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
|
\documentclass[12pt]{report}
\usepackage{manual}
\usepackage[english]{babel}
\usepackage[autolanguage]{numprint}
\usepackage{dcolumn}
\newcommand*\boi{\textbackslash}
\newcommand*\at{@}
\fvset{label=source}% english
\renewcommand\parameter[1]{\texttt{#1}\index{#1@\texttt{#1}}%
\index{parameter!\texttt{#1}}}
\begin{document}
\begin{titlepage}
\null\par\vfill
\begin{center}
\begin{minipage}{0.75\linewidth}
\hrule width\linewidth height2pt depth0pt
\hrule width0pt height3pt depth0pt
\hrule width\linewidth height1pt depth0pt
\hrule width0pt height18pt depth0pt
\begin{center}
\Huge\bfseries XLOP v \fileversion\par\vskip18pt
User Manual
\end{center}
\hrule width0pt height6pt depth0pt
\hrule width\linewidth height1pt depth0pt
\hrule width0pt height3pt depth0pt
\hrule width\linewidth height2pt depth0pt
\end{minipage}
\end{center}
\vfill
\begin{center}
Jean-Côme Charpentier\\
\today
\end{center}
\vfill\null\par
\end{titlepage}
\newpage
\pagenumbering{roman}
\tableofcontents
\newpage
\pagenumbering{arabic}
\chapter{Overview}
\label{chap:Présentation}
The \package{xlop} package is intended to make automatic arithmetic
operation on arbitrary sized numbers and to display result either on
display mode or inline mode. Here is a first exemple for an overview
of the syntax:
\begin{SideBySideExample}
\opadd{45,05}{78,4}
\end{SideBySideExample}
We comment this first example in order to give an idea about how use
\package{xlop}.
Addition is displayed ``like in school'': this is the default
displaying. We have an alignment on dots (operand's dot and result's
dot), operator symbol is put on the left and it is vertically centered
between the operands, and the decimal separator is a dot even though we
have specified operands with comma. Finally, note that there is a
carry above the first operand.
Alignment on dot is obligatory. The other points above are deal with
options. Many macros accept an optional argument which controls some
aspects of displaying or computing operation. For that, we use a
``keyval-like'' syntax: we specify a sequence of parameter's
modifications through an affectation's comma separated sequence. One
affectation has one of the two possible syntax below:
\begin{verbatim}
<parameter>=<value>
<parameter>
\end{verbatim}
the second one is a shorthand for:
\begin{verbatim}
<parameter>=true
\end{verbatim}
In this affectation sequence, we can put space(s) after comma. But
don't put space around the equal sign nor before comma: if you put
space(s) here, that means that parameter name or value has a space.
So, if you want a comma as decimal separator , an operator symbol side
by side with the second operand, and no carry, you have just to say:
\begin{SideBySideExample}
\opadd[decimalsepsymbol={,},
voperator=bottom,
carryadd=false]{45.05}{78.4}
\end{SideBySideExample}
Note the trick which consists to put the comma between braces in the
decimal separator symbol definition. In fact, if you say:
\begin{Verbatim}[xrightmargin=0pt]
\opadd[decimalsepsymbol=,,voperator=bottom,
carryadd=false]{45.05}{78.4}
\end{Verbatim}
\package{xlop} drives mad! It don't understand what is this sort of
list!
Another important point, though it is less apparent, is that the
figures are put in very precise places. Each figure is put in a box of
fixed width and fixed height (user can change these values), decimal
separator is put in a null-width box (by default), and the lines have
a regular interspace (with or without horizontal rule). This allows
exact spacing and to place what we want where we want.
\begin{SideBySideExample}
\psset{xunit=\opcolumnwidth,
yunit=\oplineheight}
\opadd{45.05}{78.4}
\oplput(1.5,3){carry}
\psline{->}(1,3.15)(-3.25,3.15)
\end{SideBySideExample}
This example uses package
\package{pstricks}\index{pstricks@\package{pstricks}}
We have said that \package{xlop} package is able to deal with
arbitrary sized numbers. We come again about this subject and, for
now, we just give an example which shows what is possible. Don't look
at the code, some explanations will be given later in this manual, for
now just admire the result!
\begin{CenterExample}[xrightmargin=0pt]
\opdiv[style=text,period]{1}{49}
\end{CenterExample}
The package \package{xlop} provides some other features. It is
possible to manipulate numbers through variables. These variables can
be created with an assignation or as a computation result. You can
also manipulate the figures individually:
\begin{SideBySideExample}
\opadd*{45.05}{78.4}{r}%
The first figure after dot of
$45.05+78.4$ is
\opgetdecimaldigit{r}{1}{d}%
$\opprint{d}$.
\end{SideBySideExample}
you can make tests:
\begin{SideBySideExample}
\opadd*{45.05}{78.4}{r}%
The sum $45.05+78.4$ is
\opcmp{r}{100}%
\ifopgt greater than
\else\ifoplt less than
\else equal to
\fi\fi
$100$.
\end{SideBySideExample}
you can use some operations and some functions:
\begin{SideBySideExample}
gcd of $182$ and $442$ is
\opgcd{182}{442}{d}$\opprint{d}$
\end{SideBySideExample}
you can compute complex expression in infix form:
\begin{SideBySideExample}
\opexpr{(2+3^2)/(gcd(22,33))}{r}%
$$\frac{2+3^2}{\gcd(22,33)} =
\opprint{r}$$
\end{SideBySideExample}
\chapter{\package{xlop} Instructions}
Except some macros which will be examined later, the \package{xlop}'s
macros can have an optional argument between squared braces in order
to localy modify parameter's values. The other arguments (mandatory)
are (nearly) always numbers. The two sections of this chapter describe
in details what is a number for \package{xlop} and how use parameters.
\section{In the Beginning Was the Number}
\label{sec:Au début etait le nombre}
\subsection{Size}
\label{subsec:Taille}
Before we see the general syntax of number, we examin the very
particular \package{xlop} feature: the ability to deal with arbitrary
sized number.
\index{number!size}To be precise, the theoric maximum size of a number
is $2^{31}-1$ digits\index{number!limit}. In practice, this limit
can't be reached for two essential reasons. The first one is that a
multiplication with two numbers with $2^{25}$~digits needs more than
$7\,000$ years to be performed on the author computer! The second one
is more restrictive because it is linked to \TeX{} stack size limits.
Here is a table showing a \TeX{} compilation for a multiplication with
two operands of same size, on a linux computer, pentium~II~600 and
256~Mb RAM:\footnote{In fact it was the author computer in 2004. The
actual author computer is \emph{more} powerfull but the author is
lazy, and he have not remake the tests!}
\begin{center}
\begin{tabular}{|l|*{6}{c|}}
\hline
number of digits & 100 & 200 & 300 & 400 & 425 & 450 \\\hline
compilation time (s) & 2 & 8 & 18 & 32 & 36 & crash \\\hline
\end{tabular}
\end{center}
The ``crash'' in the table is due to an overstack for hash table.
\index{hash table}%
\index{overflow}%
On \LaTeX{}, the limit before crash will be reduced. These tests are
made on a minimal file. With a typical document, this limit will be
reduced too. The spool size is another limit quickly reached.
\index{spool size}%
To typeset this document which contain many calls to the
\package{xlop} macros, the author has grown up the spool size
to~$250000$ ($125\,000$ was insufficient) editing the line
\verb+pool_size+ in the \file{texmf.cnf} file. Also, the author has
grown up the hash table to~\texttt{1000} in the line
\verb+hash_extra+.
\subsection{Syntax}
\label{subsec:Syntaxe}
Now we present the syntax using the BNF grammar. There will be human
explanations later:
\begin{syntaxBNF}
\*number* & \{\*sign*\}\*positive* \alt \*name* \\
\*sign* & + \alt - \\
\*positive* & \*integer* \alt \*sep*\*integer* \alt \\
\sameline \*integer*\*sep* \alt \*integer*\*sep*\*integer* \\
\*sep* & . \alt , \\
\*integer* & \*digit*\{\*digit*\} \\
\*name* & \*start*\{character\} \\
\*start* & character \textnormal{except } \*sign*\textnormal{,}
\*sep* \\
\sameline \textnormal{, and } \*digit*
\end{syntaxBNF}
\index{syntax!BNF}\index{BNF grammar}
The \texttt{character} symbol means nearly any character accepted by
\TeX{}. The exceptions are characters \verb+%+ and \verb+#+ which are
completely prohibited. In fact, the use of active characters is
risked. For instance, on \LaTeX{}, the \verb+~+ definition prohibits the
use of it inside a variable name. In the other hand, the \verb+\ +is
always the escape char, that is, the variable name will be the name
\emph{after} all is expanded. There isn't any other restraint as the
following code show it:
\begin{SideBySideExample}
\newcommand\prefix{a/b}
\opadd*{2}{2}{a/b_{^c}!&$}
\opprint{\prefix_{^c}!&$}
\end{SideBySideExample}
\index{number!name}%
Note particullary that \verb+a/b_{^c}!&$+ and \verb+\prefix_{^c}!&$+
produce exactly the same name\ldots{} obviously if \verb+\prefix+ have
the right definition! This possibility to have a name using macro
could seem useless but it is not true. For instance, you can realize
loops\index{loop} with names as \verb+r1+, \verb+r2+, \ldots,
\verb+r<n>+ using the code \verb+r\the\cpt+ as variable name, where
\verb+cpt+ is a counter in the \TeX{} meaning. With \LaTeX{}, the code
is more verbose with \verb+r\number\value{cpt}+ where \verb+cpt+ is
now a \LaTeX{} counter. We will see an example using this syntax in
the section~\ref{sec:Creation d'operations complexes}
page~\pageref{sec:Creation d'operations complexes}.
\index{number!valid}In practice, what does it mean all these rules?
First, they means that a number writes in a decimal form can be
preceded by any sequence of plus or minus signs. Obviously, if there
is a odd number of minus signs, the number will be negative. Next, a
decimal number admits only one decimal separator symbol which can
be a dot or a comma, this one can be put anywhere in the
number. Finally, a number is write in basis~10. Be carefull: these
rules mean that \verb+-a+ is not valid.
The package uses some private names and it is safe to not begin a
variable name with the character \texttt{@}.
\section{\package{xlop} Parameters}
\label{sec:Parametres de xlop}
\index{parameter!syntax|(}
Parameter assignments are local to the macro when they are indicated
in the optional argument. To make global a parameter assignment, you
have to use the \macro{opset} macro. For example:
\begin{Verbatim}[xrightmargin=0pt]
\opset{decimalsepsymbol={,}}
\end{Verbatim}
give the comma as decimal separator symbol for the whole document, at
least, until another redefinition with \verb+\opset+.
\subsection{Symbols}
\label{subsecSymboles}
The \parameter{afterperiodsymbol} parameter indicates the symbol that
follows a quotient in line in a division with period
search\index{division!period}. Its default value is \verb+$\ldots$+
The \parameter{equalsymbol} parameter indicates the symbol used for
equality. Its default value is \verb+$=$+. In fact, this parameter is
defined with:
\begin{Verbatim}[xrightmargin=0pt]
\opset{equalsymbol={$=$}}
\end{Verbatim}
that is, with braces in order to protect the equal sign. Without
theses braces, there will be a compilation error. You have to process
like that when there is an equal sign or a comma in the
value.\index{parameter!with ``='' or ``,''\quad}
The parameter \parameter{approxsymbol} indicates the symbol used for
approximations. Its default value is \verb+$\approx$+.
