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I don't want to make this article an enormous encomium to the benefits of multiply-and-add, but I wonder if this general statement in the lead is still true enough "for modern processors" to be stated that way. Of course, all floating-point instructions are implicitly multiply-and-add anyway, and the
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So either use the above as an example or change the phrase to "the first and third bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the first and third positions" and keep the current example, which I guess would be better because it demonstrates XOR flipping both a 0 and a 1.
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It seems that bit shifting is actually for compressing bytes by moving bits to save space and it turned out to not work since the innformation needs to be preserved. I think the wikipedia page on this topic needs to mention something about this but will likely be rejected due to dislike of it being
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Modern processors such as Intel
Itanium and Xeon have a combined "multiply and add" instruction as, I believe, their *only* variants of these instructions, and execute it in one cycle. (Of course, a straight add or multiply without the other is achieved just by using the identity functions x + 0 = x
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The description of C/C++ is incorrect insofar as unsigned integers (representing ) act with the character of a "logical shift", whereas signed integers (representing ) are in some circumstances not defined and are left up to the implementation, regarding the presence of upper order 1 bits subsequent
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Just noticed the truth table is quite inconsistent in how it chooses to represent the logical operators. Swapping out ↛ for NIMPLY and If/then for IMPLY would be more fitting for an article about logic in computers, no? There's also the inconsistency in
Converse NIMPLY being represented here as Xq
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There is no doubt at all, that a first bit toggles only a first bit, a second bit only a second bit, and a third bit only third bit, and so on. So your phrase "the first and third bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the first and third positions" is correct, and
2104:
No, bit shifting isn't necessarily a scam! You do not know beforehand where the "information" is and which "innformation needs to be preserved". I'm absolutely sure that YOU haven't read everything that is available to be read and that YOU do not want to read everything. So in what you select, YOU
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beneficial in real applications where multiply-then-add is extremely common, for example, for array indexing (of course an optimizer might well have other strategies for dealing with that) and for very common linear equations, eg. graphics transforms (again, this may well be done these days on the
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indication on how to make sense of large, title graphics for each operation. by contrast, the caption provides a link for 4bit, which has digressive, lateral value but anyone trying to understand bitwise operation would understand what 4 bits are and have a sense of what a 4 bit integer might be.
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this is a basic failure to be encyclical and accessible as even to a reader with a basic and rough coding background (this author) they are illegible. that's fine, it's an esoteric subject—the failure is in not providing any key or name for further investigation for any non computer scientist.
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Of course, if an overflow (carry out of the registers' width) occurs, then the sum of the original values won't be preserved and won't eventually be returned, though the sum modulo 2 would be both preserved and eventually returned. The carry occurs in the left shift, which in a way is the only
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the 4 bit integer illustrations for different operations have no reference on how to interpret them—and are not self evident—and effectively have no communicative value except as technical reference. that is to say, if you come to the page as an introduction to bitwise operation you have no
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The article states that on modern architectures, bitwise operations are not usually faster than addition, but does not specifically make that claim for bitshifting. Does this mean that x * 2 will generally be no faster than x + x, for example? what about x * 2 + x vs. x * 3?
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Hello, I should have looked at the discussion page first! I also noticed this issue and I edited a sentence that stated C/C++ compilers always use logical shifts even with signed integers. It was probably a wrong formulation, results are always undefined only if the
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There is a caveat in the article mentioning shifts are not technically bit-wise because it does not apply to corresponding pairs of bits. Would it then make sense to apply the same caveat to the NOT operator section, as it applies to only one set of bits?
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I've seen extensive development of bitwise "tricks" in practice, but don't see it mentioned in this article. Is there such an article that this could link to, as a "See Also" item, or would it make sense to develop the idea within this article?
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The text "This example uses an 8-bit register:" is given for the shift example. But for consistency, surely the NOT example needs to say "This example uses an 4-bit register:". A 3 bit register would convert from 111 to 000
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The first line is unneeded, because register c is always initialised first in the loop and not used at the end outside the loop. With that line removed and furthermore, with # marking a comment until the end of a line:
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He's probably talking about the operation that reverses the order of bits in a n-bytes integer. I don't know whether it deserves a section as it is built upon other basic bit-wise operators.
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you will see that the result of the first equation is multiplication, but with the second equation, which is the same as the example mentioned in the page, is summation not multiplication.
