# Math Operators and Formulas

Important: Starting with version 5.7.1 PCGen has incorporated the JEP (Java Mathematical Expression Parser) library. This was done because the original code which has evolved over time is problematic due to its complexity and lack of documentation. The JEP library has a clearly defined grammar which is available on the web site. JEP supports user defined variables, constants, and functions. A number of common mathematical functions and constants are included. As a fall back, if the JEP parser fails to parse the function then the old code is called. At some point in the future the old code support will be dropped and all formulas must be in JEP syntax.

The library we are using to parse math expressions defines the syntax they want to test for string equality. If you are curious you can check out the JEP library at Singular Sys

To reverse the sign (go from positive number to negative) use -1*(). EXAMPLE:

`BONUS:CHECKS|BASE.Will|CL/3` is a positive 1 at 3rd level and

`BONUS:CHECKS|BASE.Will|-1*(CL/3)` is a -1 at 3rd level.

PCGen *does* round each tag down rather than add the tags together and then round down. See example before 'Operators'

Using variables within JEP expressions

In most cases variables can be used directly in an expression, however there are some cases when you must use the var() function. This is because some variables can contain characters which are not valid JEP variables. For example the variable CL can be used in a formula without a problem but the variable CL=Fighter cannot be used because of the "=" symbol. In these cases you must use var("CL=Fighter") in the formula for it to parse correctly. The formal description of a JEP variable is "a letter followed by one or more letters and digits" where a letter is defined as: '$', '_', a-z and A-Z.

Examples of variables that may be used alone:

`CL, TL, ARMORACCHECK, BardicKnowledgeLevel, TirelessRage.`,

Examples of variables that must be called with the getvar() function:

`var("CL=Fighter"), var("COUNT[FEATS]"), var("COUNT[FEATTYPE=type]").`

Consult the DEFINE page for the list of hard coded variables available for use in formulas.

Operator order of processing:

Anything within ()'s are done first, and processing is done left-to-right.

`2+(3*5+2)/2`

Would become 2+(15+2)/2 (3*5 replaced)

then 2+17/2 (15+2 replaced)

then 19/2 (2+17 replaced)

then 9 (result of 19/2, the .5 is dropped, see below.).

PCGen truncates (or rounds down to the nearest integer) the results of each formula, so 4/3 will return a 1 and 7/3 will return a 2 etc. If you need to truncate within the formula you can use the min(x,y) or max(x,y) and floor(a) or ceil(a) tags.

## Operators

#### Mathematical Operators

Addition: `x+y`

Subtraction: `x-y`

Division: `x/y`

Multiplication: `x*y`

> Variable Used (x): Number, Variable, or Formula

> Variable Used (y): Number, Variable, or Formula

> What They Do:

> - These are the four traditional mathematical operators.
> - Order of Operation:
>   - For JEP Commands - Per standard mathematical order of operation. (i.e. Parenthises -> Multiplication/Division -> Addition/Subtraction)
>   - For Non-JEP Commands - Parenthesis are resolved first, then operators will be processed from left to right.
>   - Parenthesis may be nested with the inner-most parenthesis being processed first.

> Examples:

> `2+1`

> Returns a value of 3.

> `CL-1`

> Returns a value equal to the Class Level minus 1.

> `CL/2`

> Returns a value equal to the Class Level divided by 2.

> `CL*3`

> Returns a value equal to the Class Level multiplied by 3.

> `((CL+1)+(3*TL)/2)+4` (JEP Expression)

> Returns the result of three multiplied by Total Level divided by two, plus Class Level plus 1, plus four. Assuming CL=TL=4, this expression returns 15.

> `((CL+1)+(3*TL)/2)+4` (Non-JEP Expression)

> Returns the result of Class Level plus 1, plus three multiplied by Total Level, divided by two, plus four. Assuming CL=TL=4, this expression returns 12.

#### Boolean Operators

Equal: `x==y`

Not Equal: `x!=y`

Greater Than: `x>y`

Less Than: `x<y`

Greater Than or Equal: `x>=y`

Less Than or Equal: `x<=y`

Logical AND: `x&&y`

Logical OR: `x||y`

> Variable Used (x): Number, Variable, or Formula

> Variable Used (y): Number, Variable, or Formula

> What They Do:

> Boolean expressions are evaluated to be either 1 or 0 (true or false respectively).

