Bitwise integer operations
These functions enable integers to be manipulated as bit patterns representing
two'scomplement values, where bit position N
has weight
2**N
.
Bits are numbered from 0 upward. These operations act as though the sign bit of an integer is extended indefinitely to the left. Thus, everywhere above its most significant bit, a positive integer has 0 bits and a negative integer has 1 bit.
Function  Result  Description 

~~ INT1

Integer  Produces the bitwise complement of the integer INT1. That is, there is a 1 in the
result for each bit position for which INT1 has 0. It is always true that ~~ INT =
–(INT + 1) . 
INT1  INT2

Integer  The result of this operation is the bitwise "inclusive or" of INT1 and INT2. That is, there is a 1 in the result for each bit position for which there is a 1 in either INT1 or INT2 or both. 
INT1 /& INT2

Integer  The result of this operation is the bitwise "exclusive or" of INT1 and INT2. That is, there is a 1 in the result for each bit position for which there is a 1 in either INT1 or INT2 but not in both. 
INT1 && INT2

Integer  Produces the bitwise "and" of the integers INT1 and INT2. That is, there is a 1 in the result for each bit position for which there is a 1 in both INT1 and INT2. 
INT1 &&~~ INT2

Integer  Produces the bitwise "and" of INT1 and the bitwise complement of INT2. That is,
there is a 1 in the result for each bit position for which there is a 1 in INT1 and a 0 in
INT2. This is the same as INT1
&& (~~INT2) and is useful for clearing bits of INT1 set in
INT2. 
INT << N

Integer  Produces the bit pattern of INT1 shifted left by N positions. A negative value for N produces a right shift. 
INT >> N

Integer  Produces the bit pattern of INT1 shifted right by N positions. A negative value for N produces a left shift. 
INT1 &&=_0 INT2

Boolean  Equivalent to the Boolean expression INT1 && INT2 /== 0 but is more
efficient. 
INT1 &&/=_0 INT2

Boolean  Equivalent to the Boolean expression INT1 && INT2 == 0 but is more
efficient. 
integer_bitcount(INT)

Integer  Counts the number of 1 or 0 bits in the two'scomplement representation of INT. If
INT is nonnegative, N is the number of 1 bits. If INT is negative, it is the
number of 0 bits. Owing to the sign extension, there are an infinite number of 0 bits in a
nonnegative integer or 1 bits in a negative integer. It is always the case that
integer_bitcount(INT) = integer_bitcount((INT+1)) . 
integer_leastbit(INT)

Integer  Returns the bit position N of the leastsignificant bit set in the integer INT. N is the highest power of 2 by which INT divides exactly. 
integer_length(INT)

Integer  Returns the length in bits of INT as a two'scomplement integer. That is, N is
the smallest integer such that INT < (1 << N) if INT >= 0 INT >= (–1 <<
N) if INT < 0 . If INT is nonnegative, then the representation of INT as
an unsigned integer requires a field of at least N bits. Alternatively, a minimum of
N+1 bits is required to represent INT as a signed integer, regardless of its
sign. 
testbit(INT, N)

Boolean  Tests the bit at position N in the integer INT and returns the state of bit N as a Boolean value, which is true for 1 and false for 0. 