Functions, prefixes, and algebraic operators

Equations and parameters

You can use equations wherever you can enter a numeric value. For example, you can write equations in the Edit Dimensions dialog box, feature dialog boxes, and the Parameters dialog box. Equations can vary in complexity, and you can use them to calculate feature sizes, calculate assembly constraints offsets or angles, or simulate motion among several components.

Equations can be simple or contain many algebraic operators, prefixes, and functions. For example, here is a simple equation:

2 ul *(6+3)

The following complex equation uses internal parameters such as pi:

(PI rad/5 ul +(25 deg *PI rad)/180 deg))

Algebraic operators

The following are the algebraic operators supported by ProdName.

+: addition
-: subtraction
%: floating point modulo
*: multiplication
/: division
^: power
( or ): expression delimiters
;: delimiter for multi-argument functions

Unit prefixes

The following table lists the unit prefixes supported by ProdName.

exa: Symbol E
Value1.0e18
peta: Symbol P
Value1.0e15
tera: Symbol T
Value 1.0e12
giga: Symbol G
Value 1.0e9
mega: Symbol M
Value 1.0e6
kilo: Symbol k
Value 1.0e3
hecto: Symbol v
Value1.0e2
deca: Symbol da
Value 1.0e1
deci: Symbol d
Value 1.0e-1
centi: Symbol c
Value 1.0e-2
milli: Symbol m
Value 1.0e-3
micro: Symbol micro
Value 1.0-6
nano: Symbol n
Value 1.0-9
Pi co: Symbol p
Value 1.0e-12
femto: Symbol f
Value 1.0-15
atto: Symbol a
Value 1.0e-18

When you use unit prefixes in an equation, enter the prefix symbol. Do not enter the prefix itself. For example, an equation that includes the unit "nanometer" might look like this equation: 3.5 ul * 2.6 nm.

When you add the unit prefix for name to the meter unit, your equation is calculated based on the length of 2.6 nanometers.

Note: Prefix symbols are case sensitive. Enter them exactly as they appear in the previous table.

Functions

You can use the following functions in edit boxes.

Syntax	Returns Unit Type	Expected Unit Type
cos(expr)	unitless	angle
sin(expr)	unitless	angle
tan(expr)	unitless	angle
acos(expr)	angle	unitless
asin(expr)	angle	unitless
atan(expr)	angle	unitless
cosh(expr)	unitless	angle
sinh(expr)	unitless	angle
tanh(expr)	unitless	angle
acosh(expr)	unitless	unitless
asinh(expr)	unitless	unitless
atanh(expr)	unitless	unitless
sqrt(expr)	unit^1/2	any
sign(expr)	unitless	any (Return 0 if negative, 1 if positive.)
exp(expr)	unitless	any (Return exponential power of expression: for example, return 2 for 100, 3 for 1000, and so on.)
floor(expr)	unitless	unitless (Next lowest whole number.)
ceil(expr)	unitless	unitless (Next highest whole number.)
round(expr)	unitless	unitless (Closest whole number.)
abs(expr)	any	any
max(expr1;expr2)	any	any
min(expr1;expr2)	any	any
ln(expr)	unitless	unitless
log(expr)	unitless	unitless
pow(expr1;expr2)	unit^expr2	Can construct unit valid equation that can go invalid "pow(3.0; d12)". Decimal powers rounds at eighth decimal place. any and unitless, respectively
random(expr)	unitless	unitless
isolate(expr;unit;unit)	any	any

Note: Function names are case sensitive. Enter them exactly as they appear in the previous table.

Reserved system parameters

The following are the reserved system parameters supported by ProdName.

PI: Value3.14159265358979323846264338328

E: Value 2.71828182845904523536

Unit types

The unit type that you use with an equation depends on the type of data that you are evaluating. For example, to evaluate a linear or angular value, you typically use a unit type of millimeters, inches, or degrees (mm, in, or deg).

Some equations must return a unitless value, for example, an equation to solve the number of occurrences in a pattern. You designate a unitless value with the characters ul. For example, 5 ul means that the equation has been evaluated and returned the number 5, as in the number of occurrences in a pattern.

Note: Keep units consistent within equations containing parameters that represent different unit types. You can do this using the Isolate function. For example, to calculate the number of occurrences for a pattern that is based on one occurrence for each unit of a parameter named Width, your linear equation would be:

isolate(Width;mm;ul)

The number of Occurrences value in a dialog box requires a unitless (ul) result, but you are referencing the unit width, which is a linear value. Convert the Width parameter to a unitless value.