43 bitwise

The package bitwise provides functions that allow to manipulate bits of integer constants. As always maxima attempts to simplify the result of the operation if the actual value of a constant isn’t known considering attributes that might be known for the variables, see the declare mechanism.

43.1 Functions and Variables for bitwise

Function: bit_not (int)

Inverts all bits of a signed integer. The result of this action reads -int - 1.

(%i1) load("bitwise")$

(%i2) bit_not(i);
(%o2)                      bit_not(i)

(%i3) bit_not(bit_not(i));
(%o3)                           i

(%i4) bit_not(3);
(%o4)                          - 4

(%i5) bit_not(100);
(%o5)                         - 101

(%i6) bit_not(-101);
(%o6)                          100

Categories:  Number theory Binary operations Package bitwise

Function: bit_and (int1, ...)

This function calculates a bitwise and of two or more signed integers.

(%i1) load("bitwise")$

(%i2) bit_and(i,i);
(%o2)                           i

(%i3) bit_and(i,i,i);
(%o3)                           i

(%i4) bit_and(1,3);
(%o4)                           1

(%i5) bit_and(-7,7);
(%o5)                           1

If it is known if one of the parameters to bit_and is even this information is taken into consideration by the function.

(%i1) load("bitwise")$

(%i2) declare(e,even,o,odd);
(%o2)                         done

(%i3) bit_and(1,e);
(%o3)                           0

(%i4) bit_and(1,o);
(%o4)                           1

Categories:  Number theory Binary operations Package bitwise

Function: bit_or (int1, ...)

This function calculates a bitwise or of two or more signed integers.

(%i1) load("bitwise")$

(%i2) bit_or(i,i);
(%o2)                           i

(%i3) bit_or(i,i,i);
(%o3)                           i

(%i4) bit_or(1,3);
(%o4)                           3

(%i5) bit_or(-7,7);
(%o5)                          - 1

If it is known if one of the parameters to bit_or is even this information is taken into consideration by the function.

(%i1) load("bitwise")$

(%i2) declare(e,even,o,odd);
(%o2)                         done

(%i3) bit_or(1,e);
(%o3)                         e + 1

(%i4) bit_or(1,o);
(%o4)                           o

Categories:  Number theory Binary operations Package bitwise

Function: bit_xor (int1, ...)

This function calculates a bitwise or of two or more signed integers.

(%i1) load("bitwise")$

(%i2) bit_xor(i,i);
(%o2)                           0

(%i3) bit_xor(i,i,i);
(%o3)                           i

(%i4) bit_xor(1,3);
(%o4)                           2

(%i5) bit_xor(-7,7);
(%o5)                          - 2

If it is known if one of the parameters to bit_xor is even this information is taken into consideration by the function.

(%i1) load("bitwise")$

(%i2) declare(e,even,o,odd);
(%o2)                         done

(%i3) bit_xor(1,e);
(%o3)                         e + 1

(%i4) bit_xor(1,o);
(%o4)                         o - 1

Categories:  Number theory Binary operations Package bitwise

Function: bit_lsh (int, nBits)

This function shifts all bits of the signed integer int to the left by nBits bits. The width of the integer is extended by nBits for this process. The result of bit_lsh therefore is int * 2.

(%i1) load("bitwise")$

(%i2) bit_lsh(0,1);
(%o2)                           0

(%i3) bit_lsh(1,0);
(%o3)                           1

(%i4) bit_lsh(1,1);
(%o4)                           2

(%i5) bit_lsh(1,i);
(%o5)                     bit_lsh(1, i)

(%i6) bit_lsh(-3,1);
(%o6)                          - 6

(%i7) bit_lsh(-2,1);
(%o7)                          - 4

Categories:  Number theory Binary operations Package bitwise

Function: bit_rsh (int, nBits)

This function shifts all bits of the signed integer int to the right by nBits bits. The width of the integer is reduced by nBits for this process.

(%i1) load("bitwise")$

(%i2) bit_rsh(0,1);
(%o2)                           0

(%i3) bit_rsh(2,0);
(%o3)                           2

(%i4) bit_rsh(2,1);
(%o4)                           1

(%i5) bit_rsh(2,2);
(%o5)                           0

(%i6) bit_rsh(-3,1);
(%o6)                          - 2

(%i7) bit_rsh(-2,1);
(%o7)                          - 1

(%i8) bit_rsh(-2,2);
(%o8)                          - 1

Categories:  Number theory Binary operations Package bitwise

Function: bit_length (int)

determines how many bits a variable needs to be long in order to store the number int. This function only operates on positive numbers.

(%i1) load("bitwise")$

(%i2) bit_length(0);
(%o2)                           0

(%i3) bit_length(1);
(%o3)                           1

(%i4) bit_length(7);
(%o4)                           3

(%i5) bit_length(8);
(%o5)                           4

Categories:  Number theory Binary operations Package bitwise

Function: bit_onep (int, nBit)

determines if bits nBit is set in the signed integer int.

(%i1) load("bitwise")$

(%i2) bit_onep(85,0);
(%o2)                         true

(%i3) bit_onep(85,1);
(%o3)                         false

(%i4) bit_onep(85,2);
(%o4)                         true

(%i5) bit_onep(85,3);
(%o5)                         false

(%i6) bit_onep(85,100);
(%o6)                         false

(%i7) bit_onep(i,100);
(%o7)                   bit_onep(i, 100)

For signed numbers the sign bit is interpreted to be more than nBit to the left of the leftmost bit of int that reads 1.

(%i1) load("bitwise")$

(%i2) bit_onep(-2,0);
(%o2)                         false

(%i3) bit_onep(-2,1);
(%o3)                         true

(%i4) bit_onep(-2,2);
(%o4)                         true

(%i5) bit_onep(-2,3);
(%o5)                         true

(%i6) bit_onep(-2,4);
(%o6)                         true

If it is known if the number to be tested is even this information is taken into consideration by the function.

(%i1) load("bitwise")$

(%i2) declare(e,even,o,odd);
(%o2)                         done

(%i3) bit_onep(e,0);
(%o3)                         false

(%i4) bit_onep(o,0);
(%o4)                         true

Categories:  Number theory Binary operations Package bitwise