The parameter \parameter{decimalsepsymbol} indicates the symbol used
for the decimal separator. Its default value is a dot.
Parameters \parameter{addsymbol}, \parameter{subsymbol},
\parameter{mulsymbol}, and \parameter{divsymbol} indicate the symbols
used for the four arithmetic operations. The default value are
\verb!$+$!, \verb!$-$!, \verb!$\times$! et \verb!$\div$! respectively.
\subsection{General Displaying}
\label{subsec:Presentation generale}
The \parameter{voperation} parameter indicates the way a dispayed
operation is put with respect to the baseline. The possible values are
\verb+top+, \verb+center+, and \verb+bottom+, the latter one is the
default value.
\begin{SideBySideExample}
top\quad
\opadd[voperation=top]{45}{172}\par
center\quad
\opadd[voperation=center]{45}{172}\par
bottom\quad
\opadd[voperation=bottom]{45}{172}
\end{SideBySideExample}
The \parameter{voperator} parameter indicates how the operator symbol
is put with repect to operands. The possible values are \verb+top+,
\verb+center+ (default value), and \verb+bottom+.
\begin{SideBySideExample}
top\quad
\opadd[voperator=top]{45}{172}\par
center\quad
\opadd[voperator=center]{45}{172}\par
bottom\quad
\opadd[voperator=bottom]{45}{172}
\end{SideBySideExample}
The \parameter{deletezero} parameter indicates if some numbers in
operation should be displayed with or whithout non-significant
zeros. Exact rôle of this parameter depends of the actual
operation. We will see that when we will study the different
operations.
The \parameter{style} parameter indicates the way an operation is
displayed: display with \verb+display+ value (default value) or inline
with \verb+text+ value. We will see when we will study division
because there is many possibilities with this operation.
\begin{SideBySideExample}
\opadd[style=text]{45}{172}
\end{SideBySideExample}
In inline operations, \package{xlop} takes care to not typeset the
formula in mathematic mode in a direct way. This allow to specify what
you want as in the next example, and it is also for that that you have
to specify the classical values of symbols between mathematic
delimiters.
\begin{SideBySideExample}
\opadd[addsymbol=plus,
equalsymbol=equal,
style=text]{42}{172}
\end{SideBySideExample}
Meanwhile, \package{xlop} introduces exactly the same penalities and
the same spaces as for a mathematic formula.
The \parameter{parenthesisnegative} parameter indicates how to typeset
negative numbers in inline operations. The possible values are:
\begin{itemize}
\item \texttt{none} which typesets negative numbers without
parenthesis;
\item \texttt{all} which typesets negative numbers with parenthesis;
\item \texttt{last} which typesets negative numbers with parenthesis
but the first one.
\end{itemize}
\begin{SideBySideExample}
\opadd[style=text,
parenthesisnegative=none]
{-12}{-23}\par
\opadd[style=text,
parenthesisnegative=all]
{-12}{-23}\par
\opadd[style=text,
parenthesisnegative=last]
{-12}{-23}
\end{SideBySideExample}
\subsection{Dimensions}
\label{subsec:Dimensions}
In displayed operations, figures are put in fixed size boxes. The
width is given by the \parameter{lineheight} parameter and the height
is given by the \parameter{lineheight} parameter. The default value of
\texttt{lineheight} is \verb+\baselineskip+ that is, interline space
in operation is the same (by default) as in the normal text. The
default value for \texttt{columnwidth} is \texttt{2ex} because the
``normal'' width of figures would give bad results.
\begin{SideBySideExample}
\opadd[columnwidth=0.5em]
{45.89}{127.5}
\end{SideBySideExample}
One reason for this bad result is that the decimal separator is put in
a box which width is controlled by the \parameter{decimalsepwidth}
parameter and the default value of this parameter is null. You can
improve this presentation giving a ``normal'' width to the dot.
\begin{SideBySideExample}
\opadd[columnwidth=0.5em,
decimalsepwidth=0.27778em]
{45.89}{127.5}
\end{SideBySideExample}
It is better but give a positive width to the box that contain the
decimal separator is risked. It will be more difficult to place
extern object and it is counter against the idea to have a fixed
grid. You should avoid this in normal time.
The \parameter{columnwidth} and \parameter{lineheight} parameters
correspond to the only dimensions that \package{xlop} provides as
public one, that is,
\verb+\opcolumnwidth+\index{opcolumnwidth@\texttt{$\backslash$opcolumnwidth}}
and
\verb+\oplineheight+\index{oplineheight@\texttt{$\backslash$oplineheight}}
respectively. It is dangerous to directly modify these dimensions
since a modification in a ``normal'' way doesn't only change the
dimension value. Package \package{xlop} make these dimensions public
only for reading, not for writting.
The two next parameters allow to specify width of horizontal and
vertical rules stroked by \package{xlop}. We have
\parameter{hrulewidth} and \parameter{vrulewidth} parameters. The
default values are both \texttt{0.4pt}.
These rules are typeset with no change on grid. That is, with no space
added. Therefore, with great values for thickness, the rules could
run over numbers.
\begin{SideBySideExample}
\opadd[hrulewidth=8pt]{42}{172}
\end{SideBySideExample}
There is also a paramater which allows to control the horizontal shift
of decimal separator. It is the \parameter{decimalsepoffset} paramater
with a default value of~\texttt{-0.35}. This value indicates a length
with the unit \verb+\opcolumnwidth+. We will see an example at
section~\ref{sec:Division} page~\pageref{sec:Division}.
\subsection{Figure's Styles}
\label{subsec:Styles des chiffres}
The \package{xlop} package provides five types of numbers and
associates five style paramaters:
\begin{itemize}
\item operands with \parameter{operandstyle};
\item result with \parameter{resultstyle};
\item remainders with \parameter{remainderstyle};
\item intermediary numbers with \parameter{intermediarystyle};
\item carries with \parameter{carrystyle}.
\end{itemize}
\begin{SideBySideExample}
\opadd[operandstyle=\blue,
resultstyle=\red,
carrystyle=\scriptsize\green]
{45.89}{127.5}
\end{SideBySideExample}
Keep in mind that, in this manual, we use
\package{pstricks}\index{pstricks} package.
\index{parameter!index|(}%
In fact, the management of these styles is even more powerfull since
you can distingish different number of a same class. In one operation,
you have several operands, and, possibly several remainders and
several intermediary numbers. You can access to the style of these
numbers adding an index to the matching style.
\begin{SideBySideExample}
\opadd[operandstyle=\blue,
operandstyle.1=\lightgray,
resultstyle=\red,
carrystyle=\scriptsize\green]
{45.89}{127.5}
\end{SideBySideExample}
In this example, we indicate that the first operand must be typesetted
with the \verb+\lightgray+ style. We don't indicate anything for the
second operand, so it takes the basic style for its class. (Then with
\verb+\blue+ style.)
This mechanism is even more powerfull since you can write two level
index for operands, carries, and intermediary numbers (one level for
result and carry) in order to access to each style figure of these
numbers. To simplify index, a positive index indicates the rank of a
figure in the integer part (right to left order, index~1 is for the
unit figure) and a negative index indicates the rank of a figure in
the decimal part (left to right order, $-1$ is for the tenth figure).
\begin{SideBySideExample}
\opadd[operandstyle.1.1=\white,
operandstyle.1.-2=\white,
operandstyle.2.3=\white,
resultstyle.2=\white,
deletezero=false]
{045.89}{127.50}
\end{SideBySideExample}
You can also use a macro with one parameter as a style.
\begin{SideBySideExample}
\newcommand\hole[1]{$\bullet$}
\opadd[operandstyle.1.1=\hole,
operandstyle.1.-2=\hole,
operandstyle.2.3=\hole,
resultstyle.2=\hole]
{45.89}{127.5}
\end{SideBySideExample}
\index{operation!with hole}%
When the style is a macro with argument, this one is the figure. Here
is a more complicated example using \package{pst-node} package of the
\package{pstricks} bundle:
\begin{SideBySideExample}
\newcommand\OPoval[3]{%
\dimen1=#2\opcolumnwidth
\ovalnode{#1}
{\kern\dimen1 #3\kern\dimen1}}
\opadd[voperation=top,
operandstyle.1.1=\OPoval{A}{0},
operandstyle.2.2=\OPoval{C}{0.8}]
{45}{172}\qquad
\begin{minipage}[t]{2cm}
\pnode(0,0.2em){B}\ figure
\ncarc{->}{A}{B}\par
\pnode(0,0.2em){D}\ number
\ncarc{<-}{D}{C}
\end{minipage}
\end{SideBySideExample}
As for figures, the decimal separator take account to number style. To
access individually to the decimal separator style, you have to use
\texttt{d} index, numeric indexes are for figures.
\begin{SideBySideExample}
\newcommand\hole[1]{\texttt{\_}}
\opmul[intermediarystyle=\hole,
resultstyle=\hole,
resultstyle.d=\white]{2.46}{35.7}
\end{SideBySideExample}
\index{parameter!index|)}%
\index{parameter!syntax|)}
\chapter{Arithmetic Operations}
\label{chap:Opérations arithmétiques}
\section{Addition}
\label{sec:Addition}
Addition is deal by the \macro{opadd} macro. When it is in display
mode, it display only nonnegative numbers. Then, it displays a
substraction when one of the operands is nonpositive.%
\index{number!nonpositive in displayed operation}
\begin{SideBySideExample}
\opadd{-245}{72}
\end{SideBySideExample}
In a general manner, the principle is to display the operation that
allows to find the result as you make it ``by hand''. On the contrary,
the inline mode shows always an addition since we can now write
nonpositive numbers.
\begin{SideBySideExample}
\opadd[style=text]{-245}{72}
\end{SideBySideExample}
In addition to the general parameters discussed in the
section~\ref{sec:Parametres de xlop}, the macro \verb+\opadd+ uses
parameters \texttt{carryadd}, \texttt{lastcarry}, and
\texttt{deletezero}.
The \parameter{carryadd} parameter is a boolean
parameter\index{parameter!boolean}, that is, it accepts only the
values \texttt{true} and \texttt{false}. By habit, when you don't
specify the value and the equal sign, that is like assignment
\texttt{=true}. This parameter indicates if the carries must be showed
or not. Its default value is \texttt{true}.
