Mathematical functions in expressions

Mathematical functions

The following table lists mathematical functions that are commonly used in formulas for CAE expressions. In the table, v denotes the dimensional or dimensionless numerical argument of the function. To avoid unintended results from expressions, always follow the recommendations in the table for the dimensionality of the arguments for the mathematical functions.

For some mathematical functions, the software can issue a warning message when the dimensionality of the argument is inconsistent with that required by the function. For more information, see Inconsistent units warnings.

Function	Description	Recommended dimensions for the argument
ABS(v)	Returns the absolute value of the argument while stripping the units	Dimensionless
ABS(v,USEUNITS,TRUE)	Alternate form of ABS(v) that returns the absolute value of the argument while preserving the units	Any
ABSU(v)	Returns the absolute value of the argument while preserving the units	Any except temperature arguments with the units of C, K, F, and R
ACOSINE(v)	Returns the inverse cosine of the argument	Dimensionless arguments that range between –1 and 1
ASINE(v)	Returns the inverse sine of the argument	Dimensionless arguments that range between –1 and 1
ATANGENT(v)	Returns the inverse tangent of the argument	Dimensionless
ATANGENT2(v1,v2)	Returns the inverse tangent for the quotient v2/v1	Any with both of the arguments having the same dimensionality
AVG(v1,v2,v3,......)	Returns the arithmetic mean of the arguments	Any with all of the arguments having the same dimensionality
CEILING(v)	Rounds the argument to the next highest integer	Any
CEILING(v1,BASE,v2)	Alternate form of CEILING(v) that rounds the argument to the next highest integer independent of the units for the expression	Any with both of the arguments having the same dimensionality
COS(v)	Returns the cosine of the argument	Radians, degrees, or dimensionlessDimensionless arguments are taken to be in degrees
EXP(v)	Returns the exponential function evaluated at v	Dimensionless
FLOOR(v)	Rounds the argument to the next lowest integer	Any
FLOOR(v1,BASE,v2)	Alternate form of FLOOR(v) that rounds the argument to the next lowest integer independent of the units for the expression	Any with both of the arguments having the same dimensionality
HYPCOS(v)	Returns the hyperbolic cosine of the argument	Radians
HYPSIN(v)	Returns the hyperbolic sine of the argument	Radians
HYPTAN(v)	Returns the hyperbolic tangent of the argument	Radians
LOG(v)	Returns the natural logarithm of the argument	Dimensionless and greater than zero
LOG10(v)	Returns the base 10 logarithm of the argument	Dimensionless and greater than zero
MAX(v1,v2,v3,.....)	Returns the largest argument from the set of arguments	Any with all of the arguments having the same dimensionality
MINIMUM(v1,v2,v3,.....)orMIN(v1,v2,v3,.....)	Returns the smallest argument from the set of arguments	Any with all of the arguments having the same dimensionality
MOD(v1,v2)	Returns the modulo of the arguments	Any
MOD(v1,v2,USEUNITS,TRUE)	Alternate form of MOD(v1,v2) that returns the modulo of the arguments independent of the units for the expression	Any with both of the arguments having the same dimensionality
PI()	Returns the number π	N/A(1)
ROUND(v)	Rounds the argument to the closest integer	Any
ROUND(v1,BASE,v2)	Alternate form of ROUND(v) that rounds the argument to the closest integer independent of the units for the expression	Any with both of the arguments having the same dimensionality
SIGN(v)	Returns the sign of the argument or returns zero if the argument is zero	Dimensionless
SIN(v)	Returns the sine of the argument	Radians, degrees, or dimensionlessDimensionless arguments are taken to be in degrees
SQRT(v)	Returns the square root of the argument	Dimensionless arguments and arguments that have dimensions that are perfect squares
TAN(v)	Returns the tangent of the argument	Radians, degrees, or dimensionlessDimensionless arguments are taken to be in degrees
(1) Even though there is no argument for the pi function, it is still necessary to include the parentheses.

Examples of mathematical functions

The following table provides examples of how the expression system evaluates dimensional and dimensionless numerical arguments for each mathematical function when the expression is dimensional or dimensionless and the mathematical function is the formula for the expression.

