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Math and String Functions In addition to performing simple arithmetic and string operations with the arithmetic and string operators, Visual Basic programs can take advantage of several built-in mathematical functions and string functions to perform useful processing that, otherwise, could require highly complex original code. Mathematical Functions Popular mathematical functions are summarized in the following table. Note that certain functions do not require the Math. prefix. Function
Use
Math.Abs()
Returns the absolute value. Math.Abs(-10) returns 10.
Math.Ceiling()
Returns an integer that is greater than or equal to a number. Math.Ceiling(5.333) returns 6.
Fix()
Returns the integer portion of a number. Fix(5.3333) returns 5.
Math.Floor()
Returns an integer that is less than or equal to a number. Fix(5.3333) returns 5.
Int()
Returns the integer portion of a number. Int(5.3333) returns 5.
Math.Max()
Returns the larger of two numbers. Math.Max(5,7) returns 7.
Math.Min()
Returns the smaller of two numbers. Math.Min(5,7) returns 5.
Math.Pow()
Returns a number raised to a power. Math.Pow(12,2) returns 144.
Rnd()
Returns a random number between 0 and 1. Used in conjunction with Randomizestatement to initialize the random number generator.
Rounds a number to a specified number of decimal places. Rounds up on Math.Round() .5. Math.Round(1.1234567,5) returns 1.12346. Math.Sign()
Returns the sign of a number. Returns -1 if negative and 1 if positive. Math.Sign(-5) returns -1.
Math.Sqrt()
Returns the square root of a positive number. Math.Sqrt(144) returns 12.
Random Numbers
The Rnd() function returns a random number between 0 and 1. More likely, the need is to generate a number within a particular range, between a given low and high number. This is accomplished with the following formula. Math.floor((high - low + 1) * Rnd() + low) For instance, to generate a random number between 0 and 10 the formula becomes Math.floor((10 - 0 + 1) * Rnd() + 0)
String Functions Several built-in string functions perform string manipulations to augment simple concatenation with the "&" operator. These functions are summarized in the following table. Function
Use
Asc()
Returns the character code of the first character of a string. Asc("A") returns 65.
Chr()
Returns the display character of a character code. Chr(65) returns "A".
GetChar()
Returns the character at a specified position in a string, counting from 1. GetChar("This is a string", 7) returns "s".
InStr()
Returns the starting position in a string of a substring, counting from 1. InStr("This is a string", "string") returns 11.
InStrRev()
Returns the starting position in a string of a substring, searching from the end of the string. InStr("This is a string", "string") returns 11.
LCase()
Returns the lower-case conversion of a string. LCase("THIS IS A STRING") returns "this is a string".
Left()
Returns the left-most specified number of characters of a string. Left("This is a string", 4) returns "This".
Len()
Returns the length of a string. Len("This is a string") returns 16.
LTrim()
Removes any leading spaces from a string. LTrim(" This is a string") returns "This is a string".
Mid()
Returns a substring from a string, specified as the starting position
(counting from 1) and the number of characters. Mid("This is a string", 6, 4) returns "is a". Replace()
Replaces all occurences of a substring in a string. Replace("This is a string", " s", " longer s") returns "This are a longer string" (replaces an "s" preceded by a blank space).
Right()
Returns the right-most specified number of characters of a string. Right("This is a string", 6) returns "string".
RTrim()
Removes any trailing spaces from a string. RTrim("This is a string ") returns "This is a string".
Str()
Returns the string equivalent of a number. Str(100) returns "100".
Space()
Fills a string with a given number of spaces. "This" & Space(5) & "string" returns "This string".
StrComp()
Compares two strings. Return values are 0 (strings are equal), 1 (first string has the greater value), or -1 (second string has the greater value) based on sorting sequence. StrComp("This is a string", "This string") returns -1.
StrReverse()
Reverses the characters in a string. StrReverse("This is a string") returns "gnirts a si sihT".
Trim()
Removes any leading and trailing spaces from a string. Trim(" This is a string ") returns "This is a string".
UCase()
Returns the upper-case conversion of a string. UCase("This is a string") returns "THIS IS A STRING".