The \parameter{lastcarry} parameter is also a boolean parameter. It
indicates if a carry without matching digit for the two operands must
be showed or not. Its default value is \texttt{false}. Take care to
the exact rôle of this parameter. For instance, if the second operand
in the following example is~15307, the last carry would be showed for
any value of the \texttt{lastcarry} parameter since there is a
matching digit in the second operand.
\begin{SideBySideExample}
\opadd{4825}{5307}
\end{SideBySideExample}
\begin{SideBySideExample}
\opadd[carryadd=false]{4825}{5307}
\end{SideBySideExample}
\begin{SideBySideExample}
\opadd[lastcarry]{4825}{5307}
\end{SideBySideExample}
The \parameter{deletezero} parameter is also a boolean parameter. It
indicates if non-significant zeros must be deleted or not. Its default
value is \texttt{true}. When this parameter is \texttt{false}, the
operands and the result have the same number of digits. For that,
\package{xlop} package adds non-significant zeros. Also, the
non-significant zeros of operands are not removed.
\begin{SideBySideExample}
\opadd{012.3427}{5.2773}\par
\opadd[deletezero=false]
{012.3427}{5.2773}
\end{SideBySideExample}
This parameter has exactly the same rôle for inline mode than for
displayed mode.
\begin{SideBySideExample}
\opadd[style=text]{02.8}{1.2}\par
\opadd[style=text,
deletezero=false]{02.8}{1.2}\par
\end{SideBySideExample}
\section{Substraction}
\label{sec:soustraction}
Substraction is made by \macro{opsub} macro. In displayed mode, the
substraction shows only nonnegative numbers. For that, it shows an
addition when one operand is nonpositive.
\begin{SideBySideExample}
\opsub{-245}{72}
\end{SideBySideExample}
In a general way, the principle is to display the operation which
allow to find the result as you make it ``by hand''. On the contrary,
inline mode shows always a substraction since you can now write
nonpositive numbers.
\begin{SideBySideExample}
\opsub[style=text]{-245}{72}
\end{SideBySideExample}
This principle apply also when the first operand is less than the
second one (positive case). In this case, we have an operand
inversion.
\begin{SideBySideExample}
\opsub{1.2}{2.45}
\end{SideBySideExample}
Of course, inline operation gives an exact result.
\begin{SideBySideExample}
\opsub[style=text]{1.2}{2.45}
\end{SideBySideExample}
In addition to general parameters we have seen at
section~\ref{sec:Parametres de xlop}, \verb+\opsub+ takes account of
\texttt{carrysub}, \texttt{lastcarry}, \texttt{offsetcarry},
\texttt{deletezero}, and \texttt{behaviorsub} parameters.
The \parameter{carrysub} parameter is a boolean one which indicates if
carries must be present or not. Its default value is \texttt{false}.
(Remember that the default value of \texttt{carryadd} parameter is
\texttt{true}.)
\begin{SideBySideExample}
\opsub[carrysub]{1234}{567}
\end{SideBySideExample}
In the last example, you can see that there is no carry above the last
digit of 1234. This is quite common (at least in France). If you want
display this last carry, you have to use the \parameter{lastcarry}
parameter. This parameter does not have the same behavior in
substraction and in addition since here, the last carry is not
displayed when the second operand does not have correspondent
digit. (For addition, last carry is not displayed when \emph{all} the
operands do not have correspondent digit.)
\begin{SideBySideExample}
\opsub[carrysub,lastcarry]{1234}{567}
\end{SideBySideExample}
Note that, in this case, it is better to set the
\parameter{deletezero} parameter to \texttt{false} in order to have a
nicer result.
\begin{SideBySideExample}
\opsub[carrysub,
lastcarry,
deletezero=false]{1234}{567}
\end{SideBySideExample}
Perhaps it seems to you that showing carries for substraction is a bit
more dense. You can enlarge the figure box with the
\parameter{opcolumnwidth} parameter. You can also indicate the carry
horizontal shift using the \parameter{offsetcarry} parameter. Its
default value is \texttt{-0.35}.
\begin{SideBySideExample}
\opsub[carrysub,
lastcarry,
deletezero=false]{12.34}{5.67}
\bigskip
\opsub[carrysub,
lastcarry,
columnwidth=2.5ex,
offsetcarry=-0.4,
decimalsepoffset=-3pt,
deletezero=false]{12.34}{5.67}
\end{SideBySideExample}
It is possible that a substraction with two positive numbers and with
the first one less than the second one signs an user error. In this
case, and only in this case, the \parameter{behaviorsub} parameter
allows a call to order. The three possible values are:
\begin{itemize}
\item \texttt{silent} which is the default value and which gives the
result;
\item \texttt{warning} which gives also the result but shows the
warning message:
\begin{Verbatim}[xrightmargin=0pt,frame=none]
xlop warning. Substraction with first operand less than second one
See documentation for further information.
\end{Verbatim}
\item \texttt{error} which shows the error message:
\begin{Verbatim}[xrightmargin=0pt,frame=none]
xlop error. See documentation for further information.
Type H <return> for immediate help.
! Substraction with first operand less than second one.
\end{Verbatim}
and the operation is not performed.
\end{itemize}
\section{Multiplication}
\label{sec:Multiplication}
The multiplication is under the control of the \macro{opmul} macro.
The parameters we will see below are \texttt{hfactor},
\texttt{displayintermediary}, \texttt{shiftintermediarysymbol}, and
\texttt{deletezero}. We studied the other parameters in
section~\ref{sec:Parametres de xlop}.
The \parameter{shiftintermediarysymbol} parameter indicates what is
the symbol used for showing the shifting of intermediary numbers
(default value is \verb+$\cdot$+). The
\parameter{displayshiftintermediary} parameter can take value
\texttt{shift} (default value) which shows this symbol only for
shifting greater than one level, value \texttt{all} which shows this
symbol for all the shiftings, and the value \texttt{none} which means
that this symbol will be never showed.
\begin{CenterExample}[xrightmargin=0pt]
\opmul[displayshiftintermediary=shift]{453}{1001205}\qquad
\opmul[displayshiftintermediary=all]{453}{1001205}\qquad
\opmul[displayshiftintermediary=none]{453}{1001205}
\end{CenterExample}
In fact, null intermediary numbers are not display because of the
default value \texttt{none} of the \parameter{displayintermediary}
parameter. The value \texttt{all} shows all the intermediary numbers,
even null intermediary numbers.
\begin{SideBySideExample}
\opmul[displayintermediary=all]
{453}{1001205}
\end{SideBySideExample}
Note that null intermediary numbers are displayed with the same width
than the first factor width.
The \parameter{displayintermediary} parameter accepts the value
\texttt{nonzero} which means the same than the \texttt{none} value
except when second factor has only one digit.
\begin{CenterExample}[xrightmargin=0pt]
\opmul{3.14159}{4}\qquad
\opmul[displayintermediary=nonzero]{3.14159}{4}
\end{CenterExample}
The \parameter{hfactor} parameter indicates how align operands. The
default value, \texttt{right}, gives a raggedleft alignment. The
\texttt{decimal} value gives an alignment on dot.
\begin{CenterExample}[xrightmargin=0pt]
\opmul{3.1416}{12.8}\qquad\opmul[hfactor=decimal]{3.1416}{12.8}
\end{CenterExample}
For displayed multiplication, the \parameter{deletezero} parameter is
only for operands. The result keeps its non-significant zeros since
there are necessary in order to make a correct dot shifting when we
work ``by hand''.
\begin{CenterExample}[xrightmargin=0pt]
\opmul[deletezero=false]{01.44}{25}\qquad
\opmul{01.44}{25}
\end{CenterExample}
In the other hand, this parameter has its usual behaviour in inline
multiplication.
\begin{CenterExample}[xrightmargin=0pt]
\opmul[deletezero=false,style=text]{01.44}{25}\qquad
\opmul[style=text]{01.44}{25}
\end{CenterExample}
\section{Division}
\label{sec:Division}
The \package{xlop} package deals with ``normal'' division via
\macro{opdiv} macro and with euclidean division via \macro{opidiv}
macro. Division is a very complex operation so it is not strange that
there are many parameters to control it.
Pay attention that the \package{xlop} package v. 0.23 is unable to
deal with ``english'' division. In this package version, the division
is the ``french'' one, which is more or less used as it in some other
countries. The \package{xlop} package v. 0.3 will allow ``enlish''
division (and many more feautures).
\subsection{End Control}
\label{subsec:Controle de l'arret}
In the following text, term \emph{step} means the set of process which
allow to get one digit for the quotient. This number of steps is (not
only) under the control of \parameter{maxdivstep},
\parameter{safedivstep}, and \parameter{period} parameters. It is only
partially true because a classical division will stop automatically
when a remainder will be zero, whatever the values of these three
parameters and a euclidean division will stop with an integer quotient
without attention for these three parameters.
\begin{SideBySideExample}
\opdiv{25}{7}
\end{SideBySideExample}
\begin{SideBySideExample}
\opidiv{25}{7}
\end{SideBySideExample}
The first example stops because of the value of \parameter{maxdivstep}
which is 10 by default. Pay attention that the maximum step number
could cause strange result when it is too small.
\begin{SideBySideExample}
\opdiv[maxdivstep=2]{1248}{3}
\end{SideBySideExample}
Clearly, the last result is false. In the other hand, \package{xlop}
package did what we have ask, that is, obtain two digits (maximum) for
the quotient.
The inline mode differ with zero remainder or not and with the type of
division (classical or euclidean).
\begin{SideBySideExample}
\opdiv[style=text]{3.14}{2}\par
\opdiv[style=text]{3.14}{3}\par
\opidiv[style=text]{314}{2}\par
\opidiv[style=text]{314}{3}
\end{SideBySideExample}
Note the use of \parameter{equalsymbol} or \parameter{approxsymbol}
parameter according to the case. Note also that \package{xlop}
displays results with floor, not with round. We will see how obtain a
round in section~\ref{sec:Operations evoluees}.
For inline mode of \verb+\opdiv+, \package{xlop} take account of
\parameter{maxdivstep}. It means that we can obtain results very false
with too small values of this parametrer and, unlike with display mode
division, inline mode don't allow to understand what is wrong.
\begin{SideBySideExample}
\opdiv[maxdivstep=2,style=text]
{1248}{3}
\end{SideBySideExample}
In addition, if the last remainder is zero, we obtain a must:
\begin{SideBySideExample}
\opdiv[maxdivstep=1,style=text]
{1208}{3}
\end{SideBySideExample}
because there is no approximation at all!
A classical division can stop with period detection. For that, you
have just to give the value \texttt{true} for the \parameter{period}
parameter\index{division!period}.
\begin{SideBySideExample}
\opdiv[period]{100}{3}
\end{SideBySideExample}
To avoid comparizons between each remainder with all previous
remainder, \package{xlop} calculates immediatly the period
length. That allows to process only one comparizon for each step, then
to have a much more efficient process.\footnote{Thanks to Olivier
Viennet about mathematic precisions that allows to implement these
calculations.} Unfortunately, these calculations are made with
numbers that are directly accesible to \TeX{}. As consequence, you
can't use operand with absolute value greater than
$\left\lfloor\frac{2^{31}-1}{10}\right\rfloor = 214748364$.
In order to avoid too long calculations, \package{xlop} don't process
beyond the value of \parameter{safedivstep} parameter in division with
period. Its default value is~50. However, \package{xlop} package show
this problem. For example, if you ask for such a division with the
code:
\begin{Verbatim}[xrightmargin=0pt,frame=none]
\opdiv[period]{1}{289}
\end{Verbatim}
you obtain the warning message:
\begin{Verbatim}[xrightmargin=0pt,frame=none]
xlop warning. Period of division is too big (272 > safedivstep).
Division will stop before reach it.
See documentation for further information.
\end{Verbatim}
which indicates that this division period is~272 and that it can be
achieved because of the \texttt{safedivstep} value.
