- Elementary Functions
- Discrete mathematics
- Floating point
- Integer representation
- &, &&
- |, ||
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Binary AND between integers. Logical AND over/between booleans and numbers
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
- intA, intB
Arrays of encoded integers of any inttype.
intBmust have the same sizes to be processed element-wise. If
intBis a scalar, it is priorly replicated to the size of the other operand before processing.
intBhave 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.
Array of encoded integers with the same sizes of
intB, and of the wider inttype of both (see hereabove). For any index
intMat(i) = bitand(intA(i), intB(i))
intA & and
 & intAreturn the boolean array
- A, B
Arrays of booleans or of numbers: encoded integers of any inttype, real or complex numbers.
Bmay have distinct types, and may be one or both sparse-encoded. The special case where
Bare both encoded integers is excluded (see here-above).
Bmust have the same sizes to be processed element-wise. If
Bis a scalar, it is priorly replicated to the size of the other operand before processing.
Boolean array with the same sizes of
Bis sparse-encoded, so is
For any index
%For zero. Otherwise,
tfMat(i)is set to
A & and
 & Areturn
- 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.
Vmay have distinct data types, number of dimensions, and sizes.
single boolean: Set to
and(U) & and(V), without evaluating
and(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.
For any boolean or numerical operands
G = U && Vis equivalent to
if ~and(U), G = %F, else G = and(V), end.
&operator is used inside a logical condition tested by a
whileor by an
ifcontrol structure, it is equivalent to the
&&operator (see above).
&has two different actions:
- When both operands are encoded integers,
intA & intBis processed element-wise and yields an array of integers resulting from the bitwise
ANDbetween 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,
and(A)is equivalent to
A && %T, whereas
and(A, side)has no equivalence with
intA & intBaccepts negative integers, while
bitand(intA, intB)does not.
bitand(A,B)works bitwise with decimal-encoded integers.
The overloading code for
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.
- 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
|6.0||&& operator added|
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