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- &, &&
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See the recommended documentation of this function
&, &&
Binary AND between integers. Logical AND over/between booleans and numbers
Syntax
Element-wise operator:
intMat = intA & intB tfMat = A & B
and()-like short-circuited 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 element-wise. 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 sparse-encoded. The special case whereA
andB
are both encoded integers is excluded (see here-above).A
andB
must have the same sizes to be processed element-wise. 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 sparse-encoded, 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 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
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 so-called short-circuited).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 element-wise 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 element-wise. 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 decimal-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 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 short-circuited 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 short-circuited && : // 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 — logical AND between the elements of a boolean or numerical array
- bitand — bitwise logical AND between element-wise integers of 2 arrays
- or operator (|) — Binary OR between integers. Logical OR over/between booleans and numbers
- not ~ — (~) 論理否定
- if — 条件付き実行
- while — while キーワード
- overloading — 表示,関数および演算子オーバーロード機能
History
バージョン | 記述 |
6.0 | && operator added |
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