The inline mode for division with period have some particularities.
\begin{SideBySideExample}
\opdiv[period,style=text]{150}{7}
\end{SideBySideExample}
We obtain an equality rather than an approximation, there is a rule
under the period, and there is ellipsis after the period. All these
components can be configured. The equality symbol is given
by the \parameter{equalsymbol} parameter (default value is
\verb+{$=$}+). The rule thickness is given by
the \parameter{hrulewidth} parameter (default value is
\texttt{0.4pt}). The vertical offset of this rule is given
by \parameter{vruleperiod} parameter (default value is \texttt{-0.2})
which indicates a vertical offset taking \verb+\oplineheight+ as
unit. The ellipsis are given by the
parameter \parameter{afterperiodsymbol} (default value
\verb+$\ldots$+).
\begin{SideBySideExample}
\opdiv[period,style=text,
equalsymbol=$\approx$,
hrulewidth=0.2pt,
vruleperiod=0.7,
afterperiodsymbol=]
{150}{7}
\end{SideBySideExample}
\subsection{Other Features}
\label{subsec:Elements supplementaires}
Displayed divisions can include successive substractions which allow
remainder calculations. For \package{xlop}, the numbers which are
substracted are intermediary numbers, so the different ways to
represent substractions use \parameter{displayintermediary} parameter
see for multiplication. The default value, valeur \texttt{none}, don't
display any substraction; the value \texttt{all} displays all the
substractions, and the value \texttt{nonzero} displays substractions
with non-zero numbers
\begin{CenterExample}[xrightmargin=0pt]
\opdiv[displayintermediary=none,voperation=top]
{251}{25}\quad
\opdiv[displayintermediary=nonzero,voperation=top]
{251}{25}\quad
\opdiv[displayintermediary=all,voperation=top]
{251}{25}
\end{CenterExample}
When we write a display division, we can draw a ``bridge'' over the
part of dividend which is taken in count for the first step of
calculation. The \package{xlop} package allow to draw this symbol
thanks to the boolean parameter \parameter{dividendbridge} (default
value is \texttt{false}).
\begin{SideBySideExample}
\opdiv[dividendbridge]{1254}{30}
\end{SideBySideExample}
\subsection{Non Integer Numbers and Negative Numbers}
\label{subsec:Nombres non entiers et negatifs}
The \parameter{shiftdecimalsep} parameter governs non integer operands
aspect/ Its default value is \texttt{both} which indicates that
decimal separator is shifted in order to obtain integer divisor and
integer dividend. The value \texttt{divisor} indicates that there is
the shifting that allows an integer divisor. The value \texttt{none}
indicates that there isn't any shifting.
\begin{CenterExample}[xrightmargin=0pt]
\opdiv[shiftdecimalsep=both]{3.456}{25.6}\quad
\opdiv[shiftdecimalsep=divisor]{3.456}{25.6}\quad
\opdiv[shiftdecimalsep=none]{3.456}{25.6}
\end{CenterExample}
Parameter \parameter{strikedecimalsepsymbol} gives the symbol used
to show the old place of decimal separator when this one is
shifted. The default value is empty, that is, there isn't any
symbol. This explain why you don't see anything on previous examples.
\begin{CenterExample}[xrightmargin=0pt]
\opset{strikedecimalsepsymbol={\rlap{,}\rule[-1pt]{3pt}{0.4pt}}}
\opdiv[shiftdecimalsep=both]{3.456}{25.6}\quad
\opdiv[shiftdecimalsep=divisor]{3.456}{25.6}\quad
\opdiv[shiftdecimalsep=none]{3.456}{25.6}
\end{CenterExample}
When there is a non empty symbol for the striked decimal separator, it
is possible to have non-significant zeros in operands.
\begin{SideBySideExample}
\opdiv[shiftdecimalsep=divisor,
strikedecimalsepsymbol=%
\hspace{-3pt}\tiny$\times$]
{0.03456}{2.56}
\end{SideBySideExample}
We have already seen that \macro{opidiv} macro gives integer
quotient. This is true even with non integer operands. It is somewhere
strange to perform an euclidian division with non integer operands. The
\macro{opidiv} macro will be strict about the
presentation. Parameters \parameter{maxdivstep}, \parameter{safedivstep},
and \parameter{period} haven't any effect, as
for \parameter{shiftdecimalsep} parameter since operands are changed
to integer ones.
\begin{SideBySideExample}
\opidiv[strikedecimalsepsymbol=%
\hspace{-3pt}\tiny$\times$]
{34.57}{7}
\end{SideBySideExample}
When operands are negative, the inline \macro{opidiv} numbers is
different from the displayed \macro{opidiv} ones. Remainder will be
between zero (include) and absolute value of divisor (exclude).
\begin{SideBySideExample}
\opdiv[style=text]{124}{7}\par
\opidiv[style=text]{124}{7}\par
\opidiv[style=text]{124}{-7}\par
\opidiv[style=text]{-124}{7}\par
\opidiv[style=text]{-124}{-7}
\end{SideBySideExample}
This condition for remainder is valid even with non integer divisor.
\begin{SideBySideExample}
\opidiv[style=text]{1.24}{0.7}\par
\opidiv[style=text]{1.24}{-0.7}\par
\opidiv[style=text]{-1.24}{0.7}\par
\opidiv[style=text]{-1.24}{-0.7}
\end{SideBySideExample}
\chapter{Other Commands}
\label{chap:Autres commandes}
\section{Starred Macros}
\label{sec:Macros etoilees}
The five macros seen in previous chapter have a starred version. These
starred macros perform the calculation and don't display
anything. Result is record in a variable given as argument.
Since these commands don't display anything, parameters don't make
sens and aren't allowed for \macro{opadd*}, \macro{opsub*},
\macro{opmul*}, and \macro{opidiv*}. In the other hand,
parameters \parameter{maxdivestep}, \parameter{safedivstep},
and \parameter{period} influence calculations, then \macro{opdiv*}
macro accepts an optional argument to take account of them.
\begin{SideBySideExample}
\opmul*{2}{2}{a}%
\opmul*{a}{a}{a}\opmul*{a}{a}{a}%
\opadd[style=text]{a}{1}
\end{SideBySideExample}
For macros \macro{opdiv} and \macro{opidiv}, there are two extra
arguments to record quotient and final remainder.
\begin{SideBySideExample}
\opdiv*[maxdivstep=1]{-88}{16}{q}{r}%
\opmul*{q}{16}{bq}%
\opmul[style=text]{16}{q}\par
\opadd[style=text]{bq}{r}
\end{SideBySideExample}
\section{Input-Output}
\label{sec:Entree-sorties}
The \macro{opcopy} macro copies its first argument into its second
one. Then, the first argument is a number write in decimal form or
\emph{via} a variable, whereas the second one is a variable name.
The \macro{opprint} macro displays its argument. The following example
uses the counter \macro{time} which indicates numbers of minutes since
midnight.
\begin{SideBySideExample}
\opidiv*{\the\time}{60}{h}{m}%
It is \opprint{h}~hours
\opprint{m}~minutes
\end{SideBySideExample}
We will see at section~\ref{sec:Comparaisons} how to improve this
example with tests.
The \macro{opdisplay} macro also displays a number but here, each
figure is in a box. The width of this box is given
by \parameter{columnwidth} and the height of this box is given
by \parameter{lineheight}. Style is specified by the first
argument. This macro accepts an optional argument in order to give a
specific style for individual figures.
\begin{SideBySideExample}
\opdisplay[resultstyle.1=\bfseries,
resultstyle.-2=\bfseries]
{resultstyle}{129.192}
\end{SideBySideExample}
Macros \macro{oplput} and \macro{oprput} allow to put anything
anywhere. The syntax of both of them is different from the other ones
of \package{xlop} since the place is indicated with coordinates
between parenthesis. The coordinates use \macro{opcolumnwidth} and
\macro{oplineheight} as units. Then user is able to build his own
``operations''.
\begin{SideBySideExample}
\psset{xunit=\opcolumnwidth,
yunit=\oplineheight}%
\psgrid[subgriddiv=1,gridlabels=7pt,
griddots=5](0,1)(10,-2)
\oplput(2,0){Hello}
\oprput(8,-1){world!}
$\bullet$
\end{SideBySideExample}
On example above, note that these macros don't move the reference
point. As a precaution, they kill the trailing space and then, there
is no need to protect the end of line with a \verb+%+.
Macros \macro{ophline} and \macro{opvline} complete the previous ones
to give all the tools the user needs to build its own operations.
\macro{ophline} allows to draw a horizontal rule; its length is given
by the parameter after coordinates. \macro{opvline} does the same for
vertical rules. Remember that parameters \parameter{hrulewidth}
and \parameter{vrulewidth} indicate the thickness of these rules.
\begin{CenterExample}[xrightmargin=0pt]
\par\vspace{2\oplineheight}
\oplput(1,2){O}\oplput(2,2){N}\oplput(3,2){E}
\oplput(0,1.5){$+$}
\oplput(1,1){O}\oplput(2,1){N}\oplput(3,1){E}
\ophline(0,0.8){4}
\oplput(1,0){T}\oplput(2,0){W}\oplput(3,0){O}
\end{CenterExample}
Macro \macro{opexport}\refstepcounter{stuff}\label{macro-opexport}
allow to export a number in a macro. It's an extra to version~0.23
which is very usefull to exchange datas between \package{xlop} and the
outside world. The first argument is a number in the \package{xlop}
sense, that is, either a number write with figures, or a variable
name. The number is translated in a form directly acceptable for
\TeX{} and hold in the second argument which should be a macro
name. However, note that decimal separator will be the one specified
by \parameter{decimalsepsymbol} (without its possible braces).
\begin{SideBySideExample}
\opmul*{5}{3.141592654}{F}
\opexport{F}{\fivepi}
\texttt{\meaning\fivepi}
\end{SideBySideExample}
We can use this macro to typeset numbers calculated by \package{xlop}
in an array with a decimal alignment, or to initialize a counter or a
length (don't forget the unit in the last case).
\section{Figures of Numbers}
\label{sec:Chiffres d'un nombre}
Macros \macro{opwidth}, \macro{opintegerwidth}, and
\macro{opdecimalwidth} indicate number of digits of the whole number,
of its integer part, of its decimal part respectively. The first
argument is the examined number and the second one indicates the
variable where result will be record.
\begin{SideBySideExample}
\opcopy{123456.1234}{a}%
\opwidth{a}{na}%
\opintegerwidth{a}{ia}%
\opdecimalwidth{a}{da}%
\opprint{a} is written with
\opprint{na} figures (\opprint{ia} in
the integer part and \opprint{da} in
the decimal part).
\end{SideBySideExample}
Macro \macro{opunzero} delete all the non-significant
zeros\index{non-significant zero} of the number passed as argument.
\begin{SideBySideExample}
\opcopy{00150.00250}{a}%
Before : \opprint{a}\par
\opunzero{a}%
After : \opprint{a}
\end{SideBySideExample}
Macros \macro{integer} and \macro{opdecimal} give the integer part and
the decimal part of a number respectively.
