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# bitand

bitwise logical AND between element-wise integers of 2 arrays

### Syntax

`w = bitand(u, v)`

### 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

For each pair of components `u(i)` and `v(i)`, `bitand(u, v)` computes and returns in `w(i)` the bitwise AND conjunction of `u(i)` and `v(i)` bits: Bits of `w(i)` set to 1 are met in `u(i)` AND in `v(i)`. Otherwise, they are set to 0.
 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```