestructor)(void*) /* Destructor for the extra data */
){
RtreeGeomCallback *pGeomCtx; /* Context object for new user-function */
/* Allocate and populate the context object. */
pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
if( !pGeomCtx ){
if( xDestructor ) xDestructor(pContext);
return SQLITE_NOMEM;
}
pGeomCtx->xGeom = 0;
pGeomCtx->xQueryFunc = xQueryFunc;
pGeomCtx->xDestructor = xDestructor;
pGeomCtx->pContext = pContext;
return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY,
(void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback
);
}
#if !SQLITE_CORE
#ifdef _WIN32
__declspec(dllexport)
#endif
int sqlite3_rtree_init(
sqlite3 *db,
char **pzErrMsg,
const sqlite3_api_routines *pApi
){
SQLITE_EXTENSION_INIT2(pApi)
return sqlite3RtreeInit(db);
}
#endif
#endif
|