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Expressions are sequences of variables and literals punctuated by operators. Operators determine how the variables and literals are combined, compared, selected, and so on. The operators include:

Operator NameOperators
Additive and Multiplicative Operators+, -, *, /, %
Array Operator[i]
Assignment Operators=, +=, -=, *=, /=, %=
Binary CastsC rules for float and int, C rules or HLSL intrinsics for bool
Bitwise Operators~, <<, >>, &, , ^, <<=, >>=, &=, =, ^=
Boolean Math Operators& &, , ?:
Cast Operator(type)
Comma Operator,
Comparison Operators<, >, , !=, <=, >=
Prefix or Postfix Operators++, --
Structure Operator.
Unary Operators!, -, +
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Many of the operators are per-component, which means that the operation is performed independently for each component of each variable. For example, a single component variable has one operation performed. On the other hand, a four-component variable has four operations performed, one for each component.

All of the operators that do something to the value, such as + and *, work per component.

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The comparison operators require a single component to work unless you use the all or any intrinsic function with a multiple-component variable. The following operation fails because the if statement requires a single bool but receives a bool4:

The following operations succeed:

The binary cast operators asfloat, asint, and so on work per component except for asdouble whose special rules are documented.

Selection operators like period, comma, and array brackets do not work per component.

Cast operators change the number of components. The following cast operations show their equivalence:

Additive and Multiplicative Operators

The additive and multiplicative operators are: +, -, *, /, %

The modulus operator returns the remainder of a division. This produces different results when using integers and floating-point numbers. Integer remainders that are fractional will be truncated.

The modulus operator truncates a fractional remainder when using integers.

The % operator is defined only in cases where either both sides are positive or both sides are negative. Unlike C, it also operates on floating-point data types, as well as integers.

Array Operator

The array member selection operator '[i]' selects one or more components in an array. It is a set of square brackets that contain a zero-based index.

The array operator can also be used to access a vector.

By adding an additional index, the array operator can also access a matrix.

The first index is the zero-based row index. The second index is the zero-based column index.

Assignment Operators

The assignment operators are: =, +=, -=, *=, /=

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Variables can be assigned literal values:

Variables can also be assigned the result of a mathematical operation:

A variable can be used on either side of the equals sign:

Division for floating-point variables is as expected because decimal remainders are not a problem.

Be careful if you are using integers that may get divided, especially when truncation affects the result. This example is identical to the previous example, except for the data type. The truncation causes a very different result.

Binary Casts

Casting operation between int and float will convert the numeric value into the appropriate representations following C rules for truncating an int type. Casting a value from a float to an int and back to a float will result in a lossy conversion based on the precision of the target.

Binary casts may also be performed using Intrinsic Functions (DirectX HLSL), which reinterpret the bit representation of a number into the target data type.

Bitwise Operators

HLSL supports the following bitwise operators, which follow the same precedence as C with regard to other operators. The following table describes the operators.

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Bitwise operators require Shader Model 4_0 with Direct3D 10 and higher hardware.

~Logical Not
<<Left Shift
>>Right Shift
&Logical And
Logical Or
^Logical Xor
<<=Left Shift Equal
>>=Right Shift Equal
&=And Equal
=Or Equal
^=Xor Equal

Bitwise operators are defined to operate only on int and uint data types. Attempting to use bitwise operators on float, or struct data types will result in an error.

Boolean Math Operators


The Boolean math operators are: &&, , ?:

Unlike short-circuit evaluation of &&, , and ?: in C, HLSL expressions never short-circuit an evaluation because they are vector operations. All sides of the expression are always evaluated.

Boolean operators function on a per-component basis. This means that if you compare two vectors, the result is a vector containing the Boolean result of the comparison for each component.

For expressions that use Boolean operators, the size and component type of each variable are promoted to be the same before the operation occurs. The promoted type determines the resolution at which the operation takes place, as well as the result type of the expression. For example an int3 + float expression would be promoted to float3 + float3 for evaluation, and its result would be of type float3.

Cast Operator

An expression preceded by a type name in parenthesis is an explicit type cast. A type cast converts the original expression to the data type of the cast. In general, the simple data types can be cast to the more complex data types (with a promotion cast), but only some complex data types can be cast into simple data types (with a demotion cast).

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Only right hand side type casting is legal. For example, expressions such as (int)myFloat = myInt; are illegal. Use myFloat = (float)myInt; instead.

The compiler also performs implicit type cast. For example, the following two expressions are equivalent:

Comma Operator

The comma operator (,) separates one or more expressions that are to be evaluated in order. The value of the last expression in the sequence is used as the value of the sequence.

Here is one case worth calling attention to. If the constructor type is accidentally left off the right side of the equals sign, the right side now contains four expressions, separated by three commas.

The comma operator evaluates an expression from left to right. This reduces the right hand side to:

HLSL uses scalar promotion in this case, so the result is as if this were written as follows:

In this instance, leaving off the float4 type from the right side is probably a mistake that the compiler is unable to detect because this is a valid statement.

Comparison Operators

The comparison operators are: <, >, , !=, <=, >=.

Compare values that are greater than (or less than) any scalar value:

Or, compare values equal to (or not equal to) any scalar value:

Or combine both and compare values that are greater than or equal to (or less than or equal to) any scalar value:

Each of these comparisons can be done with any scalar data type.

To use comparison operators with vector and matrix types, use the all or any intrinsic function.

This operation fails because the if statement requires a single bool but receives a bool4:

These operations succeed:

Prefix or Postfix Operators

The prefix and postfix operators are: ++, --. Prefix operators change the contents of the variable before the expression is evaluated. Postfix operators change the contents of the variable after the expression is evaluated.

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In this case, a loop uses the contents of i to keep track of the loop count.

Because the postfix increment operator (++) is used, arrayOfFloats[i] is multiplied by 2 before i is incremented. This could be slightly rearranged to use the prefix increment operator. This one is harder to read, although both examples are equivalent.

Because the prefix operator (++) is used, arrayOfFloats[i+1 - 1] is multiplied by 2 after i is incremented.

The prefix decrement and postfix decrement operator (--) are applied in the same sequence as the increment operator. The difference is that decrement subtracts 1 instead of adding 1.

Structure Operator

The structure member selection operator (.) is a period. Given this structure:

It can be read like this:

Each member can be read or written with the structure operator:

Unary Operators

The unary operators are: !, -, +

Unary operators operate on a single operand.

Operator Precedence

When an expression contains more than one operator, operator precedence determines the order of evaluation. Operator precedence for HLSL follows the same precedence as C.


Curly braces ({,}) start and end a statement block. When a statement block uses a single statement, the curly braces are optional.

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