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
|
;; Calculator for GNU Emacs, part II [calc-rewr.el]
;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
;; Written by Dave Gillespie, daveg@synaptics.com.
;; This file is part of GNU Emacs.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY. No author or distributor
;; accepts responsibility to anyone for the consequences of using it
;; or for whether it serves any particular purpose or works at all,
;; unless he says so in writing. Refer to the GNU Emacs General Public
;; License for full details.
;; Everyone is granted permission to copy, modify and redistribute
;; GNU Emacs, but only under the conditions described in the
;; GNU Emacs General Public License. A copy of this license is
;; supposed to have been given to you along with GNU Emacs so you
;; can know your rights and responsibilities. It should be in a
;; file named COPYING. Among other things, the copyright notice
;; and this notice must be preserved on all copies.
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(defun calc-Need-calc-rewr () nil)
(defun calc-rewrite-selection (rules-str &optional many prefix)
(interactive "sRewrite rule(s): \np")
(calc-slow-wrapper
(calc-preserve-point)
(let* ((num (max 1 (calc-locate-cursor-element (point))))
(reselect t)
(pop-rules nil)
(entry (calc-top num 'entry))
(expr (car entry))
(sel (calc-auto-selection entry))
(math-rewrite-selections t)
(math-rewrite-default-iters 1))
(if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
(if (= num 1)
(error "Can't use same stack entry for formula and rules.")
(setq rules (calc-top-n 1 t)
pop-rules t))
(setq rules (if (stringp rules-str)
(math-read-exprs rules-str) rules-str))
(if (eq (car-safe rules) 'error)
(error "Bad format in expression: %s" (nth 1 rules)))
(if (= (length rules) 1)
(setq rules (car rules))
(setq rules (cons 'vec rules)))
(or (memq (car-safe rules) '(vec var calcFunc-assign
calcFunc-condition))
(let ((rhs (math-read-expr
(read-string (concat "Rewrite from: " rules-str
" to: ")))))
(if (eq (car-safe rhs) 'error)
(error "Bad format in expression: %s" (nth 1 rhs)))
(setq rules (list 'calcFunc-assign rules rhs))))
(or (eq (car-safe rules) 'var)
(calc-record rules "rule")))
(if (eq many 0)
(setq many '(var inf var-inf))
(if many (setq many (prefix-numeric-value many))))
(if sel
(setq expr (calc-replace-sub-formula (car entry)
sel
(list 'calcFunc-select sel)))
(setq expr (car entry)
reselect nil
math-rewrite-selections nil))
(setq expr (calc-encase-atoms
(calc-normalize
(math-rewrite
(calc-normalize expr)
rules many)))
sel nil
expr (calc-locate-select-marker expr))
(or (consp sel) (setq sel nil))
(if pop-rules (calc-pop-stack 1))
(calc-pop-push-record-list 1 (or prefix "rwrt") (list expr)
(- num (if pop-rules 1 0))
(list (and reselect sel))))
(calc-handle-whys))
)
(defun calc-locate-select-marker (expr) ; changes "sel"
(if (Math-primp expr)
expr
(if (and (eq (car expr) 'calcFunc-select)
(= (length expr) 2))
(progn
(setq sel (if sel t (nth 1 expr)))
(nth 1 expr))
(cons (car expr)
(mapcar 'calc-locate-select-marker (cdr expr)))))
)
(defun calc-rewrite (rules-str many)
(interactive "sRewrite rule(s): \nP")
(calc-slow-wrapper
(let (n rules expr)
(if (or (null rules-str) (equal rules-str "") (equal rules-str "$"))
(setq expr (calc-top-n 2)
rules (calc-top-n 1 t)
n 2)
(setq rules (if (stringp rules-str)
(math-read-exprs rules-str) rules-str))
(if (eq (car-safe rules) 'error)
(error "Bad format in expression: %s" (nth 1 rules)))
(if (= (length rules) 1)
(setq rules (car rules))
(setq rules (cons 'vec rules)))
(or (memq (car-safe rules) '(vec var calcFunc-assign
calcFunc-condition))
(let ((rhs (math-read-expr
(read-string (concat "Rewrite from: " rules-str
" to: ")))))
(if (eq (car-safe rhs) 'error)
(error "Bad format in expression: %s" (nth 1 rhs)))
(setq rules (list 'calcFunc-assign rules rhs))))
(or (eq (car-safe rules) 'var)
(calc-record rules "rule"))
(setq expr (calc-top-n 1)
n 1))
(if (eq many 0)
(setq many '(var inf var-inf))
(if many (setq many (prefix-numeric-value many))))
(setq expr (calc-normalize (math-rewrite expr rules many)))
(let (sel)
(setq expr (calc-locate-select-marker expr)))
(calc-pop-push-record-list n "rwrt" (list expr)))
(calc-handle-whys))
)
(defun calc-match (pat)
(interactive "sPattern: \n")
(calc-slow-wrapper
(let (n expr)
(if (or (null pat) (equal pat "") (equal pat "$"))
(setq expr (calc-top-n 2)
pat (calc-top-n 1)
n 2)
(if (interactive-p) (setq calc-previous-alg-entry pat))
(setq pat (if (stringp pat) (math-read-expr pat) pat))
(if (eq (car-safe pat) 'error)
(error "Bad format in expression: %s" (nth 1 pat)))
(if (not (eq (car-safe pat) 'var))
(calc-record pat "pat"))
(setq expr (calc-top-n 1)
n 1))
(or (math-vectorp expr) (error "Argument must be a vector"))
(if (calc-is-inverse)
(calc-enter-result n "mtcn" (math-match-patterns pat expr t))
(calc-enter-result n "mtch" (math-match-patterns pat expr nil)))))
)
(defun math-rewrite (whole-expr rules &optional mmt-many)
(let ((crules (math-compile-rewrites rules))
(heads (math-rewrite-heads whole-expr))
(trace-buffer (get-buffer "*Trace*"))
(calc-display-just 'center)
(calc-display-origin 39)
(calc-line-breaking 78)
(calc-line-numbering nil)
(calc-show-selections t)
(calc-why nil)
(mmt-func (function
(lambda (x)
(let ((result (math-apply-rewrites x (cdr crules)
heads crules)))
(if result
(progn
(if trace-buffer
(let ((fmt (math-format-stack-value
(list result nil nil))))
(save-excursion
(set-buffer trace-buffer)
(insert "\nrewrite to\n" fmt "\n"))))
(setq heads (math-rewrite-heads result heads t))))
result)))))
(if trace-buffer
(let ((fmt (math-format-stack-value (list whole-expr nil nil))))
(save-excursion
(set-buffer trace-buffer)
(setq truncate-lines t)
(goto-char (point-max))
(insert "\n\nBegin rewriting\n" fmt "\n"))))
(or mmt-many (setq mmt-many (or (nth 1 (car crules))
math-rewrite-default-iters)))
(if (equal mmt-many '(var inf var-inf)) (setq mmt-many 1000000))
(if (equal mmt-many '(neg (var inf var-inf))) (setq mmt-many -1000000))
(math-rewrite-phase (nth 3 (car crules)))
(if trace-buffer
(let ((fmt (math-format-stack-value (list whole-expr nil nil))))
(save-excursion
(set-buffer trace-buffer)
(insert "\nDone rewriting"
(if (= mmt-many 0) " (reached iteration limit)" "")
":\n" fmt "\n"))))
whole-expr)
)
(setq math-rewrite-default-iters 100)
(defun math-rewrite-phase (sched)
(while (and sched (/= mmt-many 0))
(if (listp (car sched))
(while (let ((save-expr whole-expr))
(math-rewrite-phase (car sched))
(not (equal whole-expr save-expr))))
(if (symbolp (car sched))
(progn
(setq whole-expr (math-normalize (list (car sched) whole-expr)))
(if trace-buffer
(let ((fmt (math-format-stack-value
(list whole-expr nil nil))))
(save-excursion
(set-buffer trace-buffer)
(insert "\ncall "
(substring (symbol-name (car sched)) 9)
":\n" fmt "\n")))))
(let ((math-rewrite-phase (car sched)))
(if trace-buffer
(save-excursion
(set-buffer trace-buffer)
(insert (format "\n(Phase %d)\n" math-rewrite-phase))))
(while (let ((save-expr whole-expr))
(setq whole-expr (math-normalize
(math-map-tree-rec whole-expr)))
(not (equal whole-expr save-expr)))))))
(setq sched (cdr sched)))
)
(defun calcFunc-rewrite (expr rules &optional many)
(or (null many) (integerp many)
(equal many '(var inf var-inf)) (equal many '(neg (var inf var-inf)))
(math-reject-arg many 'fixnump))
(condition-case err
(math-rewrite expr rules (or many 1))
(error (math-reject-arg rules (nth 1 err))))
)
(defun calcFunc-match (pat vec)
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
(condition-case err
(math-match-patterns pat vec nil)
(error (math-reject-arg pat (nth 1 err))))
)
(defun calcFunc-matchnot (pat vec)
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
(condition-case err
(math-match-patterns pat vec t)
(error (math-reject-arg pat (nth 1 err))))
)
(defun math-match-patterns (pat vec &optional not-flag)
(let ((newvec nil)
(crules (math-compile-patterns pat)))
(while (setq vec (cdr vec))
(if (eq (not (math-apply-rewrites (car vec) crules))
not-flag)
(setq newvec (cons (car vec) newvec))))
(cons 'vec (nreverse newvec)))
)
(defun calcFunc-matches (expr pat)
(condition-case err
(if (math-apply-rewrites expr (math-compile-patterns pat))
1
0)
(error (math-reject-arg pat (nth 1 err))))
)
(defun calcFunc-vmatches (expr pat)
(condition-case err
(or (math-apply-rewrites expr (math-compile-patterns pat))
0)
(error (math-reject-arg pat (nth 1 err))))
)
;;; A compiled rule set is an a-list of entries whose cars are functors,
;;; and whose cdrs are lists of rules. If there are rules with no
;;; well-defined head functor, they are included on all lists and also
;;; on an extra list whose car is nil.