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as well. But there is no real toggling in your example, because the two operands do not have two 1s on a matching position. And a 0 does not toggle anything.
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called a scam? It doesn't seem to be a valid science to shift bits when information is lost as the whole idea is to preserve the information
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operand is negative. Here is the source for the C language: JTC1/SC22/WG14 N843, section 6.5.7: "Bitwise shift operators", pages 91 and 92 (
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Left here because it doesn't seem appropriate to put any of this into the article, except for the removal of the unneeded line. --
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To determine whether the third bit is 1, a bitwise AND is applied to it and another bit pattern containing 1 in the third bit:
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As described in the ANSI C standard section 6.5.7 , the operation is actually only indeterminate if the number is negative:
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Isn't that toggling the first and third bits instead of the second and fourth bits? I guess the correct example would be:
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on
Knowledge. If you would like to participate, you can choose to edit the article attached to this page, or visit the
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So the speed of multiply/divide is as fast as bitwise operations in current cpus. But what about power consumption?
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Maybe, the indexing of the positions is the problem? The first position is index 0 and the fourth position index 3:
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related articles on
Knowledge. If you would like to participate, please visit the project page, where you can join
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993:"AND 1" clears all bits except the LSB (bit 0). I think it is more clear to write "if (B AND 1) = 1 then".
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Should some of the representations for the logical operators be swapped out for more fitting versions?
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The article currently (2013-08-11Z) contains this example at the end of the "Applications" section:
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I'm surprised nobody has mentioned how bitwise operators are useful for enums. something like this:
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1191:"On some older computers is was faster to shift instead of multiply or divide by a power of two."
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Is it fair to say, as the lead does in other words, that multiplication is slower than addition?
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In principle, everything is already said in the section "Bitwise operators​". But the operators
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Thanks for pointing out. Perhaps you or someone can improve them by editing their captions. –
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This article does not answer the above question. please add following to the passage:
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if (b and 1) ≠0 c := c + a shift a left by one shift b right by one
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I do not recognize your "inversion" example. As for complementing you are describing
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Requested articles/Applied arts and sciences/Computer science, computing, and
Internet
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The last example, ancient
Egyptian multiplication, is a summation not multiplication
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But processor designs may allocate faster and/or more execution units to compensate.
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383:, where you can join the project and see a list of open tasks. Leave messages at the
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http://www.codeproject.com/Articles/13740/The-Beginner-s-Guide-to-Using-Enum-Flags
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You seem to know that the decimal representation is not input, but result only. —
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The section on bitwise NOT describes two's complement as negating the value and
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lead does not narrow it down to integer instructions, which it probably should.
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I am very reluctant to support real details in this section beyond the link to
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Third bit? That took me a while to comprehend. Well, I would rather count bits
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If you want to test bit 3 for example you'll write "if (B AND 8) = 8 then".
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2003:, and the second is an implementation of addition. Please check it out. —
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No. (b and 1) is implying a bitwise operation, not a logical operation.
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the article; the first pseudocode sample is in fact an implementation of
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operation that moves any bits to have them act in other bits' positions.
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It would be adding one. But I think in the section you are referring to,
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should be mentioned in this section in addition to AND, OR, NOT, XOR. –
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Addition in bit operations and zero-testing, corrected & commented
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1460:# This clears in b the bits set in both a, b (previously saved to c),
1493:# this iteration's b. Loop until no carry occurs (until a is zero).
1469:# thus a xor b adds each bit pair of a, b while discarding carries.
824:). I do not have any information concerning C++ about this subject.
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Besides the already contained errors and missing statements, e.g.
1490:# The saved value is this iteration's carry value, to be added to
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tables for 4 bit integers unreferenced and thus non-communcative
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Shifts considered not "bit-wise" but NOT considered "bitwise"?
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Find pictures for the biographies of computer scientists (see
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Isn't the second example for the XOR bitwise operation wrong?
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1483:# This results in the carry bits, which form the carry value.
1466:# To xor is, in fact, the same operation as bit-wise addition
1449:# All these bits would carry if bits were added individually,
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arithmetic value. Perhaps it could do with some clarifying.
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http://www.fredosaurus.com/notes-cpp/expressions/bitops.html
1452:# that is, if the bits in a, b were to be added bit-wise.
