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drop table if exists t1_30237_bool; create table t1_30237_bool(A boolean, B boolean, C boolean); insert into t1_30237_bool values (FALSE, FALSE, FALSE), (FALSE, FALSE, NULL), (FALSE, FALSE, TRUE), (FALSE, NULL, FALSE), (FALSE, NULL, NULL), (FALSE, NULL, TRUE), (FALSE, TRUE, FALSE), (FALSE, TRUE, NULL), (FALSE, TRUE, TRUE), (NULL, FALSE, FALSE), (NULL, FALSE, NULL), (NULL, FALSE, TRUE), (NULL, NULL, FALSE), (NULL, NULL, NULL), (NULL, NULL, TRUE), (NULL, TRUE, FALSE), (NULL, TRUE, NULL), (NULL, TRUE, TRUE), (TRUE, FALSE, FALSE), (TRUE, FALSE, NULL), (TRUE, FALSE, TRUE), (TRUE, NULL, FALSE), (TRUE, NULL, NULL), (TRUE, NULL, TRUE), (TRUE, TRUE, FALSE), (TRUE, TRUE, NULL), (TRUE, TRUE, TRUE) ; Testing OR, XOR, AND select A, B, A OR B, A XOR B, A AND B from t1_30237_bool where C is null order by A, B; A B A OR B A XOR B A AND B NULL NULL NULL NULL NULL NULL 0 NULL NULL 0 NULL 1 1 NULL NULL 0 NULL NULL NULL 0 0 0 0 0 0 0 1 1 1 0 1 NULL 1 NULL NULL 1 0 1 1 0 1 1 1 0 1 Testing that OR is associative select A, B, C, (A OR B) OR C, A OR (B OR C), A OR B OR C from t1_30237_bool order by A, B, C; A B C (A OR B) OR C A OR (B OR C) A OR B OR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 1 1 1 NULL 0 NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 0 1 1 1 1 NULL 1 NULL 1 1 1 NULL 1 0 1 1 1 NULL 1 1 1 1 1 0 NULL NULL NULL NULL NULL 0 NULL 0 NULL NULL NULL 0 NULL 1 1 1 1 0 0 NULL NULL NULL NULL 0 0 0 0 0 0 0 0 1 1 1 1 0 1 NULL 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 NULL NULL 1 1 1 1 NULL 0 1 1 1 1 NULL 1 1 1 1 1 0 NULL 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 NULL 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 select count(*) from t1_30237_bool where ((A OR B) OR C) != (A OR (B OR C)); count(*) 0 Testing that XOR is associative select A, B, C, (A XOR B) XOR C, A XOR (B XOR C), A XOR B XOR C from t1_30237_bool order by A, B, C; A B C (A XOR B) XOR C A XOR (B XOR C) A XOR B XOR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 0 1 NULL NULL NULL NULL 1 NULL NULL NULL NULL NULL 1 0 NULL NULL NULL NULL 1 1 NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 NULL 0 NULL NULL NULL 0 NULL 1 NULL NULL NULL 0 0 NULL NULL NULL NULL 0 0 0 0 0 0 0 0 1 1 1 1 0 1 NULL NULL NULL NULL 0 1 0 1 1 1 0 1 1 0 0 0 1 NULL NULL NULL NULL NULL 1 NULL 0 NULL NULL NULL 1 NULL 1 NULL NULL NULL 1 0 NULL NULL NULL NULL 1 0 0 1 1 1 1 0 1 0 0 0 1 1 NULL NULL NULL NULL 1 1 0 0 0 0 1 1 1 1 1 1 select count(*) from t1_30237_bool where ((A XOR B) XOR C) != (A XOR (B XOR C)); count(*) 0 Testing that AND is associative select A, B, C, (A AND B) AND C, A AND (B AND C), A AND B AND C from t1_30237_bool order by A, B, C; A B C (A AND B) AND C A AND (B AND C) A AND B AND C NULL NULL NULL NULL NULL NULL NULL NULL 0 0 0 0 NULL NULL 1 NULL NULL NULL NULL 0 NULL 0 0 0 NULL 0 0 0 0 0 NULL 0 1 0 0 0 NULL 1 NULL NULL NULL NULL NULL 1 0 0 0 0 NULL 1 1 NULL NULL NULL 0 NULL NULL 0 0 0 0 NULL 0 0 0 0 0 NULL 1 0 0 0 0 0 NULL 