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
// Copyright © 2016–2017 University of Malta // This program is free software: you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public License // as published by the Free Software Foundation, either version 3 of // the License, or (at your option) any later version. // // This program is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // // You should have received a copy of the GNU Lesser General Public // License and a copy of the GNU General Public License along with // this program. If not, see <http://www.gnu.org/licenses/>. use Assign; use ext::gmp as xgmp; use gmp_mpfr_sys::gmp::{self, mpz_t}; use inner::{Inner, InnerMut}; use ops::{AddFrom, BitAndFrom, BitOrFrom, BitXorFrom, DivFrom, MulFrom, NegAssign, NotAssign, Pow, PowAssign, RemFrom, SubFrom}; #[cfg(feature = "rand")] use rand::RandState; use std::{i32, u32}; use std::cmp::Ordering; use std::error::Error; use std::ffi::CStr; use std::fmt::{self, Binary, Debug, Display, Formatter, LowerHex, Octal, UpperHex}; use std::mem; use std::ops::{Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign, Mul, MulAssign, Neg, Not, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign}; use std::os::raw::{c_char, c_int, c_long, c_ulong}; use std::str::FromStr; /// An arbitrary-precision integer. /// /// Standard arithmetic operations, bitwise operations and comparisons /// are supported. In standard arithmetic operations such as addition, /// you can mix `Integer` and primitive integer types; the result will /// be an `Integer`. /// /// Internally the integer is not stored using two’s-complement /// representation, however, for bitwise operations and shifts, the /// functionality is the same as if the representation was using two’s /// complement. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// // Create an integer initialized as zero. /// let mut int = Integer::new(); /// assert_eq!(int, 0); /// assert_eq!(int.to_u32(), Some(0)); /// int.assign(-14); /// assert_eq!(int, -14); /// assert_eq!(int.to_u32(), None); /// assert_eq!(int.to_i32(), Some(-14)); /// ``` /// /// Arithmetic operations with mixed arbitrary and primitive types are /// allowed. Note that in the following example, there is only one /// allocation. The `Integer` instance is moved into the shift /// operation so that the result can be stored in the same instance, /// then that result is similarly consumed by the addition operation. /// /// ```rust /// use rug::Integer; /// let mut a = Integer::from(0xc); /// a = (a << 80) + 0xffee; /// assert_eq!(a.to_string_radix(16), "c0000000000000000ffee"); /// // ^ ^ ^ ^ ^ /// // 80 64 48 32 16 /// ``` /// /// Bitwise operations on `Integer` values behave as if the value uses /// two’s-complement representation. /// /// ```rust /// use rug::Integer; /// /// let mut i = Integer::from(1); /// i = i << 1000; /// // i is now 1000000... (1000 zeros) /// assert_eq!(i.significant_bits(), 1001); /// assert_eq!(i.find_one(0), Some(1000)); /// i -= 1; /// // i is now 111111... (1000 ones) /// assert_eq!(i.count_ones(), Some(1000)); /// /// let a = Integer::from(0xf00d); /// let all_ones_xor_a = Integer::from(-1) ^ &a; /// // a is unchanged as we borrowed it /// let complement_a = !a; /// // now a has been moved, so this would cause an error: /// // assert!(a > 0); /// assert_eq!(all_ones_xor_a, complement_a); /// assert_eq!(complement_a, -0xf00e); /// assert_eq!(format!("{:x}", complement_a), "-f00e"); /// ``` /// /// To initialize a large `Integer` that does not fit in a primitive /// type, you can parse a string. /// /// ```rust /// use rug::Integer; /// let s1 = "123456789012345678901234567890"; /// let i1 = s1.parse::<Integer>().unwrap(); /// assert_eq!(i1.significant_bits(), 97); /// let s2 = "ffff0000ffff0000ffff0000ffff0000ffff0000"; /// let i2 = Integer::from_str_radix(s2, 16).unwrap(); /// assert_eq!(i2.significant_bits(), 160); /// assert_eq!(i2.count_ones(), Some(80)); /// ``` /// /// Operations on two borrowed `Integer` values result in an /// intermediate value that has to be assigned to a new `Integer` /// value. /// /// ```rust /// use rug::Integer; /// let a = Integer::from(10); /// let b = Integer::from(3); /// let a_b_ref = &a + &b; /// let a_b = Integer::from(a_b_ref); /// assert_eq!(a_b, 13); /// ``` /// /// The `Integer` type supports various functions. Most functions have /// three versions: one that consumes the operand, one that mutates /// the operand, and one that borrows the operand. /// /// ```rust /// use rug::Integer; /// // 1. consume the operand /// let a = Integer::from(-15); /// let abs_a = a.abs(); /// assert_eq!(abs_a, 15); /// // 2. mutate the operand /// let mut b = Integer::from(-16); /// b.abs_mut(); /// assert_eq!(b, 16); /// // 3. borrow the operand /// let c = Integer::from(-17); /// let r = c.abs_ref(); /// let abs_c = Integer::from(r); /// assert_eq!(abs_c, 17); /// // c was not consumed /// assert_eq!(c, -17); /// ``` pub struct Integer { inner: mpz_t, } impl Default for Integer { #[inline] fn default() -> Integer { Integer::new() } } impl Clone for Integer { #[inline] fn clone(&self) -> Integer { let mut ret = Integer::new(); ret.assign(self); ret } #[inline] fn clone_from(&mut self, source: &Integer) { self.assign(source); } } impl Drop for Integer { #[inline] fn drop(&mut self) { unsafe { gmp::mpz_clear(self.inner_mut()); } } } impl Integer { /// Constructs a new arbitrary-precision integer with value 0. /// /// # Examples /// ```rust /// use rug::Integer; /// let i = Integer::new(); /// assert_eq!(i, 0); /// ``` #[inline] pub fn new() -> Integer { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init(ret.inner_mut()); ret } } /// Constructs a new arbitrary-precision integer with at least the /// specified capacity. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::with_capacity(137); /// assert!(i.capacity() >= 137); /// ``` #[inline] pub fn with_capacity(bits: usize) -> Integer { assert_eq!(bits as gmp::bitcnt_t as usize, bits, "overflow"); unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init2(ret.inner_mut(), bits as gmp::bitcnt_t); ret } } /// Returns the capacity in bits that can be stored without reallocating. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::with_capacity(137); /// assert!(i.capacity() >= 137); /// ``` #[inline] pub fn capacity(&self) -> usize { let limbs = self.inner().alloc; let bits = limbs as usize * gmp::LIMB_BITS as usize; assert_eq!( limbs, (bits / gmp::LIMB_BITS as usize) as c_int, "overflow" ); bits } /// Reserves capacity for at least `additional` more bits in the /// `Integer`. If the integer already has enough excess capacity, /// this function does nothing. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // 0x2000_0000 needs 30 bits. /// let mut i = Integer::from(0x2000_0000); /// i.reserve(34); /// let capacity = i.capacity(); /// assert!(capacity >= 64); /// i.reserve(34); /// assert!(i.capacity() == capacity); /// i.reserve(35); /// assert!(i.capacity() >= 65); /// ``` pub fn reserve(&mut self, additional: usize) { if additional == 0 { return; } let used_bits = if self.inner().size == 0 { 0 } else { unsafe { gmp::mpz_sizeinbase(self.inner(), 2) } }; let req_bits = used_bits.checked_add(additional).expect("overflow"); assert_eq!(req_bits as gmp::bitcnt_t as usize, req_bits, "overflow"); unsafe { gmp::mpz_realloc2(self.inner_mut(), req_bits as gmp::bitcnt_t); } } /// Reserves capacity for at least `additional` more bits in the /// `Integer`. If the integer already has enough excess capacity, /// this function does nothing. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // let i be 100 bits wide /// let mut i = Integer::from_str_radix("fffff12345678901234567890", 16) /// .unwrap(); /// assert!(i.capacity() >= 100); /// i >>= 80; /// i.shrink_to_fit(); /// assert!(i.capacity() >= 20); /// ``` pub fn shrink_to_fit(&mut self) { let used_bits = unsafe { gmp::mpz_sizeinbase(self.inner(), 2) }; assert_eq!(used_bits as gmp::bitcnt_t as usize, used_bits, "overflow"); unsafe { gmp::mpz_realloc2(self.inner_mut(), used_bits as gmp::bitcnt_t); } } /// Creates an `Integer` from an `f32` if it is finite, rounding /// towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::f32; /// let i = Integer::from_f32(-5.6).unwrap(); /// assert_eq!(i, -5); /// let neg_inf = Integer::from_f32(f32::NEG_INFINITY); /// assert!(neg_inf.is_none()); /// ``` #[inline] pub fn from_f32(val: f32) -> Option<Integer> { Integer::from_f64(val as f64) } /// Creates an `Integer` from an `f64` if it is finite, rounding /// towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::f64; /// let i = Integer::from_f64(1e20).unwrap(); /// assert_eq!(i, "100000000000000000000".parse::<Integer>().unwrap()); /// let inf = Integer::from_f64(f64::INFINITY); /// assert!(inf.is_none()); /// ``` #[inline] pub fn from_f64(val: f64) -> Option<Integer> { if val.is_finite() { unsafe { let mut i: Integer = mem::uninitialized(); gmp::mpz_init_set_d(i.inner_mut(), val); Some(i) } } else { None } } /// Parses an `Integer` using the given radix. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from_str_radix("-ff", 16).unwrap(); /// assert_eq!(i, -0xff); /// ``` /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. #[inline] pub fn from_str_radix( src: &str, radix: i32, ) -> Result<Integer, ParseIntegerError> { let mut i = Integer::new(); i.assign_str_radix(src, radix)?; Ok(i) } /// Checks if an `Integer` can be parsed. /// /// If this method does not return an error, neither will any /// other function that parses an `Integer`. If this method /// returns an error, the other functions will return the same /// error. /// /// The string can start with an optional minus or plus sign. /// Whitespace is not allowed anywhere in the string, including in /// the beginning and end. /// /// # Examples /// /// ```rust /// use rug::Integer; /// /// let valid1 = Integer::valid_str_radix("1223", 4); /// let i1 = Integer::from(valid1.unwrap()); /// assert_eq!