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bits may be toggled by a bitwise XOR with a bit pattern
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I'm not sure how much detail to go into here, though.
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It says "given the bit pattern 0010 (decimal 2) the
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http://std.dkuug.dk/JTC1/SC22/WG14/www/docs/n843.htm
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http://std.dkuug.dk/JTC1/SC22/WG14/www/docs/n843.htm
467:, a collaborative effort to improve the coverage of
270:, a collaborative effort to improve the coverage of
1435:# Each iteration results in the same sum for a + b,
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http://graphics.stanford.edu/~seander/bithacks.html
965:Isn't "if (b and 1) ≠0" equivalent to "if b ≠0"?
1438:# until a is zero at which point b holds the sum.
579:Computer science articles needing expert attention
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2352:while Converse IMPLY is represented as Then/if.
1226:Need to specify register length for NOT operator
33:for general discussion of the article's subject.
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1446:# This separates out all bits set in both a, b.
719:WikiProject Computer science/Unreferenced BLPs
2254:4321 (-th position) 3210 (bit index)
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1463:# and sets in b all the other bits set in a.
1143:Multiply is inherently more complex than add.
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1480:# Multiply the carrying bits' values by two.
930:This algorithm is wrong. Try a = 2, b = 10
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1487:# Save value to add in the next iteration.
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2105:are already cheating yourselves. –
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1180:Furthermore, the first reference (
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1258:bitwise OR operator in C: |
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1588:
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1564:
1561:
1558:
1555:
1549:
1529:
1504:
1501:
1499:
1428:
1425:
1417:
1414:
1412:
1389:
1386:
1381:
1358:
1319:actually means
1294:
1283:
1259:
1249:
1228:
1209:
1163:
1118:
1103:212.114.254.107
1095:
1087:
1079:
1015:
963:
947:137.151.174.176
940:
937:
925:
861:—The preceding
845:
794:—The preceding
779:
777:C/C++ incorrect
754:
751:
746:
740:
728:Project-related
723:
704:
685:
659:
640:
621:
602:
583:
559:
503:High-importance
486:
483:
480:
477:
476:
444:High‑importance
443:
397:
394:
391:
388:
387:
362:
355:
335:
289:
286:
283:
280:
279:
257:
250:
230:
201:on Knowledge's
198:
121:
116:
115:
114:
91:
61:
12:
11:
5:
2424:
2422:
2414:
2413:
2408:
2403:
2398:
2393:
2388:
2383:
2378:
2368:
2367:
2348:
2345:
2344:
2343:
2302:
2299:
2298:
2297:
2283:
2253:
2252:
2251:
2248:
2218:
2217:
2216:
2168:
2163:0 (decimal 8)
2139:
2122:
2119:
2118:
2117:
2070:
2067:
2048:
2047:
2040:
2039:
2034:
2024:
2021:
2020:
2019:
1639:
1554:
1548:
1545:
1528:
1525:
1514:82.113.121.184
1429:
1390:
1380:
1377:
1357:
1354:
1353:
1352:
1323:complement or
1282:
1279:
1278:
