Programmer Guide/General Descriptions/Numerical Expressions - Revision history

Jw at 14:38, 14 December 2017

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	====General====		====General====

Jw at 14:36, 14 December 2017

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	====General====		====General====
	A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:		A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

Jw: /* General */

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General

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	===General===		====General====
	A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:		A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

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Numerical Expressions

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	==~~Numerical Expressions~~==		===General===

	~~'''General'''~~
	A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:		A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

Jw: /* Numerical Expressions */

2016-09-12T07:51:52Z

Numerical Expressions

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	'''General'''		'''General'''

	A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:		A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

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	The conversion to (32 bit) integer values is performed (if necessary) after expression evaluation.		The conversion to (32 bit) integer values is performed (if necessary) after expression evaluation.

	Expressions should be enclosed in quotes to allow blanks inside the expression and to disable parsing of special characters (e.g. the slash '<code>/</code>', which is used in expressions as divide-operator and in commands to mark options).====Operators====		Expressions should be enclosed in quotes to allow blanks inside the expression and to disable parsing of special characters (e.g. the slash '<code>/</code>', which is used in expressions as divide-operator and in commands to mark options).

			====Operators====

	The following operators are supported:		The following operators are supported:

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	'''General'''		'''General'''

	A numerical expression is a combination of symbols which represent some numerical value. In ~~S_TOOLS-STx~~ numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:		A numerical expression is a combination of symbols which represent some numerical value. In {{STX}} numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

	*any integer or decimal number		*any integer or decimal number
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	the operators addition '<code>+</code>', subtraction '<code>-</code>', multiplication '<code></code>', division '<code>/</code>', modulus '<code>%'</code>, logical and '<code>&</code>', logical or '<code>\|</code>', power '<code>^</code>' , NOT '<code>!'</code> , unary minus '<code>-</code>' and parenthesis '<code>(</code>' and '<code>)</code>'.		the operators addition '<code>+</code>', subtraction '<code>-</code>', multiplication '<code></code>', division '<code>/</code>', modulus '<code>%'</code>, logical and '<code>&</code>', logical or '<code>\|</code>', power '<code>^</code>' , NOT '<code>!'</code> , unary minus '<code>-</code>' and parenthesis '<code>(</code>' and '<code>)</code>'.
	*mathematical functions		*mathematical functions
	All calculations are performed using 64 bit floating point numbers. Since the default data format in ~~S_TOOLS-STx~~ macros is the string, the commands <code>NUM</code><code>,</code> <code>INT</code> or <code>EVAL</code> must be used to evaluate numerical expressions when assigning them to a variable (e.g. '<code>#value := PI</code>' assigns the string '<code>PI</code>' to '<code>#value</code>', whereas '<code>#value := NUM PI</code>' assigns '<code>3.14159</code>' to '<code>#value</code>').		All calculations are performed using 64 bit floating point numbers. Since the default data format in {{STX}} macros is the string, the commands <code>NUM</code><code>,</code> <code>INT</code> or <code>EVAL</code> must be used to evaluate numerical expressions when assigning them to a variable (e.g. '<code>#value := PI</code>' assigns the string '<code>PI</code>' to '<code>#value</code>', whereas '<code>#value := NUM PI</code>' assigns '<code>3.14159</code>' to '<code>#value</code>').

	If you use the <code>EVAL</code> command, you can also perform calculations using vectors and matrices. Please see the <code>EVAL</code> command documentation in the Command Reference for details.		If you use the <code>EVAL</code> command, you can also perform calculations using vectors and matrices. Please see the <code>EVAL</code> command documentation in the Command Reference for details.

Admin: 1 revision: Initial import

2010-11-18T16:31:46Z

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initial import

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{{DISPLAYTITLE:{{SUBPAGENAME}}}}
==Numerical Expressions==

'''General'''

A numerical expression is a combination of symbols which represent some numerical value. In S_TOOLS-STx numerical expressions can be used in many places (e.g. in evaluation commands, as an argument, ...) and may contain the following parts:

*any integer or decimal number
*the contents of a numerical variable
*the operators addition '<code>+</code>', subtraction '<code>-</code>', multiplication '<code>*</code>', division '<code>/</code>', modulus '<code>%'</code>, logical and '<code>&</code>', logical or '<code>|</code>', power '<code>^</code>' , NOT '<code>!'</code> , unary minus '<code>-</code>' and parenthesis '<code>(</code>' and '<code>)</code>'.
*mathematical functions
All calculations are performed using 64 bit floating point numbers. Since the default data format in S_TOOLS-STx macros is the string, the commands <code>NUM</code><code>,</code> <code>INT</code> or <code>EVAL</code> must be used to evaluate numerical expressions when assigning them to a variable (e.g. '<code>#value := PI</code>' assigns the string '<code>PI</code>' to '<code>#value</code>', whereas '<code>#value := NUM PI</code>' assigns '<code>3.14159</code>' to '<code>#value</code>').

If you use the <code>EVAL</code> command, you can also perform calculations using vectors and matrices. Please see the <code>EVAL</code> command documentation in the Command Reference for details.