(i1, 3 + 4 * (2 + 4 * (2 + 4 * 1))); /// let valid2 = Integer::valid_str_radix("12yz", 36); /// let i2 = Integer::from(valid2.unwrap()); /// assert_eq!(i2, 35 + 36 * (34 + 36 * (2 + 36 * 1))); /// /// let invalid = Integer::valid_str_radix("123", 3); /// let invalid_f = Integer::from_str_radix("123", 3); /// assert_eq!(invalid.unwrap_err(), invalid_f.unwrap_err()); /// ``` /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. pub fn valid_str_radix( src: &str, radix: i32, ) -> Result<ValidInteger, ParseIntegerError> { use self::ParseIntegerError as Error; use self::ParseErrorKind as Kind; assert!(radix >= 2 && radix <= 36, "radix out of range"); let bytes = src.as_bytes(); let (skip_plus, iter) = match bytes.get(0) { Some(&b'+') => (&bytes[1..], bytes[1..].iter()), Some(&b'-') => (bytes, bytes[1..].iter()), _ => (bytes, bytes.iter()), }; let mut got_digit = false; for b in iter { let digit_value = match *b { b'0'...b'9' => *b - b'0', b'a'...b'z' => *b - b'a' + 10, b'A'...b'Z' => *b - b'A' + 10, _ => return Err(Error { kind: Kind::InvalidDigit }), }; if digit_value >= radix as u8 { return Err(Error { kind: Kind::InvalidDigit }); } got_digit = true; } if !got_digit { return Err(Error { kind: Kind::NoDigits }); } let v = ValidInteger { bytes: skip_plus, radix: radix, }; Ok(v) } /// Converts to an `i32` if the value fits. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(-50); /// assert_eq!(fits.to_i32(), Some(-50)); /// let small = Integer::from(-123456789012345_i64); /// assert_eq!(small.to_i32(), None); /// let large = Integer::from(123456789012345_u64); /// assert_eq!(large.to_i32(), None); /// ``` #[inline] pub fn to_i32(&self) -> Option<i32> { if unsafe { xgmp::mpz_fits_i32(self.inner()) } { Some(self.to_i32_wrapping()) } else { None } } /// Converts to an `i64` if the value fits. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(-50); /// assert_eq!(fits.to_i64(), Some(-50)); /// let small = Integer::from_str_radix("-fedcba9876543210", 16).unwrap(); /// assert_eq!(small.to_i64(), None); /// let large = Integer::from_str_radix("fedcba9876543210", 16).unwrap(); /// assert_eq!(large.to_i64(), None); /// ``` #[inline] pub fn to_i64(&self) -> Option<i64> { if unsafe { xgmp::mpz_fits_i64(self.inner()) } { Some(self.to_i64_wrapping()) } else { None } } /// Converts to a `u32` if the value fits. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(1234567890); /// assert_eq!(fits.to_u32(), Some(1234567890)); /// let neg = Integer::from(-1); /// assert_eq!(neg.to_u32(), None); /// let large = "123456789012345".parse::<Integer>().unwrap(); /// assert_eq!(large.to_u32(), None); /// ``` #[inline] pub fn to_u32(&self) -> Option<u32> { if unsafe { xgmp::mpz_fits_u32(self.inner()) } { Some(self.to_u32_wrapping()) } else { None } } /// Converts to a `u64` if the value fits. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(123456789012345_u64); /// assert_eq!(fits.to_u64(), Some(123456789012345)); /// let neg = Integer::from(-1); /// assert_eq!(neg.to_u64(), None); /// let large = "1234567890123456789012345".parse::<Integer>().unwrap(); /// assert_eq!(large.to_u64(), None); /// ``` #[inline] pub fn to_u64(&self) -> Option<u64> { if unsafe { xgmp::mpz_fits_u64(self.inner()) } { Some(self.to_u64_wrapping()) } else { None } } /// Converts to an `i32`, wrapping if the value does not fit. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(-0xabcdef_i32); /// assert_eq!(fits.to_i32_wrapping(), -0xabcdef); /// let small = Integer::from(0x1_ffff_ffff_u64); /// assert_eq!(small.to_i32_wrapping(), -1); /// let large = Integer::from_str_radix("1234567890abcdef", 16).unwrap(); /// assert_eq!(large.to_i32_wrapping(), 0x90abcdef_u32 as i32); /// ``` #[inline] pub fn to_i32_wrapping(&self) -> i32 { self.to_u32_wrapping() as i32 } /// Converts to an `i64`, wrapping if the value does not fit. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(-0xabcdef); /// assert_eq!(fits.to_i64_wrapping(), -0xabcdef); /// let small = Integer::from_str_radix("1ffffffffffffffff", 16).unwrap(); /// assert_eq!(small.to_i64_wrapping(), -1); /// let large = Integer::from_str_radix("f1234567890abcdef", 16).unwrap(); /// assert_eq!(large.to_i64_wrapping(), 0x1234567890abcdef_i64); /// ``` #[inline] pub fn to_i64_wrapping(&self) -> i64 { self.to_u64_wrapping() as i64 } /// Converts to a `u32`, wrapping if the value does not fit. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(0x90abcdef_u32); /// assert_eq!(fits.to_u32_wrapping(), 0x90abcdef); /// let neg = Integer::from(-1); /// assert_eq!(neg.to_u32_wrapping(), 0xffffffff); /// let large = Integer::from_str_radix("1234567890abcdef", 16).unwrap(); /// assert_eq!(large.to_u32_wrapping(), 0x90abcdef); /// ``` #[inline] pub fn to_u32_wrapping(&self) -> u32 { let u = unsafe { xgmp::mpz_get_abs_u32(self.inner()) }; if self.sign() == Ordering::Less { u.wrapping_neg() } else { u } } /// Converts to a `u64`, wrapping if the value does not fit. /// /// # Examples /// ```rust /// use rug::Integer; /// let fits = Integer::from(0x90abcdef_u64); /// assert_eq!(fits.to_u64_wrapping(), 0x90abcdef); /// let neg = Integer::from(-1); /// assert_eq!(neg.to_u64_wrapping(), 0xffff_ffff_ffff_ffff); /// let large = Integer::from_str_radix("f123456789abcdef0", 16).unwrap(); /// assert_eq!(large.to_u64_wrapping(), 0x123456789abcdef0); /// ``` #[inline] pub fn to_u64_wrapping(&self) -> u64 { let u = unsafe { xgmp::mpz_get_abs_u64(self.inner()) }; if self.sign() == Ordering::Less { u.wrapping_neg() } else { u } } /// Converts to an `f32`, rounding towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::f32; /// let min = Integer::from_f32(f32::MIN).unwrap(); /// let minus_one = min - 1u32; /// // minus_one is truncated to f32::MIN /// assert_eq!(minus_one.to_f32(), f32::MIN); /// let times_two = minus_one * 2u32; /// // times_two is too small /// assert_eq!(times_two.to_f32(), f32::NEG_INFINITY); /// ``` #[inline] pub fn to_f32(&self) -> f32 { trunc_f64_to_f32(self.to_f64()) } /// Converts to an `f64`, rounding towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::f64; /// /// // An `f64` has 53 bits of precision. /// let exact = 0x1f_ffff_ffff_ffff_u64; /// let i = Integer::from(exact); /// assert_eq!(i.to_f64(), exact as f64); /// /// // large has 56 ones /// let large = 0xff_ffff_ffff_ffff_u64; /// // trunc has 53 ones followed by 3 zeros /// let trunc = 0xff_ffff_ffff_fff8_u64; /// let j = Integer::from(large); /// assert_eq!(j.to_f64(), trunc as f64); /// /// let max = Integer::from_f64(f64::MAX).unwrap(); /// let plus_one = max + 1u32; /// // plus_one is truncated to f64::MAX /// assert_eq!(plus_one.to_f64(), f64::MAX); /// let times_two = plus_one * 2u32; /// // times_two is too large /// assert_eq!(times_two.to_f64(), f64::INFINITY); /// ``` #[inline] pub fn to_f64(&self) -> f64 { unsafe { gmp::mpz_get_d(self.inner()) } } /// Converts to an `f32` and an exponent, rounding towards zero. /// /// The returned `f32` is in the range 0.5 ≤ *x* < 1. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let zero = Integer::new(); /// let (d0, exp0) = zero.to_f32_exp(); /// assert_eq!((d0, exp0), (0.0, 0)); /// let fifteen = Integer::from(15); /// let (d15, exp15) = fifteen.to_f32_exp(); /// assert_eq!((d15, exp15), (15.0 / 16.0, 4)); /// ``` #[inline] pub fn to_f32_exp(&self) -> (f32, u32) { let (f, exp) = self.to_f64_exp(); let trunc_f = trunc_f64_to_f32(f); (trunc_f, exp) } /// Converts to an `f64` and an exponent, rounding towards zero. /// /// The returned `f64` is in the range 0.5 ≤ *x* < 1. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let zero = Integer::new(); /// let (d0, exp0) = zero.to_f64_exp(); /// assert_eq!((d0, exp0), (0.0, 0)); /// let fifteen = Integer::from(15); /// let (d15, exp15) = fifteen.to_f64_exp(); /// assert_eq!((d15, exp15), (15.0 / 16.0, 4)); /// ``` #[inline] pub fn to_f64_exp(&self) -> (f64, u32) { let mut exp: c_long = 0; let f = unsafe { gmp::mpz_get_d_2exp(&mut exp, self.inner()) }; assert_eq!(exp as u32 as c_long, exp, "overflow"); (f, exp as u32) } /// Returns a string representation of the number for the /// specified `radix`. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut i = Integer::new(); /// assert_eq!(i.to_string_radix(10), "0"); /// i.assign(-10); /// assert_eq!(i.to_string_radix(16), "-a"); /// i.assign(0x1234cdef); /// assert_eq!(i.to_string_radix(4), "102031030313233"); /// i.assign_str_radix("1234567890aAbBcCdDeEfF", 16).unwrap(); /// assert_eq!(i.to_string_radix(16), "1234567890aabbccddeeff"); /// ``` /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. #[inline] pub fn to_string_radix(&self, radix: i32) -> String { make_string(self, radix, false) } /// Assigns from an `f32` if it is finite, rounding towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::f32; /// let mut i = Integer::new(); /// let ret = i.assign_f64(-12.7); /// assert!(ret.is_ok()); /// assert_eq!(i, -12); /// let ret = i.assign_f32(f32::NAN); /// assert!(ret.is_err()); /// assert_eq!(i, -12); /// ``` #[inline] pub fn assign_f32(&mut self, val: f32) -> Result<(), ()> { self.assign_f64(val as f64) } /// Assigns from an `f64` if it is finite, rounding towards zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// let ret = i.assign_f64(12.7); /// assert!(ret.is_ok()); /// assert_eq!(i, 12); /// let ret = i.assign_f64(1.0 / 0.0); /// assert!(ret.is_err()); /// assert_eq!(i, 12); /// ``` #[inline] pub fn assign_f64(&mut self, val: f64) -> Result<(), ()> { if val.is_finite() { unsafe { gmp::mpz_set_d(self.inner_mut(), val); } Ok(()) } else { Err(()) } } /// Parses an `Integer` from a string in decimal. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_str("123").unwrap(); /// assert_eq!(i, 123); /// let ret = i.assign_str("bad"); /// assert!