> Examples:

> `CL==1`

> Will return "True" if Class Level is equal to 1.

> `CL!=1`

> Will return "True" if Class Level is not equal to 1.

> `CL>1`

> Will return "True" if Class Level is greater than 1.

> `CL<1`

> Will return "True" if Class Level is less than 1.

> `CL>=1`

> Will return "True" if Class Level is greater than or equal to 1.

> `CL<=1`

> Will return "True" if Class Level is less than or equal to 1.

> `(CL>5)&&(TL>5)`

> Will return "True" if Class Level and Total Level are greater than 5.

> `(CL>5)||(TL>5)`

> Will return "True" if Class Level or Total Level is greater than 5.

#### Symbol Operators

Choice: `%CHOICE`

> What it does:

> The %CHOICE will put the input from a CHOOSE tag into its place.

> Where it is used:

> - In conjunction with the CHOOSE tag.
> - May be used within math computations.

> Example:

> `SPROP:Unreliable (%CHOICE) <tab> CHOOSE:5%|10%|15%|20%|25%|30%|35%|40%|45%|50%|55%|60%|65%|70%|75%|80%|85%|90%|95%|100%`

> Chooser to select the level of unreliablty.

List: `%LIST`

> What it does:

> The %LIST will put the input from a CHOOSE tag into its place.

> Where it is used:

> - In conjunction with the CHOOSE tag.
> - May not be used within math computations.

> Example:

> `CHOOSE:NUMCHOICES=1|FORTITUDE|REFLEX|WILL <tab> BONUS:CHECKS|%LIST|1`

> Will insert the "Choice" made in the "CHOOSE:" tag into the "Bonus" tag and apply the bonus of "1" to the chosen "Checks" bonus.

Not: `!`

> What it does:

> Performs a logical NOT operation.

> Example:

> `BONUS:SKILL|Swim|1|!PRESKILL:1,Swim=1.`

> If the character does not have swim, add 1 to it.

Replacement/Substitution: `%`

> What it does:

> The Replacement/Substitution Operator is used in the SAB tag.

> Example:

> `SAB:Resistance to % 5|MyFooVariable`

> Will substitute the value of "MyFooVariable" for the "%" in the SAB tag.

## Formulas/Functions

Modulus/Remainder

Formula: `x%y`

> Variables Used (x): Variable (Dividend)

> Variables Used (y): Number (Divisor)

> What it Does:

> Performs a modulus, returning the remainder for the operation.

> Examples:

> `CL%3`

> Divides the character's class level by 3 and returns the remainder

> If the class level was 7, the remainder is 1.

Minimums and Maximums (JEP Expression)

Formula: `min(x,x)` or `max(x,x)`

> Variables Used (x): Number, Variable, or Formula (Value list)

> What it Does:

> - Returns the lowest (min) or highest (max) value from the value list.
> - The value list is a comma-delimited (",") list of values to be compared.
> - The value-list may contain any number of values desired.

> Exqmples:

> `min(10,CL,TL/2)` given a multi-class character: Wiz8/Ftr6 and looking at it from the Wizard's perspective.

> Evaluating: min(10,[CL=8],[TL/2 -> (8+6)/2 -> (14/2)=7]) -> min returns the value "7".

> `max(3,CL,TL/2)` given a multi-class character: Wiz4/Rog6 and looking at it from the Rogue's perspective.

> Evaluating: max(3,[CL=6],[TL/2 -> (4+6)/2 -> (10/2)=5]) -> max returns the value "6".

Truncation, Rounding Up or Down (JEP Expression)

Formula: `floor(x)` or `ceil(x)`

> Variables Used (x): Number, Variable, or Formula

> What it Does:

> The function "floor" returns the highest integer that is less than 'x'.

> The function "ceil" returns the lowest integer that is greater than 'x'.

> Examples:

> `floor((FooVariable+4)/6)` Assume FooVariable is "7"

> Evaluate: (FooVariable+4)/6 -> (7+4)/6 -> 11/6 -> 1 5/6 - > floor returns 1.

> `ceil(STR/2)` Assume STR=15

> Evaluate: STR/2 -> 15/2 -> 7 1/2 -> ceil returns 8.