Val()
Converts a numeric expression to a number. Val( (1 + 2 + 3)^2 ) returns 36.
The above summaries give you a basic idea of the uses of these arithmetic and string functions. There are occasions throughout these tutorials to see them in action and in combination as they are applied to various processing needs.
Introduction
My company needed a small expression evaluator to use in our .NET application. Using the .NET framework compilation capabilities seem to be the most obvious way to make an evaluator. However, in practice this technique has a nasty side effect, it looks like it creates a new DLL in memory each time you evaluate your function and it seems nearly impossible to unload the DLL. You can refer to remarks at the end of the article Evaluating Mathematical Expressions by Compiling C# Code at Runtime for more details. This evaluator is neither using CodeDOM nor trying to compile VB source. On the contrary, it parses your expression and evaluates its value. Compared to other projects that I have seen, this evaluator can do the following: •
access and process string expressions. You can evaluate "Hello" + " " + "world"
•
access and process objects. You can evaluate ThisForm.Left.
•
it also offers easy extensibility.
You can add any number of custom functions without having to change the evaluator code.
Using the code The evaluator can be run with just two lines of code: Dim mEvaluator As New Evaluator Dim res As integer = CInt(mEvaluator.Eval("1+1"))
How to provide variables for the evaluator The evaluator raises an event GetVariable when a keyword is not detected. There is no need for you to publish all the variables and then run the eval. On the contrary, you can provide an on demand function which provides only the needed variables:
Private Sub Evaluator1_GetVariable(ByVal name As String, _ ByRef value As Object) Handles Evaluator1.GetVariable Select Case name Case "anumber" value = 5.0 Case "theForm" value = Me Case "adate" value = #1/1/2005# End Select End Sub
How to extend the evaluator with custom functions The member functions found in the class EvalFunctions are automatically used by the evaluator. In this example, you can see how we can make the evaluator implement the sin and now functions: Public Class EvalFunctions Function sin(ByVal v As Double) As Double Return Math.Sin(v) End Function Function now() As DateTime Return Microsoft.VisualBasic.Now End Function
As you can see you don't need much wrapping, the function can be written and used straightaway in this class. Note however that the evaluator does not make any distinction between the Integers and Doubles. Therefore, remember to use Doubles and not Integers for your function parameters.
How does this work? The evaluator is made of a classic Tokenizer followed by a classic Parser. I wrote both of them in VB, without using any Lex or Bisons tools. The aim was readability over speed. Tokenizing, parsing and execution is done in one pass. This is elegant and at the same time quite efficient because the evaluator never looks ahead or back, more than one character.
The tokenizer
It reads the characters one by one and changes its state according to the characters it encounters. When it recognizes one of the recognized Token types, it returns it to the parser. If it does not recognize a character, it will raise a syntax error exception. Collapse ' Recognized token types : Private Enum eTokenType none ' temporary state end_of_formula ' when the tokenizer reach the end operator_plus ' + operator_minus ' operator_mul ' * operator_div ' / operator_percent ' % open_parenthesis ' ( comma ' , dot ' . close_parenthesis ' ) operator_ne ' <> operator_gt ' <= operator_ge ' >= operator_eq ' = operator_le ' <= operator_lt ' < operator_and ' AND operator_or ' OR operator_not ' NOT operator_concat ' & value_identifier ' any word starting with a letter or _ value_true ' TRUE value_false ' FALSE value_number ' any number starting 0-9 or . value_string ' any string starting ' or " open_bracket ' [ close_bracket ' ] End Enum
The Tokenizer is fairly simple, it accepts a loose VB/Excel syntax. The evaluator is split into two classes, one does the tokenization and the second processes the tokens. This is the standard way of doing it. This is quite flexible also. This way, if you wish you could amend it to accept a C++ syntax by changing the way the parser detects the operators eq, ne, and, or, not... Changing the Tokenizer will not force you to reprogram the rest of the evaluator.
