|, ||

Arguments

intA, intB

Arrays of encoded integers of any inttype.

intA and intB must have the same sizes to be processed element-wise. If intA or intB is a scalar, it is priorly replicated to the size of the other operand before processing.

If intA and intB have not the same integer inttype, the operand with the smaller encoding is converted to the wider according to the following ranks: int8 < uint8 < int16 < uint16 < int32 < uint32 < int64 < uint64.

intMat

Array of encoded integers with the same sizes of intA and intB, and of the wider inttype of both (see hereabove). For any index i, intMat(i) = bitor(intA(i), intB(i))

intA | [] and [] | intA return the boolean array intA~=%nan.

A, B

Arrays of booleans or of numbers: encoded integers of any inttype, real or complex numbers. A and B may have distinct types, and may be one or both sparse-encoded. The special case where A and B are both encoded integers is excluded (see here-above).

A and B must have the same sizes to be processed element-wise. If A or B is a scalar, it is priorly replicated to the size of the other operand before processing.

tfMat

Boolean array with the same sizes of A and B. If A or B is sparse-encoded, so is tfMat.

For any index i, tfMat(i) is %T if either A(i) or B(i) is %T or not zero. Otherwise, tfMat(i) is set to %F.

A | [] and [] | A return [].

U, V

Arrays of full or sparse-encoded booleans or of numbers of any types and encoding: any inttype of encoded integers, full or sparse-encoded real or complex numbers.

U and V may have distinct data types, number of dimensions, and sizes.

tf

single boolean: U || V is equal to or(U) | or(V), without evaluating or(V) if or(U) is true (this is why the || operator is so-called short-circuited).

See or() for the definition of the evaluation to true depending on type and encoding.

Description

||

For any boolean or numerical operands U and V, G = U || V is equivalent to

if and(U) // none of U components is null or false
    G = %t
    // V is not assessed
else
    G = and(V)
end

• U and V may have distinct sizes or numbers of dimensions.
• The result is always a single boolean.
• and(V) is evaluated only if and(U) is false. This mainly avoids yielding errors when further operations with V are meaningless or prone to error when and(U) is true. See examples.

|| is useful mainly out of if .. and while .. conditions. Otherwise, it is just equivalent to the simple |.

|

When the | operator is used inside a logical condition tested by a while or by an if control structure, it is equivalent to the || operator (see above): U|V is equivalent to and(U)|and(V), without assessing V if and(U) is true.

Otherwise, | has two different actions:

1. When both operands are encoded integers,

   intA | intB is processed element-wise and yields an array of integers resulting from the bitwise AND between corresponding components.

   Comparison with bitor() : intA | intB accepts negative integers, while bitor(intA, intB) does not. bitor(A,B) works bitwise with decimal-encoded integers.

2. Otherwise,

   when operands are arrays of numbers or/and booleans, they are still processed element-wise. Null numbers being considered as booleans false, the result is an array of booleans.

The overloading code for | and || operators is g.

%nan is true. A polynomial or rational is not considered as a number and is not an acceptable operand for | or ||.

Examples

A = [0 1; 1 0];   // equivalent to [%f %t ; %t %f]
B = [1 1; 0 0];   // equivalent to [%t %t ; %f %f]
spA = sparse(A);
spB = sparse(B);
spbA = sparse(A<>0);
spbB = sparse(B<>0);
iA = int8(A);
iB = int8(B);
cA = A + 0*%i;
cB = B + 0*%i;

// | as bitwise (and elementwise) operation
// ----------------------------------------
// Both operands and the result are arrays of encoded integers

iA | iB

Ai8 = int8([ -1, 1; 127, -128]);
// Integer representation of Ai8:
// [ 1111 1111, 0000 0001 ;
//   0111 1111, 1000 0000 ]

Bi8 = int8([-2, 0; 126, -127]);
// Integer representation of Bi8:
// [ 1111 1110, 0000 0000 ;
//   0111 1110, 1000 0001 ]

Ai8 | Bi8

// Integer promotion
Ai16  = int16(Ai8);
Bui32 = uint32(Bi8);

r = Ai16 | Bui32, typeof(r)

// | as logical elementwise operation
// ----------------------------------
// Operands are arrays of booleans or of numbers. The result is an array of booleans

A | B
A | spB    // Result is sparse encoded
iA | spB   // Result is sparse encoded
cA | iB
A | %nan   // %nan is %t

// Shorted and scalared  | or ||:
// -----------------------------
// Operands are arrays of booleans or of numbers. The result is a single boolean

function res=foo()
    error("foo() shall not be called")
endfunction

// | (simple) is always shorted in any if's condition:
if  %T | foo() then
    // foo() is not called and this is not executed
end

// || is scalared and shorted in any boolean expression, even out of if or while ones:
T = [-2 1];
T  || foo()        // T has only true (non zero) components, and so is "true as a whole".
int8(T) || foo()   // Therefore, foo() as right operand is not assessed / called.
T+0*%i || foo()

Avoiding conditional errors in or out of if and while conditions:

A = [ 1 3 -2 ; 4 -1  2]
c = ~issquare(A) | det(A)~=0
// det(A) is evaluated despite ~issquare(A) is true (so c is true anyway)
// But A should be square to be able to compute its det(). ==> ERROR

// Now, we use the short-circuited || :
// det(A) is NO LONGER computed, since ~issquare(A) is true => anyway c is true
c = ~issquare(A) || det(A)~=0     // => NO ERROR

// In an "if" (or "while") tested condition, | is equivalent to ||
if ~issquare(A) | det(A)~=0       // => NO ERROR
   B = A * A.'
end

--> A = [ 1 3 -2 ; 4 -1  2]
 A  =
   1.   3.  -2.
   4.  -1.   2.

--> c = ~issquare(A) | det(A)~=0
det: Wrong type for input argument #1: Square matrix expected.

--> c = ~issquare(A) || det(A)~=0    // => NO ERROR
 c  =
  T

--> if ~issquare(A) | det(A)~=0      // => NO ERROR
  >    B = A * A.'
  > end
 B  =
   14.  -3.
  -3.    21.

Constant polynomials or rationals can't be processed with | or ||:

p = 1 + 0*%z
typeof(p)
p | 1

--> p = 1 + 0*%z
 p  =
   1

--> typeof(p)
 ans  =
 polynomial

--> p | 1
Undefined operation for the given operands.
check or define function %p_g_s for overloading.

See also

• or — logical OR over the elements of a boolean or numerical array
• bitor — bitwise logical OR between element-wise integers of 2 arrays
• and operator (&) — Binary AND between integers. Logical AND over/between booleans and numbers
• not ~ — (~) logical not
• if — keyword for conditional execution
• while — while keyword
• overloading — display, functions and operators overloading capabilities

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