Function	Description	Example
Expression dimensionality (units)	Formula for the expression	Value for the expression
ABS(v) (1)	Returns the absolute value of the argument while stripping the units	Unitless	abs(–5)	5
abs(–5[sec])	5
abs(–5[min])	300
Length (mm)	abs(–5)	5[mm]
abs(–5[sec])	5[mm]
abs(–5[min])	300[mm]
Time (sec)	abs(–5)	5[sec]
abs(–5[sec])	5[sec]
abs(–5[min])	300[sec]
ABS(v,USEUNITS,TRUE)	Alternate form of ABS(v) that returns the absolute value of the argument while preserving the units	Unitless	abs(–5,useunits,true)	5
abs(–5[sec],useunits,true)	5
abs(–5[min],useunits,true)	300
Length (mm)	abs(–5,useunits,true)	5[mm]
abs(–5[sec],useunits,true)	Invalid (3)
abs(–5[min],useunits,true)	Invalid (3)
Time (sec)	abs(–5,useunits,true)	5[sec]
abs(–5[sec],useunits,true)	5[sec]
abs(–5[min],useunits,true)	300[sec]
ABSU(v) (2)	Returns the absolute value of the argument while preserving the units	Unitless	absu(–5)	5
absu(–5[sec])	5[sec]
absu(–5[min])	5[min]
Length (mm)	absu(–5)	5[mm]
absu(–5[sec])	Invalid (3)
absu(–5[min])	Invalid (3)
Time (sec)	absu(–5)	5[sec]
absu(–5[sec])	5[sec]
absu(–5[min])	300[sec]
ACOSINE(v) (1) (4)	Returns the inverse cosine of the argument	Unitless	acosine(0.5)	60
acosine(0.5[mm])	60
acosine(0.0005[m])	60
Angle (degrees) (5)	acosine(0.5)	60[degrees]
acosine(0.5[mm])	60[degrees]
acosine(0.0005[m])	60[degrees]
ASINE(v) (1) (4)	Returns the inverse sine of the argument	Unitless	asine(0.5)	30
asine(0.5[mm])	30
asine(0.0005[m])	30
Angle (degrees) (5)	asine(0.5)	30[degrees]
asine(0.5[mm])	30[degrees]
asine(0.0005[m])	30[degrees]
ATANGENT(v) (1)	Returns the inverse tangent of the argument	Unitless	atangent(1)	45
atangent(1[mm])	45
atangent(0.001[m])	45
Angle (degrees) (5)	atangent(1)	45[degrees]
atangent(1[mm])	45[degrees]
atangent(0.001[m])	45[degrees]
ATANGENT2(v1,v2) (1)	Returns the inverse tangent for the quotient v2/v1	Unitless	atangent2(1,1)	45
atangent2(1[mm],1[mm])	45
atangent2(1[mm],1)	45
atangent2(1,1[mm])	45
atangent2(0.001[m],0.001[m])	45
atangent2(0.001[m],1)	45
atangent2(1,0.001[m])	45
Angle (degrees) (5)	atangent2(1,1)	45[degrees]
atangent2(1[mm],1[mm])	45[degrees]
atangent2(1[mm],1)	45[degrees]
atangent2(1,1[mm])	45[degrees]
atangent2(0.001[m],0.001[m])	45[degrees]
atangent2(0.001[m],1)	45[degrees]
atangent2(1,0.001[m])	45[degrees]
AVG(v1,v2,v3,......)	Returns the arithmetic mean of the arguments	Unitless	avg(1,2)	1.5
avg(1[mm],2)	1.5
avg(1[mm],2[mm])	1.5
avg(1[mm],0.002[m])	1.5
Length (mm)	avg(1,2)	1.5[mm]
avg(1[mm],2)	1.5[mm]
avg(1[mm],2[mm])	1.5[mm]
avg(1[mm],0.002[m])	1.5[mm]
CEILING(v)	Rounds the argument to the next highest integer	See Ceiling function.
CEILING(v1,BASE,v2)	Alternate form of CEILING(v) that rounds the argument to the next highest integer independent of the units for the expression
COS(v) (1)	Returns the cosine of the argument	Unitless	cos(60)	0.5
cos(60[degrees])	0.5
cos(pi()*1[radians]/3)	0.5
cos(60[mm])	0.5