The Parser The Parser is a bit more complicated than a Tokenizer. It is like the Tokenizer with a sort of flow machine, a bit
like a pipe. It will process the token one by one without looking ahead or back. In this article, I speak about operators, left parts and right parts. In the expression 1 + 2, I call + the operator, 1 is the left part and 2 is the right part. One of the complicated concepts of the Parser is priorities. For example, the expression: 1 + 2 * 3
is not treated the same way as the expression: 1 * 2 + 3
The evaluator operates using a standard set of priorities. The multiplication has more priority than addition. Therefore: 1 + 2 * 3 = 1 + 6 = 7 1 * 2 + 3 = 2 + 3 = 5
In the above cases, we need to do the multiplication first.
So how can this be done in one pass? At any time, the parser knows what is its level of priority. Private Enum ePriority none = 0 [concat] = 1 [or] = 2 [and] = 3 [not] = 4 equality = 5 plusminus = 6 muldiv = 7 percent = 8 unaryminus = 9 End Enum
When the parser encounters an operator, it will recursively call the parser to get the right part. When the parser returns the right part, the operator can apply its operation (for example +) and the parsing continues.
The interesting part is that while calculating the right part, the Tokenizer already knows its current level of priority. Therefore, while parsing the right part, if it detects an operator with more priority, it will continue its parsing and return only the resulting value.
You said it supports object? Yes, the evaluator supports the . operator. If you enter the expression theForm.text then the evaluator will return the title of the form. If you enter the expression theForm.left, it will return its runtime left position. This feature is only experimental and has not been tested yet. That is why I have put this code here, hoping others will find its features valuable and submit their improvements.
How does this work? In fact the object came free. I used System.Reflection to evaluate the custom functions. And the same code is used to access the object's methods and properties. When the parser encounters an identifier that is a keyword without any meaning for it, it will try to reflect the CurrentObject to see if it can find a method or a property with the same name. mi = CurrentObject.GetType().GetMethod(func, _ _Reflection.BindingFlags.IgnoreCase _ Or Reflection.BindingFlags.Public _ Or Reflection.BindingFlags.Instance)
If a method or a property is found, it will feed its parameters. valueleft = mi.Invoke(CurrentObject, _ _ System.Reflection.BindingFlags.Default, Nothing, _ DirectCast(parameters.ToArray(GetType(Object)), Object()), Nothing)
Use
Math.Abs()
Returns the absolute value. Math.Abs(-10) returns 10.
Math.Ceiling()
Returns an integer that is greater than or equal to a number. Math.Ceiling(5.333) returns 6.
Fix()
Returns the integer portion of a number. Fix(5.3333) returns 5.
Math.Floor()
Returns an integer that is less than or equal to a number. Fix(5.3333) returns 5.
Int()
Returns the integer portion of a number. Int(5.3333) returns 5.
Math.Max()
Returns the larger of two numbers. Math.Max(5,7) returns 7.
Math.Min()
Returns the smaller of two numbers. Math.Min(5,7) returns 5.
Math.Pow()
Returns a number raised to a power. Math.Pow(12,2) returns 144.
Rnd()
Returns a random number between 0 and 1. Used in conjunction with Randomizestatement to initialize the random number generator.
Rounds a number to a specified number of decimal places. Rounds up on Math.Round() .5. Math.Round(1.1234567,5) returns 1.12346. Math.Sign()
Returns the sign of a number. Returns -1 if negative and 1 if positive. Math.Sign(-5) returns -1.
Math.Sqrt()
Returns the square root of a positive number. Math.Sqrt(144) returns 12.
Random Numbers
The Rnd() function returns a random number between 0 and 1. More likely, the need is to generate a number within a particular range, between a given low and high number. This is accomplished with the following formula. Math.floor((high - low + 1) * Rnd() + low) For instance, to generate a random number between 0 and 10 the formula becomes Math.floor((10 - 0 + 1) * Rnd() + 0)
String Functions Several built-in string functions perform string manipulations to augment simple concatenation with the "&" operator. These functions are summarized in the following table. Function
Use
Asc()
Returns the character code of the first character of a string. Asc("A") returns 65.
Chr()
Returns the display character of a character code. Chr(65) returns "A".