;;;
;;; The first entry in the a-list is of the form (schedule A B C ...).
;;;
;;; Rule list entries take the form (regs prog head phases), where:
;;;
;;; regs is a vector of match registers.
;;;
;;; prog is a match program (see below).
;;;
;;; head is a rare function name appearing in the rule body (but not the
;;; head of the whole rule), or nil if none.
;;;
;;; phases is a list of phase numbers for which the rule is enabled.
;;;
;;; A match program is a list of match instructions.
;;;
;;; In the following, "part" is a register number that contains the
;;; subexpression to be operated on.
;;;
;;; Register 0 is the whole expression being matched. The others are
;;; meta-variables in the pattern, temporaries used for matching and
;;; backtracking, and constant expressions.
;;;
;;; (same part reg)
;;; The selected part must be math-equal to the contents of "reg".
;;;
;;; (same-neg part reg)
;;; The selected part must be math-equal to the negative of "reg".
;;;
;;; (copy part reg)
;;; The selected part is copied into "reg". (Rarely used.)
;;;
;;; (copy-neg part reg)
;;; The negative of the selected part is copied into "reg".
;;;
;;; (integer part)
;;; The selected part must be an integer.
;;;
;;; (real part)
;;; The selected part must be a real.
;;;
;;; (constant part)
;;; The selected part must be a constant.
;;;
;;; (negative part)
;;; The selected part must "look" negative.
;;;
;;; (rel part op reg)
;;; The selected part must satisfy "part op reg", where "op"
;;; is one of the 6 relational ops, and "reg" is a register.
;;;
;;; (mod part modulo value)
;;; The selected part must satisfy "part % modulo = value", where
;;; "modulo" and "value" are constants.
;;;
;;; (func part head reg1 reg2 ... regn)
;;; The selected part must be an n-ary call to function "head".
;;; The arguments are stored in "reg1" through "regn".
;;;
;;; (func-def part head defs reg1 reg2 ... regn)
;;; The selected part must be an n-ary call to function "head".
;;; "Defs" is a list of value/register number pairs for default args.
;;; If a match, assign default values to registers and then skip
;;; immediately over any following "func-def" instructions and
;;; the following "func" instruction. If wrong number of arguments,
;;; proceed to the following "func-def" or "func" instruction.
;;;
;;; (func-opt part head defs reg1)
;;; Like func-def with "n=1", except that if the selected part is
;;; not a call to "head", then the part itself successfully matches
;;; "reg1" (and the defaults are assigned).
;;;
;;; (try part heads mark reg1 [def])
;;; The selected part must be a function of the correct type which is
;;; associative and/or commutative. "Heads" is a list of acceptable
;;; types. An initial assignment of arguments to "reg1" is tried.
;;; If the program later fails, it backtracks to this instruction
;;; and tries other assignments of arguments to "reg1".
;;; If "def" exists and normal matching fails, backtrack and assign
;;; "part" to "reg1", and "def" to "reg2" in the following "try2".
;;; The "mark" is a vector of size 5; only "mark[3-4]" are initialized.
;;; "mark[0]" points to the argument list; "mark[1]" points to the
;;; current argument; "mark[2]" is 0 if there are two arguments,
;;; 1 if reg1 is matching single arguments, 2 if reg2 is matching
;;; single arguments (a+b+c+d is never split as (a+b)+(c+d)), or
;;; 3 if reg2 is matching "def"; "mark[3]" is 0 if the function must
;;; have two arguments, 1 if phase-2 can be skipped, 2 if full
;;; backtracking is necessary; "mark[4]" is t if the arguments have
;;; been switched from the order given in the original pattern.
;;;
;;; (try2 try reg2)
;;; Every "try" will be followed by a "try2" whose "try" field is
;;; a pointer to the corresponding "try". The arguments which were
;;; not stored in "reg1" by that "try" are now stored in "reg2".
;;;
;;; (alt instr nil mark)
;;; Basic backtracking. Execute the instruction sequence "instr".
;;; If this fails, back up and execute following the "alt" instruction.
;;; The "mark" must be the vector "[nil nil 4]". The "instr" sequence
;;; should execute "end-alt" at the end.
;;;
;;; (end-alt ptr)
;;; Register success of the first alternative of a previous "alt".
;;; "Ptr" is a pointer to the next instruction following that "alt".
;;;
;;; (apply part reg1 reg2)
;;; The selected part must be a function call. The functor
;;; (as a variable name) is stored in "reg1"; the arguments
;;; (as a vector) are stored in "reg2".
;;;
;;; (cons part reg1 reg2)
;;; The selected part must be a nonempty vector. The first element
;;; of the vector is stored in "reg1"; the rest of the vector
;;; (as another vector) is stored in "reg2".
;;;
;;; (rcons part reg1 reg2)
;;; The selected part must be a nonempty vector. The last element
;;; of the vector is stored in "reg2"; the rest of the vector
;;; (as another vector) is stored in "reg1".
;;;
;;; (select part reg)
;;; If the selected part is a unary call to function "select", its
;;; argument is stored in "reg"; otherwise (provided this is an `a r'
;;; and not a `g r' command) the selected part is stored in "reg".
;;;
;;; (cond expr)
;;; The "expr", with registers substituted, must simplify to
;;; a non-zero value.
;;;
;;; (let reg expr)
;;; Evaluate "expr" and store the result in "reg". Always succeeds.
;;;
;;; (done rhs remember)
;;; Rewrite the expression to "rhs", with register substituted.
;;; Normalize; if the result is different from the original
;;; expression, the match has succeeded. This is the last
;;; instruction of every program. If "remember" is non-nil,
;;; record the result of the match as a new literal rule.
;;; Pseudo-functions related to rewrites:
;;;
;;; In patterns: quote, plain, condition, opt, apply, cons, select
;;;
;;; In righthand sides: quote, plain, eval, evalsimp, evalextsimp,
;;; apply, cons, select
;;;
;;; In conditions: let + same as for righthand sides
;;; Some optimizations that would be nice to have:
;;;
;;; * Merge registers with disjoint lifetimes.
;;; * Merge constant registers with equivalent values.
;;;
;;; * If an argument of a commutative op math-depends neither on the
;;; rest of the pattern nor on any of the conditions, then no backtracking
;;; should be done for that argument. (This won't apply to very many
;;; cases.)
;;;
;;; * If top functor is "select", and its argument is a unique function,
;;; add the rule to the lists for both "select" and that function.
;;; (Currently rules like this go on the "nil" list.)
;;; Same for "func-opt" functions. (Though not urgent for these.)
;;;
;;; * Shouldn't evaluate a "let" condition until the end, or until it
;;; would enable another condition to be evaluated.
;;;
;;; Some additional features to add / things to think about:
;;;
;;; * Figure out what happens to "a +/- b" and "a +/- opt(b)".
;;;
;;; * Same for interval forms.
;;;
;;; * Have a name(v,pat) pattern which matches pat, and gives the
;;; whole match the name v. Beware of circular structures!