(ret.is_err()); /// ``` #[inline] pub fn assign_str(&mut self, src: &str) -> Result<(), ParseIntegerError> { self.assign_str_radix(src, 10) } /// Parses an `Integer` from a string with the specified radix. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_str_radix("ff", 16).unwrap(); /// assert_eq!(i, 0xff); /// ``` /// /// # Panics /// /// Panics if `radix` is less than 2 or greater than 36. #[inline] pub fn assign_str_radix( &mut self, src: &str, radix: i32, ) -> Result<(), ParseIntegerError> { self.assign(Integer::valid_str_radix(src, radix)?); Ok(()) } /// Returns `true` if the number is even. /// /// # Examples /// /// ```rust /// use rug::Integer; /// assert!(!(Integer::from(13).is_even())); /// assert!(Integer::from(-14).is_even()); /// ``` #[inline] pub fn is_even(&self) -> bool { unsafe { gmp::mpz_even_p(self.inner()) != 0 } } /// Returns `true` if the number is odd. /// /// # Examples /// /// ```rust /// use rug::Integer; /// assert!(Integer::from(13).is_odd()); /// assert!(!Integer::from(-14).is_odd()); /// ``` #[inline] pub fn is_odd(&self) -> bool { unsafe { gmp::mpz_odd_p(self.inner()) != 0 } } /// Returns `true` if the number is divisible by `divisor`. Unlike /// other division functions, `divisor` can be zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(230); /// assert!(i.is_divisible(&Integer::from(10))); /// assert!(!i.is_divisible(&Integer::from(100))); /// assert!(!i.is_divisible(&Integer::new())); /// ``` #[inline] pub fn is_divisible(&self, divisor: &Integer) -> bool { unsafe { gmp::mpz_divisible_p(self.inner(), divisor.inner()) != 0 } } /// Returns `true` if the number is divisible by `divisor`. Unlike /// other division functions, `divisor` can be zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(230); /// assert!(i.is_divisible_u(23)); /// assert!(!i.is_divisible_u(100)); /// assert!(!i.is_divisible_u(0)); /// ``` #[inline] pub fn is_divisible_u(&self, divisor: u32) -> bool { unsafe { gmp::mpz_divisible_ui_p(self.inner(), divisor.into()) != 0 } } /// Returns `true` if the number is divisible by 2<sup>*b*</sup>. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(15 << 17); /// assert!(i.is_divisible_2pow(16)); /// assert!(i.is_divisible_2pow(17)); /// assert!(!i.is_divisible_2pow(18)); /// ``` #[inline] pub fn is_divisible_2pow(&self, b: u32) -> bool { unsafe { gmp::mpz_divisible_2exp_p(self.inner(), b.into()) != 0 } } /// Returns `true` if the number is congruent to *c* mod /// *divisor*, that is, if there exists a *q* such that `self` = /// *c* + *q* × *divisor*. Unlike other division functions, /// `divisor` can be zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let n = Integer::from(105); /// let divisor = Integer::from(10); /// assert!(n.is_congruent(&Integer::from(5), &divisor)); /// assert!(n.is_congruent(&Integer::from(25), &divisor)); /// assert!(!n.is_congruent(&Integer::from(7), &divisor)); /// // n is congruent to itself if divisor is 0 /// assert!(n.is_congruent(&n, &Integer::from(0))); /// ``` #[inline] pub fn is_congruent(&self, c: &Integer, divisor: &Integer) -> bool { unsafe { gmp::mpz_congruent_p(self.inner(), c.inner(), divisor.inner()) != 0 } } /// Returns `true` if the number is congruent to *c* mod /// *divisor*, that is, if there exists a *q* such that `self` = /// *c* + *q* × *divisor*. Unlike other division functions, /// `divisor` can be zero. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let n = Integer::from(105); /// assert!(n.is_congruent_u(3335, 10)); /// assert!(!n.is_congruent_u(107, 10)); /// // n is congruent to itself if divisor is 0 /// assert!(n.is_congruent_u(105, 0)); /// ``` #[inline] pub fn is_congruent_u(&self, c: u32, divisor: u32) -> bool { unsafe { gmp::mpz_congruent_ui_p(self.inner(), c.into(), divisor.into()) != 0 } } /// Returns `true` if the number is congruent to *c* mod /// 2<sup>*b*</sup>, that is, if there exists a *q* such that /// `self` = *c* + *q* × 2<sup>*b*</sup>. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let n = Integer::from(13 << 17 | 21); /// assert!(n.is_congruent_2pow(&Integer::from(7 << 17 | 21), 17)); /// assert!(!n.is_congruent_2pow(&Integer::from(13 << 17 | 22), 17)); /// ``` #[inline] pub fn is_congruent_2pow(&self, c: &Integer, b: u32) -> bool { unsafe { gmp::mpz_congruent_2exp_p(self.inner(), c.inner(), b.into()) != 0 } } /// Returns `true` if the number is a perfect power. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// // 0 is 0 to the power of anything /// let mut i = Integer::from(0); /// assert!(i.is_perfect_power()); /// // 243 is 3 to the power of 5 /// i.assign(243); /// assert!(i.is_perfect_power()); /// // 10 is not a perfect power /// i.assign(10); /// assert!(!i.is_perfect_power()); /// ``` #[inline] pub fn is_perfect_power(&self) -> bool { unsafe { gmp::mpz_perfect_power_p(self.inner()) != 0 } } /// Returns `true` if the number is a perfect square. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut i = Integer::from(1); /// assert!(i.is_perfect_square()); /// i.assign(9); /// assert!(i.is_perfect_square()); /// i.assign(15); /// assert!(!i.is_perfect_square()); /// ``` #[inline] pub fn is_perfect_square(&self) -> bool { unsafe { gmp::mpz_perfect_square_p(self.inner()) != 0 } } /// Returns the same result as `self.cmp(&0)`, but is faster. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::cmp::Ordering; /// assert_eq!(Integer::from(-5).sign(), Ordering::Less); /// assert_eq!(Integer::from(0).sign(), Ordering::Equal); /// assert_eq!(Integer::from(5).sign(), Ordering::Greater); /// ``` #[inline] pub fn sign(&self) -> Ordering { unsafe { gmp::mpz_sgn(self.inner()).cmp(&0) } } /// Compares the absolute values. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use std::cmp::Ordering; /// let a = Integer::from(-10); /// let b = Integer::from(4); /// assert_eq!(a.cmp(&b), Ordering::Less); /// assert_eq!(a.cmp_abs(&b), Ordering::Greater); /// ``` #[inline] pub fn cmp_abs(&self, other: &Integer) -> Ordering { unsafe { gmp::mpz_cmpabs(self.inner(), other.inner()).cmp(&0) } } /// Returns the number of bits required to represent the absolute /// value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// /// assert_eq!(Integer::from(0).significant_bits(), 0); /// assert_eq!(Integer::from(1).significant_bits(), 1); /// assert_eq!(Integer::from(-1).significant_bits(), 1); /// assert_eq!(Integer::from(4).significant_bits(), 3); /// assert_eq!(Integer::from(-4).significant_bits(), 3); /// assert_eq!(Integer::from(7).significant_bits(), 3); /// assert_eq!(Integer::from(-7).significant_bits(), 3); /// ``` #[inline] pub fn significant_bits(&self) -> u32 { let bits = unsafe { gmp::mpz_sizeinbase(self.inner(), 2) }; if bits > u32::MAX as usize { panic!("overflow"); } // sizeinbase returns 1 if number is 0 if bits == 1 && *self == 0 { 0 } else { bits as u32 } } /// Returns the number of one bits if the value ≥ 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// assert_eq!(Integer::from(0).count_ones(), Some(0)); /// assert_eq!(Integer::from(15).count_ones(), Some(4)); /// assert_eq!(Integer::from(-1).count_ones(), None); /// ``` #[inline] pub fn count_ones(&self) -> Option<u32> { bitcount_to_u32(unsafe { gmp::mpz_popcount(self.inner()) }) } /// Returns the number of zero bits if the value < 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// assert_eq!(Integer::from(0).count_zeros(), None); /// assert_eq!(Integer::from(1).count_zeros(), None); /// assert_eq!(Integer::from(-1).count_zeros(), Some(0)); /// assert_eq!(Integer::from(-2).count_zeros(), Some(1)); /// assert_eq!(Integer::from(-7).count_zeros(), Some(2)); /// assert_eq!(Integer::from(-8).count_zeros(), Some(3)); /// ``` #[inline] pub fn count_zeros(&self) -> Option<u32> { bitcount_to_u32(unsafe { xgmp::mpz_zerocount(self.inner()) }) } /// Returns the location of the first zero, starting at `start`. /// If the bit at location `start` is zero, returns `start`. /// /// ```rust /// use rug::Integer; /// assert_eq!(Integer::from(-2).find_zero(0), Some(0)); /// assert_eq!(Integer::from(-2).find_zero(1), None); /// assert_eq!(Integer::from(15).find_zero(0), Some(4)); /// assert_eq!(Integer::from(15).find_zero(20), Some(20)); #[inline] pub fn find_zero(&self, start: u32) -> Option<u32> { bitcount_to_u32(unsafe { gmp::mpz_scan0(self.inner(), start.into()) }) } /// Returns the location of the first one, starting at `start`. /// If the bit at location `start` is one, returns `start`. /// /// ```rust /// use rug::Integer; /// assert_eq!(Integer::from(1).find_one(0), Some(0)); /// assert_eq!(Integer::from(1).find_one(1), None); /// assert_eq!(Integer::from(-16).find_one(0), Some(4)); /// assert_eq!(Integer::from(-16).find_one(20), Some(20)); #[inline] pub fn find_one(&self, start: u32) -> Option<u32> { bitcount_to_u32(unsafe { gmp::mpz_scan1(self.inner(), start.into()) }) } /// Sets the bit at location `index` to 1 if `val` is `true` or 0 /// if `val` is `false`. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut i = Integer::from(-1); /// assert_eq!(*i.set_bit(0, false), -2); /// i.assign(0xff); /// assert_eq!(*i.set_bit(11, true), 0x8ff); /// ``` #[inline] pub fn set_bit(&mut self, index: u32, val: bool) -> &mut Integer { unsafe { if val { gmp::mpz_setbit(self.inner_mut(), index.into()); } else { gmp::mpz_clrbit(self.inner_mut(), index.into()); } } self } /// Returns `true` if the bit at location `index` is 1 or `false` /// if the bit is 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(0b100101); /// assert!(i.get_bit(0)); /// assert!(!i.get_bit(1)); /// assert!(i.get_bit(5)); /// let neg = Integer::from(-1); /// assert!(neg.get_bit(1000)); /// ``` #[inline] pub fn get_bit(&self, index: u32) -> bool { unsafe { gmp::mpz_tstbit(self.inner(), index.into()) != 0 } } /// Toggles the bit at location `index`. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(0b100101); /// i.toggle_bit(5); /// assert_eq!