# Mathematical Functions

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## Contents

# Maths Functions

The PGM Language supports the maths functions in the Table below.

**Notes:**

- All Function names are NOT case sensitive.
- To use the negative of a value in any of these functions (where allowable), users must enter -1 * value;
- For example y = exp(-x) is
**NOT**allowed, use y = exp(-1 * x)

- For example y = exp(-x) is
- Angles in trigonometric functions are specified in units of radians, not degrees. 1 radian is approximately 57.3 degrees, 1 degree is approximately 0.01745 radians.
- [math]\mathbf{\mathit{radians = \dfrac {180^{o}}{\pi}}}[/math] (Please see Example 4 for sample conversion functions.)

See Also: Math Function Examples
Mathematical Functions | ||||

Function |
Syntax |
Description
| ||
---|---|---|---|---|

Sin |
variable = Sin(variable1) | The Sin function, returns the sine of the argument in radians. Variable1 = an angle in radians
| ||

aSin Implemented in Build137 |
variable1 = aSin(variable) | The aSin function, is the inverse of the sine function. Returns Variable1, an angle in radians. NOTE: Valid range: -1 <= Variable <= 1, for out of range variables, variable1 will be limited by the range, math error will be given in the GControl. | ||

Cos |
variable = Cos(variable1) | The Cos function, returns the cosine of the argument in radians. Variable1 = an angle in radians
| ||

aCos Implemented in Build137 |
variable1 = aCos(variable) | The aCos function, is the inverse of the cosine function. Returns Variable1, an angle in radians. NOTE: Valid range: -1 <= Variable <= 1, for out of range variables, variable1 will be limited by the range, math error will be given in the GControl. | ||

Tan |
variable = Tan(variable1) | The Tan function, returns the tangent of the argument in radians. Variable1 = an angle in radians
| ||

aTan Implemented in Build137 |
variable1 = aTan(variable) | The aTan function, is the inverse of the tangent function. Returns Variable1, an angle in radians.
| ||

ATan2 |
variable = ATan2(y1, y2, x1, x2) | The ATan2 function, returns the angle, in radians, given by the two points. | ||

Degrees Implemented in Build137 |
variable = Degrees(variable1) | This function is used to convert radians to degrees. Can be used to interpret results from the trigonometric functions above. Returns Variable, an angle in degrees from Variable1, an angle in radians. | ||

RadiansImplemented in Build137 |
variable = Radians(variable1) | This function is used to convert degrees to radians. Can be used as input for the trigonometric functions above. Returns Variable, an angle in radians from Variable1, an angle in degrees. | ||

Abs |
variable = Abs(variable1) | The Abs function, returns the absolute value of variable1
| ||

Sqrt |
variable = Sqrt(variable1) | The Sqrt function, returns the square root of variable1. Note: If variable1 is negative an error occurs as the operation is undefined.
| ||

Exp |
variable = Exp(variable1) | The Exp function, returns the exponential of variable1. Note: If the user wishes to use the negative of variable1, the correct syntax is: variable = Exp(-1 * variable1), NOT variable = Exp(-variable1)
| ||

Ln |
variable = Ln(variable1) | The Ln function, returns the natural logarithm of variable1. Note: If variable1 is zero or negative an error occurs as the operation is undefined and the function returns 0.
| ||

Log |
variable = Log(variable1) | The Log function, returns the logarithm of variable1.Note: If variable1 is zero or negative an error occurs as the operation is undefined and the function returns 0.
| ||

Pow |
variable = Pow(variable1, variable2) OR variable = variable1^variable2 |
The Pow function, raises variable1 to the power of variable2. Alternatively, the ^ operator can be used. Notes:
- If
*variable1*is negative and*variable2*is not an integer an error occurs as the operation is undefined. - If the user wishes to use the negative of
*variable2*, the correct syntax is either variable = Pow(variable1, -1 * variable2) OR variable = variable1^(-1 * variable2),**NOT**variable = Pow(variable1, -variable2)
| ||

Max |
variable = Max(variable1, variable2) | The Max function, returns the maximum of variable1 and variable2.
| ||

Min |
variable = Min(variable1, variable2) | The Min function, returns the minimum of variable1 and variable2.
| ||

Range |
variable = Range(low_limit, variable1, hi_limit) | The Range function, ranges variable1 between the two limits.
| ||

Trunc |
variable = Trunc(variable1) | The Trunc function, returns the integer part of variable1.
| ||

Round |
variable = Round(variable1) | The Round function, rounds variable1 to the closest integer variable.
| ||

Roundup |
variable = RoundUp(variable1, decimals) | Variable1: is any real number that you want rounded up; decimals - is the number of digits to which you want to round number. If decimals is 0, then number is rounded up to the nearest integer. If decimals is less than 0, then number is rounded up to the left of the decimal point. | ||

Mod |
variable = Mod(numerator, denominator) | The Mod function, returns the remainder of numerator divided by denominator. The result and the variables may be double variable types. See also Div.Note: Division by zero will result in an error as it is undefined.
| ||

Div |
variable = Div(numerator, denominator) | The Div function, returns the quotient of numerator divided by denominator. The result is a long data type and the parameters may be double variable types. See also Mod.Note: Division by zero will result in an error as it is undefined.
| ||

erf |
variable = erf(variable1) | The erf function returns the the error function integrated between 0 and variable1.
The form of the function is: [math]\operatorname{erf}(z) = \frac{2}{\sqrt{\Pi}}\int\limits_{0}^{z}e^{-t^2} dt\,[/math] | ||