;;;
(defun math-compile-patterns (pats)
(if (and (eq (car-safe pats) 'var)
(calc-var-value (nth 2 pats)))
(let ((prop (get (nth 2 pats) 'math-pattern-cache)))
(or prop
(put (nth 2 pats) 'math-pattern-cache (setq prop (list nil))))
(or (eq (car prop) (symbol-value (nth 2 pats)))
(progn
(setcdr prop (math-compile-patterns
(symbol-value (nth 2 pats))))
(setcar prop (symbol-value (nth 2 pats)))))
(cdr prop))
(let ((math-rewrite-whole t))
(cdr (math-compile-rewrites (cons
'vec
(mapcar (function (lambda (x)
(list 'vec x t)))
(if (eq (car-safe pats) 'vec)
(cdr pats)
(list pats))))))))
)
(setq math-rewrite-whole nil)
(setq math-make-import-list nil)
(defun math-compile-rewrites (rules &optional name)
(if (eq (car-safe rules) 'var)
(let ((prop (get (nth 2 rules) 'math-rewrite-cache))
(math-import-list nil)
(math-make-import-list t)
p)
(or (calc-var-value (nth 2 rules))
(error "Rules variable %s has no stored value" (nth 1 rules)))
(or prop
(put (nth 2 rules) 'math-rewrite-cache
(setq prop (list (list (cons (nth 2 rules) nil))))))
(setq p (car prop))
(while (and p (eq (symbol-value (car (car p))) (cdr (car p))))
(setq p (cdr p)))
(or (null p)
(progn
(message "Compiling rule set %s..." (nth 1 rules))
(setcdr prop (math-compile-rewrites
(symbol-value (nth 2 rules))
(nth 2 rules)))
(message "Compiling rule set %s...done" (nth 1 rules))
(setcar prop (cons (cons (nth 2 rules)
(symbol-value (nth 2 rules)))
math-import-list))))
(cdr prop))
(if (or (not (eq (car-safe rules) 'vec))
(and (memq (length rules) '(3 4))
(let ((p rules))
(while (and (setq p (cdr p))
(memq (car-safe (car p))
'(vec
calcFunc-assign
calcFunc-condition
calcFunc-import
calcFunc-phase
calcFunc-schedule
calcFunc-iterations))))
p)))
(setq rules (list rules))
(setq rules (cdr rules)))
(if (assq 'calcFunc-import rules)
(let ((pp (setq rules (copy-sequence rules)))
p part)
(while (setq p (car (cdr pp)))
(if (eq (car-safe p) 'calcFunc-import)
(progn
(setcdr pp (cdr (cdr pp)))
(or (and (eq (car-safe (nth 1 p)) 'var)
(setq part (calc-var-value (nth 2 (nth 1 p))))
(memq (car-safe part) '(vec
calcFunc-assign
calcFunc-condition)))
(error "Argument of import() must be a rules variable"))
(if math-make-import-list
(setq math-import-list
(cons (cons (nth 2 (nth 1 p))
(symbol-value (nth 2 (nth 1 p))))
math-import-list)))
(while (setq p (cdr (cdr p)))
(or (cdr p)
(error "import() must have odd number of arguments"))
(setq part (math-rwcomp-substitute part
(car p) (nth 1 p))))
(if (eq (car-safe part) 'vec)
(setq part (cdr part))
(setq part (list part)))
(setcdr pp (append part (cdr pp))))
(setq pp (cdr pp))))))
(let ((rule-set nil)
(all-heads nil)
(nil-rules nil)
(rule-count 0)
(math-schedule nil)
(math-iterations nil)
(math-phases nil)
(math-all-phases nil)
(math-remembering nil)
math-pattern math-rhs math-conds)
(while rules
(cond
((and (eq (car-safe (car rules)) 'calcFunc-iterations)
(= (length (car rules)) 2))
(or (integerp (nth 1 (car rules)))
(equal (nth 1 (car rules)) '(var inf var-inf))
(equal (nth 1 (car rules)) '(neg (var inf var-inf)))
(error "Invalid argument for iterations(n)"))
(or math-iterations
(setq math-iterations (nth 1 (car rules)))))
((eq (car-safe (car rules)) 'calcFunc-schedule)
(or math-schedule
(setq math-schedule (math-parse-schedule (cdr (car rules))))))
((eq (car-safe (car rules)) 'calcFunc-phase)
(setq math-phases (cdr (car rules)))
(if (equal math-phases '((var all var-all)))
(setq math-phases nil))
(let ((p math-phases))
(while p
(or (integerp (car p))
(error "Phase numbers must be small integers"))
(or (memq (car p) math-all-phases)
(setq math-all-phases (cons (car p) math-all-phases)))
(setq p (cdr p)))))
((or (and (eq (car-safe (car rules)) 'vec)
(cdr (cdr (car rules)))
(not (nthcdr 4 (car rules)))
(setq math-conds (nth 3 (car rules))
math-rhs (nth 2 (car rules))
math-pattern (nth 1 (car rules))))
(progn
(setq math-conds nil
math-pattern (car rules))
(while (and (eq (car-safe math-pattern) 'calcFunc-condition)
(= (length math-pattern) 3))
(let ((cond (nth 2 math-pattern)))
(setq math-conds (if math-conds
(list 'calcFunc-land math-conds cond)
cond)
math-pattern (nth 1 math-pattern))))
(and (eq (car-safe math-pattern) 'calcFunc-assign)
(= (length math-pattern) 3)
(setq math-rhs (nth 2 math-pattern)
math-pattern (nth 1 math-pattern)))))
(let* ((math-prog (list nil))
(math-prog-last math-prog)
(math-num-regs 1)
(math-regs (list (list nil 0 nil nil)))
(math-bound-vars nil)
(math-aliased-vars nil)
(math-copy-neg nil))
(setq math-conds (and math-conds (math-flatten-lands math-conds)))
(math-rwcomp-pattern math-pattern 0)
(while math-conds
(let ((expr (car math-conds)))
(setq math-conds (cdr math-conds))
(math-rwcomp-cond-instr expr)))
(math-rwcomp-instr 'done
(if (eq math-rhs t)
(cons 'vec
(delq
nil
(nreverse
(mapcar
(function
(lambda (v)
(and (car v)
(list
'calcFunc-assign
(math-build-var-name
(car v))
(math-rwcomp-register-expr
(nth 1 v))))))
math-regs))))
(math-rwcomp-match-vars math-rhs))
math-remembering)
(setq math-prog (cdr math-prog))
(let* ((heads (math-rewrite-heads math-pattern))
(rule (list (vconcat
(nreverse
(mapcar (function (lambda (x) (nth 3 x)))
math-regs)))
math-prog
heads
math-phases))
(head (and (not (Math-primp math-pattern))
(not (and (eq (car (car math-prog)) 'try)
(nth 5 (car math-prog))))
(not (memq (car (car math-prog)) '(func-opt
apply
select
alt)))
(if (memq (car (car math-prog)) '(func
func-def))
(nth 2 (car math-prog))
(if (eq (car math-pattern) 'calcFunc-quote)
(car-safe (nth 1 math-pattern))
(car math-pattern))))))
(let (found)
(while heads
(if (setq found (assq (car heads) all-heads))
(setcdr found (1+ (cdr found)))
(setq all-heads (cons (cons (car heads) 1) all-heads)))
(setq heads (cdr heads))))
(if (eq head '-) (setq head '+))
(if (memq head '(calcFunc-cons calcFunc-rcons)) (setq head 'vec))
(if head
(progn
(nconc (or (assq head rule-set)
(car (setq rule-set (cons (cons head
(copy-sequence
nil-rules))
rule-set))))
(list rule))
(if (eq head '*)
(nconc (or (assq '/ rule-set)
(car (setq rule-set (cons (cons
'/
(copy-sequence
nil-rules))
rule-set))))
(list rule))))
(setq nil-rules (nconc nil-rules (list rule)))
(let ((ptr rule-set))
(while ptr
(nconc (car ptr) (list rule))
(setq ptr (cdr ptr))))))))
(t
(error "Rewrite rule set must be a vector of A := B rules")))
(setq rules (cdr rules)))
(if nil-rules
(setq rule-set (cons (cons nil nil-rules) rule-set)))
(setq all-heads (mapcar 'car
(sort all-heads (function
(lambda (x y)
(< (cdr x) (cdr y)))))))
(let ((set rule-set)
rule heads ptr)
(while set
(setq rule (cdr (car set)))
(while rule
(if (consp (setq heads (nth 2 (car rule))))
(progn
(setq heads (delq (car (car set)) heads)
ptr all-heads)
(while (and ptr (not (memq (car ptr) heads)))
(setq ptr (cdr ptr)))
(setcar (nthcdr 2 (car rule)) (car ptr))))
(setq rule (cdr rule)))
(setq set (cdr set))))
(let ((plus (assq '+ rule-set)))
(if plus
(setq rule-set (cons (cons '- (cdr plus)) rule-set))))
(cons (list 'schedule math-iterations name
(or math-schedule
(sort math-all-phases '<)
(list 1)))
rule-set)))
)
(defun math-flatten-lands (expr)
(if (eq (car-safe expr) 'calcFunc-land)
(append (math-flatten-lands (nth 1 expr))