\index{number!integer part}\index{integer part}%
\index{number!decimal part}\index{decimal part}%
First argument is the number to process, and the second one is the
variable name which hold the result.
\begin{SideBySideExample}
\opcopy{-37.69911}{a}%
\opinteger{a}{ia}%
\opdecimal{a}{da}%
Integer part: \opprint{ia}\par
Decimal part: \opprint{da}
\end{SideBySideExample}
Six macros allow to write or read a figure of a number. You can read
or read a figure according to its place in the whole number, or in the
integer part, or in the decimal part. Figures for whole number and for
decimal part are numbered from right to left, figures for integer part
are numbered from left to right. For instance, with the number
1234.56789, the second figure is 8, the second figure of the integer
part is 3, and the second figure of the decimal part is 6. It is now
easy to guess the rôle of the six next macros:
\begin{itemize}
\item \parameter{opgetdigit} ;
\item \parameter{opsetdigit} ;
\item \parameter{opgetintegerdigit} ;
\item \parameter{opsetintegerdigit} ;
\item \parameter{opgetdecimaldigit} ;
\item \parameter{opsetdecimaldigit} ;
\end{itemize}
Syntax is the same for these macros. The first argument is the
processed number (reading or writting), the second one is the index of
te figure, and the third one is the variable name which hold the
result (figure read or changed number). If index is out of the range,
the reading macros give \texttt{0} as result and writing macros
extend the number in order to reach this index (for that, zero will be
created in new slots).
\section{Comparisons}
\label{sec:Comparaisons}
When you want complex macros, often you need to realize tests. For
that, \package{xlop} gives the macro \macro{opcmp}. The two
arguments are numbers and this macro setup the tests \macro{ifopgt},
\macro{ifopge}, \macro{ifople}, \macro{ifoplt}, \macro{ifopeq}, and
\macro{ifopneq} to indicate that first operand is greater, greater or
equal, less or equal, less, equal, or different to the second operand
respectively.
For technical reasons, \package{xlop} give global definitions for the
six tests above. Then, they are not protected by groups. Since these
tests are used by many \package{xlop} macros, you must \emph{always}
use tests \verb+\ifop...+ immediately after \macro{opcmp}, or, at
least, before any use of a \package{xlop} macro. Otherwise, there will
be bugs hard to fix!
Let's resume the hour display macro see at
section~\ref{sec:Entree-sorties}. But now, we check if argument is
between 0 (include) and 1440 (exclude), then we process tests in order
to know if ``hour'' is plural or not, as for ``minute''.
\begin{CenterExample}[xrightmargin=0pt]
\newcommand\hour[1]{%
\opcmp{#1}{0}\ifopge
\opcmp{#1}{1440}\ifoplt
\opidiv*{#1}{60}{h}{m}%
\opprint{h} hour%
\opcmp{h}{1}\ifopgt
s%
\fi
\opcmp{m}{0}\ifopneq
\space\opprint{m} minute%
\opcmp{m}{1}\ifopgt
s%
\fi
\fi
\fi\fi
}
\hour{60} -- \hour{1080} -- \hour{1081} -- \hour{1082}
\end{CenterExample}
\section{Advanced Operations}
\label{sec:Operations evoluees}
The macros left to be examined are either internal macros and which it
will be a shame to keep private , or macro asked for users.
Internal macros are \macro{opgcd}\index{gcd} which gives gcd of two
numbers and macro \macro{opdivperiod}\index{division!period} which
gives the period length of quotient of two numbers. For efficiency
reason, these macros don't use \package{xlop} number, they rather use
numbers directly understand by \TeX{}. There are two consequences: the
numbers can't be greater than \texttt{2147483647} for \macro{opgcd};
it can't be greater than \texttt{214748364} for
\macro{opdivperiod}. A warning is displayed for an overflow. Result is
put in the third parameter.
There is also some checks on the two first parameters: a gcd mustn't
have null argument; length of period can't be processed with null
quotient. Futhermore, if an argument is a non integer number, only the
integer part will be take account.
\begin{SideBySideExample}
\opcopy{5376}{a}%
\opcopy{2304}{b}%
\opgcd{a}{b}{gcd(ab)}%
$\gcd(\opprint{a},\opprint{b}) =
\opprint{gcd(ab)}$
\end{SideBySideExample}
You can play and find long period of divisions. Without going into
mathematical details, square of prime numbers are good choices. For
instance with $257^2=66049$ you obtain:
\begin{SideBySideExample}
\opdivperiod{1}{66049}{p}%
$\frac{1}{66049}$ have a period
of length $\opprint{p}$.
\end{SideBySideExample}
With macros \macro{opcastingoutnines}\index{casting out of nines} and
\macro{opcastingoutelevens}\index{casting out of elevens} you can
build casting out of nines and casting out of elevens. \package{xlop}
don't typeset directly these ``operations'' since they need diagonal
rules, and then, need some particular packages. In fact, macro
\macro{opcastingoutnines} calculates the sum modulo~9 of first
argument digits and put the result in second argument. Macro
\macro{opcastingoutelevens} calculates the sum modulo~11 of the even
rank digits of first argument, calculates the sum moldulo~11 of the
odd rank digits of first argument, and calculates the difference of
these two sums.
\begin{SideBySideExample}
\newcommand\castingoutnines[3]{%
\opcastingoutnines{#1}{cna}%
\opcastingoutnines{#2}{cnb}%
\opmul*{cna}{cnb}{cna*cnb}
\opcastingoutnines{cna*cnb}{cna*cnb}%
\opcastingoutnines{#3}{cn(a*b)}%
\begin{pspicture}(-3.5ex,-3.5ex)%
(3.5ex,3.5ex)
\psline(-3.5ex,-3.5ex)(3.5ex,3.5ex)
\psline(-3.5ex,3.5ex)(3.5ex,-3.5ex)
\rput(-2.75ex,0){\opprint{cna}}
\rput(2.75ex,0){\opprint{cnb}}
\rput(0,2.75ex){\opprint{cna*cnb}}
\rput(0,-2.75ex){\opprint{cn(a*b)}}
\end{pspicture}
}
\castingoutnines{157}{317}{49669}
\end{SideBySideExample}
In passing, this example shows that $157\times317\neq49669$! The right
operation is \opmul[style=text]{157}{317}.
The two next macros are very simple. We have \macro{opneg} which
calculates the opposite of its first argument and store it in the
variable indicated by the second argument. We have also \macro{opabs}
which does the same with absolute value.
Macro \macro{oppower} calculates integer powers of numbers. This macro
has three parameters. The third one store the first argument to the
power of the second argument. When the first argument is zero: if the
second argument is zero, result is~1; if the second argument is
positive, result is~0; if the second argument is negative, there is an
error. There isn't any limitation on first parameter. This leads to
some problems, for instance:
\begin{CenterExample}[xrightmargin=0pt]
\opcopy{0.8}{a}\opcopy{-17}{n}%
\oppower{a}{n}{r}%
$\opprint{a}^{\opprint{n}} = \opprint{r}$
\end{CenterExample}
With $0.7$ rather than $0.8$, problem is worse:
\begin{CenterExample}[xrightmargin=0pt]
\opcopy{0.7}{a}\opcopy{-8}{n}%
\oppower{a}{n}{r}%
\opdecimalwidth{r}{dr}
$\opprint{a}^{\opprint{n}}$ has \opprint{dr}
figures after dot.
\end{CenterExample}
In fact, when exponent is negative, \emph{first} \package{xlop}
calulates inverse of the number and \emph{after that}, it calculates
the power with opposite of the exponent. In this example, if we had
left $-17$ rather than $-8$, then there will be a capacity overflow
capacity of \TeX{}.
Three macros allow a control about precision. They allow to
approximate a number giving the rank of the approximation. There are
\macro{opfloor}, \macro{opceil}, and \macro{opround}. They need three
parameters which are (in order): start number, rank of approximation,
variable name to store the result.
Rank is an integer value giving number of digits after decimal
separator which must be present. If this rank is negative,
approximation will be done before the decimal separator. If rank
is positive and indicates more digits than decimal part has, then
zeros will be added. If rank is negative and indicates more digits
than integer part has, then approximation will be locked in order to
give the first digit of the number at least.
Here is a summary table which allow to understand how these macros
work.
\begin{center}
\opcopy{3838.3838}{a}
\begin{tabular}{|r|l|l|l|}
\hline
\multicolumn{4}{|c|}{\textbf{\texttt{\textbackslash
op\ldots{}\{3838.3838\}\{n\}\{r\}}}}\\\hline
\multicolumn{1}{|c|}{\textbf{\texttt{n}}} &
\multicolumn{1}{c|}{\textbf{\texttt{floor}}} &
\multicolumn{1}{c|}{\textbf{\texttt{ceil}}} &
\multicolumn{1}{c|}{\textbf{\texttt{round}}} \\\hline
\opcopy{6}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{4}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{3}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{0}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-1}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-2}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-6}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\\hline
\end{tabular}
\opcopy{-3838.3838}{a}
\begin{tabular}{|r|l|l|l|}
\hline
\multicolumn{4}{|c|}{\textbf{\texttt{\textbackslash
op\ldots{}\{-3838.3838\}\{n\}\{r\}}}}\\\hline
\multicolumn{1}{|c|}{\textbf{\texttt{n}}} &
\multicolumn{1}{c|}{\textbf{\texttt{floor}}} &
\multicolumn{1}{c|}{\textbf{\texttt{ceil}}} &
\multicolumn{1}{c|}{\textbf{\texttt{round}}} \\\hline
\opcopy{6}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{4}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{3}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{0}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-1}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-2}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\
\opcopy{-6}{n}$\opprint{n}$ &
\opfloor{a}{n}{r}$\opprint{r}$ &
\opceil{a}{n}{r}$\opprint{r}$ &
\opround{a}{n}{r}$\opprint{r}$ \\\hline
\end{tabular}
\end{center}
\index{complex expression|(}
The very last macro we have to study is \macro{opexpr}. It calculates
a complex expression. This macro needs two parameters: the first one
is the expression in infix form (the natural one for human), the
second one is the variable name where the result is stored.
Initially, expression must have been polish one (for instance,
notation used on old HP calculator, or PostScript language), but
another work with Christophe Jorssen has given the actual form for
expression in \package{xlop}, more pleasant for users.
Formulas accept usual arithmetic operators \texttt{+}, \texttt{-},
\texttt{*}, and \texttt{/}. They accept also \texttt{:} operator for
euclidian division, and \verb+^+ for power. The \texttt{-} operator
has both rôle of substraction and unary operator for opposite. The
\texttt{+} has also these rôles, here the unary operator do\dots{}
nothing! Operands are written in decimal form or \emph{via} variable
name. However, \macro{opexpr} introduces a restriction about variable
name since variable names must be different to function names
recognized by \macro{opexpr}. Accessible functions are:
\begin{itemize}
\item \texttt{abs(a)} ;
\item \texttt{ceil(a,i)} ;
\item \texttt{decimal(a)} ;
\item \texttt{floor(a,i)} ;
\item \texttt{gcd(a,b)} ;
\item \texttt{integer(a)} ;
\item \texttt{mod(a,b)} gives result of \texttt{a} modulo
\texttt{b} ;
\item \texttt{rest(a,b)} gives remainder of \texttt{a} divide by
\texttt{b} (difference between remainider and modulo is the same as
between non euclidian division and euclidian division);
\item \texttt{round(a,i)}.
\end{itemize}
where functions that aren't listed above ask the matching macros.
(function \texttt{xxx} calls macro \verb+\opxxx+) For functions
\texttt{ceil}, \texttt{floor}, and \texttt{round}, the number
\texttt{i} indicates rank for approximation.
