bitand

Parameters

u, v, w

scalars, vectors, matrices or hypermatrices of null or positive integers encoded as decimal or integer numbers of any signed or unsigned inttype.

Sparse-encoded matrices are not accepted.

If u and v have the same type and inttype, this one is the working one. Otherwise,

• if u or v is decimal-encoded, the working inttype is 0 (real decimal), even if the other operand is int64- or uint64-encoded.
• if u and v are both encoded integers, the working inttype is the widest of both: int8 < uint8 < int16 < uint16 < int32 < uint32 < int64 < uint64.

The result w gets the type of the working encoding.

u and v are processed element-wise.

• If u is a single value (scalar) and v is a vector, matrix or hypermatrix, u is priorly expanded as u*ones(v) in order to operate u with every v component.
• Conversely, v is priorly expanded as v*ones(u) if it is a single value.
• If neither u nor v are scalars, they must have the same sizes.

The result w gets the sizes of u or/and v arrays.

Description

With encoded integers, bitand(u, v) is equivalent to u & v. However, u & v demands that u and v have the same inttype, while bitand(..) accepts mixed operands.

For any decimal integer u greater than 2^52, only its bits from log2(u) down to log2(u)-52 are encoded and can be actually taken into account. Lower bits are not stored and are then ignored.

Examples

bitand(54, 107)
dec2bin([54 107 34]')  // binary representations

--> bitand(54, 107)
 ans  =
   34.

--> dec2bin([54 107 34]')
 ans  =
!0110110  !
!1101011  !
!0100010  !

// Between 2 simple rows with zeros and ones
u = [0 1 0 1];
v = [0 0 1 1];
bitand(u, v)    // [0 0 0 1] expected

// Encoded integers such as int8 are accepted:
u = int8([0 1 0 1]);
v = int8([0 0 1 1]);
bitand(u, v)

// Operands of mixed types are accepted.
// The type of the result is decimal if a decimal operand is involved,
// or the widest integer one otherwise:
u = [0 1 0 1];
v = [0 0 1 1];
z = bitand(u, int64(v));         type(z)      // 1 : decimal representation
z = bitand(uint8(u), int8(v));   typeof(z)    // uint8
z = bitand(uint8(u), int32(v));  typeof(z)    // int32

// Usage with 2 matrices
u = [  0  1   0   1
      54 107 107 54 ];
v = [  0  0   1   1
      107 54 34  34 ];
bitand(u, v)     //  [ 0 0 0 1 ;  34 34 34 34 ]   expected

// Usage with a distributed scalar:
bitand([1 2 4 8 9 10 12], 8)  // == bitand([1 2 4 8 9 10 12], [8 8 8 8 8 8 8])
bitand(4, [1 2 4 8 9 10 12])  // == bitand([4 4 4 4 4 4 4], [1 2 4 8 9 10 12])

// With encoded integers, bitand(u,v) and u & v are equivalent:
u = int8([2 3 10]);
v = int8(13);
[bitand(u, v) ; u & v]
// ... but "&" demands operands having the same type:
u & 13    // mismatching int8- | decimal- encodings

--> u = int8([2 3 10]);
--> v = int8(13);
--> [bitand(u, v) ; u & v]
 ans  =
  0  1  8
  0  1  8
--> u & 13
Undefined operation for the given operands.
check or define function %i_h_s for overloading.

// Examples with big decimal integers:

u = sum(2 .^(600+[0 3 9 20 45]))        // ~ 1.46D+194
bitand(u, 2^601) == 0    // True: The bit #601 is set to 0 in u
v = 2 .^[603 610];
bitand(u, v) == 2^603    // True: the bit #603 is the only one common to u and v
bitand(u, 2^646-1) == 0  // True: 2^646-1 has theoretically bits #1 to #645 set to 1
                         // BUT -1/(2^646) is <<< %eps and is then ignored:
                         // 2^646 is actually used instead of 2^646-1.
                         // Now, 2^646 has bits #1 to #645set to 0. So the result.
bitand(u, 2^646-2^599)==u  // %T: 2^646-2^599 has actually bits #599 to #645 set to 1
//
n = fix(log2(u))       // == 645: Index of the heaviest bit of u
bitand(u, u+2^(n-53)) == u   // True: Addressing bits below the lightest one has no effect
bitand(u, u-2^(n-53)) == u   // True: idem

See also

• & — Binary AND between integers. Logical AND over/between booleans and numbers
• and — logical AND between the elements of a boolean or numerical array
• bitor — bitwise logical OR between element-wise integers of 2 arrays
• dec2bin — 10進数から2進数への変換

History