(i, 0b101); /// ``` #[inline] pub fn toggle_bit(&mut self, index: u32) -> &mut Integer { unsafe { gmp::mpz_combit(self.inner_mut(), index.into()); } self } /// Retuns the Hamming distance if the two numbers have the same /// sign. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-1); /// assert_eq!(Integer::from(0).hamming_dist(&i), None); /// assert_eq!(Integer::from(-1).hamming_dist(&i), Some(0)); /// // -1 is ...11111111 and -13 is ...11110011 /// assert_eq!(Integer::from(-13).hamming_dist(&i), Some(2)); /// ``` #[inline] pub fn hamming_dist(&self, other: &Integer) -> Option<u32> { bitcount_to_u32( unsafe { gmp::mpz_hamdist(self.inner(), other.inner()) }, ) } math_op1! { Integer; gmp::mpz_abs; /// Computes the absolute value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-100); /// let abs = i.abs(); /// assert_eq!(abs, 100); /// ``` fn abs(); /// Computes the absolute value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(-100); /// i.abs_mut(); /// assert_eq!(i, 100); /// ``` fn abs_mut; /// Computes the absolute value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-100); /// let r = i.abs_ref(); /// let abs = Integer::from(r); /// assert_eq!(abs, 100); /// assert_eq!(i, -100); /// ``` fn abs_ref -> AbsRef; } math_op1! { Integer; gmp::mpz_fdiv_r_2exp; /// Keeps the *n* least significant bits only. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-1); /// let keep_8 = i.keep_bits(8); /// assert_eq!(keep_8, 0xff); /// ``` fn keep_bits(n: u32); /// Keeps the *n* least significant bits only. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(-1); /// i.keep_bits_mut(8); /// assert_eq!(i, 0xff); /// ``` fn keep_bits_mut; /// Keeps the *n* least significant bits only. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-1); /// let r = i.keep_bits_ref(8); /// let eight_bits = Integer::from(r); /// assert_eq!(eight_bits, 0xff); /// ``` fn keep_bits_ref -> KeepBitsRef; } math_op1! { Integer; xgmp::mpz_next_pow_of_two; /// Finds the next power of two, or 1 if the number ≤ 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(-3).next_power_of_two(); /// assert_eq!(i, 1); /// let i = Integer::from(4).next_power_of_two(); /// assert_eq!(i, 4); /// let i = Integer::from(7).next_power_of_two(); /// assert_eq!(i, 8); /// ``` fn next_power_of_two(); /// Finds the next power of two, or 1 if the number ≤ 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(53); /// i.next_power_of_two_mut(); /// assert_eq!(i, 64); /// ``` fn next_power_of_two_mut; /// Finds the next power of two, or 1 if the number ≤ 0. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(53); /// let r = i.next_power_of_two_ref(); /// let next = Integer::from(r); /// assert_eq!(next, 64); /// ``` fn next_power_of_two_ref -> NextPowerTwoRef; } math_op2_2! { Integer; xgmp::mpz_tdiv_qr_check_0; /// Performs a division producing both the quotient and /// remainder. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let dividend = Integer::from(23); /// let divisor = Integer::from(10); /// let (quotient, rem) = dividend.div_rem(divisor); /// assert_eq!(quotient, 2); /// assert_eq!(rem, 3); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_rem(divisor); /// Performs a division producing both the quotient and /// remainder. /// /// The quotient is stored in `self` and the remainder is /// stored in `divisor`. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut dividend_quotient = Integer::from(23); /// let mut divisor_rem = Integer::from(10); /// dividend_quotient.div_rem_mut(&mut divisor_rem); /// assert_eq!(dividend_quotient, 2); /// assert_eq!(divisor_rem, 3); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_rem_mut; /// Performs a division producing both the quotient and /// remainder. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let dividend = Integer::from(23); /// let divisor = Integer::from(10); /// let r = dividend.div_rem_ref(&divisor); /// let (quotient, rem) = <(Integer, Integer)>::from(r); /// assert_eq!(quotient, 2); /// assert_eq!(rem, 3); /// ``` fn div_rem_ref -> DivRemRef; } math_op2! { Integer; xgmp::mpz_divexact_check_0; /// Performs an exact division. /// /// This is much faster than normal division, but produces /// correct results only when the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(12345 * 54321); /// let quotient = i.div_exact(&Integer::from(12345)); /// assert_eq!(quotient, 54321); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_exact(divisor); /// Performs an exact division. /// /// This is much faster than normal division, but produces /// correct results only when the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(12345 * 54321); /// i.div_exact_mut(&Integer::from(12345)); /// assert_eq!(i, 54321); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_exact_mut; /// Performs an exact division. /// /// This is much faster than normal division, but produces /// correct results only when the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(12345 * 54321); /// let divisor = Integer::from(12345); /// let r = i.div_exact_ref(&divisor); /// let quotient = Integer::from(r); /// assert_eq!(quotient, 54321); /// ``` fn div_exact_ref -> DivExactRef; } math_op1! { Integer; xgmp::mpz_divexact_ui_check_0; /// Performs an exact division. This is much faster than /// normal division, but produces correct results only when /// the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(12345 * 54321); /// let q = i.div_exact_u(12345); /// assert_eq!(q, 54321); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_exact_u(divisor: u32); /// Performs an exact division. This is much faster than /// normal division, but produces correct results only when /// the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(12345 * 54321); /// i.div_exact_u_mut(12345); /// assert_eq!(i, 54321); /// ``` /// /// # Panics /// /// Panics if `divisor` is zero. fn div_exact_u_mut; /// Performs an exact division. This is much faster than /// normal division, but produces correct results only when /// the division is exact. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(12345 * 54321); /// let r = i.div_exact_u_ref(12345); /// assert_eq!(Integer::from(r), 54321); /// ``` fn div_exact_u_ref -> DivExactURef; } /// Finds the inverse modulo `modulo` and returns `Ok(inverse)` if /// it exists, or `Err(unchanged)` if the inverse does not exist. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let n = Integer::from(2); /// // Modulo 4, 2 has no inverse: there is no x such that 2 * x = 1. /// let inv_mod_4 = match n.invert(&Integer::from(4)) { /// Ok(_) => unreachable!(), /// Err(unchanged) => unchanged, /// }; /// // no inverse exists, so value is unchanged /// assert_eq!(inv_mod_4, 2); /// let n = inv_mod_4; /// // Modulo 5, the inverse of 2 is 3, as 2 * 3 = 1. /// let inv_mod_5 = match n.invert(&Integer::from(5)) { /// Ok(inverse) => inverse, /// Err(_) => unreachable!(), /// }; /// assert_eq!(inv_mod_5, 3); /// ``` /// /// # Panics /// /// Panics if `modulo` is zero. #[inline] pub fn invert(mut self, modulo: &Integer) -> Result<Integer, Integer> { if self.invert_mut(modulo) { Ok(self) } else { Err(self) } } /// Finds the inverse modulo `modulo` and returns `true` if an /// inverse exists. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut n = Integer::from(2); /// // Modulo 4, 2 has no inverse: there is no x such that 2 * x = 1. /// let exists_4 = n.invert_mut(&Integer::from(4)); /// assert!(!exists_4); /// assert_eq!(n, 2); /// // Modulo 5, the inverse of 2 is 3, as 2 * 3 = 1. /// let exists_5 = n.invert_mut(&Integer::from(5)); /// assert!(exists_5); /// assert_eq!(n, 3); /// ``` /// /// # Panics /// /// Panics if `modulo` is zero. #[inline] pub fn invert_mut(&mut self, modulo: &Integer) -> bool { unsafe { xgmp::mpz_invert_check_0( self.inner_mut(), self.inner(), modulo.inner(), ) != 0 } } /// Finds the inverse modulo `modulo` if an inverse exists. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let n = Integer::from(2); /// // Modulo 4, 2 has no inverse, there is no x such that 2 * x = 1. /// // For this conversion, if no inverse exists, the Integer /// // created is left unchanged as 0. /// let mut ans = Result::from(n.invert_ref(&Integer::from(4))); /// match ans { /// Ok(_) => unreachable!(), /// Err(ref unchanged) => assert_eq!(*unchanged, 0), /// } /// // Modulo 5, the inverse of 2 is 3, as 2 * 3 = 1. /// ans.assign(n.invert_ref(&Integer::from(5))); /// match ans { /// Ok(ref inverse) => assert_eq!(*inverse, 3), /// Err(_) => unreachable!(), /// }; /// ``` #[inline] pub fn invert_ref<'a>(&'a self, modulo: &'a Integer) -> InvertRef<'a> { InvertRef { ref_self: self, modulo: modulo, } } /// Raises a number to the power of `power` modulo `modulo` and /// returns `Ok(raised)` if an answer exists, or `Err(unchanged)` /// if it does not. /// /// If `power` is negative, then the number must have an inverse /// modulo `modulo` for an answer to exist. /// /// # Examples /// /// When the power is positive, an answer always exists. /// /// ```rust /// use rug::Integer; /// // 7 ^ 5 = 16807 /// let n = Integer::from(7); /// let pow = Integer::from(5); /// let m = Integer::from(1000); /// let raised = match n.pow_mod(&pow, &m) { /// Ok(raised) => raised, /// Err(_) => unreachable!(), /// }; /// assert_eq!(raised, 807); /// ``` /// /// When the power is negative, an answer exists if an inverse /// exists. /// /// ```rust /// use rug::Integer; /// // 7 * 143 modulo 1000 = 1, so 7 has an inverse 143. /// // 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943. /// let n = Integer::from(7); /// let pow = Integer::from(-5); /// let m = Integer::from(1000); /// let raised = match n.pow_mod(&pow, &m) { /// Ok(raised) => raised, /// Err(_) => unreachable!(), /// }; /// assert_eq!