Vocabulary/bdot
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(m b.) y x (m b.) y Boolean/Bitwise/Bitwise Shift Adverb
Rank Infinity -- operates on [x and] y as a whole -- WHY IS THIS IMPORTANT?
Creates a verb to perform logic on the bit(s) of y (and x, if present).
The operand m (an integer) selects the appropriate logic to apply, according to this table:
For m ... The value of x must fit in: The value of y must fit in: Action _16 to _1 boolean boolean (same as m+16) 0 to 15 boolean boolean logical function: x F y 16 to 31 integer integer bitwise logical function: x L y 32 integer integer left-rotate bits of y by x positions 33 integer integer (unsigned) left-shift bits of y by x positions 34 integer integer (signed) left-shift bits of y by x positions
Notes on the above table:
- (monad) (m b.)y is the same as (dyad) x(m b.)y with x=0
- To shift (or rotate) right instead of left, use a negative value for x
- Left shift fills the vacated positions with 0
- (Unsigned) right shift fills the vacated positions with 0
- (Signed) right shift fills the vacated positions by the value (0|1) of the sign bit.
Examples:
1. Create the logical function of x and y which has its truth table encoded by the number m=2
xandnoty =: 2 b. NB. m=2 gives logical function: (x and not-y) 0 1 0 1 xandnoty 0 0 1 1 0 1 0 0
Note[1]: To encode the truth table t into an integer m, ravel t and treat it as a binary numeral
] t=: 2 2 $ 0 0 1 0 NB. sample truth table: (x and not-y) 0 0 1 0 ] m=: #. , t NB. encode truth table t into an integer m 2 ] m=: 2b0010 NB. or write m directly in base 2 2 ] m=: 2b10010 NB. add 16 for the bitwise verbs 18
Note[2]: To verify the truth table corresponding to a given choice of integer m, use table to show truth table of the created logical function
] m =: 2b0010 NB. ravel of desired truth table: 0 0 ,: 1 0 2 xandnoty =: m b. NB. create corresponding logical fn 0 1 xandnoty table 0 1 +--------+---+ |xandnoty|0 1| +--------+---+ |0 |0 0| |1 |1 0| +--------+---+
table is a
- Standard Library word(s) residing in the 'z'-locale
- Defined in the factory script stdlib.ijs which is located in ~system/main/stdlib.ijs
- View the definition(s) in a JQt session by entering: open '~system/main/stdlib.ijs'
2 Create a bitwise logical function (here, x and not-y) that independently combines corresponding bits of x and y
xandnotybw =: 18 b. NB. (m=16+2) same as (m=2) but combines integers x and y bitwise
showbin =: '01' {~ (32#2)&#: NB. verb to display (list of) integers as (table of) bits
showbin 12 5 , (12 xandnotybw 5)
00000000000000000000000000001100
00000000000000000000000000000101
00000000000000000000000000001000
3. Create a verb to perform rotate left or shift left on the bits of integer y
y=: _12345 NB. non-trivial bit pattern with sign-bit set to 1 showbin y , 4 (32 b.) y NB. (m=32) - rotate left 4 places 11111111111111111100111111000111 11111111111111001111110001111111 showbin y , _4 (33 b.) y NB. (m=33) unsigned shift-right 4 places 11111111111111111100111111000111 00001111111111111111110011111100 showbin y , _4 (34 b.) y NB. signed shift-right 4 places 11111111111111111100111111000111 11111111111111111111110011111100
Note: shift-right 4 places is: shift-left _4 places.
Common Uses
1. Construct a logical verb (e.g. xor) from its truth table
but xor already has a J primitive: ~: . See below: More Information [1])
] m =: 2b0110 NB. from ravel of desired truth table: 0 1 ,: 1 0 6 xor =: m b. NB. create corresponding logical fn 0 1 xor table 0 1 NB. verify truth table of xor +---+---+ |xor|0 1| +---+---+ |0 |0 1| |1 |1 0| +---+---+
2. Find the largest power of 2 that divides a given number, e.g. 448
(17 b. -) 448 NB. y BITWISE_AND (-y) gives the required result 64
3. Implement CRC polynomials using bit-shifting.
More Information
1. Every logical function has an equivalent J primitive.
m Equivalent m Equivalent m Equivalent m Equivalent 0 0"0 4 x < y 8 x +: y (NOR) 12 -. x 1 x *. y (AND) 5 y 9 x = y (XNOR) 13 x <: y 2 x > y 6 x ~: y (XOR) 10 -. y 14 x *: y (NAND) 3 x 7 x +. y (OR) 11 x >: y 15 1"0
Note: the primitive equivalents are faster than (m b.)
2. Operand m may be an array, in which case each result cell will be the array of the results of the logical functions specified by m.
Use These Combinations
Combinations using b. y that have exceptionally good performance include:
What it does Type;
Precisions;
RanksSyntax Variants;
Restrictions
Benefits;
Bug Warnings
Integer reductions on infixes integer x (17 b.)/\ y also (22 b.) (23 b.) (25 b.) in place of (17 b.) much faster than alternatives Integer reductions on partitions integer x (17 b.)//. y (22 b.) (23 b.) (25 b.) in place of (17 b.) avoids building argument cells Polynomial Multiplication (bitwise) integer x (22 b.)//.@(17 b./) y avoids building argument cells Bitwise reductions along diagonals integer (17 b.)//. y (22 b.) (23 b.) in place of (17 b.) avoids building argument cells Integer [quotient/]remainder of power of 2 integer x | y with x a power of 2 If x is positive, (-x) 17 b. y is better to get remainder Bitwise reduction and scan integer x (m b.)/ y
m is 16 to 31
/\ /\. in place of / much faster than alternatives Bitwise operations on bytes byte u&.(a.&i.) y (u y) -: u"0 y avoids conversion to integer (m b.)/&.(a.&i.) y
x (m b.)&.(a.&i.) y
m is 16 to 31