Macro \macro{opexpr} accept optional argument since it can realize
division which can be controlled
by \parameter{maxdivstep},\parameter{safedivstep},
and \parameter{period} parameters. Our first example is quite basic:
\begin{CenterExample}[xrightmargin=0pt]
\opexpr{3--gcd(15*17,25*27)*2}{r}%
$3--\gcd(15\times17,25\times27)\times2 = \opprint{r}$
\end{CenterExample}
Here is another example that shows that datas can come from a macro:
\begin{CenterExample}[xrightmargin=0pt]
\newcommand\try{2}%
\opexpr{\try+1/
(\try+1/
(\try+1/
(\try+1/
(\try+1/
(\try)))))}{r}
Continued fraction of base $u_n=2$ equal \opprint{r} at rank~5.
\end{CenterExample}
\index{complex expression|)}
\appendix
\chapter{Short Summary}
\label{chap:Aide-mémoire}
\section{Compilation times}
\label{sec:Temps de compilation}
Compilation times was measured on a computer with
processor Pentium II 600\,MHz, RAM 256\,MB, on linux system (Debian
woody).\footnote{In fact, these measures was done in 2004, when the
0.2 version was released. Author is somewhere lasy and he doesn't
measure with his new computer (more efficient)!}. The principle is
to do a minimal file \texttt{.tex}. The general canvas is:
\begin{verbatim}
\input xlop
\count255=0
\loop
\ifnum\count255<1000
<operation to test>
\advance\count255 by1
\repeat
\bye
\end{verbatim}
Compilation time with \verb+<operation to test>+ empty was substract
from the others test. Only the user time was take account. Results are
given in millisecond and should be read with great precautions.
\index{compilation time|(}\index{time (calculation)|(}%
Next table gives operation times in milliseconds. Operands used had
decimal notation but some trails with variable has shown that times
was very closed.
First line indicates the numbers of digits for both operands.
Operands were build like this:
\begin{itemize}
\item $\mathrm{A} = 1$ et $\mathrm{B} = 9$ for one digit;
\item $\mathrm{A} = 12$ et $\mathrm{B} = 98$ for two digits;
\item $\mathrm{A} = 123$ et $\mathrm{B} = 987$ for three digits;
\item $\mathrm{A} = 12345$ et $\mathrm{B} = 98765$ for five digits;
\item $\mathrm{A} = 1234567890$ et $\mathrm{B} = 9876543210$ for ten
digits;
\item $\mathrm{A} = 12345678901234567890$ et $\mathrm{B} =
98765432109876543210$ for twenty digits;
\end{itemize}
Here is results, some comments follow:
\bigskip\noindent\hbox to\linewidth{\hss
\begin{tabular}{|r|*{6}{l|}}
\cline{2-7}
\multicolumn{1}{l|}{} &
\multicolumn{1}{c|}{1} &
\multicolumn{1}{c|}{2} &
\multicolumn{1}{c|}{3} &
\multicolumn{1}{c|}{5} &
\multicolumn{1}{c|}{10} &
\multicolumn{1}{c|}{20} \\\hline
\verb+\opadd*{A}{B}{r}+ &
1.1 & 1.4 & 1.6 & 2.1 & 3.3 & 5.8 \\\cline{2-7}
\verb+\opadd*{B}{A}{r}+ &
1.1 & 1.4 & 1.6 & 2.1 & 3.3 & 5.8 \\\hline
\verb+\opsub*{A}{B}{r}+ &
1.7 & 2.1 & 2.4 & 3.0 & 4.8 & 8.3 \\\cline{2-7}
\verb+\opsub*{B}{A}{r}+ &
1.5 & 1.7 & 2.0 & 2.6 & 4.0 & 7.0 \\\hline
\verb+\opmul*{A}{B}{r}+ &
4.6 & 6.3 & 8.2 & 12.8 & 29.9 & 87.0 \\\cline{2-7}
\verb+\opmul*{B}{A}{r}+ &
5.0 & 6.6 & 8.5 & 13.2 & 30.3 & 87.8 \\\hline
\verb+\opdiv*{A}{B}{q}{r}+ &
46.4 & 53.8 & 53.8 & 64.3 & 85.8 & 124.7 \\\cline{2-7}
\verb+\opdiv*{B}{A}{q}{r}+ &
12.4 & 48.9 & 55.7 & 58.6 & 72.8 & 111.0 \\\hline
\verb+\opdiv*[maxdivstep=5]{A}{B}{q}{r}+ &
26.8 & 30.0 & 32.6 & 37.6 & 49.5 & 73.5 \\\cline{2-7}
\verb+\opdiv*[maxdivstep=5]{B}{A}{q}{r}+ &
12.4 & 29.1 & 32.6 & 35.2 & 43.3 & 67.9 \\\hline
\verb+\opidiv*{A}{B}{q}{r}+ &
10.8 & 12.2 & 13.5 & 16.0 & 22.3 & 35.5 \\\cline{2-7}
\verb+\opidiv*{B}{A}{q}{r}+ &
11.6 & 13.0 & 14.2 & 16.6 & 23.0 & 36.7 \\\hline
\verb+\opidiv*{A}{2}{q}{r}+ &
10.7 & 12.0 & 15.3 & 22.3 & 42.9 & 83.0 \\\hline
\end{tabular}
\hss
}
\par\bigskip
It is normal that inversion of operands don't have sensible influence
for addition. Then, it could be strange that there is influence for
substraction. In fact, when the second operand is bigger than the
second one, there is additional process (double inversion, operation
on the sign of the result).
It is normal that division time is greater than the multiplication
one. It could be abnormal that division seems catch up! In fact, the
multiplication complexity grows quickly with the operand length. In
the other hand, division complexity is stopped
by \parameter{maxdivstep} parameter. It is clear on example where
there is only five steps.
Some results seems odd. For instance \verb+\opdiv*{9}{1}{q}{r}+ is
very fast. These is due to the one digit quotient.
\verb+\opdiv*{123}{987}{q}{r}+, even more odd, is rather fast. Here,
explanation is quite subtle: this is due to many zeros in the
quotient.
When operands have comparable length, euclidian division is much
faster than non euclidian one. This is because quotient has few
digits (only one for all the numbers \texttt{A} and \texttt{B}). The
last line of the table is more relevant for this operation time.
All these remarks are written to put the emphasis on the difficulty to
evaluate the compilation time: it depends on too many parameters. On
the other hand, this table give a pretty good idea of what can be
expected.
\index{compilation time|)}\index{time (calculation)|)}%
\newpage
\section{Macros List}
\label{sec:Liste des macros}
\index{macros!table of|(}%
\noindent\begin{longtable}{|l|p{6.3cm}|}
\hline
\multicolumn{1}{|c|}{\textbf{Macro}} &
\multicolumn{1}{c|}{\textbf{Description}} \\\hline\hline
\endfirsthead
\hline
\multicolumn{1}{|c|}{\textbf{Macro}} &
\multicolumn{1}{c|}{\textbf{Description}} \\\hline\hline
\endhead
\hline
\multicolumn{2}{|c|}{$\ldots$ to be continued $\ldots$}\\
\hline
\endfoot
\hline
\endlastfoot
\verb+\opabs{n}{N}+ &
\verb+N+ stores the absolute value of \verb+n+. \\\hline
\verb+\opadd[P]{n1}{n2}+ &
Displays result of \verb-n1+n2-. \\\hline
\verb+\opadd*{n1}{n2}{N}+ &
Calcules \verb-n1+n2- and put result in \verb+N+. \\\hline
\verb+\opcastingoutelevens{n}{N}+ &
Calcules difference (modulo 11) of sum of rank odd digits and sum of
rank even digits of \verb+n+ and put the result in \verb+N+.\\\hline
\verb+\opcastingoutnines{n}{N}+. &
Calcules sum modulo 9 of digits of \verb+n+ and put result in
\verb+N+. \\\hline
\verb+\opceil{n}{T}{N}+ &
Places in \verb+N+ the approximation (ceiling) of \verb+n+ to rank
\verb+T+. \\\hline
\verb+\opcmp{n1}{n2}+ &
Compares numbers \verb+n1+ and \verb+n2+ and setup the tests
\verb+\ifopeq+, \verb+\ifopneq+, \verb+\ifopgt+, \verb+\ifopge+,
\verb+\ifople+ et \verb+\ifoplt+. \\\hline
\verb+\opcopy{n}{N}+ &
Copy number \verb+n+ in \verb+N+. \\\hline
\verb+\opdecimal{n}{N}+ &
Copy decimal part (positive integer number) of \verb+n+ in
\verb+N+. \\\hline
\verb+\opdecimalwidth{n}{N}+ &
\verb+N+ stores the width of decimal part of number \verb+n+.
\\\hline
\verb+\opdisplay[P]{S}{n}+ &
Display number \verb+n+ width style \verb+S+ puting each figure in a
box which have a width of \verb+\opcolumnwidth+ and a height of
\verb+\oplineheight+. \\\hline
\verb+\opdiv[P]{n1}{n2}+ &
Display result of n1/n2. \\\hline
\verb+\opdiv*[P]{n1}{n2}{N1}{N2}+ &
Calculates \verb+n1/n2+, put the quotient in \verb+N1+ and the
remainder in \verb+N2+. \\\hline
\verb+\opdivperiod{T1}{T2}{N}+ &
Calculates length of period of \verb+T1+ divide by \verb+T2+ and put
the result in \verb+N+. \\\hline
\verb+\opexport[P]{n}\cmd+ &
Copy number \verb+n+ in macro \verb+\cmd+. \\\hline
\verb+\opexpr[P]{F}{N}+ &
Evaluates formula \texttt{F} and put the final result in
\texttt{N}. \\\hline
\verb+\opfloor{n}{T}{N}+ &
Put in \verb+N+ the apprimation (floor) of \verb+n+ at rank
\verb+T+. \\\hline
\verb+\opgcd{T1}{T2}{N}+ &
Calculates gcd of \verb+T1+ and \verb+T2+ and put result in
\verb+N+. \\\hline
\verb+\opgetdecimaldigit{n}{T}{N}+ &
Build the number \verb+N+ with the only digit in slot
\verb+T+ of decimal part of \verb+n+. \\\hline
\verb+\opgetdigit{n}{T}{N}+ &
Build the number \verb+N+ with the only digit in slot
\verb+T+ of number \verb+n+. \\\hline
\verb+\opgetintegerdigit{n}{T}{N}+ &
Build the number \verb+N+ width the only digit in slot
\verb+T+ of integer part of \verb+n+. \\\hline
\verb+\ophline(T1,T2){T3}+ &
Draw a horizontal rule of length \verb+T3+, of thickness
\verb+hrulewidth+, and which begin at \verb+(T1,T2)+ in relation to
reference point. \\\hline
\verb+\opidiv[P]{n1}{n2}+ &
Display the result of \verb+n1/n2+. (euclidian division, that is,
with integer division) \\\hline
\verb+\opidiv*{n1}{n2}{N1}{N2}+ &
Calculates \verb+n1/n2+ (euclidian division), put quotient
(integer) in \verb+N1+ and remainder (between 0 (include) and
\verb+|n2|+ (exclude)) in \verb+N2+. \\\hline
\verb+\opinteger{n}{N}+ &
Copy integer part (positive integer number) of \verb+n+
in \verb+N+. \\\hline
\verb+\opintegerwidth{n}{N}+ &
Number \verb+N+ stores the width of integer part of number \verb+n+.