(raised, 943); /// ``` #[inline] pub fn pow_mod( mut self, power: &Integer, modulo: &Integer, ) -> Result<Integer, Integer> { if self.pow_mod_mut(power, modulo) { Ok(self) } else { Err(self) } } /// Raises a number to the power of `power` modulo `modulo` and /// returns `true` if an answer exists. /// /// If `power` is negative, then the number must have an inverse /// modulo `modulo` for an answer to exist. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// // Modulo 1000, 2 has no inverse: there is no x such that 2 * x = 1. /// let mut n = Integer::from(2); /// let pow = Integer::from(-5); /// let m = Integer::from(1000); /// let exists = n.pow_mod_mut(&pow, &m); /// assert!(!exists); /// assert_eq!(n, 2); /// // 7 * 143 modulo 1000 = 1, so 7 has an inverse 143. /// // 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943. /// n.assign(7); /// let exists = n.pow_mod_mut(&pow, &m); /// assert!(exists); /// assert_eq!(n, 943); /// ``` pub fn pow_mod_mut(&mut self, power: &Integer, modulo: &Integer) -> bool { let abs_pow; let pow_inner = if power.sign() == Ordering::Less { if !(self.invert_mut(modulo)) { return false; } abs_pow = mpz_t { alloc: power.inner().alloc, size: power.inner().size.checked_neg().expect("overflow"), d: power.inner().d, }; &abs_pow } else { power.inner() }; unsafe { gmp::mpz_powm( self.inner_mut(), self.inner(), pow_inner, modulo.inner(), ); } true } /// Raises a number to the power of `power` modulo `modulo` if an /// answer exists. /// /// If `power` is negative, then the number must have an inverse /// modulo `modulo` for an answer to exist. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// // Modulo 1000, 2 has no inverse: there is no x such that 2 * x = 1. /// let two = Integer::from(2); /// let pow = Integer::from(-5); /// let m = Integer::from(1000); /// let mut ans = Result::from(two.pow_mod_ref(&pow, &m)); /// match ans { /// Ok(_) => unreachable!(), /// Err(ref unchanged) => assert_eq!(*unchanged, 0), /// } /// // 7 * 143 modulo 1000 = 1, so 7 has an inverse 143. /// // 7 ^ -5 modulo 1000 = 143 ^ 5 modulo 1000 = 943. /// let seven = Integer::from(7); /// ans.assign(seven.pow_mod_ref(&pow, &m)); /// match ans { /// Ok(ref raised) => assert_eq!(*raised, 943), /// Err(_) => unreachable!(), /// } /// ``` #[inline] pub fn pow_mod_ref<'a>( &'a self, power: &'a Integer, modulo: &'a Integer, ) -> PowModRef<'a> { PowModRef { ref_self: self, power: power, modulo: modulo, } } /// Raises `base` to the power of `power`. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_u_pow_u(13, 12); /// assert_eq!(i, 13_u64.pow(12)); /// ``` #[inline] pub fn assign_u_pow_u(&mut self, base: u32, power: u32) { unsafe { gmp::mpz_ui_pow_ui(self.inner_mut(), base.into(), power.into()); } } /// Raises `base` to the power of `power`. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_i_pow_u(-13, 12); /// assert_eq!(i, (-13_i64).pow(12)); /// i.assign_i_pow_u(-13, 13); /// assert_eq!(i, (-13_i64).pow(13)); /// ``` #[inline] pub fn assign_i_pow_u(&mut self, base: i32, power: u32) { if base >= 0 { self.assign_u_pow_u(base as u32, power); } else { self.assign_u_pow_u(base.wrapping_neg() as u32, power); if (power & 1) == 1 { self.neg_assign(); } } } math_op1! { Integer; gmp::mpz_root; /// Computes the <i>n</i>th root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(1004); /// let root = i.root(3); /// assert_eq!(root, 10); /// ``` fn root(n: u32); /// Computes the <i>n</i>th root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(1004); /// i.root_mut(3); /// assert_eq!(i, 10); /// ``` fn root_mut; /// Computes the <i>n</i>th root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(1004); /// assert_eq!(Integer::from(i.root_ref(3)), 10); /// ``` fn root_ref -> RootRef; } math_op1_2! { Integer; gmp::mpz_rootrem; /// Computes the <i>n</i>th root and returns the truncated /// root and the remainder. /// /// The remainder is the original number minus the truncated /// root raised to the power of *n*. /// /// The initial value of `remainder` is ignored. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(1004); /// let (root, rem) = i.root_rem(Integer::new(), 3); /// assert_eq!(root, 10); /// assert_eq!(rem, 4); /// ``` fn root_rem(remainder, n: u32); /// Computes the <i>n</i>th root and returns the truncated /// root and the remainder. /// /// The remainder is the original number minus the truncated /// root raised to the power of *n*. /// /// The initial value of `remainder` is ignored. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(1004); /// let mut rem = Integer::new(); /// i.root_rem_mut(&mut rem, 3); /// assert_eq!(i, 10); /// assert_eq!(rem, 4); /// ``` fn root_rem_mut; /// Computes the <i>n</i>th root and returns the truncated /// root and the remainder. /// /// The remainder is the original number minus the truncated /// root raised to the power of *n*. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let i = Integer::from(1004); /// let r = i.root_rem_ref(3); /// let mut root = Integer::new(); /// let mut rem = Integer::new(); /// (&mut root, &mut rem).assign(r); /// assert_eq!(root, 10); /// assert_eq!(rem, 4); /// let (other_root, other_rem) = <(Integer, Integer)>::from(r); /// assert_eq!(other_root, 10); /// assert_eq!(other_rem, 4); /// ``` fn root_rem_ref -> RootRemRef; } math_op1! { Integer; gmp::mpz_sqrt; /// Computes the square root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(104); /// let sqrt = i.sqrt(); /// assert_eq!(sqrt, 10); /// ``` fn sqrt(); /// Computes the square root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(104); /// i.sqrt_mut(); /// assert_eq!(i, 10); /// ``` fn sqrt_mut; /// Computes the square root and truncates the result. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(104); /// assert_eq!(Integer::from(i.sqrt_ref()), 10); /// ``` fn sqrt_ref -> SqrtRef; } math_op1_2! { Integer; gmp::mpz_sqrtrem; /// Computes the square root and the remainder. /// /// The remainder is the original number minus the truncated /// root squared. /// /// The initial value of `remainder` is ignored. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let i = Integer::from(104); /// let (sqrt, rem) = i.sqrt_rem(Integer::new()); /// assert_eq!(sqrt, 10); /// assert_eq!(rem, 4); /// ``` fn sqrt_rem(remainder); /// Computes the square root and the remainder. /// /// The remainder is the original number minus the truncated /// root squared. /// /// The initial value of `remainder` is ignored. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::from(104); /// let mut rem = Integer::new(); /// i.sqrt_rem_mut(&mut rem); /// assert_eq!(i, 10); /// assert_eq!(rem, 4); /// ``` fn sqrt_rem_mut; /// Computes the square root and the remainder. /// /// The remainder is the original number minus the truncated /// root squared. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let i = Integer::from(104); /// let r = i.sqrt_rem_ref(); /// let mut sqrt = Integer::new(); /// let mut rem = Integer::new(); /// (&mut sqrt, &mut rem).assign(r); /// assert_eq!(sqrt, 10); /// assert_eq!(rem, 4); /// let (other_sqrt, other_rem) = <(Integer, Integer)>::from(r); /// assert_eq!(other_sqrt, 10); /// assert_eq!(other_rem, 4); /// ``` fn sqrt_rem_ref -> SqrtRemRef; } /// Determines wheter a number is prime using some trial /// divisions, then `reps` Miller-Rabin probabilistic primality /// tests. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use rug::integer::IsPrime; /// let no = Integer::from(163 * 4003); /// assert_eq!(no.is_probably_prime(15), IsPrime::No); /// let yes = Integer::from(21_751); /// assert_eq!(yes.is_probably_prime(15), IsPrime::Yes); /// // 817_504_243 is actually a prime. /// let probably = Integer::from(817_504_243); /// assert_eq!(probably.is_probably_prime(15), IsPrime::Probably); /// ``` #[inline] pub fn is_probably_prime(&self, reps: u32) -> IsPrime { let p = unsafe { gmp::mpz_probab_prime_p(self.inner(), reps as c_int) }; match p { 0 => IsPrime::No, 1 => IsPrime::Probably, 2 => IsPrime::Yes, _ => unreachable!(), } } math_op1! { Integer; gmp::mpz_nextprime; /// Identifies primes using a probabilistic algorithm; the /// chance of a composite passing will be extremely small. fn next_prime(); /// Identifies primes using a probabilistic algorithm; the /// chance of a composite passing will be extremely small. fn next_prime_mut; /// Identifies primes using a probabilistic algorithm; the /// chance of a composite passing will be extremely small. fn next_prime_ref -> NextPrimeRef; } math_op2! { Integer; gmp::mpz_gcd; /// Finds the greatest common divisor. /// /// The result is always positive except when both inputs are /// zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let a = Integer::new(); /// let mut b = Integer::new(); /// // gcd of 0, 0 is 0 /// let gcd1 = a.gcd(&b); /// assert_eq!(gcd1, 0); /// b.assign(10); /// // gcd of 0, 10 is 10 /// let gcd2 = gcd1.gcd(&b); /// assert_eq!(gcd2, 10); /// b.assign(25); /// // gcd of 10, 25 is 5 /// let gcd3 = gcd2.gcd(&b); /// assert_eq!(gcd3, 5); /// ``` fn gcd(other); /// Finds the greatest common divisor. /// /// The result is always positive except when both inputs are /// zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut a = Integer::new(); /// let mut b = Integer::new(); /// // gcd of 0, 0 is 0 /// a.gcd_mut(&b); /// assert_eq!(a, 0); /// b.assign(10); /// // gcd of 0, 10 is 10 /// a.gcd_mut(&b); /// assert_eq!(a, 10); /// b.assign(25); /// // gcd of 10, 25 is 5 /// a.gcd_mut(&b); /// assert_eq!(a, 5); /// ``` fn gcd_mut; /// Finds the greatest common divisor. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let a = Integer::from(100); /// let b = Integer::from(125); /// let r = a.gcd_ref(&b); /// // gcd of 100, 125 is 25 /// assert_eq!(Integer::from(r), 25); /// ``` fn gcd_ref -> GcdRef; } math_op2! { Integer; gmp::mpz_lcm; /// Finds the least common multiple. /// /// The result is always positive except when one or both /// inputs are zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let a = Integer::from(10); /// let mut b = Integer::from(25); /// // lcm of 10, 25 is 50 /// let lcm1 = a.lcm(&b); /// assert_eq!