bitxor bitwise logical XOR between element-wise integers of 2 arrays

## Syntax

                w = bitxor(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)`, `bitxor(u, v)` computes and returns in `w(i)` the bitwise XOR eXclusive-OR conjunction of `u(i)` and `v(i)` bits.
With encoded integers, `bitxor(u,v)` is equivalent to `(u | v) & ~(u & v)`. However, both `|` and `&` operators demand that `u` and `v` have the same inttype, while `bitxor(..)` 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

    bitxor(25, 33)
    dec2bin([25 33 56]')  // binary representations

    --> bitxor(25, 33)
     ans  =
       56.

    --> dec2bin([25 33 56]'))
     ans  =
    !011001  !
    !100001  !
    !111000  !

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

    // Encoded integers such as int8 are accepted:
    u = int8([0 1 0 1]);
    v = int8([0 0 1 1]);
    bitxor(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 = bitxor(u, int64(v));          type(z)       // 1 : decimal representation
    z = bitxor(uint8(u), int8(v));    typeof(z)     // uint8
    z = bitxor(uint8(u), int32(v));   typeof(z)     // int32

    // Usage with 2 matrices
    u = [  1    2    4   8
          25   33   25  33 ];
    v = [  2  2+4  4+8  16
          33   25   56  56 ];
    bitxor(u, v)      //  [ 3 4 8 24 ;  56 56 33 25 ]   expected

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

    // Examples with big decimal integers:

    u = sum(2 .^(600+[0 3 9 20 45]))        // ~ 1.46D+194
    bitxor(u, 2^630) == u+2^630  // true: XOR sets to 1 the missing bit #630 of u, so adds it
    bitxor(u, 2^645) == u-2^645  // true: XOR sets to 0 the existing bit #645 of u, so removes it
    bitxor(u, 2^601) == u        // false: The bit #601 is 0 in u. XOR changes it.
    //
    n = fix(log2(u))           // 645 == Index of the heaviest bit of u
    bitxor(u, 2^(n-52)) == u   // false: The lightest bit of u was at 0 => This changes it
    bitxor(u, 2^(n-53)) == u   // true: Addressing bits below the lightest one doesn't change u

## See also

- |
- or
- bitor
- bitand
- dec2bin

## History

6.0

- Extension to positive signed encoded integers
- Extension to new int64 and uint64 inttypes
- Operands of mixed types or inttypes are now accepted.
- bitxor(scalar, array) and bitxor(array, scalar) are now supported.
- Extension to decimal numbers greater than 2^32 and even than 2^52, up to 1.80D+308 (== number_properties("huge")), for the 52 heaviest encoded bits of their unsigned mantissa.