&, &&
Binary AND between integers. Logical AND over/between booleans and numbers
Syntax
Elementwise operator:
intMat = intA & intB tfMat = A & B
and()like 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) = bitand(intA(i), intB(i))
intA & []
and[] & intA
return the boolean arrayintA~=0
. 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 neitherA(i)
norB(i)
are%F
or 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: Set to
and(U) & and(V)
, without evaluatingand(V)
ifand(U)
is false (this is why the&&
operator is socalled shortcircuited).See and() for the definition of the evaluation to false depending on type and encoding.
Description
 &&
For any boolean or numerical operands
U
andV
,G = U && V
is equivalent toif ~and(U), G = %F, else G = and(V), end
. &
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).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.  Otherwise, when operands are arrays of numbers or/and booleans, they are still processed elementwise. Provided that null numbers are equivalent to false booleans, the result is an array of booleans.
 When both operands are encoded integers,
Comparing &
and
&&
with bitand()
and
and()
:
and(A)
is equivalent toA && %T
, whereasand(A, side)
has no equivalence with&&
.intA & intB
accepts negative integers, whilebitand(intA, intB)
does not.bitand(A,B)
works bitwise with decimalencoded 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 logical operation A & B A & spB // Result is sparse encoded iA & spB // Result is sparse encoded cA & iB A & %nan // %nan is %t // & as bitwise operation 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) // Shorted & or &&: //  function res=foo() error("foo() shall not be called") endfunction // & (simple) is always shorted in any if's condition: if %F & foo() then // foo() is not called and this is not executed end A && foo() // A, iA and cA have at least one element equals to 0. iA && foo() // Therefore, foo() is not called cA && foo() iA && iB // iA is evaluated as false resulting in the shortcircuited operation
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 false (so c is false anyway) // But A should be square to be able to compute its det(). This leads to the error // Now, we use the shortcircuited && : // det(A) is NO LONGER computed, since issquare(A) is false => anyway c is false 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: here & is meant as && B = inv(A) else disp("A is not square") 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 c = F > if issquare(A) & det(A)~=0 // => no error: here & is meant as && > B = inv(A) > else > disp("A is not square") > end A is not square
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_h_s for overloading.
See also
 and — ET logique entre éléments d'un tableau booléen ou numérique
 bitand — bitwise logical AND between elementwise integers of 2 arrays
 or operator () — Binary OR between integers. Logical OR over/between booleans and numbers
 not ~ — négation logique
 if — Motclé utilisé pour une exécution conditionnelle
 while — motclé utilisé dans une structure while ... end
 overloading — display, functions and operators overloading capabilities
History
Version  Description 
6.0  && operator added 
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