(lcm1, 50); /// b.assign(0); /// // lcm of 50, 0 is 0 /// let lcm2 = lcm1.lcm(&b); /// assert_eq!(lcm2, 0); /// ``` fn lcm(other); /// Finds the least common multiple. /// /// The result is always positive except when one or both /// inputs are zero. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut a = Integer::from(10); /// let mut b = Integer::from(25); /// // lcm of 10, 25 is 50 /// a.lcm_mut(&b); /// assert_eq!(a, 50); /// b.assign(0); /// // lcm of 50, 0 is 0 /// a.lcm_mut(&b); /// assert_eq!(a, 0); /// ``` fn lcm_mut; /// Finds the least common multiple. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let a = Integer::from(100); /// let b = Integer::from(125); /// let r = a.lcm_ref(&b); /// // lcm of 100, 125 is 500 /// assert_eq!(Integer::from(r), 500); /// ``` fn lcm_ref -> LcmRef; } /// Calculates the Jacobi symbol (`self`/<i>n</i>). #[inline] pub fn jacobi(&self, n: &Integer) -> i32 { unsafe { gmp::mpz_jacobi(self.inner(), n.inner()) as i32 } } /// Calculates the Legendre symbol (`self`/<i>p</i>). #[inline] pub fn legendre(&self, p: &Integer) -> i32 { unsafe { gmp::mpz_legendre(self.inner(), p.inner()) as i32 } } /// Calculates the Jacobi symbol (`self`/<i>n</i>) with the /// Kronecker extension. #[inline] pub fn kronecker(&self, n: &Integer) -> i32 { unsafe { gmp::mpz_kronecker(self.inner(), n.inner()) as i32 } } /// Removes all occurrences of `factor`, and returns the number of /// occurrences removed. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_u_pow_u(13, 50); /// i *= 1000; /// let (remove, count) = i.remove_factor(&Integer::from(13)); /// assert_eq!(remove, 1000); /// assert_eq!(count, 50); /// ``` #[inline] pub fn remove_factor(mut self, factor: &Integer) -> (Integer, u32) { let count = self.remove_factor_mut(factor); (self, count) } /// Removes all occurrences of `factor`, and returns the number of /// occurrences removed. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_u_pow_u(13, 50); /// i *= 1000; /// let count = i.remove_factor_mut(&Integer::from(13)); /// assert_eq!(i, 1000); /// assert_eq!(count, 50); /// ``` #[inline] pub fn remove_factor_mut(&mut self, factor: &Integer) -> u32 { let cnt = unsafe { gmp::mpz_remove(self.inner_mut(), self.inner(), factor.inner()) }; assert_eq!(cnt as u32 as gmp::bitcnt_t, cnt, "overflow"); cnt as u32 } /// Removes all occurrences of `factor`, and counts the number of /// occurrences removed. /// /// # Examples /// /// ```rust /// use rug::{Assign, Integer}; /// let mut i = Integer::new(); /// i.assign_u_pow_u(13, 50); /// i *= 1000; /// let (mut j, mut count) = (Integer::new(), 0); /// (&mut j, &mut count).assign(i.remove_factor_ref(&Integer::from(13))); /// assert_eq!(count, 50); /// assert_eq!(j, 1000); /// ``` #[inline] pub fn remove_factor_ref<'a>( &'a self, factor: &'a Integer, ) -> RemoveFactorRef<'a> { RemoveFactorRef { ref_self: self, factor: factor, } } /// Computes the factorial of *n*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// // 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 /// i.assign_factorial(10); /// assert_eq!(i, 3628800); /// ``` #[inline] pub fn assign_factorial(&mut self, n: u32) { unsafe { gmp::mpz_fac_ui(self.inner_mut(), n.into()); } } /// Computes the double factorial of *n*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// // 10 * 8 * 6 * 4 * 2 /// i.assign_factorial_2(10); /// assert_eq!(i, 3840); /// ``` #[inline] pub fn assign_factorial_2(&mut self, n: u32) { unsafe { gmp::mpz_2fac_ui(self.inner_mut(), n.into()); } } /// Computes the *m*-multi factorial of *n*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// // 10 * 7 * 4 * 1 /// i.assign_factorial_m(10, 3); /// assert_eq!(i, 280); /// ``` #[inline] pub fn assign_factorial_m(&mut self, n: u32, m: u32) { unsafe { gmp::mpz_mfac_uiui(self.inner_mut(), n.into(), m.into()); } } /// Computes the primorial of *n*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// // 7 * 5 * 3 * 2 /// i.assign_primorial(10); /// assert_eq!(i, 210); /// ``` #[inline] pub fn assign_primorial(&mut self, n: u32) { unsafe { gmp::mpz_primorial_ui(self.inner_mut(), n.into()); } } math_op1! { Integer; gmp::mpz_bin_ui; /// Computes the binomial coefficient over *k*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // 7 choose 2 is 21 /// let i = Integer::from(7); /// let bin = i.binomial(2); /// assert_eq!(bin, 21); /// ``` fn binomial(k: u32); /// Computes the binomial coefficient over *k*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // 7 choose 2 is 21 /// let mut i = Integer::from(7); /// i.binomial_mut(2); /// assert_eq!(i, 21); /// ``` fn binomial_mut; /// Computes the binomial coefficient over *k*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // 7 choose 2 is 21 /// let i = Integer::from(7); /// assert_eq!(Integer::from(i.binomial_ref(2)), 21); /// ``` fn binomial_ref -> BinomialRef; } /// Computes the binomial coefficient *n* over *k*. /// /// # Examples /// /// ```rust /// use rug::Integer; /// // 7 choose 2 is 21 /// let mut i = Integer::new(); /// i.assign_binomial_u(7, 2); /// assert_eq!(i, 21); /// ``` #[inline] pub fn assign_binomial_u(&mut self, n: u32, k: u32) { unsafe { gmp::mpz_bin_uiui(self.inner_mut(), n.into(), k.into()); } } /// Computes the Fibonacci number. /// /// This function is meant for an isolated number. If a sequence /// of Fibonacci numbers is required, the first two values of the /// sequence should be computed with the /// [`assign_fibonacci_2`](#method.assign_fibonacci_2) method, /// then iterations should be used. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_fibonacci(12); /// assert_eq!(i, 144); /// ``` #[inline] pub fn assign_fibonacci(&mut self, n: u32) { unsafe { gmp::mpz_fib_ui(self.inner_mut(), n.into()); } } /// Computes a Fibonacci number, and the previous Fibonacci number. /// /// This function is meant to calculate isolated numbers. If a /// sequence of Fibonacci numbers is required, the first two /// values of the sequence should be computed with this function, /// then iterations should be used. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// let mut j = Integer::new(); /// i.assign_fibonacci_2(&mut j, 12); /// assert_eq!(i, 144); /// assert_eq!(j, 89); /// // Fibonacci number F[-1] is 1 /// i.assign_fibonacci_2(&mut j, 0); /// assert_eq!(i, 0); /// assert_eq!(j, 1); /// ``` #[inline] pub fn assign_fibonacci_2(&mut self, previous: &mut Integer, n: u32) { unsafe { gmp::mpz_fib2_ui(self.inner_mut(), previous.inner_mut(), n.into()); } } /// Computes the Lucas number. /// /// This function is meant for an isolated number. If a sequence /// of Lucas numbers is required, the first two values of the /// sequence should be computed with the /// [`assign_lucas_2`](#method.assign_lucas_2) method, then /// iterations should be used. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// i.assign_lucas(12); /// assert_eq!(i, 322); /// ``` #[inline] pub fn assign_lucas(&mut self, n: u32) { unsafe { gmp::mpz_lucnum_ui(self.inner_mut(), n.into()); } } /// Computes a Lucas number, and the previous Lucas number. /// /// This function is meant to calculate isolated numbers. If a /// sequence of Lucas numbers is required, the first two values of /// the sequence should be computed with this function, then /// iterations should be used. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let mut i = Integer::new(); /// let mut j = Integer::new(); /// i.assign_lucas_2(&mut j, 12); /// assert_eq!(i, 322); /// assert_eq!(j, 199); /// i.assign_lucas_2(&mut j, 0); /// assert_eq!(i, 2); /// assert_eq!(j, -1); /// ``` #[inline] pub fn assign_lucas_2(&mut self, previous: &mut Integer, n: u32) { unsafe { gmp::mpz_lucnum2_ui( self.inner_mut(), previous.inner_mut(), n.into(), ); } } #[cfg(feature = "rand")] /// Generates a random number with a specified maximum number of /// bits. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use rug::rand::RandState; /// let mut rand = RandState::new(); /// let mut i = Integer::new(); /// i.assign_random_bits(0, &mut rand); /// assert_eq!(i, 0); /// i.assign_random_bits(80, &mut rand); /// assert!(i.significant_bits() <= 80); /// ``` #[inline] pub fn assign_random_bits(&mut self, bits: u32, rng: &mut RandState) { unsafe { gmp::mpz_urandomb(self.inner_mut(), rng.inner_mut(), bits.into()); } } #[cfg(feature = "rand")] /// Generates a non-negative random number below the given /// boundary value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use rug::rand::RandState; /// let mut rand = RandState::new(); /// let i = Integer::from(15); /// let below = i.random_below(&mut rand); /// println!("0 <= {} < 15", below); /// assert!(below < 15); /// ``` /// /// # Panics /// /// Panics if the boundary value is less than or equal to zero. #[inline] pub fn random_below(mut self, rng: &mut RandState) -> Integer { self.random_below_mut(rng); self } #[cfg(feature = "rand")] /// Generates a non-negative random number below the given /// boundary value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use rug::rand::RandState; /// let mut rand = RandState::new(); /// let mut i = Integer::from(15); /// i.random_below_mut(&mut rand); /// println!("0 <= {} < 15", i); /// assert!(i < 15); /// ``` /// /// # Panics /// /// Panics if the boundary value is less than or equal to zero. #[inline] pub fn random_below_mut(&mut self, rng: &mut RandState) { assert_eq!(self.sign(), Ordering::Greater, "cannot be below zero"); unsafe { gmp::mpz_urandomm(self.inner_mut(), rng.inner_mut(), self.inner()); } } #[cfg(feature = "rand")] /// Generates a non-negative random number below the given /// boundary value. /// /// # Examples /// /// ```rust /// use rug::Integer; /// use rug::rand::RandState; /// let mut rand = RandState::new(); /// let bound = Integer::from(15); /// let mut i = Integer::new(); /// i.assign_random_below(&bound, &mut rand); /// println!