(math-flatten-lands (nth 2 expr)))
(list expr))
)
(defun math-rewrite-heads (expr &optional more all)
(let ((heads more)
(skips (and (not all)
'(calcFunc-apply calcFunc-condition calcFunc-opt
calcFunc-por calcFunc-pnot)))
(blanks (and (not all)
'(calcFunc-quote calcFunc-plain calcFunc-select
calcFunc-cons calcFunc-rcons
calcFunc-pand))))
(or (Math-primp expr)
(math-rewrite-heads-rec expr))
heads)
)
(defun math-rewrite-heads-rec (expr)
(or (memq (car expr) skips)
(progn
(or (memq (car expr) heads)
(memq (car expr) blanks)
(memq 'algebraic (get (car expr) 'math-rewrite-props))
(setq heads (cons (car expr) heads)))
(while (setq expr (cdr expr))
(or (Math-primp (car expr))
(math-rewrite-heads-rec (car expr))))))
)
(defun math-parse-schedule (sched)
(mapcar (function
(lambda (s)
(if (integerp s)
s
(if (math-vectorp s)
(math-parse-schedule (cdr s))
(if (eq (car-safe s) 'var)
(math-var-to-calcFunc s)
(error "Improper component in rewrite schedule"))))))
sched)
)
(defun math-rwcomp-match-vars (expr)
(if (Math-primp expr)
(if (eq (car-safe expr) 'var)
(let ((entry (assq (nth 2 expr) math-regs)))
(if entry
(math-rwcomp-register-expr (nth 1 entry))
expr))
expr)
(if (and (eq (car expr) 'calcFunc-quote)
(= (length expr) 2))
(math-rwcomp-match-vars (nth 1 expr))
(if (and (eq (car expr) 'calcFunc-plain)
(= (length expr) 2)
(not (Math-primp (nth 1 expr))))
(list (car expr)
(cons (car (nth 1 expr))
(mapcar 'math-rwcomp-match-vars (cdr (nth 1 expr)))))
(cons (car expr)
(mapcar 'math-rwcomp-match-vars (cdr expr))))))
)
(defun math-rwcomp-register-expr (num)
(let ((entry (nth (1- (- math-num-regs num)) math-regs)))
(if (nth 2 entry)
(list 'neg (list 'calcFunc-register (nth 1 entry)))
(list 'calcFunc-register (nth 1 entry))))
)
(defun math-rwcomp-substitute (expr old new)
(if (and (eq (car-safe old) 'var)
(memq (car-safe new) '(var calcFunc-lambda)))
(let ((old-func (math-var-to-calcFunc old))
(new-func (math-var-to-calcFunc new)))
(math-rwcomp-subst-rec expr))
(let ((old-func nil))
(math-rwcomp-subst-rec expr)))
)
(defun math-rwcomp-subst-rec (expr)
(cond ((equal expr old) new)
((Math-primp expr) expr)
(t (if (eq (car expr) old-func)
(math-build-call new-func (mapcar 'math-rwcomp-subst-rec
(cdr expr)))
(cons (car expr)
(mapcar 'math-rwcomp-subst-rec (cdr expr))))))
)
(setq math-rwcomp-tracing nil)
(defun math-rwcomp-trace (instr)
(if math-rwcomp-tracing (progn (terpri) (princ instr)))
instr
)
(defun math-rwcomp-instr (&rest instr)
(setcdr math-prog-last
(setq math-prog-last (list (math-rwcomp-trace instr))))
)
(defun math-rwcomp-multi-instr (tail &rest instr)
(setcdr math-prog-last
(setq math-prog-last (list (math-rwcomp-trace (append instr tail)))))
)
(defun math-rwcomp-bind-var (reg var)
(setcar (math-rwcomp-reg-entry reg) (nth 2 var))
(setq math-bound-vars (cons (nth 2 var) math-bound-vars))
(math-rwcomp-do-conditions)
)
(defun math-rwcomp-unbind-vars (mark)
(while (not (eq math-bound-vars mark))
(setcar (assq (car math-bound-vars) math-regs) nil)
(setq math-bound-vars (cdr math-bound-vars)))
)
(defun math-rwcomp-do-conditions ()
(let ((cond math-conds))
(while cond
(if (math-rwcomp-all-regs-done (car cond))
(let ((expr (car cond)))
(setq math-conds (delq (car cond) math-conds))
(setcar cond 1)
(math-rwcomp-cond-instr expr)))
(setq cond (cdr cond))))
)
(defun math-rwcomp-cond-instr (expr)
(let (op arg)
(cond ((and (eq (car-safe expr) 'calcFunc-matches)
(= (length expr) 3)
(eq (car-safe (setq arg (math-rwcomp-match-vars (nth 1 expr))))
'calcFunc-register))
(math-rwcomp-pattern (nth 2 expr) (nth 1 arg)))
((math-numberp (setq expr (math-rwcomp-match-vars expr)))
(if (Math-zerop expr)
(math-rwcomp-instr 'backtrack)))
((and (eq (car expr) 'calcFunc-let)
(= (length expr) 3))
(let ((reg (math-rwcomp-reg)))
(math-rwcomp-instr 'let reg (nth 2 expr))
(math-rwcomp-pattern (nth 1 expr) reg)))
((and (eq (car expr) 'calcFunc-let)
(= (length expr) 2)
(eq (car-safe (nth 1 expr)) 'calcFunc-assign)
(= (length (nth 1 expr)) 3))
(let ((reg (math-rwcomp-reg)))
(math-rwcomp-instr 'let reg (nth 2 (nth 1 expr)))
(math-rwcomp-pattern (nth 1 (nth 1 expr)) reg)))
((and (setq op (cdr (assq (car-safe expr)
'( (calcFunc-integer . integer)
(calcFunc-real . real)
(calcFunc-constant . constant)
(calcFunc-negative . negative) ))))
(= (length expr) 2)
(or (and (eq (car-safe (nth 1 expr)) 'neg)
(memq op '(integer real constant))
(setq arg (nth 1 (nth 1 expr))))
(setq arg (nth 1 expr)))
(eq (car-safe (setq arg (nth 1 expr))) 'calcFunc-register))
(math-rwcomp-instr op (nth 1 arg)))
((and (assq (car-safe expr) calc-tweak-eqn-table)
(= (length expr) 3)
(eq (car-safe (nth 1 expr)) 'calcFunc-register))
(if (math-constp (nth 2 expr))
(let ((reg (math-rwcomp-reg)))
(setcar (nthcdr 3 (car math-regs)) (nth 2 expr))
(math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
(car expr) reg))
(if (eq (car (nth 2 expr)) 'calcFunc-register)
(math-rwcomp-instr 'rel (nth 1 (nth 1 expr))
(car expr) (nth 1 (nth 2 expr)))
(math-rwcomp-instr 'cond expr))))
((and (eq (car-safe expr) 'calcFunc-eq)
(= (length expr) 3)
(eq (car-safe (nth 1 expr)) '%)
(eq (car-safe (nth 1 (nth 1 expr))) 'calcFunc-register)
(math-constp (nth 2 (nth 1 expr)))
(math-constp (nth 2 expr)))
(math-rwcomp-instr 'mod (nth 1 (nth 1 (nth 1 expr)))
(nth 2 (nth 1 expr)) (nth 2 expr)))
((equal expr '(var remember var-remember))
(setq math-remembering 1))
((and (eq (car-safe expr) 'calcFunc-remember)
(= (length expr) 2))
(setq math-remembering (if math-remembering
(list 'calcFunc-lor
math-remembering (nth 1 expr))
(nth 1 expr))))
(t (math-rwcomp-instr 'cond expr))))
)
(defun math-rwcomp-same-instr (reg1 reg2 neg)
(math-rwcomp-instr (if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
(nth 2 (math-rwcomp-reg-entry reg2)))
neg)
'same-neg
'same)
reg1 reg2)
)
(defun math-rwcomp-copy-instr (reg1 reg2 neg)
(if (eq (eq (nth 2 (math-rwcomp-reg-entry reg1))
(nth 2 (math-rwcomp-reg-entry reg2)))
neg)
(math-rwcomp-instr 'copy-neg reg1 reg2)
(or (eq reg1 reg2)
(math-rwcomp-instr 'copy reg1 reg2)))
)
(defun math-rwcomp-reg ()
(prog1
math-num-regs
(setq math-regs (cons (list nil math-num-regs nil 0) math-regs)
math-num-regs (1+ math-num-regs)))
)
(defun math-rwcomp-reg-entry (num)
(nth (1- (- math-num-regs num)) math-regs)
)
(defun math-rwcomp-pattern (expr part &optional not-direct)
(cond ((or (math-rwcomp-no-vars expr)
(and (eq (car expr) 'calcFunc-quote)
(= (length expr) 2)
(setq expr (nth 1 expr))))
(if (eq (car-safe expr) 'calcFunc-register)
(math-rwcomp-same-instr part (nth 1 expr) nil)
(let ((reg (math-rwcomp-reg)))
(setcar (nthcdr 3 (car math-regs)) expr)
(math-rwcomp-same-instr part reg nil))))
((eq (car expr) 'var)
(let ((entry (assq (nth 2 expr) math-regs)))
(if entry
(math-rwcomp-same-instr part (nth 1 entry) nil)
(if not-direct
(let ((reg (math-rwcomp-reg)))
(math-rwcomp-pattern expr reg)
(math-rwcomp-copy-instr part reg nil))
(if (setq entry (assq (nth 2 expr) math-aliased-vars))
(progn
(setcar (math-rwcomp-reg-entry (nth 1 entry))
(nth 2 expr))
(setcar entry nil)
(math-rwcomp-copy-instr part (nth 1 entry) nil))
(math-rwcomp-bind-var part expr))))))
((and (eq (car expr) 'calcFunc-select)