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 NULL 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 NULL NULL NULL NULL NULL 1 NULL 0 0 0 0 1 NULL 1 NULL NULL NULL 1 0 NULL 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 NULL NULL NULL NULL 1 1 0 0 0 0 1 1 1 1 1 1 select count(*) from t1_30237_bool where ((A AND B) AND C) != (A AND (B AND C)); count(*) 0 Testing that AND has precedence over OR select A, B, C, (A OR B) AND C, A OR (B AND C), A OR B AND C from t1_30237_bool order by A, B, C; A B C (A OR B) AND C A OR (B AND C) A OR B AND C NULL NULL NULL NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 1 NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 0 0 NULL NULL NULL 0 1 NULL NULL NULL NULL 1 NULL NULL NULL NULL NULL 1 0 0 NULL NULL NULL 1 1 1 1 1 0 NULL NULL NULL NULL NULL 0 NULL 0 0 0 0 0 NULL 1 NULL NULL NULL 0 0 NULL 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 NULL NULL NULL NULL 0 1 0 0 0 0 0 1 1 1 1 1 1 NULL NULL NULL 1 1 1 NULL 0 0 1 1 1 NULL 1 1 1 1 1 0 NULL NULL 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 NULL NULL 1 1 1 1 0 0 1 1 1 1 1 1 1 1 select count(*) from t1_30237_bool where (A OR (B AND C)) != (A OR B AND C); count(*) 0 select A, B, C, (A AND B) OR C, A AND (B OR C), A AND B OR C from t1_30237_bool order by A, B, C; A B C (A AND B) OR C A AND (B OR C) A AND B OR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 1 NULL 1 NULL 0 NULL NULL NULL NULL NULL 0 0 0 0 0 NULL 0 1 1 NULL 1 NULL 1 NULL NULL NULL NULL NULL 1 0 NULL NULL NULL NULL 1 1 1 NULL 1 0 NULL NULL NULL 0 NULL 0 NULL 0 0 0 0 0 NULL 1 1 0 1 0 0 NULL NULL 0 NULL 0 0 0 0 0 0 0 0 1 1 0 1 0 1 NULL NULL 0 NULL 0 1 0 0 0 0 0 1 1 1 0 1 1 NULL NULL NULL NULL NULL 1 NULL 0 NULL NULL NULL 1 NULL 1 1 1 1 1 0 NULL NULL NULL NULL 1 0 0 0 0 0 1 0 1 1 1 1 1 1 NULL 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 select count(*) from t1_30237_bool where ((A AND B) OR C) != (A AND B OR C); count(*) 0 Testing that AND has precedence over XOR select A, B, C, (A XOR B) AND C, A XOR (B AND C), A XOR B AND C from t1_30237_bool order by A, B, C; A B C (A XOR B) AND C A XOR (B AND C) A XOR B AND C NULL NULL NULL NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 1 NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 0 0 NULL NULL NULL 0 1 NULL NULL NULL NULL 1 NULL NULL NULL NULL NULL 1 0 0 NULL NULL NULL 1 1 NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 NULL 0 0 0 0 0 NULL 1 NULL NULL NULL 0 0 NULL 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 NULL NULL NULL NULL 0 1 0 0 0 0 0 1 1 1 1 1 1 NULL NULL NULL NULL NULL 1 NULL 0 0 1 1 1 NULL 1 NULL NULL NULL 1 0 NULL NULL 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 NULL 0 NULL NULL 1 1 0 0 1 1 1 1 1 0 0 0 select count(*) from t1_30237_bool where (A XOR (B AND C)) != (A XOR B AND C); count(*) 0 select A, B, C, (A AND B) XOR C, A AND (B XOR C), A AND B XOR C from t1_30237_bool order by A, B, C; A B C (A AND B) XOR C A AND (B XOR C) A AND B XOR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 