1277:
1256:
1248:
1245:
1227:
1224:
1208:
1205:
1204:
1203:
1189:
1162:
1159:
1158:
1157:
1144:
1117:
1114:
1091:
1085:
1078:
1075:
1050:
1049:
1039:70.250.179.253
1020:70.250.179.253
1014:
1011:
1010:
1009:
1008:
1007:
994:
988:
987:
962:
959:
935:
924:
921:
919:
917:
916:
915:
914:
900:
894:
893:
858:
857:
853:
844:
841:
840:
839:
825:
778:
775:
772:
771:
768:
767:
764:
763:
760:
759:
756:
755:
753:
752:
750:
749:
732:
724:
722:
721:
715:
705:
703:
702:
696:
686:
684:
683:
678:
670:
660:
658:
657:
651:
641:
639:
638:
632:
622:
620:
619:
613:
603:
601:
600:
594:
584:
582:
581:
576:
570:
560:
558:
557:
551:
539:
537:
536:
524:
523:
511:
510:
499:
493:
492:
490:
473:the discussion
459:
447:
446:
438:
426:
425:
422:
421:
414:Mid-importance
410:
404:
403:
401:
368:
367:
351:
339:
338:
336:Mid‑importance
330:
318:
317:
314:
313:
302:
296:
295:
293:
276:the discussion
263:
262:
246:
234:
233:
225:
213:
212:
206:
195:
181:
180:
118:
117:
113:
112:
107:
102:
93:
92:
90:
89:
82:
77:
68:
62:
60:
59:
48:
39:
38:
35:
34:
28:
13:
10:
9:
6:
4:
3:
2:
2423:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2373:
2371:
2364:
2363:
2359:
2355:
2346:
2342:
2337:
2332:
2330:
2329:Novem Linguae
2324:
2323:
2322:
2321:
2317:
2313:
2307:
2300:
2296:
2292:
2288:
2284:
2281:
2280:
2277:
2273:
2269:
2265:
2261:
2257:
2249:
2246:
2245:
2242:
2238:
2234:
2230:
2226:
2222:
2213:
2212:
2211:
2210:
2206:
2202:
2198:
2192:
2188:
2184:
2180:
2176:
2172:
2167:
2162:
2158:
2154:
2150:
2146:
2142:
2138:
2136:
2132:
2128:
2116:
2112:
2108:
2101:
2096:
2095:
2094:
2091:
2087:
2083:
2079:
2068:
2066:
2065:
2061:
2057:
2045:
2044:
2043:
2035:
2030:
2029:
2028:
2022:
2018:
2014:
2010:
2006:
2002:
1997:
1992:
1991:
1990:
1637:
1636:
1631:
1552:
1546:
1544:
1543:
1539:
1535:
1526:
1524:
1523:
1519:
1515:
1510:
1506:
1497:
1494:
1491:
1488:
1484:
1481:
1477:
1473:
1470:
1467:
1464:
1461:
1457:
1453:
1450:
1447:
1443:
1439:
1436:
1432:
1427:
1423:
1419:
1410:
1406:
1402:
1398:
1394:
1388:
1384:
1378:
1376:
1375:
1371:
1367:
1363:
1355:
1350:
1346:
1342:
1338:
1334:
1330:
1326:
1322:
1318:
1314:
1313:
1312:
1310:
1306:
1302:
1301:99.235.242.51
1298:
1292:
1288:
1275:
1271:
1267:
1266:2.145.223.233
1263:
1257:
1254:
1253:
1252:
1246:
1244:
1242:
1238:
1234:
1225:
1223:
1222:
1218:
1214:
1206:
1202:
1198:
1194:
1193:82.150.248.28
1190:
1187:
1186:
1185:
1183:
1178:
1177:
1173:
1169:
1160:
1156:
1152:
1148:
1142:
1141:
1140:
1137:
1134:
1130:
1127:
1121:
1115:
1113:
1112:
1108:
1104:
1100:
1094:
1090:
1084:
1083:
1076:
1074:
1072:
1068:
1064:
1063:108.45.150.80
1060:
1055:
1048:
1044:
1040:
1036:
1032:
1031:
1030:
1029:
1025:
1021:
1012:
1006:
1002:
998:
992:
991:
990:
989:
986:
983:
979:
978:
977:
976:
972:
968:
960:
958:
956:
952:
948:
944:
934:
931:
928:
922:
920:
913:
909:
905:
901:
898:
897:
896:
895:
892:
889:
885:
881:
880:
879:
876:
872:
868:
867:88.72.207.149
864:
854:
850:
849:
848:
842:
838:
834:
830:
826:
823:
819:
814:
813:
812:
809:
805:
801:
797:
791:
790:
786:
783:
776:
745:
738:
734:
733:
731:
729:
725:
720:
717:
716:
714:
712:
711:
706:
701:
698:
697:
695:
693:
692:
687:
682:
679:
676:
672:
671:
669:
667:
666:
661:
656:
653:
652:
650:
648:
647:
642:
637:
634:
633:
631:
629:
628:
623:
618:
615:
614:
612:
610:
609:
604:
599:
596:
595:
593:
591:
590:
585:
580:
577:
575:
572:
571:
569:
567:
566:
561:
556:
553:
552:
550:
548:
547:
542:
541:
538:
534:
530:
529:
526:
525:
521:
517:
516:
512:
508:
504:
498:
495:
494:
491:
474:
470:
466:
465:
460:
457:
453:
452:
448:
442:
439:
436:
432:
419:
415:
409:
406:
405:
402:
386:
382:
378:
374:
373:
365:
359:
354:
352:
349:
345:
344:
340:
334:
331:
328:
324:
311:
307:
301:
298:
297:
294:
277:
273:
269:
268:
260:
254:
249:
247:
244:
240:
239:
235:
229:
226:
223:
219:
214:
210:
204:
196:
192:
187:
186:
177:
173:
170:
167:
163:
159:
155:
152:
149:
146:
143:
140:
137:
134:
131:
127:
124:
123:Find sources:
120:
119:
111:
110:Verifiability
108:
106:
103:
101:
98:
97:
96:
87:
83:
81:
78:
76:
72:
69:
67:
64:
63:
57:
53:
52:Learn to edit
49:
46:
41:
40:
37:
36:
32:
26:
22:
18:
17:
2350:
2328:
2308:
2304:
2275:
2271:
2267:
2263:
2259:
2255:
2243:(decimal 7)
2240:
2236:
2232:
2228:
2224:
2220:
2215:your example
2199:
2195:
2193:(decimal 7)
2190:
2186:
2182:
2178:
2174:
2170:
2165:
2160:
2156:
2152:
2148:
2144:
2140:
2134:
2130:
2126:
2124:
2076:— Preceding
2072:
2049:
2041:
2026:
1988:
1632:
1629:
1550:
1530:
1511:
1507:
1503:
1495:
1492:
1489:
1486:
1482:
1479:
1475:
1471:
1468:
1465:
1462:
1459:
1455:
1451:
1448:
1445:
1441:
1437:
1434:
1430:
1424:
1420:
1416:
1408:
1404:
1403:a b = b
1400:
1396:
1392:
1385:
1382:
1366:174.6.72.195
1359:
1332:
1328:
1324:
1320:
1316:
1295:— Preceding
1290:
1286:
1284:
1260:— Preceding
1250:
1229:
1210:
1179:
1164:
1138:
1135:
1131:
1125:
1122:
1119:
1098:
1096:
1093:
1088:
1081:
1080:
1077:Bit-counting
1057:— Preceding
1051:
1016:
964:
938:
932:
929:
926:
918:
859:
846:
817:
800:150.169.8.72
792:
787:
784:
780:
727:
726:
710:Unreferenced
708:
707:
689:
688:
663:
662:
644:
643:
625:
624:
606:
605:
587:
586:
563:
562:
544:
543:
502:
462:
413:
381:project page
370:
306:Mid-priority
305:
265:
231:Mid‑priority
209:WikiProjects
171:
165:
157:
150:
144:
138:
132:
122:
94:
19:This is the
2354:Iarmethodil
2312:Abaczkowski
2052:&,|,~,^
1287:subtracting
967:Robogymnast
961:Pseudo-code
941:—Preceding
389:Electronics
377:electronics
333:Electronics
281:Mathematics
272:mathematics
228:Mathematics
148:free images
31:not a forum
2370:Categories
2287:Nomen4Omen
2201:Douglasdcc
2107:Nomen4Omen
2056:Nomen4Omen
1472:left shift
939:return c
2032:x ^ x = 0
1996:corrected
1458:a
1444:a
1089:AND 0010
982:Oli Filth
598:Computing
88:if needed
71:Be polite
21:talk page
2090:contribs
2078:unsigned
2013:contribs
1885:<<
1758:<<
1534:Bcjordan
1345:contribs
1333:negative
1297:unsigned
1262:unsigned
1233:Skytopia
1059:unsigned
943:unsigned
888:Cburnett
875:contribs
863:unsigned
808:contribs
796:unsigned
646:Maintain
589:Copyedit
56:get help
29:This is
27:article.
1960:Println
1930:Println
1641:package
1454:b := b
1440:c := b
1337:Vadmium
1329:inverse
1213:Rtdrury
1147:Musaran
927:Hello,
904:Acetate
829:Acetate
627:Infobox
565:Cleanup
505:on the
416:on the
308:on the
199:C-class
154:WPÂ refs
142:scholar
2270:0 =
2262:0 XOR
2131:fourth
2127:second
2005:Dsimic
1903:return
1783:return
1647:import
1622:return
1496:return
1409:return
1391:c = b
1327:, and
1293:one?
1291:adding
1129:GPU).
1126:hugely
1092:= 0010
997:SvenPB
608:Expand
205:scale.