(= (length expr) 2))
(let ((reg (math-rwcomp-reg)))
(math-rwcomp-instr 'select part reg)
(math-rwcomp-pattern (nth 1 expr) reg)))
((and (eq (car expr) 'calcFunc-opt)
(memq (length expr) '(2 3)))
(error "opt( ) occurs in context where it is not allowed"))
((eq (car expr) 'neg)
(if (eq (car (nth 1 expr)) 'var)
(let ((entry (assq (nth 2 (nth 1 expr)) math-regs)))
(if entry
(math-rwcomp-same-instr part (nth 1 entry) t)
(if math-copy-neg
(let ((reg (math-rwcomp-best-reg (nth 1 expr))))
(math-rwcomp-copy-instr part reg t)
(math-rwcomp-pattern (nth 1 expr) reg))
(setcar (cdr (cdr (math-rwcomp-reg-entry part))) t)
(math-rwcomp-pattern (nth 1 expr) part))))
(if (math-rwcomp-is-algebraic (nth 1 expr))
(math-rwcomp-cond-instr (list 'calcFunc-eq
(math-rwcomp-register-expr part)
expr))
(let ((reg (math-rwcomp-reg)))
(math-rwcomp-instr 'func part 'neg reg)
(math-rwcomp-pattern (nth 1 expr) reg)))))
((and (eq (car expr) 'calcFunc-apply)
(= (length expr) 3))
(let ((reg1 (math-rwcomp-reg))
(reg2 (math-rwcomp-reg)))
(math-rwcomp-instr 'apply part reg1 reg2)
(math-rwcomp-pattern (nth 1 expr) reg1)
(math-rwcomp-pattern (nth 2 expr) reg2)))
((and (eq (car expr) 'calcFunc-cons)
(= (length expr) 3))
(let ((reg1 (math-rwcomp-reg))
(reg2 (math-rwcomp-reg)))
(math-rwcomp-instr 'cons part reg1 reg2)
(math-rwcomp-pattern (nth 1 expr) reg1)
(math-rwcomp-pattern (nth 2 expr) reg2)))
((and (eq (car expr) 'calcFunc-rcons)
(= (length expr) 3))
(let ((reg1 (math-rwcomp-reg))
(reg2 (math-rwcomp-reg)))
(math-rwcomp-instr 'rcons part reg1 reg2)
(math-rwcomp-pattern (nth 1 expr) reg1)
(math-rwcomp-pattern (nth 2 expr) reg2)))
((and (eq (car expr) 'calcFunc-condition)
(>= (length expr) 3))
(math-rwcomp-pattern (nth 1 expr) part)
(setq expr (cdr expr))
(while (setq expr (cdr expr))
(let ((cond (math-flatten-lands (car expr))))
(while cond
(if (math-rwcomp-all-regs-done (car cond))
(math-rwcomp-cond-instr (car cond))
(setq math-conds (cons (car cond) math-conds)))
(setq cond (cdr cond))))))
((and (eq (car expr) 'calcFunc-pand)
(= (length expr) 3))
(math-rwcomp-pattern (nth 1 expr) part)
(math-rwcomp-pattern (nth 2 expr) part))
((and (eq (car expr) 'calcFunc-por)
(= (length expr) 3))
(math-rwcomp-instr 'alt nil nil [nil nil 4])
(let ((math-conds nil)
(head math-prog-last)
(mark math-bound-vars)
(math-copy-neg t))
(math-rwcomp-pattern (nth 1 expr) part t)
(let ((amark math-aliased-vars)
(math-aliased-vars math-aliased-vars)
(tail math-prog-last)
(p math-bound-vars)
entry)
(while (not (eq p mark))
(setq entry (assq (car p) math-regs)
math-aliased-vars (cons (list (car p) (nth 1 entry) nil)
math-aliased-vars)
p (cdr p))
(setcar (math-rwcomp-reg-entry (nth 1 entry)) nil))
(setcar (cdr (car head)) (cdr head))
(setcdr head nil)
(setq math-prog-last head)
(math-rwcomp-pattern (nth 2 expr) part)
(math-rwcomp-instr 'same 0 0)
(setcdr tail math-prog-last)
(setq p math-aliased-vars)
(while (not (eq p amark))
(if (car (car p))
(setcar (math-rwcomp-reg-entry (nth 1 (car p)))
(car (car p))))
(setq p (cdr p)))))
(math-rwcomp-do-conditions))
((and (eq (car expr) 'calcFunc-pnot)
(= (length expr) 2))
(math-rwcomp-instr 'alt nil nil [nil nil 4])
(let ((head math-prog-last)
(mark math-bound-vars))
(math-rwcomp-pattern (nth 1 expr) part)
(math-rwcomp-unbind-vars mark)
(math-rwcomp-instr 'end-alt head)
(math-rwcomp-instr 'backtrack)
(setcar (cdr (car head)) (cdr head))
(setcdr head nil)
(setq math-prog-last head)))
(t (let ((props (get (car expr) 'math-rewrite-props)))
(if (and (eq (car expr) 'calcFunc-plain)
(= (length expr) 2)
(not (math-primp (nth 1 expr))))
(setq expr (nth 1 expr))) ; but "props" is still nil
(if (and (memq 'algebraic props)
(math-rwcomp-is-algebraic expr))
(math-rwcomp-cond-instr (list 'calcFunc-eq
(math-rwcomp-register-expr part)
expr))
(if (and (memq 'commut props)
(= (length expr) 3))
(let ((arg1 (nth 1 expr))
(arg2 (nth 2 expr))
try1 def code head (flip nil))
(if (eq (car expr) '-)
(setq arg2 (math-rwcomp-neg arg2)))
(setq arg1 (cons arg1 (math-rwcomp-best-reg arg1))
arg2 (cons arg2 (math-rwcomp-best-reg arg2)))
(or (math-rwcomp-order arg1 arg2)
(setq def arg1 arg1 arg2 arg2 def flip t))
(if (math-rwcomp-optional-arg (car expr) arg1)
(error "Too many opt( ) arguments in this context"))
(setq def (math-rwcomp-optional-arg (car expr) arg2)
head (if (memq (car expr) '(+ -))
'(+ -)
(if (eq (car expr) '*)
'(* /)
(list (car expr))))
code (if (math-rwcomp-is-constrained
(car arg1) head)
(if (math-rwcomp-is-constrained
(car arg2) head)
0 1)
2))
(math-rwcomp-multi-instr (and def (list def))
'try part head
(vector nil nil nil code flip)
(cdr arg1))
(setq try1 (car math-prog-last))
(math-rwcomp-pattern (car arg1) (cdr arg1))
(math-rwcomp-instr 'try2 try1 (cdr arg2))
(if (and (= part 0) (not def) (not math-rewrite-whole)
(not (eq math-rhs t))
(setq def (get (car expr)
'math-rewrite-default)))
(let ((reg1 (math-rwcomp-reg))
(reg2 (math-rwcomp-reg)))
(if (= (aref (nth 3 try1) 3) 0)
(aset (nth 3 try1) 3 1))
(math-rwcomp-instr 'try (cdr arg2)
(if (equal head '(* /))
'(*) head)
(vector nil nil nil
(if (= code 0)
1 2)
nil)
reg1 def)
(setq try1 (car math-prog-last))
(math-rwcomp-pattern (car arg2) reg1)
(math-rwcomp-instr 'try2 try1 reg2)
(setq math-rhs (list (if (eq (car expr) '-)
'+ (car expr))
math-rhs
(list 'calcFunc-register
reg2))))
(math-rwcomp-pattern (car arg2) (cdr arg2))))
(let* ((args (mapcar (function
(lambda (x)
(cons x (math-rwcomp-best-reg x))))
(cdr expr)))
(args2 (copy-sequence args))
(argp (reverse args2))
(defs nil)
(num 1))
(while argp
(let ((def (math-rwcomp-optional-arg (car expr)
(car argp))))
(if def
(progn
(setq args2 (delq (car argp) args2)
defs (cons (cons def (cdr (car argp)))
defs))
(math-rwcomp-multi-instr
(mapcar 'cdr args2)
(if (or (and (memq 'unary1 props)
(= (length args2) 1)
(eq (car args2) (car args)))
(and (memq 'unary2 props)
(= (length args) 2)
(eq (car args2) (nth 1 args))))
'func-opt
'func-def)
part (car expr)
defs))))
(setq argp (cdr argp)))
(math-rwcomp-multi-instr (mapcar 'cdr args)
'func part (car expr))
(setq args (sort args 'math-rwcomp-order))
(while args
(math-rwcomp-pattern (car (car args)) (cdr (car args)))
(setq num (1+ num)
args (cdr args)))))))))
)
(defun math-rwcomp-best-reg (x)
(or (and (eq (car-safe x) 'var)
(let ((entry (assq (nth 2 x) math-aliased-vars)))
(and entry
(not (nth 2 entry))
(not (nth 2 (math-rwcomp-reg-entry (nth 1 entry))))
(progn
(setcar (cdr (cdr entry)) t)
(nth 1 entry)))))
(math-rwcomp-reg))
)
(defun math-rwcomp-all-regs-done (expr)
(if (Math-primp expr)
(or (not (eq (car-safe expr) 'var))
(assq (nth 2 expr) math-regs)
(eq (nth 2 expr) 'var-remember)
(math-const-var expr))
(if (and (eq (car expr) 'calcFunc-let)
(= (length expr) 3))
(math-rwcomp-all-regs-done (nth 2 expr))
(if (and (eq (car expr) 'calcFunc-let)
(= (length expr) 2)
(eq (car-safe (nth 1 expr)) 'calcFunc-assign)
(= (length (nth 1 expr)) 3))
(math-rwcomp-all-regs-done (nth 2 (nth 1 expr)))
(while (and (setq expr (cdr expr))
(math-rwcomp-all-regs-done (car expr))))
(null expr))))
)
(defun math-rwcomp-no-vars (expr)
(if (Math-primp expr)
(or (not (eq (car-safe expr) 'var))
(math-const-var expr))