IsNAN |
variable = IsNAN(variable1) | variable1 = double to be tested; The IsNAN function, returns true if variable1 is NAN (not a number) otherwise it returns false. Variable1 should be a double. See also NAN in Predefined Constants and Variables. |

# Examples

## Example 1: Math Functions

REAL Sin_a@, Cos_b@, Tan_c@, aSin_a@, aCos_b@, aTan_c@, f@ INTEGER w@ BIT i* BYTE z* CONST DOUBLE g = 2.5 CONST DOUBLE h = -3.4 CONST DOUBLE a = 0.6 CONST DOUBLE b = 2 CONST DOUBLE c = -0.5 Sin_a = sin(a) ;Sin_a= 0.56464 Cos_b = cos(b) ;Cos_b=-0.41615 Tan_c = tan(c) ;Tan_c=-0.54630 aSin_a = aSin(Sin_a) ;aSin_a= 0.6, implemented in Build137 aCos_b = aCos(Cos_b) ;aCos_b=2.0, implemented in Build137 aTan_c = aTan(Tan_c) ;aTan_c=-0.5, implemented in Build137 f = atan2(1,2,1,2) ;f=0.785 f = abs(g) ;f=2.5 f = abs(h) ;f=3.4 f = sqrt(g) ;f=1.581 f = sqrt(h) ;f=* (NAN) (error) f = exp(-1 * g) ;f=0.0821 f = exp(h) ;f=0.0334 f = ln(g) ;f=0.916 f = ln(h) ;f=* (NAN) (error) f = ln(0) ;f=0 (error) f = log(g) ;f=0.398 w = log(h) ;f=-2147483648 (error) f = pow(g,h) ;f=0.044 f = pow(h,g) ;f=* (NAN) (error) f = trunc(g) ;f=2.0 f = trunc(h) ;f=-3.0 f = round(g) ;f=3.0 f = round(h) ;f=-3.0 w = mod(7,3) ;w=1 w = div(7,3) ;w=2 f = mod(3.4,1.1) ;f=0.1 f = div(3.4,1.1) ;f=3.0 f = mod(g,h) ;f=2.5 f = mod(h,g) ;f=-0.9 f = mod(h,0) ;f=* (NAN) (error) w = div(g,h) ;w=0 w = div(h,g) ;w=1 f = erf(1) ;f=0.84279 f = min(g,h) ;f=-3.4 f = max(g,h) ;f=2.5 f = range(0,h,4) ;f=0.0 f = range(0,g,4) ;f=2.5 f = range(h,-4.2,g) ;f=-3.4 f = range(g,-4.2,h) ;f=2.5 f = Round(2.5) ;rounds to 3 f = Round(0.1) ;rounds to 0 f = Round(-3.7) ;rounds to -4 f = Round(-3.4) ;rounds to -3 f = ROUNDUP(3.2,0) ;Rounds 3.2 up to zero decimal places (4) f = ROUNDUP(76.9,0) ;Rounds 76.9 up to zero decimal places (77) f = ROUNDUP(3.14159, 3) ;Rounds 3.14159 up to three decimal places (3.142) f = ROUNDUP(-3.14159, 1) ;Rounds -3.14159 up to one decimal place (-3.2) f = ROUNDUP(31415.92654, -2) ;Rounds 31415.92654 up to 2 decimal places to the left of the decimal (31500) f = ROUNDUP(3.2,-3) ;Rounds 3.2 up to 3 decimal places to the left of the decimal (1000)

## Example 2: Calculating pH

Real [email protected], [email protected]("ConcMl", "mol/L") H_Concentration = ["P_001.Qo.CMlC:LPh.HCl (mol/L)"] * 1 Tank1_pH = -1 * Log(H_Concentration) $

## Example 3: Inverse Trigonometric Functions

Inverse trigonometric functions have been Implemented in SysCAD 9.3 Build 137, see functions aSin, aCos and aTan.

For users using older versions of SysCAD, where Inverse trigonometric functions were not available, the Atan2 function can be used:

Double Z<0,1>*, ArcSinZ("Ang","rad")@, ArcCosZ("Ang","rad")@ ArcSinZ = Atan2(0, Z, 0, sqrt(1.0 - Z^2)) ArcCosZ = Atan2(0,sqrt(1.0 - Z^2) , 0, Z) Double ZZ*, ArcTanZ("Ang","rad")@ ArcTanZ = Atan2(0, ZZ, 0, 1.0)

## Example 4: Radians and Degrees Conversion

Radians and Degrees Conversion functions have been Implemented in SysCAD 9.3 Build 137, see functions Radians("Degree") and Degrees("Radians").

For users using older versions of SysCAD, where angle conversion functions were not available, the following user defined functions can be used (note that PI is a predefined function in SysCAD):

;--- variable declarations --- TextLabel(, "Convert Radians to Degrees") Real Angle_Radians_Input*<<1>>{Comment("Radians")} Real [email protected]{Comment("Degrees")} TextLabel(, "Convert Degrees to Radians") Real Angle_Degrees_Input*<<180>>{Comment("Degress")} Real [email protected]{Comment("Radians")} ;--- Define Functions --- Function RadToDeg(Real UserDefined_Radians) Return UserDefined_Radians * 180 / PI EndFunct Function DegToRad(Real UserDefined_Degrees) Return UserDefined_Degrees / 180 * PI EndFunct ;--- Convert angles --- Angle_Radians_Result = DegToRad(Angle_Degrees_Input) Angle_Degrees_Result = RadToDeg(Angle_Radians_Input) $ ; --- end of file --- |