cos(0.06[m])	0.5
Length (mm)	cos(60)	0.5[mm]
cos(60[degrees])	0.5[mm]
cos(pi()*1[radians]/3)	0.5[mm]
cos(60[mm])	0.5[mm]
cos(0.06[m])	0.5[mm]
EXP(v) (1)	Returns the exponential function evaluated at v	Unitless	exp(1)	2.71828....
exp(1[mm])	2.71828....
exp(0.001[m])	2.71828....
Length (mm)	exp(1)	2.71828....[mm]
exp(1[mm])	2.71828....[mm]
exp(0.001[m])	2.71828....[mm]
FLOOR(v)	Rounds the argument to the next lowest integer	See Floor function.
FLOOR(v1,BASE,v2)	Alternate form of FLOOR(v) that rounds the argument to the next lowest integer independent of the units for the expression
HYPCOS(v)	Returns the hyperbolic cosine of the argument	Unitless	hypcos(2)	1.000609....
hypcos(2[radians])	3.76219....
hypcos(2[degrees])	1.000609....
hypcos(2[mm])	1.000609....
hypcos(2[m])	7.2228....x1014
Length (mm)	hypcos(2)	1.000609....[mm]
hypcos(2[radians])	3.76219....[mm]
hypcos(2[degrees])	1.000609....[mm]
hypcos(2[mm])	1.000609....[mm]
hypcos(2[m])	7.2228....x1014[mm]
HYPSIN(v)	Returns the hyperbolic sine of the argument	Unitless	hypsin(2)	0.034913....
hypsin(2[radians])	3.62686....
hypsin(2[degrees])	0.034913....
hypsin(2[mm])	0.034913....
hypsin(2[m])	7.2228....x1014
Length (mm)	hypsin(2)	0.034913....[mm]
hypsin(2[radians])	3.62686....[mm]
hypsin(2[degrees])	0.034913....[mm]
hypsin(2[mm])	0.034913....[mm]
hypsin(2[m])	7.2228....x1014[mm]
HYPTAN(v)	Returns the hyperbolic tangent of the argument	Unitless	hyptan(2)	0.03489....
hyptan(2[radians])	0.96402....
hyptan(2[degrees])	0.03489....
hyptan(2[mm])	0.03489....
hyptan(2[m])	1
Length (mm)	hyptan(2)	0.03489....[mm]
hyptan(2[radians])	0.96402....[mm]
hyptan(2[degrees])	0.03489....[mm]
hyptan(2[mm])	0.03489....[mm]
hyptan(2[m])	1[mm]
LOG(v) (1)	Returns the natural logarithm of the argument	Unitless	log(exp(1))	1
log(exp(1[mm]))	1
log(exp(0.001[m]))	1
Length (mm)	log(exp(1))	1[mm]
log(exp(1[mm]))	1[mm]
log(exp(0.001[m]))	1[mm]
LOG10(v) (1)	Returns the base 10 logarithm of the argument	Unitless	log10(10)	1
log10(10[mm])	1
log10(0.01[m])	1
Length (mm)	log10(10)	1[mm]
log10(10[mm])	1[mm]
log10(0.01[m])	1[mm]
MAX(v1,v2,v3,.....)	Returns the largest argument from the set of arguments	Unitless	max(–1,0,1,2)	2
max(–1[mm],0[mm],1[mm],2[mm])	2
max(–0.001[m],0[m],0.001[m],0.002[m])	2
Length (mm)	max(–1,0,1,2)	2[mm]
max(–1[mm],0[mm],1[mm],2[mm])	2[mm]
max(–0.001[m],0[m],0.001[m],0.002[m])	2[mm]
MIN(v1,v2,v3,.....)orMINIMUM(v1,v2,v3,.....)	Returns the smallest argument from the set of arguments	Unitless	min(–1,0,1,2)	–1
min(–1[mm],0[mm],1[mm],2[mm])	–1
min(–0.001[m],0[m],0.001[m],0.002[m])	–1
Length (mm)	min(–1,0,1,2)	–1[mm]
min(–1[mm],0[mm],1[mm],2[mm])	–1[mm]
min(–0.001[m],0[m],0.001[m],0.002[m])	–1[mm]
MOD(v1,v2)	Returns the modulo of the arguments	See Modulo function.
MOD(v1,v2,USEUNITS,TRUE)	Alternate form of MOD(v1,v2) that returns the modulo of the arguments independent of the units for the expression
PI()	Returns the number π (6)	Unitless	pi()	3.14159....