("0 <= {} < {}", i, bound); /// assert!(i < bound); /// ``` /// /// # Panics /// /// Panics if the boundary value is less than or equal to zero. #[inline] pub fn assign_random_below( &mut self, bound: &Integer, rng: &mut RandState, ) { assert_eq!(bound.sign(), Ordering::Greater, "cannot be below zero"); unsafe { gmp::mpz_urandomm(self.inner_mut(), rng.inner_mut(), bound.inner()); } } } impl<'a> From<&'a Integer> for Integer { #[inline] fn from(val: &Integer) -> Integer { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init_set(ret.inner_mut(), val.inner()); ret } } } impl From<i32> for Integer { #[inline] fn from(val: i32) -> Integer { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init_set_si(ret.inner_mut(), val.into()); ret } } } impl From<i64> for Integer { #[inline] fn from(val: i64) -> Integer { if mem::size_of::<c_long>() >= 8 { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init_set_si(ret.inner_mut(), val as c_long); ret } } else { let mut i = Integer::new(); i.assign(val); i } } } impl From<u32> for Integer { #[inline] fn from(val: u32) -> Integer { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init_set_ui(ret.inner_mut(), val.into()); ret } } } impl From<u64> for Integer { #[inline] fn from(val: u64) -> Integer { if mem::size_of::<c_ulong>() >= 8 { unsafe { let mut ret: Integer = mem::uninitialized(); gmp::mpz_init_set_ui(ret.inner_mut(), val as c_ulong); ret } } else { let mut i = Integer::new(); i.assign(val); i } } } impl FromStr for Integer { type Err = ParseIntegerError; #[inline] fn from_str(src: &str) -> Result<Integer, ParseIntegerError> { let mut i = Integer::new(); i.assign_str(src)?; Ok(i) } } impl Display for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 10, false, "") } } impl Debug for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 10, false, "") } } impl Binary for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 2, false, "0b") } } impl Octal for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 8, false, "0o") } } impl LowerHex for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 16, false, "0x") } } impl UpperHex for Integer { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { fmt_radix(self, f, 16, true, "0x") } } impl Assign for Integer { #[inline] fn assign(&mut self, mut other: Integer) { mem::swap(self, &mut other); } } impl<'a> Assign<&'a Integer> for Integer { #[inline] fn assign(&mut self, other: &'a Integer) { unsafe { gmp::mpz_set(self.inner_mut(), other.inner()); } } } impl Assign<i32> for Integer { #[inline] fn assign(&mut self, val: i32) { unsafe { xgmp::mpz_set_i32(self.inner_mut(), val); } } } impl Assign<i64> for Integer { #[inline] fn assign(&mut self, val: i64) { unsafe { xgmp::mpz_set_i64(self.inner_mut(), val); } } } impl Assign<u32> for Integer { #[inline] fn assign(&mut self, val: u32) { unsafe { xgmp::mpz_set_u32(self.inner_mut(), val); } } } impl Assign<u64> for Integer { #[inline] fn assign(&mut self, val: u64) { unsafe { xgmp::mpz_set_u64(self.inner_mut(), val); } } } ref_math_op1! { Integer; gmp::mpz_abs; struct AbsRef {} } ref_math_op1! { Integer; gmp::mpz_fdiv_r_2exp; struct KeepBitsRef { n: u32 } } ref_math_op1! { Integer; xgmp::mpz_next_pow_of_two; struct NextPowerTwoRef {} } ref_math_op2_2! { Integer; xgmp::mpz_tdiv_qr_check_0; struct DivRemRef { divisor } } ref_math_op2! { Integer; xgmp::mpz_divexact_check_0; struct DivExactRef { divisor } } ref_math_op1! { Integer; xgmp::mpz_divexact_ui_check_0; struct DivExactURef { divisor: u32 } } #[derive(Clone, Copy)] pub struct PowModRef<'a> { ref_self: &'a Integer, power: &'a Integer, modulo: &'a Integer, } impl<'a> From<PowModRef<'a>> for Result<Integer, Integer> { #[inline] fn from(src: PowModRef<'a>) -> Result<Integer, Integer> { if src.power.sign() == Ordering::Less { let mut ret = Result::from(src.ref_self.invert_ref(src.modulo))?; let abs_pow = mpz_t { alloc: src.power.inner().alloc, size: src.power.inner().size.checked_neg().expect("overflow"), d: src.power.inner().d, }; unsafe { gmp::mpz_powm( ret.inner_mut(), ret.inner(), &abs_pow, src.modulo.inner(), ); } Ok(ret) } else { let mut ret = Integer::new(); unsafe { gmp::mpz_powm( ret.inner_mut(), src.ref_self.inner(), src.power.inner(), src.modulo.inner(), ); } Ok(ret) } } } impl<'a> Assign<PowModRef<'a>> for Result<Integer, Integer> { fn assign(&mut self, src: PowModRef<'a>) { if src.power.sign() == Ordering::Less { self.assign(src.ref_self.invert_ref(src.modulo)); match *self { Ok(ref mut inv) => { let abs_pow = mpz_t { alloc: src.power.inner().alloc, size: src.power .inner() .size .checked_neg() .expect("overflow"), d: src.power.inner().d, }; unsafe { gmp::mpz_powm( inv.inner_mut(), inv.inner(), &abs_pow, src.modulo.inner(), ); } } Err(_) => {} } } else { if self.is_err() { result_swap(self); } match *self { Ok(ref mut dest) => unsafe { gmp::mpz_powm( dest.inner_mut(), src.ref_self.inner(), src.power.inner(), src.modulo.inner(), ); }, Err(_) => unreachable!(), } let mut ret = Integer::new(); unsafe { gmp::mpz_powm( ret.inner_mut(), src.ref_self.inner(), src.power.inner(), src.modulo.inner(), ); } } } } ref_math_op1! { Integer; gmp::mpz_root; struct RootRef { n: u32 } } ref_math_op1_2! { Integer; gmp::mpz_rootrem; struct RootRemRef { n: u32 } } ref_math_op1! { Integer; gmp::mpz_sqrt; struct SqrtRef {} } ref_math_op1_2! { Integer; gmp::mpz_sqrtrem; struct SqrtRemRef {} } ref_math_op1! { Integer; gmp::mpz_nextprime; struct NextPrimeRef {} } ref_math_op2! { Integer; gmp::mpz_gcd; struct GcdRef { other } } ref_math_op2! { Integer; gmp::mpz_lcm; struct LcmRef { other } } #[derive(Clone, Copy)] pub struct InvertRef<'a> { ref_self: &'a Integer, modulo: &'a Integer, } impl<'a> From<InvertRef<'a>> for Result<Integer, Integer> { #[inline] fn from(src: InvertRef<'a>) -> Result<Integer, Integer> { let mut i = Integer::new(); let exists = unsafe { xgmp::mpz_invert_check_0( i.inner_mut(), src.ref_self.inner(), src.modulo.inner(), ) != 0 }; if exists { Ok(i) } else { Err(i) } } } impl<'a> Assign<InvertRef<'a>> for Result<Integer, Integer> { #[inline] fn assign(&mut self, src: InvertRef<'a>) { let exists = { let dest = match *self { Ok(ref mut i) | Err(ref mut i) => i, }; unsafe { xgmp::mpz_invert_check_0( dest.inner_mut(), src.ref_self.inner(), src.modulo.inner(), ) != 0 } }; if exists != self.is_ok() { result_swap(self); } } } #[derive(Clone, Copy)] pub struct RemoveFactorRef<'a> { ref_self: &'a Integer, factor: &'a Integer, } impl<'a> Assign<RemoveFactorRef<'a>> for (&'a mut Integer, &'a mut u32) { #[inline] fn assign(&mut self, src: RemoveFactorRef<'a>) { let cnt = unsafe { gmp::mpz_remove( self.0.inner_mut(), src.ref_self.inner(), src.factor.inner(), ) }; assert_eq!(cnt as u32 as gmp::bitcnt_t, cnt, "overflow"); *self.1 = cnt as u32; } } ref_math_op1! { Integer; gmp::mpz_bin_ui; struct BinomialRef { k: u32 } } arith_unary! { Integer; gmp::mpz_neg; Neg neg; NegAssign neg_assign; NegRef } arith_binary! { Integer; gmp::mpz_add; Add add; AddAssign add_assign; AddFrom add_from; AddRef } arith_binary! { Integer; gmp::mpz_sub; Sub sub; SubAssign sub_assign; SubFrom sub_from; SubRef } arith_binary! { Integer; gmp::mpz_mul; Mul mul; MulAssign mul_assign; MulFrom mul_from; MulRef } arith_binary! { Integer; xgmp::mpz_tdiv_q_check_0; Div div; DivAssign div_assign; DivFrom div_from; DivRef } arith_binary! { Integer; xgmp::mpz_tdiv_r_check_0; Rem rem; RemAssign rem_assign; RemFrom rem_from; RemRef } arith_unary! { Integer; gmp::mpz_com; Not not; NotAssign not_assign; NotRef } arith_binary! { Integer; gmp::mpz_and; BitAnd bitand; BitAndAssign bitand_assign; BitAndFrom bitand_from; BitAndRef } arith_binary! { Integer; gmp::mpz_ior; BitOr bitor; BitOrAssign bitor_assign; BitOrFrom bitor_from; BitOrRef } arith_binary! { Integer; gmp::mpz_xor; BitXor bitxor; BitXorAssign bitxor_assign; BitXorFrom bitxor_from; BitXorRef } arith_prim_commut! { Integer; xgmp::mpz_add_si; Add add; AddAssign add_assign; AddFrom add_from; i32; AddRefI32 } arith_prim_noncommut! { Integer; xgmp::mpz_sub_si, xgmp::mpz_si_sub; Sub sub; SubAssign sub_assign; SubFrom sub_from; i32; SubRefI32 SubFromRefI32 } arith_prim_commut! { Integer; gmp::mpz_mul_si; Mul mul; MulAssign mul_assign; MulFrom mul_from; i32; MulRefI32 } arith_prim_noncommut! { Integer; xgmp::mpz_tdiv_q_si_check_0, xgmp::mpz_si_tdiv_q_check_0; Div div; DivAssign div_assign; DivFrom div_from; i32; DivRefI32 DivFromRefI32 } arith_prim_noncommut! { Integer; xgmp::mpz_tdiv_r_si_check_0, xgmp::mpz_si_tdiv_r_check_0; Rem rem; RemAssign rem_assign; RemFrom rem_from; i32; RemRefI32 RemFromRefI32 } arith_prim! { Integer; xgmp::mpz_lshift_si; Shl shl; ShlAssign shl_assign; i32; ShlRefI32 } arith_prim! { Integer; xgmp::mpz_rshift_si; Shr shr; ShrAssign shr_assign; i32; ShrRefI32 } arith_prim_commut! { Integer; xgmp::bitand_si; BitAnd bitand; BitAndAssign bitand_assign; BitAndFrom bitand_from; i32; BitAndRefI32 } arith_prim_commut! { Integer; xgmp::bitor_si; BitOr bitor; BitOrAssign bitor_assign; BitOrFrom bitor_from; i32; BitOrRefI32 } arith_prim_commut! { Integer; xgmp::bitxor_si; BitXor bitxor; BitXorAssign bitxor_assign; BitXorFrom bitxor_from; i32; BitXorRefI32 } arith_prim_commut! { Integer; gmp::mpz_add_ui; Add add; AddAssign add_assign; AddFrom add_from; u32; AddRefU32 } arith_prim_noncommut! { Integer; gmp::mpz_sub_ui, gmp::mpz_ui_sub; Sub sub; SubAssign sub_assign; SubFrom sub_from; u32; SubRefU32 SubFromRefU32 } arith_prim_commut! { Integer; gmp::mpz_mul_ui; Mul mul; MulAssign mul_assign; MulFrom mul_from; u32; MulRefU32 } arith_prim_noncommut! { Integer; xgmp::mpz_tdiv_q_ui_check_0, xgmp::mpz_ui_tdiv_q_check_0; Div div; DivAssign div_assign; DivFrom div_from; u32; DivRefU32 DivFromRefU32 } arith_prim_noncommut! { Integer; xgmp::mpz_tdiv_r_ui_check_0, xgmp::mpz_ui_tdiv_r_check_0; Rem rem; RemAssign rem_assign; RemFrom rem_from; u32; RemRefU32 RemFromRefU32 } arith_prim! { Integer; gmp::mpz_mul_2exp; Shl shl; ShlAssign shl_assign; u32; ShlRefU32 } arith_prim! { Integer; gmp::mpz_fdiv_q_2exp; Shr shr; ShrAssign shr_assign; u32; ShrRefU32 } arith_prim! { Integer; gmp::mpz_pow_ui; Pow pow; PowAssign pow_assign; u32; PowRefU32 } arith_prim_commut! { Integer; xgmp::bitand_ui; BitAnd bitand; BitAndAssign bitand_assign; BitAndFrom bitand_from; u32; BitAndRefU32 } arith_prim_commut! { Integer; xgmp::bitor_ui; BitOr bitor; BitOrAssign bitor_assign; BitOrFrom bitor_from; u32; BitOrRefU32 } arith_prim_commut! { Integer; xgmp::bitxor_ui; BitXor bitxor; BitXorAssign bitxor_assign; BitXorFrom bitxor_from; u32; BitXorRefU32 } macro_rules! op_mul { { $(#[$attr:meta])* impl $Imp:ident $method:ident; $(#[$attr_assign:meta])* impl $ImpAssign:ident $method_assign:ident; $Ref:ident, $rhs_method:ident, $func:path } => { impl<'a> $Imp<$Ref<'a>> for Integer { type Output = Integer; $(#[$attr])* #[inline] fn $method(mut self, rhs: $Ref) -> Integer { self.