The conversion to (32 bit) integer values is performed (if necessary) after expression evaluation.

Expressions should be enclosed in quotes to allow blanks inside the expression and to disable parsing of special characters (e.g. the slash '<code>/</code>', which is used in expressions as divide-operator and in commands to mark options).====Operators====

The following operators are supported:

=====Unary Operators=====

{|
|-
|sign
|<code>-</code>
|<nowiki>-</nowiki>expr
|-
|logical not
|<code>!</code>
|!expr
|}

=====Binary Operators=====

{|
|-
|add
|<code>+</code>
|exprA+exprB
|-
|subtract
|<code>-</code>
|exprA<nowiki>-</nowiki>exprB
|-
|multiply
|<code>*</code>
|exprA*exprB
|-
|divide
|<code>/</code>
|exprA/exprB
|-
|modulus
|<code>%</code>
|exprA%exprB
|-
|power
|<code>^</code>
|exprA^exprB
|-
|logical and
|<code>&</code>
|exprA&exprB
|-
|logical or
|<code>|</code>
|exprA<nowiki>|</nowiki>exprB
|}

=====Precedence=====

Precedence of operators (Operators on the same level are evaluated from left to right):

*parenthesis ( )

*unary minus '<code>-</code>', logical not '<code>!</code>'

*power '<code>^</code>', logical and '<code>&</code>', logical or '<code>|</code>'

*multiplication '<code>*</code>', division '<code>/</code>', modulus '<code>%</code>'

*addition '<code>+</code>', subtraction '<code>-</code>'

====Functions====

The following mathematical functions are available in [[Programmer Guide/General Descriptions/Numerical Expressions|numerical expressions]]:

=====abs=====

The absolute value of <var>x</var>.{|
|-
|Usage:
|abs(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====acos=====

The inverse cosine of x.{|
|-
|Usage:
|acos(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|<nowiki>-</nowiki>1 <= <var>x</var> <= 1
|}

|
|}

=====asin=====

The inverse sine of x.{|
|-
|Usage:
|asin(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|<nowiki>-</nowiki>1 <= <var>x</var> <= 1
|}

|
|}

=====atan=====

The inverse tangent of x.

{|
|-
|Usage:
|atan(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====bark2hz=====

Computes the Hertz equivalent of the Bark value x.{|
|-
|Usage:
|bark2hz(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value in Bark
|}

|
|}

=====bit=====

Computes 2 ^ x (0 <= <var>x</var> < 32). Use this to compute bit masks.

{|
|-
|Usage:
|bit(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|An integer value (0 <= x <= 32).
|}

|
|}

=====cos=====

The cosine of x.{|
|-
|Usage:
|cos(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A value in radians.
|}

|
|}

=====db=====

The value of x in converted thus: 10 ^ (<var>x</var> / 20)

{|
|-
|Usage:
|db(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====exp=====

The value <code>e</code> raised to the power of <var>x</var>.{|
|-
|Usage:
|exp(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|a numerical value
|}

|
|}

=====floor=====

The floor of x.{|
|-
|Usage:
|floor(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|any real number
|}

|
|}

=====hz2bark=====

Computes the Bark equivalent of the Hertz value x.{|
|-
|Usage:
|hz2bark(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value in Hertz (0 <= x <= 20000).
|}

|
|}

=====int=====

The integer value of x. This function truncates the value <var>x</var>.{|
|-
|Usage:
|int(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====ln=====

The natural logarithm of x.{|
|-
|Usage:
|ln(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value (x > 0)
|}

|
|}

=====log=====

The 10 base logarithm of the argument x.{|
|-
|Usage:
|log(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value (x > 0)
|}

|
|}

=====lran=====

A linear distributed random number (Interval = [0,1]).

=====pi=====

The constant p to 16 decimal places.

=====round=====

Round the number x to the nearest integer.{|
|-
|Usage:
|round(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|The value to round.
|}

|
|}

=====setlran=====

Set the random seed for the lran function to x or the current time.

{|
|-
|Usage:
|setlran(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|Set the random seed to the current time (x = 0) or to the value of <var>x</var> (0 < <var>x</var> < 1).
|}

|
|}

=====sign=====

<nowiki>-</nowiki>1 if <var>x</var> is negative, otherwise 1.

{|
|-
|Usage:
|sign(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====sin=====

The sine of x.{|
|-
|Usage:
|sin(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A value in radians.
|}

|
|}

=====sinc=====

The sinc function of x.

{|
|-
|Usage:
|sinc(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value
|}

|
|}

=====sinx=====

1 if x = 0, otherwise sin(<var>x</var>)/<var>x</var>{|
|-
|Usage:
|sinx(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====sqrt=====

The square root of x.{|
|-
|Usage:
|sqrt(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A numerical value.
|}

|
|}

=====tan=====

The tangent of x.{|
|-
|Usage:
|tan(x)
|-
|Arguments:
|{|
|-
|<var>x</var>
|A value in radians.
|}

|
|}