Length (mm)	pi()	3.14159....[mm]
ROUND(v)	Rounds the argument to the closest integer	See Rounding function.
ROUND(v1,BASE,v2)	Alternate form of ROUND(v) that rounds the argument to the closest integer independent of the units for the expression
SIGN(v) (1)	Returns the sign of the argument or returns zero if the argument is zero	Unitless	sign(2)	1
sign(0)	0
sign(–2)	–1
sign(–2[mm])	–1
sign(–2[m])	–1
Length (mm)	sign(2)	1[mm]
sign(0)	0[mm]
sign(–2)	–1[mm]
sign(–2[mm])	–1[mm]
sign(–2[m])	–1[mm]
SIN(v) (1)	Returns the sine of the argument	Unitless	sin(30)	0.5
sin(30[degrees])	0.5
sin(pi()*1[radians]/6)	0.5
sin(30[mm])	0.5
sin(0.03[m])	0.5
Length (mm)	sin(30)	0.5[mm]
sin(30[degrees])	0.5[mm]
sin(pi()*1[radians]/6)	0.5[mm]
sin(30[mm])	0.5[mm]
sin(0.03[m])	0.5[mm]
SQRT(v)	Returns the square root of the argument (7)	Unitless	sqrt(4)	2
sqrt(4[mm^2])	2
sqrt(0.000004[m^2])	2
Length (mm)	sqrt(4)	2[mm]
sqrt(4[mm^2])	2[mm]
sqrt(0.000004[m^2])	2[mm]
TAN(v) (1)	Returns the tangent of the argument	Unitless	tan(45)	1
tan(45[degrees])	1
tan(pi()*1[radians]/4)	1
tan(45[mm])	1
tan(0.045[m])	1
Length (mm)	tan(45)	1[mm]
tan(45[degrees])	1[mm]
tan(pi()*1[radians]/4)	1[mm]
tan(45[mm])	1[mm]
tan(0.045[m])	1[mm]
(1) Mathematical function that strips units from the argument. For more information, see Unit stripping mathematical functions. (2) Temperature in units of C, K, F, and R is not a valid argument. However, temperature difference in units of dC, dK, dF, and dR is a valid argument. (3) For the argument to be valid, it must have the same dimensionality as the expression, or be dimensionless. (4) If the argument is dimensionless, valid arguments range between –1 and 1. If the argument is dimensional, valid arguments range between –1[base unit] and 1[base unit]. Thus, 0.0005[m] is a valid argument, but 0.5[m] is not a valid argument because the expression system converts it to 500[mm] prior to evaluating the function. (5) For this formula, angle is the only valid dimensionality for the expression. (6) Even though there is no argument for the pi function, it is still necessary to include the parentheses. (7) Only dimensionless input or input having dimensions that are perfect squares are allowed.

Unit stripping mathematical functions

Some mathematical functions strip the units from the argument before perfoming the mathematical operation.

For example, if the formula for an expression is ABS(-50[sec]), the software begins by stripping the unit from the argument. Then it takes the absolute value of the now dimensionless and unitless argument. If the expression for which the formula is defined has dimensionality and units, the software then assigns that dimensionality and units to the value for the expression. Thus, if the expression dimensionality and units are length and millimeters, the software returns +50 mm as the result.

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