(and (not (memq (car expr) '(calcFunc-condition
calcFunc-select calcFunc-quote
calcFunc-plain calcFunc-opt
calcFunc-por calcFunc-pand
calcFunc-pnot calcFunc-apply
calcFunc-cons calcFunc-rcons)))
(progn
(while (and (setq expr (cdr expr))
(math-rwcomp-no-vars (car expr))))
(null expr))))
)
(defun math-rwcomp-is-algebraic (expr)
(if (Math-primp expr)
(or (not (eq (car-safe expr) 'var))
(math-const-var expr)
(assq (nth 2 expr) math-regs))
(and (memq 'algebraic (get (car expr) 'math-rewrite-props))
(progn
(while (and (setq expr (cdr expr))
(math-rwcomp-is-algebraic (car expr))))
(null expr))))
)
(defun math-rwcomp-is-constrained (expr not-these)
(if (Math-primp expr)
(not (eq (car-safe expr) 'var))
(if (eq (car expr) 'calcFunc-plain)
(math-rwcomp-is-constrained (nth 1 expr) not-these)
(not (or (memq (car expr) '(neg calcFunc-select))
(memq (car expr) not-these)
(and (memq 'commut (get (car expr) 'math-rewrite-props))
(or (eq (car-safe (nth 1 expr)) 'calcFunc-opt)
(eq (car-safe (nth 2 expr)) 'calcFunc-opt)))))))
)
(defun math-rwcomp-optional-arg (head argp)
(let ((arg (car argp)))
(if (eq (car-safe arg) 'calcFunc-opt)
(and (memq (length arg) '(2 3))
(progn
(or (eq (car-safe (nth 1 arg)) 'var)
(error "First argument of opt( ) must be a variable"))
(setcar argp (nth 1 arg))
(if (= (length arg) 2)
(or (get head 'math-rewrite-default)
(error "opt( ) must include a default in this context"))
(nth 2 arg))))
(and (eq (car-safe arg) 'neg)
(let* ((part (list (nth 1 arg)))
(partp (math-rwcomp-optional-arg head part)))
(and partp
(setcar argp (math-rwcomp-neg (car part)))
(math-neg partp))))))
)
(defun math-rwcomp-neg (expr)
(if (memq (car-safe expr) '(* /))
(if (eq (car-safe (nth 1 expr)) 'var)
(list (car expr) (list 'neg (nth 1 expr)) (nth 2 expr))
(if (eq (car-safe (nth 2 expr)) 'var)
(list (car expr) (nth 1 expr) (list 'neg (nth 2 expr)))
(math-neg expr)))
(math-neg expr))
)
(defun math-rwcomp-assoc-args (expr)
(if (and (eq (car-safe (nth 1 expr)) (car expr))
(= (length (nth 1 expr)) 3))
(math-rwcomp-assoc-args (nth 1 expr))
(setq math-args (cons (nth 1 expr) math-args)))
(if (and (eq (car-safe (nth 2 expr)) (car expr))
(= (length (nth 2 expr)) 3))
(math-rwcomp-assoc-args (nth 2 expr))
(setq math-args (cons (nth 2 expr) math-args)))
)
(defun math-rwcomp-addsub-args (expr)
(if (memq (car-safe (nth 1 expr)) '(+ -))
(math-rwcomp-addsub-args (nth 1 expr))
(setq math-args (cons (nth 1 expr) math-args)))
(if (eq (car expr) '-)
(setq math-args (cons (math-rwcomp-neg (nth 2 expr)) math-args))
(if (eq (car-safe (nth 2 expr)) '+)
(math-rwcomp-addsub-args (nth 2 expr))
(setq math-args (cons (nth 2 expr) math-args))))
)
(defun math-rwcomp-order (a b)
(< (math-rwcomp-priority (car a))
(math-rwcomp-priority (car b)))
)
;;; Order of priority: 0 Constants and other exact matches (first)
;;; 10 Functions (except below)
;;; 20 Meta-variables which occur more than once
;;; 30 Algebraic functions
;;; 40 Commutative/associative functions
;;; 50 Meta-variables which occur only once
;;; +100 for every "!!!" (pnot) in the pattern
;;; 10000 Optional arguments (last)
(defun math-rwcomp-priority (expr)
(+ (math-rwcomp-count-pnots expr)
(cond ((eq (car-safe expr) 'calcFunc-opt)
10000)
((math-rwcomp-no-vars expr)
0)
((eq (car expr) 'calcFunc-quote)
0)
((eq (car expr) 'var)
(if (assq (nth 2 expr) math-regs)
0
(if (= (math-rwcomp-count-refs expr) 1)
50
20)))
(t (let ((props (get (car expr) 'math-rewrite-props)))
(if (or (memq 'commut props)
(memq 'assoc props))
40
(if (memq 'algebraic props)
30
10))))))
)
(defun math-rwcomp-count-refs (var)
(let ((count (or (math-expr-contains-count math-pattern var) 0))
(p math-conds))
(while p
(if (eq (car-safe (car p)) 'calcFunc-let)
(if (= (length (car p)) 3)
(setq count (+ count
(or (math-expr-contains-count (nth 2 (car p)) var)
0)))
(if (and (= (length (car p)) 2)
(eq (car-safe (nth 1 (car p))) 'calcFunc-assign)
(= (length (nth 1 (car p))) 3))
(setq count (+ count
(or (math-expr-contains-count
(nth 2 (nth 1 (car p))) var) 0))))))
(setq p (cdr p)))
count)
)
(defun math-rwcomp-count-pnots (expr)
(if (Math-primp expr)
0
(if (eq (car expr) 'calcFunc-pnot)
100
(let ((count 0))
(while (setq expr (cdr expr))
(setq count (+ count (math-rwcomp-count-pnots (car expr)))))
count)))
)
;;; In the current implementation, all associative functions must
;;; also be commutative.
(put '+ 'math-rewrite-props '(algebraic assoc commut))
(put '- 'math-rewrite-props '(algebraic assoc commut)) ; see below
(put '* 'math-rewrite-props '(algebraic assoc commut)) ; see below
(put '/ 'math-rewrite-props '(algebraic unary1))
(put '^ 'math-rewrite-props '(algebraic unary1))
(put '% 'math-rewrite-props '(algebraic))
(put 'neg 'math-rewrite-props '(algebraic))
(put 'calcFunc-idiv 'math-rewrite-props '(algebraic))
(put 'calcFunc-abs 'math-rewrite-props '(algebraic))
(put 'calcFunc-sign 'math-rewrite-props '(algebraic))
(put 'calcFunc-round 'math-rewrite-props '(algebraic))
(put 'calcFunc-rounde 'math-rewrite-props '(algebraic))
(put 'calcFunc-roundu 'math-rewrite-props '(algebraic))
(put 'calcFunc-trunc 'math-rewrite-props '(algebraic))
(put 'calcFunc-floor 'math-rewrite-props '(algebraic))
(put 'calcFunc-ceil 'math-rewrite-props '(algebraic))
(put 'calcFunc-re 'math-rewrite-props '(algebraic))
(put 'calcFunc-im 'math-rewrite-props '(algebraic))
(put 'calcFunc-conj 'math-rewrite-props '(algebraic))
(put 'calcFunc-arg 'math-rewrite-props '(algebraic))
(put 'calcFunc-and 'math-rewrite-props '(assoc commut))
(put 'calcFunc-or 'math-rewrite-props '(assoc commut))
(put 'calcFunc-xor 'math-rewrite-props '(assoc commut))
(put 'calcFunc-eq 'math-rewrite-props '(commut))
(put 'calcFunc-neq 'math-rewrite-props '(commut))
(put 'calcFunc-land 'math-rewrite-props '(assoc commut))
(put 'calcFunc-lor 'math-rewrite-props '(assoc commut))
(put 'calcFunc-beta 'math-rewrite-props '(commut))
(put 'calcFunc-gcd 'math-rewrite-props '(assoc commut))
(put 'calcFunc-lcm 'math-rewrite-props '(assoc commut))
(put 'calcFunc-max 'math-rewrite-props '(algebraic assoc commut))
(put 'calcFunc-min 'math-rewrite-props '(algebraic assoc commut))
(put 'calcFunc-vunion 'math-rewrite-props '(assoc commut))
(put 'calcFunc-vint 'math-rewrite-props '(assoc commut))
(put 'calcFunc-vxor 'math-rewrite-props '(assoc commut))
;;; Note: "*" is not commutative for matrix args, but we pretend it is.
;;; Also, "-" is not commutative but the code tweaks things so that it is.
(put '+ 'math-rewrite-default 0)
(put '- 'math-rewrite-default 0)
(put '* 'math-rewrite-default 1)
(put '/ 'math-rewrite-default 1)
(put '^ 'math-rewrite-default 1)
(put 'calcFunc-land 'math-rewrite-default 1)
(put 'calcFunc-lor 'math-rewrite-default 0)
(put 'calcFunc-vunion 'math-rewrite-default '(vec))
(put 'calcFunc-vint 'math-rewrite-default '(vec))
(put 'calcFunc-vdiff 'math-rewrite-default '(vec))
(put 'calcFunc-vxor 'math-rewrite-default '(vec))
(defmacro math-rwfail (&optional back)
(list 'setq 'pc
(list 'and
(if back
'(setq btrack (cdr btrack))
'btrack)
''((backtrack))))
)
;;; This monstrosity is necessary because the use of static vectors of
;;; registers makes rewrite rules non-reentrant. Yucko!