\\\hline
\verb+\oplput(T1,T2){<object>}+ &
Put \verb+<object>+ to the right of the point with coordinates
\verb+(T1,T2)+ in relation to reference point. \\\hline
\verb+\opmul[P]{n1}{n2}+ &
Display result of \verb+n1*n2+. \\\hline
\verb+\opmul*{n1}{n2}{N}+ &
Calculates \verb+n1*n2+ and put the result in \verb+N+. \\\hline
\verb+\opneg{n}{N}+ &
Number \verb+N+ stores opposite of \verb+n+. \\\hline
\verb+\oppower{n}{T}{N}+ &
Calculates \verb+n+ to the power of \verb+T+ and put the result in
\verb+N+. \\\hline
\verb+\opprint{n}+ &
Display number \verb+n+ in a direct way. \\\hline
\verb+\opround{n}{T}{N}+ &
Put in \verb+N+ the approximation of \verb+n+ at rank \verb+T+.
\\\hline
\verb+\oprput(T1,T2){<object>}+ &
Put \verb+<object>+ to the left of the point with coordinates
\verb+(T1,T2)+ in relation to reference point. \\\hline
\verb+\opset{L}+ &
Allocates globally \package{xlop} parameters given in the list
\verb+L+. \\\hline
\verb+\opsetdecimaldigit{n}{T}{N}+ &
Modify the digit of rank \verb+T+ in decimal part of \verb+N+ in
order to have the value \verb+n+ for this digit. \\\hline
\verb+\opsetdigit{n}{T}{N}+ &
Modify the digit of rank \verb+T+ of \verb+N+ in
order to have the value \verb+n+ for this digit. \\\hline
\verb+\opsetintegerdigit{n}{T}{N}+ &
Modify the digit of rank \verb+T+ in integer part of \verb+N+ in
order to have the value \verb+n+ for this digit. \\\hline
\verb+\opsub[P]{n1}{n2}+ &
Display result of \verb+n1-n2+. \\\hline
\verb+\opsub*{n1}{n2}{N}+ &
Calculates \verb+n1-n2+ and put the result in \verb+N+. \\\hline
\verb+\opunzero{N}+ &
Delete non-significant zeros of \verb+N+. \\\hline
\verb+\opvline(T1,T2){T3}+ &
Draw a vertical ruleof length \verb+T3+, of thickness
\verb+hrulewidth+ and which begin at \verb+(T1,T2)+ in relation to
reference point. \\\hline
\verb+\opwidth{n}{N}+ &
Number \verb+N+ stores number of digits of number \verb+n+. \\\hline
\end{longtable}\index{macros!table of|)}
In this table, parameters:
\begin{itemize}
\item \texttt{n} and \texttt{ni} (where \texttt{i} is an index)
indicate that parameter must be a number given in decimal form or a
variable name;
\item \texttt{N} and \texttt{Ni} (where \texttt{i} is an index)
indicate that parameter must be a number given in decimal form or a
variable name;
\item \texttt{[P]} indicates that the macro accept an optional
parameter which allow to modify parameter of \package{xlop};
\item \texttt{T} and \texttt{Ti} (where \texttt{i} is an index)
indicate that parameter must be a number given in decimal form or a
variable name but must be less than numbers acceptable by \TeX{},
that is, $-2147483648 \le \mathtt{T} \le 2147483647$.
\end{itemize}
\section{Parameter list}
\label{sec:Liste des parametres}
\index{parameter@parameter!table of|(}%
\begingroup
\advance\hoffset by-1.75cm \advance\linewidth by1.75cm
\begin{longtable}{|l|l|p{7cm}|}
\hline
\multicolumn{1}{|c|}{\textbf{Parameter}} &
\multicolumn{1}{c|}{\textbf{Default}} &
\multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline
\endfirsthead
\hline
\multicolumn{1}{|c|}{\textbf{Parameter}} &
\multicolumn{1}{c|}{\textbf{Default}} &
\multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline
\endhead
\hline
\multicolumn{3}{|c|}{$\ldots$ to be continued $\ldots$}\\
\hline
\endfoot
\hline
\endlastfoot
\verb+afterperiodsymbol+ &
\verb+$\ldots$+ &
Symbol used after a period of a division. \\\hline
\verb+approxsymbol+ &
\verb+$\approx$+ &
Symbol used as approximation relation in inline operations. \\\hline
\verb+equalsymbol+ &
\verb+{$=$}+ &
Symbol used as equality relation in inline operations. \\\hline
\verb+addsymbol+ &
\verb-$+$- &
Symbol used as addition operator. \\\hline
\verb+subsymbol+ &
\verb+$-$+ &
Symbol used as substraction operator. \\\hline
\verb+mulsymbol+ &
\verb+$\times$+ &
Symbol used as multiplication operator. \\\hline
\verb+divsymbol+ &
\verb+$\div$+ &
Symbol used as multiplication operator for inline
operations. \\\hline
\verb+decimalsepsymbol+ &
\verb+.+ &
Symbol used as decimal separator. \\\hline
\verb+strikedecimalsepsymbol+ &
&
Symbol used as decimal separator moved in dividend and divisor for
display division. \\\hline
\verb+shiftintermediarysymbol+ &
\verb+$\cdot$+ &
Symbol used to show intermediary numbers shifting for display
multiplication. \\\hline
\verb+displayshiftintermediary+ &
\verb+shift+ &
Indicates that the shifting character for multiplications will be
displayed only for additional shifting (value \verb+shift+), for
all the shifting (value \verb+all+), or never (value
\verb+none+). \\\hline
\verb+voperation+ &
\verb+bottom+ &
Vertical alignement for displayed operation. The value \verb+bottom+
indicates that the bottom of operation will be aligned with
baseline. The value \verb+top+ indicates that the top of operation
will be aligned with baseline. The value \verb+center+ indicates
that operation will be verticaly centred with baseline. \\\hline
\verb+voperator+ &
\verb+center+ &
Vertical alignement for operators in displayed operations. The value
\verb+top+ put operator at the level of first operand. The value
\verb+bottom+ put operator at the level of second operand. The value
\verb+center+ put operator between operands. \\\hline
\verb+hfactor+ &
\verb+decimal+ &
Sort of operands alignement for displayed operation. The value
\verb+decimal+ indicates an alignement on decimal separator. The
value \verb+right+ indicates a flushright alignement. \\\hline
\verb+vruleperiod+ &
\verb+-0.2+ &
Vertical position of rule which indicates period of quotient for
inline division. \\\hline
\verb+dividendbridge+ &
\verb+false+ &
Indicates if there is a ``bridge'' above dividend. \\\hline
\verb+shiftdecimalsep+ &
\verb+both+ &
Indicates how shift decimal separator into operands for a displayed
division. The value \verb+both+ indicates that shifting are made on
both divisor and dividend in order to make integer numbers. The
value \verb+divisor+ indicates that the shifting must give an
integer divisor. The value \verb+none+ indicates that there is no
shifting. \\\hline
\verb+maxdivstep+ &
\verb+10+ &
Maximal number of steps in division. \\\hline
\verb+safedivstep+ &
\verb+50+ &
Maximal number of steps in division when there is a period to
reach. \\\hline
\verb+period+ &
\verb+false+ &
Indicates if division must be stoped when a whole period is
reached. \\\hline
\verb+deletezero+ &
\verb+true+ &
Indicates that non-significant zeros are displayed (\verb+false+) or
deleted (\verb+true+). \\\hline
\verb+carryadd+ &
\verb+true+ &
Indicates that carries are displayed (\verb+true+) for displayed
additions. \\\hline
\verb+carrysub+ &
\verb+false+ &
Indicates that carries are displayed (\verb+true+) for displayed
substractions. \\\hline
\verb+offsetcarry+ &
\verb+-0.35+ &
Horizontal offset for carries into displayed substractions. \\\hline
\verb+style+ &
\verb+display+ &
Indicates tha operation are inline (\verb+text+) or displayed
(\verb+display+). \\\hline
\verb+displayintermediary+ &
\verb+nonzero+ &
Indicates that all intermediary results are displayed (\verb+all+),
only non null ones are displayed (\verb+nonzero+), or any
intermediary result isn't displayed into displayed multiplications
and divisions. \\\hline
\verb+lastcarry+ &
\verb+false+ &
Indicates that carry with no figure just below it must be displayed
(\verb+true+), or not (\verb+false+). \\\hline
\verb+parenthesisnegative+ &
\verb+none+ &
Behavior to display negative numbers in inline operations. The value
\verb+none+ displays them without parenthesis. The value \verb+all+
displays them always with parenthesis. The value \verb+last+ display
parenthesis except for first operand of an expression. \\\hline
\verb+columnwidth+ &
\verb+2ex+ &
With of box for one figure. \\\hline
\verb+lineheight+ &
\verb+\baselineskip+ &
Height of box for one figure. \\\hline
\verb+decimalsepwidth+ &
\verb+0pt+ &
Width of box that hold the decimal separator. \\\hline
\verb+decimalsepoffset+ &
\verb+0pt+ &
Horizontal offset for decimal separator. \\\hline
\verb+hrulewidth+ &
\verb+0.4pt+ &
Thickness of horizontal rules. \\\hline
\verb+vrulewidth+ &
\verb+0.4pt+ &
Thickness of vertical rules. \\\hline
\verb+behaviorsub+ &
\verb+silent+ &
\package{xlop} behavior for an ``impossible'' substraction, that is,
a substraction with two positive operands, the second greater
than the first one. The value \verb+silent+ does operation swapping
the two operands in a slient way. With the value \verb+warning+,
there are also a swapping but \package{xlop} gives a warning. The
value \verb+error+ display an error message and operation isn't
processed. \\\hline
\verb+country+ &
\verb+french+ &
Indicates the displayed operation behavior depending of
contry. Package \package{xlop} put forward only \verb+french+,
\verb+american+, and \verb+russian+ but these different ways to
display operations aren't encoded in version 0.23. \\\hline
\verb+operandstyle+ &
&
Style for operands. \\\hline
\verb+resultstyle+ &
&
Style for results. \\\hline
\verb+remainderstyle+ &
&
Style for remainders. \\\hline
\verb+intermediarystyle+ &
&
Style for intermediary results (intermediary numbers in
multiplication and number to substract in division when successive
substractions are displayed). \\\hline
\verb+carrystyle+ &
\verb+\scriptsize+ &
Style for carries. The default value when compilation are made
without \LaTeX{} is \verb+\sevenrm+. \\\hline
\end{longtable}\index{parameter@parameter!table of|)}
\endgroup
\chapter{Tricks}
\label{chap:Trucs et astuces}
\section{\package{xlop} vs. \package{calc} and \package{fp}}
You could believe that \package{xlop} can replace package such
\package{calc}\index{package!calc}\index{calc} and
\package{fp}\index{package!fp}\index{fp}. In fact, that is not so
simple. Obviously \package{xlop} can do complex calculations, on arbitrary
long numbers but, unlike \package{calc}, it don't allow to process
directly dimensions. Comparison with \package{fp} is somewhere more
realistic but remember that \package{xlop} can make memory usage too
high.
If you want to process calculations on length\index{length}, you can use
that a dimen register allocation to a counter gives a number which
correspond to this length with unit \texttt{sp}.
\begin{CenterExample}[xrightmargin=0pt]
\newcommand\getsize[2]{%
\dimen0=#1\relax
\count255=\dimen0
\opcopy{\the\count255}{#2}}
\getsize{1pt}{r}$1\,\mathrm{pt}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1pc}{r}$1\,\mathrm{pc}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1in}{r}$1\,\mathrm{in}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1bp}{r}$1\,\mathrm{bp}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1cm}{r}$1\,\mathrm{cm}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1mm}{r}$1\,\mathrm{mm}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1dd}{r}$1\,\mathrm{dd}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1cc}{r}$1\,\mathrm{cc}=\opprint{r}\,\mathrm{sp}$\quad
\getsize{1sp}{r}$1\,\mathrm{sp}=\opprint{r}\,\mathrm{sp}$\quad
\end{CenterExample}
However, don't forget that the \package{xlop} main goal is to
\emph{display} operations.
