bitor bitwise logical OR between element-wise integers of 2 arrays

## Syntax

                w = bitor(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.

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

## Description

For each pair of components `u(i)` and `v(i)`, `bitor(u, v)` computes and returns in `w(i)` the bitwise OR conjunction of `u(i)` and `v(i)` bits.
With encoded integers, `bitor(u, v)` is equivalent to `u | v`. However, `u | v` demands that `u` and `v` have the same inttype, while `bitor(..)` 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

    bitor(25, 33)
    dec2bin([25 33 57]')  // binary representations

    --> bitor(25, 33)
     ans  =
       57.

    --> dec2bin([25 33 57]'))
     ans  =
    !011001  !
    !100001  !
    !111001  !

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

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

    // Usage with 2 matrices
    u = [  1  2  4  8
          25 33 25 33 ];
    v = [  2  4  8 16
          33 25 57 57 ];
    bitor(u, v)      //  [ 3 6 12 24 ;  57 57 57 57 ]   expected

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

    // With encoded integers, bitor(u,v) and u|v are equivalent:
    u = int8([2 3 10]);
    v = int8(6);
    [bitor(u, v) ; u | v]
    // ... but "|" demands operands with the same type:
    u | 6    // mismatching int8- | decimal- encodings

    --> u = int8([2 3 10]);
    --> v = int8(6);
    --> [bitor(u, v) ; u | v]
     ans  =
      6  7  14
      6  7  14
    --> u | 6
    Undefined operation for the given operands.
    check or define function %i_g_s for overloading.

    // Examples with big decimal integers:

    u = sum(2 .^(600+[0 3 9 20 45]))        // ~ 1.46D+194
    v = 2^630                               // ~ 4.46D+189
    w = bitor(u, v)
    w == (u+v)  // must be true, since u is built without the bit #630
    bitor(u, 2^645) == u   // true, since u has already its bit #645 set to 1
    bitor(u, 2^601) == u   // false
    //
    n = fix(log2(u))       // Index of the heaviest bit of u
    bitor(u, 2^(n-52)) == u   // false: The lightest bit of u was at 0 => This changes it
    bitor(u, 2^(n-53)) == u   // true: Addressing bits below the lightest doesn't change u

## See also

- |
- or
- bitxor
- 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.
- bitor(scalar, array) and bitor(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.