GetChar()
Returns the character at a specified position in a string, counting from 1. GetChar("This is a string", 7) returns "s".
InStr()
Returns the starting position in a string of a substring, counting from 1. InStr("This is a string", "string") returns 11.
InStrRev()
Returns the starting position in a string of a substring, searching from the end of the string. InStr("This is a string", "string") returns 11.
LCase()
Returns the lower-case conversion of a string. LCase("THIS IS A STRING") returns "this is a string".
Left()
Returns the left-most specified number of characters of a string. Left("This is a string", 4) returns "This".
Len()
Returns the length of a string. Len("This is a string") returns 16.
LTrim()
Removes any leading spaces from a string. LTrim(" This is a string") returns "This is a string".
Mid()
Returns a substring from a string, specified as the starting position
(counting from 1) and the number of characters. Mid("This is a string", 6, 4) returns "is a". Replace()
Replaces all occurences of a substring in a string. Replace("This is a string", " s", " longer s") returns "This are a longer string" (replaces an "s" preceded by a blank space).
Right()
Returns the right-most specified number of characters of a string. Right("This is a string", 6) returns "string".
RTrim()
Removes any trailing spaces from a string. RTrim("This is a string ") returns "This is a string".
Str()
Returns the string equivalent of a number. Str(100) returns "100".
Space()
Fills a string with a given number of spaces. "This" & Space(5) & "string" returns "This string".
StrComp()
Compares two strings. Return values are 0 (strings are equal), 1 (first string has the greater value), or -1 (second string has the greater value) based on sorting sequence. StrComp("This is a string", "This string") returns -1.
StrReverse()
Reverses the characters in a string. StrReverse("This is a string") returns "gnirts a si sihT".
Trim()
Removes any leading and trailing spaces from a string. Trim(" This is a string ") returns "This is a string".
UCase()
Returns the upper-case conversion of a string. UCase("This is a string") returns "THIS IS A STRING".
Val()
Converts a numeric expression to a number. Val( (1 + 2 + 3)^2 ) returns 36.
The above summaries give you a basic idea of the uses of these arithmetic and string functions. There are occasions throughout these tutorials to see them in action and in combination as they are applied to various processing needs.
Introduction
My company needed a small expression evaluator to use in our .NET application. Using the .NET framework compilation capabilities seem to be the most obvious way to make an evaluator. However, in practice this technique has a nasty side effect, it looks like it creates a new DLL in memory each time you evaluate your function and it seems nearly impossible to unload the DLL. You can refer to remarks at the end of the article Evaluating Mathematical Expressions by Compiling C# Code at Runtime for more details. This evaluator is neither using CodeDOM nor trying to compile VB source. On the contrary, it parses your expression and evaluates its value. Compared to other projects that I have seen, this evaluator can do the following: •
access and process string expressions. You can evaluate "Hello" + " " + "world"
•
access and process objects. You can evaluate ThisForm.Left.
•
it also offers easy extensibility.
You can add any number of custom functions without having to change the evaluator code.
Using the code The evaluator can be run with just two lines of code: Dim mEvaluator As New Evaluator Dim res As integer = CInt(mEvaluator.Eval("1+1"))
How to provide variables for the evaluator The evaluator raises an event GetVariable when a keyword is not detected. There is no need for you to publish all the variables and then run the eval. On the contrary, you can provide an on demand function which provides only the needed variables:
Private Sub Evaluator1_GetVariable(ByVal name As String, _ ByRef value As Object) Handles Evaluator1.GetVariable Select Case name Case "anumber" value = 5.0 Case "theForm" value = Me Case "adate" value = #1/1/2005# End Select End Sub
How to extend the evaluator with custom functions The member functions found in the class EvalFunctions are automatically used by the evaluator. In this example, you can see how we can make the evaluator implement the sin and now functions: Public Class EvalFunctions Function sin(ByVal v As Double) As Double Return Math.Sin(v) End Function Function now() As DateTime Return Microsoft.VisualBasic.Now End Function
As you can see you don't need much wrapping, the function can be written and used straightaway in this class. Note however that the evaluator does not make any distinction between the Integers and Doubles. Therefore, remember to use Doubles and not Integers for your function parameters.
