An expression is a sequence of operators and operands that can be either vectors or scalars. A scalar is a vector with a length of one. It is possible, using round brackets, to nest sub-expressions. Expressions are evaluated according to a series of conversion, grouping, associativity and precedence rules depending on the operator used, the presence of round brackets and the type of operands.

Numeric values

 Numerical values should be written with scientific notation (a numerical value followed by an integer exponent such as 1.234e-5) or using the following scale suffixes:

Characters that follow a number and do not represent a scale suffix and characters that follow a scale suffix are ignored. So the numbers: 1000, 1000.0, 1000Hz, 1e3, 1.0e3, 1KHz, and 1K all represent the same value.

Hexadecimal and binary numbers

If a numeric value starts with the letters 0x or 0X, it is hexadecimal. If it starts with the letters 0b or 0B it is binary. Integer numeric values are limited to 32 bits.

Vectors

Vector names can be specified in either upper or lower case. Square brackets are used to index the elements of a vector. The notation expr[n] denotes the umpteenth element of the vector expr. For multidimensional vectors, the previous notation returns a vector of dimension dim-1 while the notation expr[m][n] returns the umpteenth element of the umpteenth subvector. To extract a sequence of elements from a vector you can use the notation expr[lower, upper] which creates a vector with only the elements between the lower and upper index.

The names of the vectors refer to the current document. To specify a vector of any document you must also specify the handle of the document separating it from the name of the vector with a dot:

document_handle.vector_name

For example:

H10AD56D4A9451745.V(1)

specifies the vector V(1) of the document whose handler is H10AD56D4A9451745.

Operators

Operators are symbols that specify which operation must be performed on the operands. They perform some operations on the vectors contained in an expression.

Arithmetic Operators

Arithmetic operators allow you to perform basic arithmetic operations.

Comma Operator

The comma operator is the sequential evaluation operator and causes the program to examine the first expression preceding the comma before passing to the examination of the second expression following it.

Quote Operator

This operator separates the two elements of a complex number: x'y equals x+j(y). Use the operator to pass complex values to the functions.

Conditional Operators

A conditional expression is in the form:

conditional_expression ? expression1 : expression2

the conditional expression evaluates expression_condition, if its value is different from zero (true condition), returns the value of expression1. Otherwise it returns the value of expression2.

Semicolon Operator

The expression to be evaluated can be single or multiple. The semicolon operator separates the single expressions of a multiple expression.

For example, the following is a single expression:

P1 * sin(P0) + P2 / 2

while the following is a multiple expression:

a = P1 * sin(P0); b = P2 / 2; a + b

In a multiple expression it is allowed to assign any intermediate results to local variables (related to the expression). The final result of a multiple expression is that of the last evaluated expression.

Assignment operators

These operators evaluate the expression on their right and assign the result to the vector specified on their left. The effect of the assignment operator has local validity to the expression.

Relational operators

These operators produce a result of 0 if the relationship is false or 1 if the relationship is true.

Logical operators

These operators produce a result of 0 or 1. Operands are worth 1 if they are different from zero otherwise they are worth zero.

Digital Operators

The following operators produce a result equal to: VLOW, VHIGH or VUNDEF. The value of the operands is determined by the variables VIL and VIH as follows:

HIGH for v>=VIH
LOW for v<=VIL
UNDEF for VIL<v<VIH

If one of the operands is worth UNDEF, the result is VUNDEF for all operators.

Bitwise operators

These operators result in a 32-bit integer number. The operands are converted to 32-bit integers and then the operator is applied.

Constants

The following constants may be used in expressions:

Functions

The following table shows the mathematical functions that can be used. The functions can return a vector or a scalar.

When a real value is required and a complex vector is provided, the module of the complex vector is used.

The subject of trigonometric functions is in radians.

User-defined functions and constants

You can define functions and constants to be used in expressions. You can define either simple functions represented by an expression or complex functions defined by a macro procedure. For more information on external functions, see Define functions and constants for expressions.

See also