126:Google
1855:&
1774:: -->
1773:: -->
1719:&
1650:"fmt"
1601:shift
1556:while
1431:while
1397:while
1321:ones’
1086:0011
1052:also
818:right
691:Stubs
665:Photo
522:with:
169:JSTOR
130:books
84:Seek
2358:talk
2336:talk
2316:talk
2291:talk
2205:talk
2129:and
2111:talk
2086:talk
2060:talk
2009:talk
1915:main
1912:func
1792:func
1653:func
1644:main
1598:left
1538:talk
1518:talk
1478:1
1370:talk
1341:talk
1305:talk
1270:talk
1237:talk
1217:talk
1197:talk
1172:talk
1151:talk
1107:talk
1067:talk
1043:talk
1024:talk
1001:talk
971:talk
951:talk
908:talk
871:talk
833:talk
804:talk
497:High
162:FENS
136:news
73:and
1966:eq2
1954:fmt
1936:eq1
1924:fmt
1831:for
1828:int
1822:var
1816:int
1810:int
1795:eq2
1695:for
1677:int
1671:int
1656:eq1
1592:xor
1577:and
1456:xor
1442:and
1405:xor
1401:and
1393:and
1325:not
1139:S.
856:001
852:011
408:Mid
300:Mid
176:TWL
2372::
2360:)
2318:)
2293:)
2278:0
2207:)
2113:)
2092:)
2088:•
2062:)
2015:)
2011:|
1981:))
1951:))
1918:()
1837:!=
1740:+=
1728:!=
1710:if
1701:!=
1607:by
1540:)
1520:)
1498:b
1476:by
1474:c
1411:b
1395:a
1372:)
1347:)
1343:,
1307:)
1272:)
1243:.
1239:)
1231:--
1219:)
1199:)
1174:)
1153:)
1109:)
1069:)
1045:)
1026:)
1003:)
973:)
953:)
910:)
902:--
886:.
877:).
873:•
835:)
827:--
810:).
806:•
747:}}
741:{{
156:)
54:;
2356:(
2338:)
2334:(
2314:(
2289:(
2276:0
2274:0
2272:1
2268:1
2266:0
2264:1
2260:1
2258:0
2256:0
2241:1
2239:1
2237:1
2233:1
2231:0
2229:1
2225:0
2223:1
2221:0
2219:0
2203:(
2191:1
2189:1
2187:1
2183:1
2181:0
2179:1
2175:0
2173:1
2171:0
2169:0
2161:0
2159:0
2157:1
2153:1
2151:0
2149:1
2145:1
2143:0
2141:0
2109:(
2102::
2098:@
2084:(
2058:(
2007:(
1984:}
1978:3
1975:,
1972:2
1969:(
1963:(
1957:.
1948:3
1945:,
1942:2
1939:(
1933:(
1927:.
1921:{
1909:}
1906:b
1900:}
1897:c
1894:=
1891:a
1888:1
1882:c
1879:=
1876:c
1873:a
1870:^
1867:b
1864:=
1861:b
1858:a
1852:b
1849:=
1846:c
1843:{
1840:0
1834:a
1825:c
1819:{
1813:)
1807:b
1804:,
1801:a
1798:(
1789:}
1786:c
1780:}
1777:1
1770:b
1767:=
1764:b
1761:1
1755:a
1752:=
1749:a
1746:}
1743:a
1737:c
1734:{
1731:0
1725:)
1722:1
1716:b
1713:(
1707:{
1704:0
1698:b
1692:0
1689:=
1686::
1683:c
1680:{
1674:)
1668:b
1665:,
1662:a
1659:(
1625:b
1619:c
1616:=
1613:a
1610:1
1604:c
1595:a
1589:b
1586:=
1583:b
1580:a
1574:b
1571:=
1568:c
1565:0
1562:â‰
1559:a
1536:(
1516:(
1368:(
1351:.
1339:(
1303:(
1268:(
1235:(
1215:(
1195:(
1170:(
1149:(
1105:(
1065:(
1041:(
1022:(
999:(
969:(
949:(
906:(
869:(
831:(
802:(
730::
713::
694::
677:)
668::
649::
630::
611::
592::
568::
549::
509:.
420:.
312:.
211::
172:·
166:·
158:·
151:·
145:·
139:·
133:·
128:(
58:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