(defmacro math-rweval (form)
(list 'let '((orig (car rules)))
'(setcar rules (quote (nil nil nil no-phase)))
(list 'unwind-protect
form
'(setcar rules orig)))
)
(setq math-rewrite-phase 1)
(defun math-apply-rewrites (expr rules &optional heads ruleset)
(and
(setq rules (cdr (or (assq (car-safe expr) rules)
(assq nil rules))))
(let ((result nil)
op regs inst part pc mark btrack
(tracing math-rwcomp-tracing)
(phase math-rewrite-phase))
(while rules
(or
(and (setq part (nth 2 (car rules)))
heads
(not (memq part heads)))
(and (setq part (nth 3 (car rules)))
(not (memq phase part)))
(progn
(setq regs (car (car rules))
pc (nth 1 (car rules))
btrack nil)
(aset regs 0 expr)
(while pc
(and tracing
(progn (terpri) (princ (car pc))
(if (and (natnump (nth 1 (car pc)))
(< (nth 1 (car pc)) (length regs)))
(princ (format "\n part = %s"
(aref regs (nth 1 (car pc))))))))
(cond ((eq (setq op (car (setq inst (car pc)))) 'func)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(eq (car part)
(car (setq inst (cdr (cdr inst)))))
(progn
(while (and (setq inst (cdr inst)
part (cdr part))
inst)
(aset regs (car inst) (car part)))
(not (or inst part))))
(setq pc (cdr pc))
(math-rwfail)))
((eq op 'same)
(if (or (equal (setq part (aref regs (nth 1 inst)))
(setq mark (aref regs (nth 2 inst))))
(Math-equal part mark))
(setq pc (cdr pc))
(math-rwfail)))
((and (eq op 'try)
calc-matrix-mode
(not (eq calc-matrix-mode 'scalar))
(eq (car (nth 2 inst)) '*)
(consp (setq part (aref regs (car (cdr inst)))))
(eq (car part) '*)
(not (math-known-scalarp part)))
(setq mark (nth 3 inst)
pc (cdr pc))
(if (aref mark 4)
(progn
(aset regs (nth 4 inst) (nth 2 part))
(aset mark 1 (cdr (cdr part))))
(aset regs (nth 4 inst) (nth 1 part))
(aset mark 1 (cdr part)))
(aset mark 0 (cdr part))
(aset mark 2 0))
((eq op 'try)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(memq (car part) (nth 2 inst))
(= (length part) 3)
(or (not (eq (car part) '/))
(Math-objectp (nth 2 part))))
(progn
(setq op nil
mark (car (cdr (setq inst (cdr (cdr inst))))))
(and
(memq 'assoc (get (car part) 'math-rewrite-props))
(not (= (aref mark 3) 0))
(while (if (and (consp (nth 1 part))
(memq (car (nth 1 part)) (car inst)))
(setq op (cons (if (eq (car part) '-)
(math-rwapply-neg
(nth 2 part))
(nth 2 part))
op)
part (nth 1 part))
(if (and (consp (nth 2 part))
(memq (car (nth 2 part))
(car inst))
(not (eq (car (nth 2 part)) '-)))
(setq op (cons (nth 1 part) op)
part (nth 2 part))))))
(setq op (cons (nth 1 part)
(cons (if (eq (car part) '-)
(math-rwapply-neg
(nth 2 part))
(if (eq (car part) '/)
(math-rwapply-inv
(nth 2 part))
(nth 2 part)))
op))
btrack (cons pc btrack)
pc (cdr pc))
(aset regs (nth 2 inst) (car op))
(aset mark 0 op)
(aset mark 1 op)
(aset mark 2 (if (cdr (cdr op)) 1 0)))
(if (nth 5 inst)
(if (and (consp part)
(eq (car part) 'neg)
(eq (car (nth 2 inst)) '*)
(eq (nth 5 inst) 1))
(progn
(setq mark (nth 3 inst)
pc (cdr pc))
(aset regs (nth 4 inst) (nth 1 part))
(aset mark 1 -1)
(aset mark 2 4))
(setq mark (nth 3 inst)
pc (cdr pc))
(aset regs (nth 4 inst) part)
(aset mark 2 3))
(math-rwfail))))
((eq op 'try2)
(setq part (nth 1 inst) ; try instr
mark (nth 3 part)
op (aref mark 2)
pc (cdr pc))
(aset regs (nth 2 inst)
(cond
((eq op 0)
(if (eq (aref mark 0) (aref mark 1))
(nth 1 (aref mark 0))
(car (aref mark 0))))
((eq op 1)
(setq mark (delq (car (aref mark 1))
(copy-sequence (aref mark 0)))
op (car (nth 2 part)))
(if (eq op '*)
(progn
(setq mark (nreverse mark)
part (list '* (nth 1 mark) (car mark))
mark (cdr mark))
(while (setq mark (cdr mark))
(setq part (list '* (car mark) part))))
(setq part (car mark)
mark (cdr mark)
part (if (and (eq op '+)
(consp (car mark))
(eq (car (car mark)) 'neg))
(list '- part
(nth 1 (car mark)))
(list op part (car mark))))
(while (setq mark (cdr mark))
(setq part (if (and (eq op '+)
(consp (car mark))
(eq (car (car mark)) 'neg))
(list '- part
(nth 1 (car mark)))
(list op part (car mark))))))
part)
((eq op 2)
(car (aref mark 1)))
((eq op 3) (nth 5 part))
(t (aref mark 1)))))
((eq op 'select)
(setq pc (cdr pc))
(if (and (consp (setq part (aref regs (nth 1 inst))))
(eq (car part) 'calcFunc-select))
(aset regs (nth 2 inst) (nth 1 part))
(if math-rewrite-selections
(math-rwfail)
(aset regs (nth 2 inst) part))))
((eq op 'same-neg)
(if (or (equal (setq part (aref regs (nth 1 inst)))
(setq mark (math-neg
(aref regs (nth 2 inst)))))
(Math-equal part mark))
(setq pc (cdr pc))
(math-rwfail)))
((eq op 'backtrack)
(setq inst (car (car btrack)) ; "try" or "alt" instr
pc (cdr (car btrack))
mark (or (nth 3 inst) [nil nil 4])
op (aref mark 2))
(cond ((eq op 0)
(if (setq op (cdr (aref mark 1)))
(aset regs (nth 4 inst) (car (aset mark 1 op)))
(if (nth 5 inst)
(progn
(aset mark 2 3)
(aset regs (nth 4 inst)
(aref regs (nth 1 inst))))
(math-rwfail t))))
((eq op 1)
(if (setq op (cdr (aref mark 1)))
(aset regs (nth 4 inst) (car (aset mark 1 op)))
(if (= (aref mark 3) 1)
(if (nth 5 inst)
(progn
(aset mark 2 3)
(aset regs (nth 4 inst)
(aref regs (nth 1 inst))))
(math-rwfail t))
(aset mark 2 2)
(aset mark 1 (cons nil (aref mark 0)))
(math-rwfail))))
((eq op 2)
(if (setq op (cdr (aref mark 1)))
(progn
(setq mark (delq (car (aset mark 1 op))
(copy-sequence
(aref mark 0)))
op (car (nth 2 inst)))
(if (eq op '*)
(progn
(setq mark (nreverse mark)
part (list '* (nth 1 mark)
(car mark))
mark (cdr mark))
(while (setq mark (cdr mark))
(setq part (list '* (car mark)
part))))
(setq part (car mark)
mark (cdr mark)
part (if (and (eq op '+)
(consp (car mark))
(eq (car (car mark))
'neg))
(list '- part
(nth 1 (car mark)))
(list op part (car mark))))
(while (setq mark (cdr mark))
(setq part (if (and (eq op '+)
(consp (car mark))
(eq (car (car mark))
'neg))
(list '- part
(nth 1 (car mark)))
(list op part (car mark))))))
(aset regs (nth 4 inst) part))
(if (nth 5 inst)
(progn
(aset mark 2 3)
(aset regs (nth 4 inst)
(aref regs (nth 1 inst))))
(math-rwfail t))))
((eq op 4)
(setq btrack (cdr btrack)))
(t (math-rwfail t))))
((eq op 'integer)
(if (Math-integerp (setq part (aref regs (nth 1 inst))))
(setq pc (cdr pc))
(if (Math-primp part)
(math-rwfail)
(setq part (math-rweval (math-simplify part)))
(if (Math-integerp part)
(setq pc (cdr pc))
(math-rwfail)))))
((eq op 'real)
(if (Math-realp (setq part (aref regs (nth 1 inst))))
(setq pc (cdr pc))
(if (Math-primp part)
(math-rwfail)
(setq part (math-rweval (math-simplify part)))
(if (Math-realp part)
(setq pc (cdr pc))
(math-rwfail)))))
((eq op 'constant)
(if (math-constp (setq part (aref regs (nth 1 inst))))
(setq pc (cdr pc))
(if (Math-primp part)
(math-rwfail)
(setq part (math-rweval (math-simplify part)))
(if (math-constp part)
(setq pc (cdr pc))
(math-rwfail)))))
((eq op 'negative)
(if (math-looks-negp (setq part (aref regs (nth 1 inst))))
(setq pc (cdr pc))
(if (Math-primp part)
(math-rwfail)
(setq part (math-rweval (math-simplify part)))
(if (math-looks-negp part)
(setq pc (cdr pc))
(math-rwfail)))))
((eq op 'rel)
(setq part (math-compare (aref regs (nth 1 inst))
(aref regs (nth 3 inst)))
op (nth 2 inst))
(if (= part 2)
(setq part (math-rweval
(math-simplify
(calcFunc-sign
(math-sub (aref regs (nth 1 inst))
(aref regs (nth 3 inst))))))))
(if (cond ((eq op 'calcFunc-eq)
(eq part 0))
((eq op 'calcFunc-neq)
(memq part '(-1 1)))
((eq op 'calcFunc-lt)
(eq part -1))
((eq op 'calcFunc-leq)
(memq part '(-1 0)))
((eq op 'calcFunc-gt)
(eq part 1))
((eq op 'calcFunc-geq)
(memq part '(0 1))))
(setq pc (cdr pc))
(math-rwfail)))
((eq op 'func-def)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(eq (car part)
(car (setq inst (cdr (cdr inst))))))
(progn
(setq inst (cdr inst)
mark (car inst))
(while (and (setq inst (cdr inst)
part (cdr part))
inst)
(aset regs (car inst) (car part)))
(if (or inst part)
(setq pc (cdr pc))
(while (eq (car (car (setq pc (cdr pc))))
'func-def))
(setq pc (cdr pc)) ; skip over "func"
(while mark
(aset regs (cdr (car mark)) (car (car mark)))
(setq mark (cdr mark)))))
(math-rwfail)))
((eq op 'func-opt)