0 0 0 0 NULL 0 1 1 NULL 1 NULL 1 NULL NULL NULL NULL NULL 1 0 NULL NULL NULL NULL 1 1 NULL 0 NULL 0 NULL NULL NULL 0 NULL 0 NULL 0 0 0 0 0 NULL 1 1 0 1 0 0 NULL NULL 0 NULL 0 0 0 0 0 0 0 0 1 1 0 1 0 1 NULL NULL 0 NULL 0 1 0 0 0 0 0 1 1 1 0 1 1 NULL NULL NULL NULL NULL 1 NULL 0 NULL NULL NULL 1 NULL 1 NULL NULL NULL 1 0 NULL NULL NULL NULL 1 0 0 0 0 0 1 0 1 1 1 1 1 1 NULL NULL NULL NULL 1 1 0 1 1 1 1 1 1 0 0 0 select count(*) from t1_30237_bool where ((A AND B) XOR C) != (A AND B XOR C); count(*) 0 Testing that XOR has precedence over OR select A, B, C, (A XOR B) OR C, A XOR (B OR C), A XOR B OR C from t1_30237_bool order by A, B, C; A B C (A XOR B) OR C A XOR (B OR C) A XOR B OR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 1 NULL 1 NULL 0 NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 0 1 1 NULL 1 NULL 1 NULL NULL NULL NULL NULL 1 0 NULL NULL NULL NULL 1 1 1 NULL 1 0 NULL NULL NULL NULL NULL 0 NULL 0 NULL NULL NULL 0 NULL 1 1 1 1 0 0 NULL NULL NULL NULL 0 0 0 0 0 0 0 0 1 1 1 1 0 1 NULL 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 NULL NULL NULL NULL NULL 1 NULL 0 NULL NULL NULL 1 NULL 1 1 0 1 1 0 NULL 1 NULL 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 NULL NULL 0 NULL 1 1 0 0 0 0 1 1 1 1 0 1 select count(*) from t1_30237_bool where ((A XOR B) OR C) != (A XOR B OR C); count(*) 0 select A, B, C, (A OR B) XOR C, A OR (B XOR C), A OR B XOR C from t1_30237_bool order by A, B, C; A B C (A OR B) XOR C A OR (B XOR C) A OR B XOR C NULL NULL NULL NULL NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 1 NULL NULL NULL NULL 0 NULL NULL NULL NULL NULL 0 0 NULL NULL NULL NULL 0 1 NULL 1 1 NULL 1 NULL NULL NULL NULL NULL 1 0 1 1 1 NULL 1 1 0 NULL NULL 0 NULL NULL NULL NULL NULL 0 NULL 0 NULL NULL NULL 0 NULL 1 NULL NULL NULL 0 0 NULL NULL NULL NULL 0 0 0 0 0 0 0 0 1 1 1 1 0 1 NULL NULL NULL NULL 0 1 0 1 1 1 0 1 1 0 0 0 1 NULL NULL NULL 1 1 1 NULL 0 1 1 1 1 NULL 1 0 1 1 1 0 NULL NULL 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 NULL NULL 1 1 1 1 0 1 1 1 1 1 1 0 1 1 select count(*) from t1_30237_bool where (A OR (B XOR C)) != (A OR B XOR C); count(*) 0 drop table t1_30237_bool; Testing that NOT has precedence over OR select (NOT FALSE) OR TRUE, NOT (FALSE OR TRUE), NOT FALSE OR TRUE; (NOT FALSE) OR TRUE NOT (FALSE OR TRUE) NOT FALSE OR TRUE 1 0 1 Testing that NOT has precedence over XOR select (NOT FALSE) XOR FALSE, NOT (FALSE XOR FALSE), NOT FALSE XOR FALSE; (NOT FALSE) XOR FALSE NOT (FALSE XOR FALSE) NOT FALSE XOR FALSE 1 1 1 Testing that NOT has precedence over AND select (NOT FALSE) AND FALSE, NOT (FALSE AND FALSE), NOT FALSE AND FALSE; (NOT FALSE) AND FALSE NOT (FALSE AND FALSE) NOT FALSE AND FALSE 0 1 0 Testing that NOT is associative select NOT NOT TRUE, NOT NOT NOT FALSE; NOT NOT TRUE NOT NOT NOT FALSE 1 1 Testing that IS has precedence over NOT select (NOT NULL) IS TRUE, NOT (NULL IS TRUE), NOT NULL IS TRUE; (NOT NULL) IS TRUE NOT (NULL IS TRUE) NOT NULL IS TRUE 0 1 1 select (NOT NULL) IS NOT TRUE, NOT (NULL IS NOT