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 Elementary Functions
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 &, &&
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, 
Binary OR between integers. Logical OR over/between booleans and numbers
Syntax
Elementwise operator:
intMat = intA  intB tfMat = A  B
Scalared shortcircuited evaluation:
tf = U  V if (U  V) then ... end if (U  V) then ... end while (U  V) then ... end while (U  V) then ... end
Arguments
 intA, intB
Arrays of encoded integers of any inttype.
intA
andintB
must have the same sizes to be processed elementwise. IfintA
orintB
is a scalar, it is priorly replicated to the size of the other operand before processing.If
intA
andintB
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
andintB
, and of the wider inttype of both (see hereabove). For any indexi
,intMat(i) = bitor(intA(i), intB(i))
intA  []
and[]  intA
return the boolean arrayintA~=%nan
. A, B
Arrays of booleans or of numbers: encoded integers of any inttype, real or complex numbers.
A
andB
may have distinct types, and may be one or both sparseencoded. The special case whereA
andB
are both encoded integers is excluded (see hereabove).A
andB
must have the same sizes to be processed elementwise. IfA
orB
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
andB
. IfA
orB
is sparseencoded, so istfMat
.For any index
i
,tfMat(i)
is%T
if eitherA(i)
orB(i)
is%T
or not zero. Otherwise,tfMat(i)
is set to%F
.A  []
and[]  A
return[]
. U, V
Arrays of full or sparseencoded booleans or of numbers of any types and encoding: any inttype of encoded integers, full or sparseencoded real or complex numbers.
U
andV
may have distinct data types, number of dimensions, and sizes. tf
single boolean:
U  V
is equal toor(U)  or(V)
, without evaluatingor(V)
ifor(U)
is true (this is why the
operator is socalled shortcircuited).See or() for the definition of the evaluation to true depending on type and encoding.
Description
 
For any boolean or numerical operands
U
andV
,G = U  V
is equivalent toif and(U) // none of U components is null or false G = %t // V is not assessed else G = and(V) end
U
andV
may have distinct sizes or numbers of dimensions. The result is always a single boolean.
and(V)
is evaluated only ifand(U)
is false. This mainly avoids yielding errors when further operations withV
are meaningless or prone to error whenand(U)
is true. See examples.

is useful mainly out ofif ..
andwhile ..
conditions. Otherwise, it is just equivalent to the simple
. 
When the

operator is used inside a logical condition tested by awhile
or by anif
control structure, it is equivalent to the
operator (see above):UV
is equivalent toand(U)and(V)
, without assessingV
ifand(U)
is true.Otherwise,

has two different actions: When both operands are encoded integers,
intA  intB
is processed elementwise and yields an array of integers resulting from the bitwiseAND
between corresponding components.Comparison withbitor()
:intA  intB
accepts negative integers, whilebitor(intA, intB)
does not.bitor(A,B)
works bitwise with decimalencoded integers.  Otherwise,
when operands are arrays of numbers or/and booleans, they are still processed elementwise. Null numbers being considered as booleans false, the result is an array of booleans.
 When both operands are encoded integers,

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 shortcircuited  : // 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 elementwise 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 — Opens a block of instructions iterated on a heading condition
 overloading — display, functions and operators overloading capabilities
History
Version  Description 
6.0   operator added 
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