(if (or (not (and (consp
(setq part (aref regs (car (cdr inst)))))
(eq (car part) (nth 2 inst))))
(and (= (length part) 2)
(setq part (nth 1 part))))
(progn
(setq mark (nth 3 inst))
(aset regs (nth 4 inst) part)
(while (eq (car (car (setq pc (cdr pc)))) 'func-def))
(setq pc (cdr pc)) ; skip over "func"
(while mark
(aset regs (cdr (car mark)) (car (car mark)))
(setq mark (cdr mark))))
(setq pc (cdr pc))))
((eq op 'mod)
(if (if (Math-zerop (setq part (aref regs (nth 1 inst))))
(Math-zerop (nth 3 inst))
(and (not (Math-zerop (nth 2 inst)))
(progn
(setq part (math-mod part (nth 2 inst)))
(or (Math-numberp part)
(setq part (math-rweval
(math-simplify part))))
(Math-equal part (nth 3 inst)))))
(setq pc (cdr pc))
(math-rwfail)))
((eq op 'apply)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(not (Math-objvecp part))
(not (eq (car part) 'var)))
(progn
(aset regs (nth 2 inst)
(math-calcFunc-to-var (car part)))
(aset regs (nth 3 inst)
(cons 'vec (cdr part)))
(setq pc (cdr pc)))
(math-rwfail)))
((eq op 'cons)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(eq (car part) 'vec)
(cdr part))
(progn
(aset regs (nth 2 inst) (nth 1 part))
(aset regs (nth 3 inst) (cons 'vec (cdr (cdr part))))
(setq pc (cdr pc)))
(math-rwfail)))
((eq op 'rcons)
(if (and (consp (setq part (aref regs (car (cdr inst)))))
(eq (car part) 'vec)
(cdr part))
(progn
(aset regs (nth 2 inst) (calcFunc-rhead part))
(aset regs (nth 3 inst) (calcFunc-rtail part))
(setq pc (cdr pc)))
(math-rwfail)))
((eq op 'cond)
(if (math-is-true
(math-rweval
(math-simplify
(math-rwapply-replace-regs (nth 1 inst)))))
(setq pc (cdr pc))
(math-rwfail)))
((eq op 'let)
(aset regs (nth 1 inst)
(math-rweval
(math-normalize
(math-rwapply-replace-regs (nth 2 inst)))))
(setq pc (cdr pc)))
((eq op 'copy)
(aset regs (nth 2 inst) (aref regs (nth 1 inst)))
(setq pc (cdr pc)))
((eq op 'copy-neg)
(aset regs (nth 2 inst)
(math-rwapply-neg (aref regs (nth 1 inst))))
(setq pc (cdr pc)))
((eq op 'alt)
(setq btrack (cons pc btrack)
pc (nth 1 inst)))
((eq op 'end-alt)
(while (and btrack (not (eq (car btrack) (nth 1 inst))))
(setq btrack (cdr btrack)))
(setq btrack (cdr btrack)
pc (cdr pc)))
((eq op 'done)
(setq result (math-rwapply-replace-regs (nth 1 inst)))
(if (or (and (eq (car-safe result) '+)
(eq (nth 2 result) 0))
(and (eq (car-safe result) '*)
(eq (nth 2 result) 1)))
(setq result (nth 1 result)))
(setq part (and (nth 2 inst)
(math-is-true
(math-rweval
(math-simplify
(math-rwapply-replace-regs
(nth 2 inst)))))))
(if (or (equal result expr)
(equal (setq result (math-normalize result)) expr))
(setq result nil)
(if part (math-rwapply-remember expr result))
(setq rules nil))
(setq pc nil))
(t (error "%s is not a valid rewrite opcode" op))))))
(setq rules (cdr rules)))
result))
)
(defun math-rwapply-neg (expr)
(if (and (consp expr)
(memq (car expr) '(* /)))
(if (Math-objectp (nth 2 expr))
(list (car expr) (nth 1 expr) (math-neg (nth 2 expr)))
(list (car expr)
(if (Math-objectp (nth 1 expr))
(math-neg (nth 1 expr))
(list '* -1 (nth 1 expr)))
(nth 2 expr)))
(math-neg expr))
)
(defun math-rwapply-inv (expr)
(if (and (Math-integerp expr)
calc-prefer-frac)
(math-make-frac 1 expr)
(list '/ 1 expr))
)
(defun math-rwapply-replace-regs (expr)
(cond ((Math-primp expr)
expr)
((eq (car expr) 'calcFunc-register)
(setq expr (aref regs (nth 1 expr)))
(if (eq (car-safe expr) '*)
(if (eq (nth 1 expr) -1)
(math-neg (nth 2 expr))
(if (eq (nth 1 expr) 1)
(nth 2 expr)
expr))
expr))
((and (eq (car expr) 'calcFunc-eval)
(= (length expr) 2))
(calc-with-default-simplification
(math-normalize (math-rwapply-replace-regs (nth 1 expr)))))
((and (eq (car expr) 'calcFunc-evalsimp)
(= (length expr) 2))
(math-simplify (math-rwapply-replace-regs (nth 1 expr))))
((and (eq (car expr) 'calcFunc-evalextsimp)
(= (length expr) 2))
(math-simplify-extended (math-rwapply-replace-regs (nth 1 expr))))
((and (eq (car expr) 'calcFunc-apply)
(= (length expr) 3))
(let ((func (math-rwapply-replace-regs (nth 1 expr)))
(args (math-rwapply-replace-regs (nth 2 expr)))
call)
(if (and (math-vectorp args)
(not (eq (car-safe (setq call (math-build-call
(math-var-to-calcFunc func)
(cdr args))))
'calcFunc-call)))
call
(list 'calcFunc-apply func args))))
((and (eq (car expr) 'calcFunc-cons)
(= (length expr) 3))
(let ((head (math-rwapply-replace-regs (nth 1 expr)))
(tail (math-rwapply-replace-regs (nth 2 expr))))
(if (math-vectorp tail)
(cons 'vec (cons head (cdr tail)))
(list 'calcFunc-cons head tail))))
((and (eq (car expr) 'calcFunc-rcons)
(= (length expr) 3))
(let ((head (math-rwapply-replace-regs (nth 1 expr)))
(tail (math-rwapply-replace-regs (nth 2 expr))))
(if (math-vectorp head)
(append head (list tail))
(list 'calcFunc-rcons head tail))))
((and (eq (car expr) 'neg)
(math-rwapply-reg-looks-negp (nth 1 expr)))
(math-rwapply-reg-neg (nth 1 expr)))
((and (eq (car expr) 'neg)
(eq (car-safe (nth 1 expr)) 'calcFunc-register)
(math-scalarp (aref regs (nth 1 (nth 1 expr)))))
(math-neg (math-rwapply-replace-regs (nth 1 expr))))
((and (eq (car expr) '+)
(math-rwapply-reg-looks-negp (nth 1 expr)))
(list '- (math-rwapply-replace-regs (nth 2 expr))
(math-rwapply-reg-neg (nth 1 expr))))
((and (eq (car expr) '+)
(math-rwapply-reg-looks-negp (nth 2 expr)))
(list '- (math-rwapply-replace-regs (nth 1 expr))
(math-rwapply-reg-neg (nth 2 expr))))
((and (eq (car expr) '-)
(math-rwapply-reg-looks-negp (nth 2 expr)))
(list '+ (math-rwapply-replace-regs (nth 1 expr))
(math-rwapply-reg-neg (nth 2 expr))))
((eq (car expr) '*)
(cond ((eq (nth 1 expr) -1)
(if (math-rwapply-reg-looks-negp (nth 2 expr))
(math-rwapply-reg-neg (nth 2 expr))
(math-neg (math-rwapply-replace-regs (nth 2 expr)))))
((eq (nth 1 expr) 1)
(math-rwapply-replace-regs (nth 2 expr)))
((eq (nth 2 expr) -1)
(if (math-rwapply-reg-looks-negp (nth 1 expr))
(math-rwapply-reg-neg (nth 1 expr))
(math-neg (math-rwapply-replace-regs (nth 1 expr)))))
((eq (nth 2 expr) 1)
(math-rwapply-replace-regs (nth 1 expr)))
(t
(let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
(arg2 (math-rwapply-replace-regs (nth 2 expr))))
(cond ((and (eq (car-safe arg1) '/)
(eq (nth 1 arg1) 1))
(list '/ arg2 (nth 2 arg1)))
((and (eq (car-safe arg2) '/)
(eq (nth 1 arg2) 1))
(list '/ arg1 (nth 2 arg2)))
(t (list '* arg1 arg2)))))))
((eq (car expr) '/)
(let ((arg1 (math-rwapply-replace-regs (nth 1 expr)))
(arg2 (math-rwapply-replace-regs (nth 2 expr))))
(if (eq (car-safe arg2) '/)
(list '/ (list '* arg1 (nth 2 arg2)) (nth 1 arg2))
(list '/ arg1 arg2))))
((and (eq (car expr) 'calcFunc-plain)
(= (length expr) 2))
(if (Math-primp (nth 1 expr))
(nth 1 expr)
(if (eq (car (nth 1 expr)) 'calcFunc-register)
(aref regs (nth 1 (nth 1 expr)))
(cons (car (nth 1 expr)) (mapcar 'math-rwapply-replace-regs
(cdr (nth 1 expr)))))))
(t (cons (car expr) (mapcar 'math-rwapply-replace-regs (cdr expr)))))
)
(defun math-rwapply-reg-looks-negp (expr)
(if (eq (car-safe expr) 'calcFunc-register)
(math-looks-negp (aref regs (nth 1 expr)))
(if (memq (car-safe expr) '(* /))
(or (math-rwapply-reg-looks-negp (nth 1 expr))
(math-rwapply-reg-looks-negp (nth 2 expr)))))
)
(defun math-rwapply-reg-neg (expr) ; expr must satisfy rwapply-reg-looks-negp
(if (eq (car expr) 'calcFunc-register)
(math-neg (math-rwapply-replace-regs expr))
(if (math-rwapply-reg-looks-negp (nth 1 expr))
(math-rwapply-replace-regs (list (car expr)
(math-rwapply-reg-neg (nth 1 expr))
(nth 2 expr)))
(math-rwapply-replace-regs (list (car expr)
(nth 1 expr)
(math-rwapply-reg-neg (nth 2 expr))))))
)
(defun math-rwapply-remember (old new)
(let ((varval (symbol-value (nth 2 (car ruleset))))
(rules (assq (car-safe old) ruleset)))
(if (and (eq (car-safe varval) 'vec)
(not (memq (car-safe old) '(nil schedule + -)))
rules)
(progn
(setcdr varval (cons (list 'calcFunc-assign
(if (math-rwcomp-no-vars old)
old
(list 'calcFunc-quote old))
new)
(cdr varval)))
(setcdr rules (cons (list (vector nil old)
(list (list 'same 0 1)
(list 'done new nil))
nil nil)
(cdr rules))))))
)
|