TRUE), NOT NULL IS NOT TRUE; (NOT NULL) IS NOT TRUE NOT (NULL IS NOT TRUE) NOT NULL IS NOT TRUE 1 0 0 select (NOT NULL) IS FALSE, NOT (NULL IS FALSE), NOT NULL IS FALSE; (NOT NULL) IS FALSE NOT (NULL IS FALSE) NOT NULL IS FALSE 0 1 1 select (NOT NULL) IS NOT FALSE, NOT (NULL IS NOT FALSE), NOT NULL IS NOT FALSE; (NOT NULL) IS NOT FALSE NOT (NULL IS NOT FALSE) NOT NULL IS NOT FALSE 1 0 0 select (NOT TRUE) IS UNKNOWN, NOT (TRUE IS UNKNOWN), NOT TRUE IS UNKNOWN; (NOT TRUE) IS UNKNOWN NOT (TRUE IS UNKNOWN) NOT TRUE IS UNKNOWN 0 1 1 select (NOT TRUE) IS NOT UNKNOWN, NOT (TRUE IS NOT UNKNOWN), NOT TRUE IS NOT UNKNOWN; (NOT TRUE) IS NOT UNKNOWN NOT (TRUE IS NOT UNKNOWN) NOT TRUE IS NOT UNKNOWN 1 0 0 select (NOT TRUE) IS NULL, NOT (TRUE IS NULL), NOT TRUE IS NULL; (NOT TRUE) IS NULL NOT (TRUE IS NULL) NOT TRUE IS NULL 0 1 1 select (NOT TRUE) IS NOT NULL, NOT (TRUE IS NOT NULL), NOT TRUE IS NOT NULL; (NOT TRUE) IS NOT NULL NOT (TRUE IS NOT NULL) NOT TRUE IS NOT NULL 1 0 0 Testing that IS [NOT] TRUE/FALSE/UNKNOWN predicates are not associative select TRUE IS TRUE IS TRUE IS TRUE; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS TRUE IS TRUE' at line 1 select FALSE IS NOT TRUE IS NOT TRUE IS NOT TRUE; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS NOT TRUE IS NOT TRUE' at line 1 select NULL IS FALSE IS FALSE IS FALSE; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS FALSE IS FALSE' at line 1 select TRUE IS NOT FALSE IS NOT FALSE IS NOT FALSE; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS NOT FALSE IS NOT FALSE' at line 1 select FALSE IS UNKNOWN IS UNKNOWN IS UNKNOWN; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS UNKNOWN IS UNKNOWN' at line 1 select TRUE IS NOT UNKNOWN IS NOT UNKNOWN IS NOT UNKNOWN; ERROR 42000: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'IS NOT UNKNOWN IS NOT UNKNOWN' at line 1 Testing that IS [NOT] NULL predicates are associative select FALSE IS NULL IS NULL IS NULL; FALSE IS NULL IS NULL IS NULL 0 select TRUE IS NOT NULL IS NOT NULL IS NOT NULL; TRUE IS NOT NULL IS NOT NULL IS NOT NULL 1 Testing that comparison operators are left associative select 1 <=> 2 <=> 2, (1 <=> 2) <=> 2, 1 <=> (2 <=> 2); 1 <=> 2 <=> 2 (1 <=> 2) <=> 2 1 <=> (2 <=> 2) 0 0 1 select 1 = 2 = 2, (1 = 2) = 2, 1 = (2 = 2); 1 = 2 = 2 (1 = 2) = 2 1 = (2 = 2) 0 0 1 select 1 != 2 != 3, (1 != 2) != 3, 1 != (2 != 3); 1 != 2 != 3 (1 != 2) != 3 1 != (2 != 3) 1 1 0 select 1 <> 2 <> 3, (1 <> 2) <> 3, 1 <> (2 <> 3); 1 <> 2 <> 3 (1 <> 2) <> 3 1 <> (2 <> 3) 1 1 0 select 1 < 2 < 3, (1 < 2) < 3, 1 < (2 < 3); 1 < 2 < 3 (1 < 2) < 3 1 < (2 < 3) 1 1 0 select 3 <= 2 <= 1, (3 <= 2) <= 1, 3 <= (2 <= 1); 3 <= 2 <= 1 (3 <= 2) <= 1 3 <= (2 <= 1) 1 1 0 select 1 > 2 > 3, (1 > 2) > 3, 1 > (2 > 3); 1 > 2 > 3 (1 > 2) > 3 1 > (2 > 3) 0 0 1 select 1 >= 2 >= 3, (1 >= 2) >= 3, 1 >= (2 >= 3); 1 >= 2 >= 3 (1 >= 2) >= 3 1 >= (2 >= 3) 0 0 1 Testing that | is associative select 0xF0 | 0x0F | 0x55, (0xF0 | 0x0F) | 0x55, 0xF0 | (0x0F | 0x55); 0xF0 | 0x0F | 0x55 (0xF0 | 0x0F) | 0x55 0xF0 | (0x0F | 0x55) 255 255 255 Testing that & is associative select 0xF5 & 0x5F & 0x55, (0xF5 & 0x5F) & 0x55, 0xF5 & (0x5F & 0x55); 0xF5 & 0x5F & 0x55 (0xF5 & 0x5F) & 0x55 0xF5 & (0x5F & 0x55) 85 85 85 Testing that << is left associative select 4 << 3 << 2, (4 << 3) << 2, 4 << (3 << 2); 4 << 3 << 2 (4 << 3) << 2 4 << (3 << 2) 128 128 16384 Testing that >> is left associative select 256 >> 3 >> 2, (256 >> 3) >> 2, 256 >> (3 >> 2); 256 >> 3 >> 2 (256 >> 3) >> 2 256 >> (3 >> 2) 8 8 256 Testing that & has precedence over | select 0xF0 & 0x0F | 0x55, (0xF0 & 0x0F) | 0x55, 0xF0 & (0x0F | 0x55); 0xF0 & 0x0F | 0x55 (0xF0 & 0x0F) | 0x55 0xF0 & (0x0F | 0x55) 85 85 80 select 0x55 | 0xF0 & 0x0F, (0x55 | 0xF0) & 0x0F, 0x55 | (0xF0 & 0x0F); 0x55 | 0xF0 & 0x0F (0x55 | 0xF0) & 0x0F 0x55 | (0xF0 & 0x0F) 85 5 85 Testing that << has precedence over | select 0x0F << 4 | 0x0F, (0x0F << 4) | 0x0F, 0x0F << (4 | 0x0F); 0x0F << 4 | 0x0F (0x0F << 4) | 0x0F 0x0F << (4 | 0x0F) 255 255 491520 select 0x0F | 0x0F << 4, (0x0F | 0x0F) << 4, 0x0F | (0x0F << 4); 0x0F | 0x0F << 4 (0x0F | 0x0F) << 4 0x0F | (0x0F << 4) 255 240 255 Testing that >> has precedence over | select 0xF0 >> 4 | 0xFF, (0xF0 >> 4) | 0xFF, 0xF0 >> (4 | 0xFF); 0xF0 >> 4 | 0xFF (0xF0 >> 4) | 0xFF 0xF0 >> (4 | 0xFF) 255 255 0 select 0xFF | 0xF0 >> 4, (0xFF | 0xF0) >> 4, 0xFF | (0xF0 >> 4); 0xFF | 0xF0 >> 4 (0xFF | 0xF0) >> 4 0xFF | (0xF0 >> 4) 255 15 255 Testing that << has precedence over & select 0x0F << 4 & 0xF0, (0x0F << 4) & 0xF0, 0x0F << (4 & 0xF0); 0x0F << 4 & 0xF0 (0x0F << 4) & 0xF0 0x0F << (4 & 0xF0) 240 240 15 select 0xF0 & 0x0F << 4, (0xF0 & 0x0F) << 4, 0xF0 & (0x0F << 4); 0xF0 & 0x0F << 4 (0xF0 & 0x0F) << 4 0xF0 & (0x0F << 4) 240 0 240 Testing that >> has precedence over & select 0xF0 >> 4 & 0x55, (0xF0 >> 4) & 0x55, 0xF0 >> (4 & 0x55); 0xF0 >> 4 & 0x55 (0xF0 >> 4) & 0x55 0xF0 >> (4 & 0x55) 5 5 15 select 0x0F & 0xF0 >> 4, (0x0F & 0xF0) >> 4, 0x0F & (0xF0 >> 4); 0x0F & 0xF0 >> 4 (0x0F & 0xF0) >> 4 0x0F & (0xF0 >> 4) 15 0 15 Testing that >> and << have the same precedence select 0xFF >> 4 << 2, (0xFF >> 4) << 2, 0xFF >> (4 << 2); 0xFF >> 4 << 2 (0xFF >> 4) << 2 0xFF >> (4 << 2) 60 60 0 select 0x0F << 4 >> 2, (0x0F << 4) >> 2, 0x0F << (4 >> 2); 0x0F << 4 >> 2 (0x0F << 4) >> 2 0x0F << (4 >> 2) 60 60 30 Testing that binary + is associative select 1 + 2 + 3, (1 + 2) + 3, 1 + (2 + 3); 1 + 2 + 3 (1 + 2) + 3 1 + (2 + 3) 6 6 6 Testing that binary - is left associative select 1 - 2 - 3, (1 - 2) - 3, 1 - (2 - 3); 1 - 2 - 3 (1 - 2) - 3 1 - (2 - 3) -4 -4 2 Testing that binary + and binary - have the same precedence select 1 + 2 - 3, (1 + 2) - 3, 1 + (2 - 3); 1 + 2 - 3 (1 + 2) - 3 1 + (2 - 3) 0 0 0 select 1 - 2 + 3, (1 - 2) + 3, 1 - (2 + 3); 1 - 2 + 3 (1 - 2) + 3 1 - (2 + 3) 2 2 -4 Testing that binary + has precedence over | select 0xF0 + 0x0F | 0x55, (0xF0 + 0x0F) | 0x55, 0xF0 + (0x0F | 0x55); 0xF0 + 0x0F | 0x55 (0xF0 + 0x0F) | 0x55 0xF0 + (0x0F | 0x55) 255 255 335 select 0x55 | 0xF0 + 0x0F, (0x55 | 0xF0) + 0x0F, 0x55 | (0xF0 + 0x0F); 0x55 | 0xF0 + 0x0F (0x55 | 0xF0) + 0x0F 0x55 | (0xF0 + 0x0F) 255 260 255 Testing that binary + has precedence over & select 0xF0 + 0x0F & 0x55, (0xF0 + 0x0F) & 0x55, 0xF0 + (0x0F & 0x55); 0xF0 + 0x0F & 0x55 (0xF0 + 0x0F) & 0x55 0xF0 + (0x0F & 0x55) 85 85 245 select 0x55 & 0xF0 + 0x0F, (0x55 & 0xF0) + 0x0F, 0x55 & (0xF0 + 0x0F); 0x55 & 0xF0 + 0x0F (0x55 & 0xF0) + 0x0F 0x55 & (0xF0 + 0x0F) 85 95 85 Testing that binary + has precedence over << select 2 + 3 << 4, (2 + 3) << 4, 2 + (3 << 4); 2 + 3 << 4 (2 + 3) << 4 2 + (3 << 4) 80 80 50 select 3 << 4 + 2, (3 << 4) + 2, 3 << (4 + 2); 3 << 4 + 2 (3 << 4) + 2 3 << (4 + 2) 192 50 192 Testing that binary + has precedence over >> select 4 + 3 >> 2, (4 + 3) >> 2, 4 + (3 >> 2); 4 + 3 >> 2 (4 + 3) >> 2 4 + (3 >> 2) 1 1 4 select 3 >> 2 + 1, (3 >> 2) + 1, 3 >> (2 + 1); 3 >> 2 + 1 (3 >> 2) + 1 3 >> (2 + 1) 0 1 0 Testing that binary - has precedence over | select 0xFF - 0x0F | 0x55, (0xFF - 0x0F) | 0x55, 0xFF - (0x0F | 0x55); 0xFF - 0x0F | 0x55 (0xFF - 0x0F) | 0x55 0xFF - (0x0F | 0x55) 245 245 160 select 0x55 | 0xFF - 0xF0, (0x55 | 0xFF) - 0xF0, 0x55 | (0xFF - 0xF0); 0x55 | 0xFF - 0xF0 (0x55 | 0xFF) - 0xF0 0x55 | (0xFF - 0xF0) 95 15 95 Testing that binary - has precedence over & select 0xFF - 0xF0 & 0x55, (0xFF - 0xF0) & 0x55, 0xFF - (0xF0 & 0x55); 0xFF - 0xF0 & 0x55 (0xFF - 0xF0) & 0x55 0xFF - (0xF0 & 0x55) 5 5 175 select 0x55 & 0xFF - 0x49, (0x55 & 0xFF) - 0x49, 0x55 & (0xFF - 0x49); 0x55 & 0xFF - 0x49 (0x55 & 0xFF) - 0x49 0x55 & (0xFF - 0x49) 20 12 20 Testing that binary - has precedence over << select 16 - 3 << 2, (16 - 3) << 2, 16 - (3 << 2); 16 - 3 << 2 (16 - 3) << 2 16 - (3 << 2) 52 52 4 select 4 << 3 - 2, (4 << 3) - 2, 4 << (3 - 2); 4 << 3 - 2 (4 << 3) - 2 4 << (3 - 2) 8 30 8 Testing that binary - has precedence over >> select 16 - 3 >> 2, (16 - 3) >> 2, 16 - (3 >> 2); 16 - 3 >> 2 (16 - 3) >> 2 16 - (3 >> 2) 3 3 16 select 16 >> 3 - 2, (16 >> 3) - 2, 16 >> (3 - 2); 16 >> 3 - 2 (16 >> 3) - 2 16 >> (3 - 2) 8 0 8 Testing that * is associative select 2 * 3 * 4, (2 * 3) * 4, 2 * (3 * 4); 2 * 3 * 4 (2 * 3) * 4 2 * (3 * 4) 24 24 24 Testing that * has precedence over | select 2 * 0x40 | 0x0F, (2 * 0x40) | 0x0F, 2 * (0x40 | 0x0F); 2 * 0x40 | 0x0F (2 * 0x40) | 0x0F 2 * (0x40 | 0x0F) 143 143 158 select 0x0F | 2 * 0x40, (0x0F | 2) * 0x40, 0x0F | (2 * 0x40); 0x0F | 2 * 0x40 (0x0F | 2) * 0x40 0x0F | (2 * 0x40) 143 960 143 Testing that * has precedence over & select 2 * 0x40 & 0x55, (2 * 0x40) & 0x55, 2 * (0x40 & 0x55); 2 * 0x40 & 0x55 (2 * 0x40) & 0x55 2 * (0x40 & 0x55) 0 0 128 select 0xF0 & 2 * 0x40, (0xF0 & 2) * 0x40, 0xF0 & (2 * 0x40); 0xF0 & 2 * 0x40 (0xF0 & 2) * 0x40 0xF0 & (2 * 0x40) 128 0 128 Testing that * has precedence over << select 5 * 3 << 4, (5 * 3) << 4, 5 * (3 << 4); 5 * 3 << 4 (5 * 3) << 4 5 * (3 << 4) 240 240 240 select 2 << 3 * 4, (2 << 3) * 4, 2 << (3 * 4); 2 << 3 * 4 (2 << 3) * 4 2 << (3 * 4) 8192 64 8192 Testing that * has precedence over >> select 3 * 4 >> 2, (3 * 4) >> 2, 3 * (4 >> 2); 3 * 4 >> 2 (3 * 4) >> 2 3 * (4 >> 2) 3 3 3 