With this \macro{getsize} macro, it is possible to realise
calculations on length.
\begin{SideBySideExample}
\newcommand\getsize[2]{%
\dimen0=#1\relax
\count255=\dimen0
\opcopy{\the\count255}{#2}}
\getsize{1cm}{u}%
\getsize{\textwidth}{w}%
\getsize{\textheight}{h}%
\opexpr{w*h/u^2}{S}%
\opround{S}{2}{S}%
Surface of spread is
\opprint{S}\,$\mathrm{cm}^2$
\end{SideBySideExample}
\section{Complex Operations}
\label{sec:Creation d'operations complexes}
Use of \package{xlop} macros with loop of \TeX{} allow to create
operations as you want. Here, we give only two examples. The first one
can express a number as a product of prime factors, the second one is
a general calculation for continued
fraction.\index{number!prime}\index{loop|(}%
\index{product of prime factors}
\begin{Verbatim}[xrightmargin=0pt]
\newcount\primeindex
\newcount\tryindex
\newif\ifprime
\newif\ifagain
\newcommand\getprime[1]{%
\opcopy{2}{P0}%
\opcopy{3}{P1}%
\opcopy{5}{try}
\primeindex=2
\loop
\ifnum\primeindex<#1\relax
\testprimality
\ifprime
\opcopy{try}{P\the\primeindex}%
\advance\primeindex by1
\fi
\opadd*{try}{2}{try}%
\ifnum\primeindex<#1\relax
\testprimality
\ifprime
\opcopy{try}{P\the\primeindex}%
\advance\primeindex by1
\fi
\opadd*{try}{4}{try}%
\fi
\repeat
}
\newcommand\testprimality{%
\begingroup
\againtrue
\global\primetrue
\tryindex=0
\loop
\opidiv*{try}{P\the\tryindex}{q}{r}%
\opcmp{r}{0}%
\ifopeq \global\primefalse \againfalse \fi
\opcmp{q}{P\the\tryindex}%
\ifoplt \againfalse \fi
\advance\tryindex by1
\ifagain
\repeat
\endgroup
}
\end{Verbatim}
\newcount\primeindex
\newcount\tryindex
\newif\ifprime
\newif\ifagain
\newcommand\getprime[1]{%
\opcopy{2}{P0}%
\opcopy{3}{P1}%
\opcopy{5}{try}
\primeindex=2
\loop
\ifnum\primeindex<#1\relax
\testprimality
\ifprime
\opcopy{try}{P\the\primeindex}%
\advance\primeindex by1
\fi
\opadd*{try}{2}{try}%
\ifnum\primeindex<#1\relax
\testprimality
\ifprime
\opcopy{try}{P\the\primeindex}%
\advance\primeindex by1
\fi
\opadd*{try}{4}{try}%
\fi
\repeat
}
\newcommand\testprimality{%
\begingroup
\againtrue
\global\primetrue
\tryindex=0
\loop
\opidiv*{try}{P\the\tryindex}{q}{r}%
\opcmp{r}{0}%
\ifopeq \global\primefalse \againfalse \fi
\opcmp{q}{P\the\tryindex}%
\ifoplt \againfalse \fi
\advance\tryindex by1
\ifagain
\repeat
\endgroup
}
With this code, we can create a prime numbers list (here the 20~first
ones).
\begin{SideBySideExample}
\getprime{20}%
\opprint{P0}, \opprint{P1}, \ldots,
\opprint{P9}, \ldots \opprint{P19}.
\end{SideBySideExample}
Note that this code is very bad: it is very slow and don't give
anything against native \TeX{} operations. It is only a educational
example. Note also that the tricks to put loop into loop with macro
\verb+\testprimality+ inside a group. \package{xlop} operations give
global results.\index{global allocation}
Once you have your prime numbers ``table'', you can use it to
write a number as product of prime number.
\begin{CenterExample}[xrightmargin=0pt]
\newcommand\primedecomp[2][nil]{%
\begingroup
\opset{#1}%
\opcopy{#2}{NbtoDecompose}%
\opabs{NbtoDecompose}{NbtoDecompose}%
\opinteger{NbtoDecompose}{NbtoDecompose}%
\opcmp{NbtoDecompose}{0}%
\ifopeq
I refuse to factorize zero.
\else
\setbox1=\hbox{\opdisplay{operandstyle.1}%
{NbtoDecompose}}%
{\setbox2=\box2{}}%
\count255=1
\primeindex=0
\loop
\opcmp{NbtoDecompose}{1}\ifopneq
\opidiv*{NbtoDecompose}{P\the\primeindex}{q}{r}%
\opcmp{0}{r}\ifopeq
\ifvoid2
\setbox2=\hbox{%
\opdisplay{intermediarystyle.\the\count255}%
{P\the\primeindex}}%
\else
\setbox2=\vtop{%
\hbox{\box2}
\hbox{%
\opdisplay{intermediarystyle.\the\count255}%
{P\the\primeindex}}}
\fi
\opcopy{q}{NbtoDecompose}%
\advance\count255 by1
\setbox1=\vtop{%
\hbox{\box1}
\hbox{%
\opdisplay{operandstyle.\the\count255}%
{NbtoDecompose}}
}%
\else
\advance\primeindex by1
\fi
\repeat
\hbox{\box1
\kern0.5\opcolumnwidth
\opvline(0,0.75){\the\count255.25}
\kern0.5\opcolumnwidth
\box2}%
\fi
\endgroup
}
\getprime{20}%
\primedecomp[operandstyle.2=\red,
intermediarystyle.2=\red]{252}
\end{CenterExample}
Note the use of group for the whole macro in order to protect
\package{xlop} parameter modifications.%
\index{parameter!local modification} Note also that void parameter
aren't allowed. It's not a bug, it's a feature. Author thinks that a
user who write brackets without anything between these brackets is
going to make a mistake. To obviate this
prohibition\index{parameter!void}, there is the particular
parameter \parameter{nil} which has exactly this rôle.
\index{loop|)}
Finally, note the trick \verb+{\setbox2=\box2}+ to obtain a void box
register, and final manipulations to show the vertical rule in a
easy-to-read way.
The second example allow to calculates a continued fraction like:
\def\dfrac#1#2{\frac{\displaystyle #1}{\displaystyle #2}}
\[a_0+\dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{a_3+\cdots}}}\]
giving the sequence $a_0,a_1,a_2,a_3,\ldots$ to the macro. This
example gives fractions corresponding to gold number, and square root
for~2 and~3.
\makeatletter
\begin{CenterExample}[xrightmargin=0pt]
\begingroup
\long\gdef\continuedfraction#1#2{%
\let\@mirror\relax
\@for\op@Nb:=#1\do
{%
\ifx\@mirror\relax
\edef\@mirror{\op@Nb}%
\else
\edef\@mirror{\op@Nb,\@mirror}%
\fi
}%
\let\Op@result\relax
\@for\op@Nb:=\@mirror\do
{%
\ifx\Op@result\relax
\opcopy{\op@Nb}{result}%
\else
\opexpr{\op@Nb+1/result}{result}%
\fi
}%
\opcopy{result}{#2}%
}
\endgroup
\continuedfraction{1,1,1,1,1,1,1,1,1,1,1,1}{r}\opprint{r}\quad
\continuedfraction{1,2,2,2,2,2,2,2,2,2,2,2}{r}\opprint{r}\quad
\continuedfraction{1,1,2,1,2,1,2,1,2,1,2,1}{r}\opprint{r}
\end{CenterExample}
\makeatother
It does no harm just this once, we use \LaTeX{} commands for the
loop.
\section{Direct Access to Number}
\label{sec:Acces direct aux nombres}
When a number is saved in a \package{xlop} variable, it is possible to
process with it in many different ways. However, in certain
situations, you would creat you own macro or use external macro giving
such numbers as parameter.
Giving directly \verb+\opprint{var}+ is ineffective since this macro
is a complex a gives side effect. It is necessary to access directly
to this number. When a variable hold a number, \package{xlop} creates
a macro
\texttt{$\backslash$Op@var}\index{Opvar@\texttt{\boi {Op\at var}}}
which contain this number. Note the uppercase ``O'' and the lowercase
``p''. The at sign is here to do this definition a private one, that
is, you have to enclose it with \macro{makeatletter} and
\macro{makeatother} to access it (or \macro{catcode @=11} in \TeX).
\begin{SideBySideExample}
\opcopy{1234}{a}\opcopy{56}{b}%
\opmul*{a}{b}{r}%
\makeatletter
\newcolumntype{.}{D{.}{.}{-1}}
\begin{tabular}{l.}
& \Op@a \\
$\times$ & \Op@b \\
$=$ & \Op@r
\end{tabular}
\makeatother
\end{SideBySideExample}
Note that this way of doing don't work when decimal separator is
between braces since macro \verb+\opprint{var}+ contain such
braces. In this case, the simplest is to use \macro{opexport} macro
(see page~\pageref{macro-opexport}).
\chapter{Future Versions}
\label{chap:Versions futures}
Version of \package{xlop} package is~0.23 which is only a debuging
version of version~0.2, which is itself a correcting version of
version~0.1 (first public release). The next release will be
version~0.3 and its ``stable'' version will be version~0.4.
The features of version~0.3 aren't definitively fixed but there are
some points planned:
\begin{itemize}
\item international version for posées;
\item opérations from 2 to 36~basis;
\item additional high level functions with roots (\macro{oproot} for
any roots and \macro{opsqrt} for square root), exponential function,
logarithm, trigonometric functions (direct, inverse, hyperbolic);
\item macro to have a formated writing, that is, write a number where
length of decimal part and integer part are given (if these widths
are not the ones of the number, there will be overflow or filling);
this macro was present in version~0.1 and allow to display numbers
decimal aligned, right aligned, or left aligned;
\item macro for addition with more than two operands;
\item parameter for scientific or engineer notation;
\item macro to allow to write a multi-line number and/or with thousand
separator;
\item carries for multiplications;
\item make public the successive remainders of a division;
\item negative values of \parameter{maxdivstep} and
\parameter{safedivstep} parameters will take acount of decimal digit
of quotient.
\end{itemize}
For all requests or bug report, the author will be grateful to you to
contact him at:
\begin{verbatim}
Jean-Come.Charpentier@wanadoo.fr
\end{verbatim}
placing the word ``xlop'' in the subject in order to help my spam killer.
It would be nice to have a hacker manual which explain in details the
source. This tool could be usefull in order to improve
\package{xlop}. Unfortunately, the current code has more
than~4000~lines and the work to do that may well be too long.
%\printindex
\chapter{Index}
\label{chap:index}
\begin{multicols}{2}
\makeatletter
\parindent \z@\relax
\parskip \z@ \@plus.3\p@\relax
\let\item\@idxitem
\makeatother
\renewenvironment{theindex}{}{}%
\input\jobname.ind
\end{multicols}
\end{document}
|