How does this work? The evaluator is made of a classic Tokenizer followed by a classic Parser. I wrote both of them in VB, without using any Lex or Bisons tools. The aim was readability over speed. Tokenizing, parsing and execution is done in one pass. This is elegant and at the same time quite efficient because the evaluator never looks ahead or back, more than one character.
The tokenizer
It reads the characters one by one and changes its state according to the characters it encounters. When it recognizes one of the recognized Token types, it returns it to the parser. If it does not recognize a character, it will raise a syntax error exception. Collapse ' Recognized token types : Private Enum eTokenType none ' temporary state end_of_formula ' when the tokenizer reach the end operator_plus ' + operator_minus ' operator_mul ' * operator_div ' / operator_percent ' % open_parenthesis ' ( comma ' , dot ' . close_parenthesis ' ) operator_ne ' <> operator_gt ' <= operator_ge ' >= operator_eq ' = operator_le ' <= operator_lt ' < operator_and ' AND operator_or ' OR operator_not ' NOT operator_concat ' & value_identifier ' any word starting with a letter or _ value_true ' TRUE value_false ' FALSE value_number ' any number starting 0-9 or . value_string ' any string starting ' or " open_bracket ' [ close_bracket ' ] End Enum
The Tokenizer is fairly simple, it accepts a loose VB/Excel syntax. The evaluator is split into two classes, one does the tokenization and the second processes the tokens. This is the standard way of doing it. This is quite flexible also. This way, if you wish you could amend it to accept a C++ syntax by changing the way the parser detects the operators eq, ne, and, or, not... Changing the Tokenizer will not force you to reprogram the rest of the evaluator.
The Parser The Parser is a bit more complicated than a Tokenizer. It is like the Tokenizer with a sort of flow machine, a bit
like a pipe. It will process the token one by one without looking ahead or back. In this article, I speak about operators, left parts and right parts. In the expression 1 + 2, I call + the operator, 1 is the left part and 2 is the right part. One of the complicated concepts of the Parser is priorities. For example, the expression: 1 + 2 * 3
is not treated the same way as the expression: 1 * 2 + 3
The evaluator operates using a standard set of priorities. The multiplication has more priority than addition. Therefore: 1 + 2 * 3 = 1 + 6 = 7 1 * 2 + 3 = 2 + 3 = 5
In the above cases, we need to do the multiplication first.
So how can this be done in one pass? At any time, the parser knows what is its level of priority. Private Enum ePriority none = 0 [concat] = 1 [or] = 2 [and] = 3 [not] = 4 equality = 5 plusminus = 6 muldiv = 7 percent = 8 unaryminus = 9 End Enum
When the parser encounters an operator, it will recursively call the parser to get the right part. When the parser returns the right part, the operator can apply its operation (for example +) and the parsing continues.
The interesting part is that while calculating the right part, the Tokenizer already knows its current level of priority. Therefore, while parsing the right part, if it detects an operator with more priority, it will continue its parsing and return only the resulting value.
You said it supports object? Yes, the evaluator supports the . operator. If you enter the expression theForm.text then the evaluator will return the title of the form. If you enter the expression theForm.left, it will return its runtime left position. This feature is only experimental and has not been tested yet. That is why I have put this code here, hoping others will find its features valuable and submit their improvements.
How does this work? In fact the object came free. I used System.Reflection to evaluate the custom functions. And the same code is used to access the object's methods and properties. When the parser encounters an identifier that is a keyword without any meaning for it, it will try to reflect the CurrentObject to see if it can find a method or a property with the same name. mi = CurrentObject.GetType().GetMethod(func, _ _Reflection.BindingFlags.IgnoreCase _ Or Reflection.BindingFlags.Public _ Or Reflection.BindingFlags.Instance)
If a method or a property is found, it will feed its parameters. valueleft = mi.Invoke(CurrentObject, _ _ System.Reflection.BindingFlags.Default, Nothing, _ DirectCast(parameters.ToArray(GetType(Object)), Object()), Nothing)