select 4 >> 2 * 3, (4 >> 2) * 3, 4 >> (2 * 3); 4 >> 2 * 3 (4 >> 2) * 3 4 >> (2 * 3) 0 3 0 Testing that * has precedence over binary + select 2 * 3 + 4, (2 * 3) + 4, 2 * (3 + 4); 2 * 3 + 4 (2 * 3) + 4 2 * (3 + 4) 10 10 14 select 2 + 3 * 4, (2 + 3) * 4, 2 + (3 * 4); 2 + 3 * 4 (2 + 3) * 4 2 + (3 * 4) 14 20 14 Testing that * has precedence over binary - select 4 * 3 - 2, (4 * 3) - 2, 4 * (3 - 2); 4 * 3 - 2 (4 * 3) - 2 4 * (3 - 2) 10 10 4 select 4 - 3 * 2, (4 - 3) * 2, 4 - (3 * 2); 4 - 3 * 2 (4 - 3) * 2 4 - (3 * 2) -2 2 -2 Testing that / is left associative select 15 / 5 / 3, (15 / 5) / 3, 15 / (5 / 3); 15 / 5 / 3 (15 / 5) / 3 15 / (5 / 3) 1.00000000 1.00000000 9.0000 Testing that / has precedence over | select 105 / 5 | 2, (105 / 5) | 2, 105 / (5 | 2); 105 / 5 | 2 (105 / 5) | 2 105 / (5 | 2) 23 23 15.0000 select 105 | 2 / 5, (105 | 2) / 5, 105 | (2 / 5); 105 | 2 / 5 (105 | 2) / 5 105 | (2 / 5) 105 21.4000 105 Testing that / has precedence over & select 105 / 5 & 0x0F, (105 / 5) & 0x0F, 105 / (5 & 0x0F); 105 / 5 & 0x0F (105 / 5) & 0x0F 105 / (5 & 0x0F) 5 5 21.0000 select 0x0F & 105 / 5, (0x0F & 105) / 5, 0x0F & (105 / 5); 0x0F & 105 / 5 (0x0F & 105) / 5 0x0F & (105 / 5) 5 1.8000 5 Testing that / has precedence over << select 0x80 / 4 << 2, (0x80 / 4) << 2, 0x80 / (4 << 2); 0x80 / 4 << 2 (0x80 / 4) << 2 0x80 / (4 << 2) 128 128 8.0000 select 0x80 << 4 / 2, (0x80 << 4) / 2, 0x80 << (4 / 2); 0x80 << 4 / 2 (0x80 << 4) / 2 0x80 << (4 / 2) 512 1024.0000 512 Testing that / has precedence over >> select 0x80 / 4 >> 2, (0x80 / 4) >> 2, 0x80 / (4 >> 2); 0x80 / 4 >> 2 (0x80 / 4) >> 2 0x80 / (4 >> 2) 8 8 128.0000 select 0x80 >> 4 / 2, (0x80 >> 4) / 2, 0x80 >> (4 / 2); 0x80 >> 4 / 2 (0x80 >> 4) / 2 0x80 >> (4 / 2) 32 4.0000 32 Testing that / has precedence over binary + select 0x80 / 2 + 2, (0x80 / 2) + 2, 0x80 / (2 + 2); 0x80 / 2 + 2 (0x80 / 2) + 2 0x80 / (2 + 2) 66.0000 66.0000 32.0000 select 0x80 + 2 / 2, (0x80 + 2) / 2, 0x80 + (2 / 2); 0x80 + 2 / 2 (0x80 + 2) / 2 0x80 + (2 / 2) 129.0000 65.0000 129.0000 Testing that / has precedence over binary - select 0x80 / 4 - 2, (0x80 / 4) - 2, 0x80 / (4 - 2); 0x80 / 4 - 2 (0x80 / 4) - 2 0x80 / (4 - 2) 30.0000 30.0000 64.0000 select 0x80 - 4 / 2, (0x80 - 4) / 2, 0x80 - (4 / 2); 0x80 - 4 / 2 (0x80 - 4) / 2 0x80 - (4 / 2) 126.0000 62.0000 126.0000 Testing that ^ is associative select 0xFF ^ 0xF0 ^ 0x0F, (0xFF ^ 0xF0) ^ 0x0F, 0xFF ^ (0xF0 ^ 0x0F); 0xFF ^ 0xF0 ^ 0x0F (0xFF ^ 0xF0) ^ 0x0F 0xFF ^ (0xF0 ^ 0x0F) 0 0 0 select 0xFF ^ 0xF0 ^ 0x55, (0xFF ^ 0xF0) ^ 0x55, 0xFF ^ (0xF0 ^ 0x55); 0xFF ^ 0xF0 ^ 0x55 (0xFF ^ 0xF0) ^ 0x55 0xFF ^ (0xF0 ^ 0x55) 90 90 90 Testing that ^ has precedence over | select 0xFF ^ 0xF0 | 0x0F, (0xFF ^ 0xF0) | 0x0F, 0xFF ^ (0xF0 | 0x0F); 0xFF ^ 0xF0 | 0x0F (0xFF ^ 0xF0) | 0x0F 0xFF ^ (0xF0 | 0x0F) 15 15 0 select 0xF0 | 0xFF ^ 0xF0, (0xF0 | 0xFF) ^ 0xF0, 0xF0 | (0xFF ^ 0xF0); 0xF0 | 0xFF ^ 0xF0 (0xF0 | 0xFF) ^ 0xF0 0xF0 | (0xFF ^ 0xF0) 255 15 255 Testing that ^ has precedence over & select 0xFF ^ 0xF0 & 0x0F, (0xFF ^ 0xF0) & 