$method_assign(rhs); self } } impl<'a> $ImpAssign<$Ref<'a>> for Integer { $(#[$attr_assign])* #[inline] fn $method_assign(&mut self, rhs: $Ref) { unsafe { $func( self.inner_mut(), rhs.lhs.inner(), rhs.rhs.$rhs_method() ); } } } }; } op_mul! { /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m1 = Integer::from(3); /// let m2 = Integer::from(7); /// let init = Integer::from(100); /// let acc = init + &m1 * &m2; /// assert_eq!(acc, 121); /// ``` impl Add add; /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m1 = Integer::from(3); /// let m2 = Integer::from(7); /// let mut acc = Integer::from(100); /// acc += &m1 * &m2; /// assert_eq!(acc, 121); /// ``` impl AddAssign add_assign; MulRef, inner, gmp::mpz_addmul } op_mul! { /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let init = Integer::from(100); /// let acc = init + &m * 7u32; /// assert_eq!(acc, 121); /// ``` impl Add add; /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let mut acc = Integer::from(100); /// acc += &m * 7u32; /// assert_eq!(acc, 121); /// ``` impl AddAssign add_assign; MulRefU32, into, gmp::mpz_addmul_ui } op_mul! { /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let init = Integer::from(100); /// let acc = init + &m * -7i32; /// assert_eq!(acc, 79); /// ``` impl Add add; /// Peforms multiplication and addition together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let mut acc = Integer::from(100); /// acc += &m * -7i32; /// assert_eq!(acc, 79); /// ``` impl AddAssign add_assign; MulRefI32, into, xgmp::mpz_addmul_si } op_mul! { /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m1 = Integer::from(3); /// let m2 = Integer::from(7); /// let init = Integer::from(100); /// let acc = init - &m1 * &m2; /// assert_eq!(acc, 79); /// ``` impl Sub sub; /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m1 = Integer::from(3); /// let m2 = Integer::from(7); /// let mut acc = Integer::from(100); /// acc -= &m1 * &m2; /// assert_eq!(acc, 79); /// ``` impl SubAssign sub_assign; MulRef, inner, gmp::mpz_submul } op_mul! { /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let init = Integer::from(100); /// let acc = init - &m * 7u32; /// assert_eq!(acc, 79); /// ``` impl Sub sub; /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let mut acc = Integer::from(100); /// acc -= &m * 7u32; /// assert_eq!(acc, 79); /// ``` impl SubAssign sub_assign; MulRefU32, into, gmp::mpz_submul_ui } op_mul! { /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let init = Integer::from(100); /// let acc = init - &m * -7i32; /// assert_eq!(acc, 121); /// ``` impl Sub sub; /// Peforms multiplication and subtraction together. /// /// # Examples /// /// ```rust /// use rug::Integer; /// let m = Integer::from(3); /// let mut acc = Integer::from(100); /// acc -= &m * -7i32; /// assert_eq!(acc, 121); /// ``` impl SubAssign sub_assign; MulRefI32, into, xgmp::mpz_submul_si } impl Eq for Integer {} impl Ord for Integer { #[inline] fn cmp(&self, other: &Integer) -> Ordering { let ord = unsafe { gmp::mpz_cmp(self.inner(), other.inner()) }; ord.cmp(&0) } } impl PartialEq for Integer { #[inline] fn eq(&self, other: &Integer) -> bool { self.cmp(other) == Ordering::Equal } } impl PartialOrd for Integer { #[inline] fn partial_cmp(&self, other: &Integer) -> Option<Ordering> { Some(self.cmp(other)) } } macro_rules! cmp { { $T:ty, $func:path } => { impl PartialEq<$T> for Integer { #[inline] fn eq(&self, other: &$T) -> bool { self.partial_cmp(other) == Some(Ordering::Equal) } } impl PartialEq<Integer> for $T { #[inline] fn eq(&self, other: &Integer) -> bool { other.eq(self) } } impl PartialOrd<$T> for Integer { #[inline] fn partial_cmp(&self, other: &$T) -> Option<Ordering> { let ord = unsafe { $func(self.inner(), (*other).into()) }; Some(ord.cmp(&0)) } } impl PartialOrd<Integer> for $T { #[inline] fn partial_cmp(&self, other: &Integer) -> Option<Ordering> { other.partial_cmp(self).map(Ordering::reverse) } } }; } cmp! { i32, xgmp::mpz_cmp_i32 } cmp! { i64, xgmp::mpz_cmp_i64 } cmp! { u32, xgmp::mpz_cmp_u32 } cmp! { u64, xgmp::mpz_cmp_u64 } impl PartialEq<f32> for Integer { #[inline] fn eq(&self, other: &f32) -> bool { let o = *other as f64; self.eq(&o) } } impl PartialEq<Integer> for f32 { #[inline] fn eq(&self, other: &Integer) -> bool { other.eq(self) } } impl PartialOrd<f32> for Integer { #[inline] fn partial_cmp(&self, other: &f32) -> Option<Ordering> { let o = *other as f64; self.partial_cmp(&o) } } impl PartialOrd<Integer> for f32 { #[inline] fn partial_cmp(&self, other: &Integer) -> Option<Ordering> { other.partial_cmp(self).map(Ordering::reverse) } } impl PartialEq<f64> for Integer { #[inline] fn eq(&self, other: &f64) -> bool { self.partial_cmp(other) == Some(Ordering::Equal) } } impl PartialEq<Integer> for f64 { #[inline] fn eq(&self, other: &Integer) -> bool { other.eq(self) } } impl PartialOrd<f64> for Integer { #[inline] fn partial_cmp(&self, other: &f64) -> Option<Ordering> { if other.is_nan() { None } else { let ord = unsafe { gmp::mpz_cmp_d(self.inner(), *other) }; Some(ord.cmp(&0)) } } } impl PartialOrd<Integer> for f64 { #[inline] fn partial_cmp(&self, other: &Integer) -> Option<Ordering> { other.partial_cmp(self).map(Ordering::reverse) } } fn make_string(i: &Integer, radix: i32, to_upper: bool) -> String { assert!(radix >= 2 && radix <= 36, "radix out of range"); let i_size = unsafe { gmp::mpz_sizeinbase(i.inner(), radix) }; // size + 2 for '-' and nul let size = i_size.checked_add(2).unwrap(); let mut buf = Vec::<u8>::with_capacity(size); let case_radix = if to_upper { -radix } else { radix }; unsafe { buf.set_len(size); gmp::mpz_get_str( buf.as_mut_ptr() as *mut c_char, case_radix as c_int, i.inner(), ); let nul_index = buf.iter().position(|&x| x == 0).unwrap(); buf.set_len(nul_index); String::from_utf8_unchecked(buf) } } fn fmt_radix( i: &Integer, f: &mut Formatter, radix: i32, to_upper: bool, prefix: &str, ) -> fmt::Result { let s = make_string(i, radix, to_upper); let (neg, buf) = if s.starts_with('-') { (true, &s[1..]) } else { (false, &s[..]) }; f.pad_integral(!neg, prefix, buf) } /// A validated string that can always be converted to an /// [`Integer`](../struct.Integer.html). /// /// See the [`Integer::valid_str_radix`] /// (../struct.Integer.html#method.valid_str_radix) method. #[derive(Clone, Debug)] pub struct ValidInteger<'a> { bytes: &'a [u8], radix: i32, } from_borrow! { ValidInteger<'a> => Integer } impl<'a> Assign<ValidInteger<'a>> for Integer { #[inline] fn assign(&mut self, rhs: ValidInteger) { let mut v = Vec::<u8>::with_capacity(rhs.bytes.len() + 1); v.extend_from_slice(rhs.bytes); v.push(0); let err = unsafe { let c_str = CStr::from_bytes_with_nul_unchecked(&v); gmp::mpz_set_str(self.inner_mut(), c_str.as_ptr(), rhs.radix.into()) }; assert_eq!(err, 0); } } #[derive(Clone, Debug, Eq, PartialEq)] /// An error which can be returned when parsing an `Integer`. pub struct ParseIntegerError { kind: ParseErrorKind, } #[derive(Clone, Debug, Eq, PartialEq)] enum ParseErrorKind { InvalidDigit, NoDigits, } impl Error for ParseIntegerError { fn description(&self) -> &str { use self::ParseErrorKind::*; match self.kind { InvalidDigit => "invalid digit found in string", NoDigits => "string has no digits", } } } impl Display for ParseIntegerError { #[inline] fn fmt(&self, f: &mut Formatter) -> fmt::Result { Debug::fmt(self, f) } } #[derive(Clone, Copy, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)] /// Whether a number is prime. pub enum IsPrime { /// The number is definitely not prime. No, /// The number is probably prime. Probably, /// The number is definitely prime. Yes, } unsafe impl Send for Integer {} unsafe impl Sync for Integer {} fn bitcount_to_u32(bits: gmp::bitcnt_t) -> Option<u32> { let max: gmp::bitcnt_t = !0; if bits == max { None } else { assert_eq!(bits as u32 as gmp::bitcnt_t, bits, "overflow"); Some(bits as u32) } } impl Inner for Integer { type Output = mpz_t; #[inline] fn inner(&self) -> &mpz_t { &self.inner } } impl InnerMut for Integer { #[inline] unsafe fn inner_mut(&mut self) -> &mut mpz_t { &mut self.inner } } fn trunc_f64_to_f32(f: f64) -> f32 { // f as f32 might round away from zero, so we need to clear // the least significant bits of f. // * If f is a nan, we do NOT want to clear any mantissa bits, // as this may change f into +/- infinity. // * If f is +/- infinity, the bits are already zero, so the // masking has no effect. // * If f is subnormal, f as f32 will be zero anyway. if !f.is_nan() { let u = unsafe { mem::transmute::<_, u64>(f) }; // f64 has 29 more significant bits than f32. let trunc_u = u & (!0 << 29); let trunc_f = unsafe { mem::transmute::<_, f64>(trunc_u) }; trunc_f as f32 } else { f as f32 } } fn result_swap<T>(r: &mut Result<T, T>) { let old = mem::replace(r, unsafe { mem::uninitialized() }); let new = match old { Ok(t) => Err(t), Err(t) => Ok(t), }; mem::forget(mem::replace(r, new)); }