0x0F, 0xFF ^ (0xF0 & 0x0F); 0xFF ^ 0xF0 & 0x0F (0xFF ^ 0xF0) & 0x0F 0xFF ^ (0xF0 & 0x0F) 15 15 255 select 0x0F & 0xFF ^ 0xF0, (0x0F & 0xFF) ^ 0xF0, 0x0F & (0xFF ^ 0xF0); 0x0F & 0xFF ^ 0xF0 (0x0F & 0xFF) ^ 0xF0 0x0F & (0xFF ^ 0xF0) 15 255 15 Testing that ^ has precedence over << select 0xFF ^ 0xF0 << 2, (0xFF ^ 0xF0) << 2, 0xFF ^ (0xF0 << 2); 0xFF ^ 0xF0 << 2 (0xFF ^ 0xF0) << 2 0xFF ^ (0xF0 << 2) 60 60 831 select 0x0F << 2 ^ 0xFF, (0x0F << 2) ^ 0xFF, 0x0F << (2 ^ 0xFF); 0x0F << 2 ^ 0xFF (0x0F << 2) ^ 0xFF 0x0F << (2 ^ 0xFF) 0 195 0 Testing that ^ has precedence over >> select 0xFF ^ 0xF0 >> 2, (0xFF ^ 0xF0) >> 2, 0xFF ^ (0xF0 >> 2); 0xFF ^ 0xF0 >> 2 (0xFF ^ 0xF0) >> 2 0xFF ^ (0xF0 >> 2) 3 3 195 select 0xFF >> 2 ^ 0xF0, (0xFF >> 2) ^ 0xF0, 0xFF >> (2 ^ 0xF0); 0xFF >> 2 ^ 0xF0 (0xFF >> 2) ^ 0xF0 0xFF >> (2 ^ 0xF0) 0 207 0 Testing that ^ has precedence over binary + select 0xFF ^ 0xF0 + 0x0F, (0xFF ^ 0xF0) + 0x0F, 0xFF ^ (0xF0 + 0x0F); 0xFF ^ 0xF0 + 0x0F (0xFF ^ 0xF0) + 0x0F 0xFF ^ (0xF0 + 0x0F) 30 30 0 select 0x0F + 0xFF ^ 0xF0, (0x0F + 0xFF) ^ 0xF0, 0x0F + (0xFF ^ 0xF0); 0x0F + 0xFF ^ 0xF0 (0x0F + 0xFF) ^ 0xF0 0x0F + (0xFF ^ 0xF0) 30 510 30 Testing that ^ has precedence over binary - select 0xFF ^ 0xF0 - 1, (0xFF ^ 0xF0) - 1, 0xFF ^ (0xF0 - 1); 0xFF ^ 0xF0 - 1 (0xFF ^ 0xF0) - 1 0xFF ^ (0xF0 - 1) 14 14 16 select 0x65 - 0x0F ^ 0x55, (0x65 - 0x0F) ^ 0x55, 0x65 - (0x0F ^ 0x55); 0x65 - 0x0F ^ 0x55 (0x65 - 0x0F) ^ 0x55 0x65 - (0x0F ^ 0x55) 11 3 11 Testing that ^ has precedence over * select 0xFF ^ 0xF0 * 2, (0xFF ^ 0xF0) * 2, 0xFF ^ (0xF0 * 2); 0xFF ^ 0xF0 * 2 (0xFF ^ 0xF0) * 2 0xFF ^ (0xF0 * 2) 30 30 287 select 2 * 0xFF ^ 0xF0, (2 * 0xFF) ^ 0xF0, 2 * (0xFF ^ 0xF0); 2 * 0xFF ^ 0xF0 (2 * 0xFF) ^ 0xF0 2 * (0xFF ^ 0xF0) 30 270 30 Testing that ^ has precedence over / select 0xFF ^ 0xF0 / 2, (0xFF ^ 0xF0) / 2, 0xFF ^ (0xF0 / 2); 0xFF ^ 0xF0 / 2 (0xFF ^ 0xF0) / 2 0xFF ^ (0xF0 / 2) 7.5000 7.5000 135 select 0xF2 / 2 ^ 0xF0, (0xF2 / 2) ^ 0xF0, 0xF2 / (2 ^ 0xF0); 0xF2 / 2 ^ 0xF0 (0xF2 / 2) ^ 0xF0 0xF2 / (2 ^ 0xF0) 1.0000 137 1.0000 Testing that ^ has precedence over % select 0xFF ^ 0xF0 % 0x20, (0xFF ^ 0xF0) % 0x20, 0xFF ^ (0xF0 % 0x20); 0xFF ^ 0xF0 % 0x20 (0xFF ^ 0xF0) % 0x20 0xFF ^ (0xF0 % 0x20) 15 15 239 select 0xFF % 0x20 ^ 0xF0, (0xFF % 0x20) ^ 0xF0, 0xFF % (0x20 ^ 0xF0); 0xFF % 0x20 ^ 0xF0 (0xFF % 0x20) ^ 0xF0 0xFF % (0x20 ^ 0xF0) 47 239 47 Testing that ^ has precedence over DIV select 0xFF ^ 0xF0 DIV 2, (0xFF ^ 0xF0) DIV 2, 0xFF ^ (0xF0 DIV 2); 0xFF ^ 0xF0 DIV 2 (0xFF ^ 0xF0) DIV 2 0xFF ^ (0xF0 DIV 2) 7 7 135 select 0xF2 DIV 2 ^ 0xF0, (0xF2 DIV 2) ^ 0xF0, 0xF2 DIV (2 ^ 0xF0); 0xF2 DIV 2 ^ 0xF0 (0xF2 DIV 2) ^ 0xF0 0xF2 DIV (2 ^ 0xF0) 1 137 1 Testing that ^ has precedence over MOD select 0xFF ^ 0xF0 MOD 0x20, (0xFF ^ 0xF0) MOD 0x20, 0xFF ^ (0xF0 MOD 0x20); 0xFF ^ 0xF0 MOD 0x20 (0xFF ^ 0xF0) MOD 0x20 0xFF ^ (0xF0 MOD 0x20) 15 15 239 select 0xFF MOD 0x20 ^ 0xF0, (0xFF MOD 0x20) ^ 0xF0, 0xFF MOD (0x20 ^ 0xF0); 0xFF MOD 0x20 ^ 0xF0 (0xFF MOD 0x20) ^ 0xF0 0xFF MOD (0x20 ^ 0xF0) 47 239 47