Boolean If

Formula: `if(x,y,z)`

> Variable Used (x): Formula (Boolean expression)

> Variable Used (y): Number (Result if True)

> Variable Used (z): Number (Result if False)

> What it Does:

> - The boolean "if" operator will return one of two results after evaluating a boolean expression.
> - When evaluating the boolean expression, any result beside "0" is "True".
> - If the boolean expression (x) is "True", i.e. not equal to "0", the "True" result (y) is returned.
> - If the boolean expression (x) is "False", i.e. equal to "0", the "False" result (z) is returned.

> Examples:

> `if(CL<10,1,2)`

> Asks if Class Level is less than 10 then returns 1 or else returns 2.

> `if(CL>=4,10,0)`

> Asks if Class Level is greater than or equal to 4 then returns 10 or else returns 0.

> `if((CL>5)||(TL>5),2,-4)`

> Asks if Class Level or Total Level is greater than 5 then returns 2 or else returns -4.

> `if(STR,5,0)`

> Asks if Strength modifier is greater than or less than 0 then returns 5 or else returns 0.

#### Random Number Generation (JEP Expression)

Formula: `roll("x")`

> Variables Used (x): Formula (JEP formula or "xdx")

> What it Does:

> - The formula used within the roll("x") function can use all the standard JEP operators and in addition it can take a dice expression in the form of xdx, for example 2d6, 1d20 and 3d4.
> - The following functions are also supported within the roll function and must be encapsulated in a roll("x") call to function properly:
>   - `min(v1,v2)`
>   - `max(v1,v2)`
>   - `pow(base, exponent)`
>   - `roll(times, sides)`
>   - `roll(times, sides, [keep])`
>   - `roll(times, [sides])`
>   - `roll(times, [sides], [keep])`

> Warning:

> Although the JEP function roll("x") can generate a random number in any formula that takes JEP there are few places in the program where this is actually useful. This is because the roll function will generate a new random number every time the formula is evaluated which happens many times while you use the program. So if you were to use roll("2d6") in a base attack bonus it would appear to add a number between 2 and 12 which would change frequently. Currently the QTY tag used FUNDS lines in Kit files is one of the few places this JEP operator functions in a useful way.

> Examples:

> `roll("3d6")`

> Simulates rolling 3 six-sided dice.

> `roll("1d20+10")`

> Simulates rolling a twenty-sided die and adds 10.

> `roll("min(4,7)")`

> Returns a value of "4".

> `roll("max(4,7)")`

> Returns a value of "7".

> `roll("pow(10,2)")`

> Returns a value of "100".

> `roll("roll(3,6)")`

> Simulates rolling 3 six-sided dice.

> `roll("roll(4,6,[2,3,4])")`

> Simulates rolling 4 six-sided dice and keeps the 3 highest rolls.

> `roll("roll(1,[3,5,7,9])")`

> Similates rolling one 3, 5, 7 or 9 sided die, randomly selected.

> `roll("roll(3,[2,3,4,5,6],[2,3])")`

> Simulates rolling three 2, 3, 4, 5, or 6 sided dice, randomly selected and keeps the highest 2.

*** Updated 6.03.04

Class Level (JEP Expression)

Formula: `classlevel("x")`

> Variables Used (x): Text (Class name)

> Variables Used (x): TYPE=Text (Class type)

> Variables Used (x): APPLIEDAS=NONEPIC

> What it Does:

> - This function returns the number of level the PC has in the specified class.
> - When specifying a Class by `TYPE`, use of a period-delimited list of types will return the level of the Class that is of all types listed.

> Examples:

> `classlevel("Bard")`

> Returns the number of levels of Bard.

> `classlevel("TYPE=PC.Prestige")`

> Returns the number of levels of the class of types PC and Prestige.

> `classlevel("APPLIEDAS=NONEPIC")`

> Returns the number of levels of applied as non-epic levels.

> Deprecated Syntax:

> `CL=<Bard>`

*** Updated 5.17.5 - Added STAT and MISC properties.

Skill Information (JEP Expression)

Formula: `skillinfo("x","y")`

> Variables Used (x): RANK (Property)

> Variables Used (x): TOTALRANK (Property)

> Variables Used (x): MODIFIER (Property)

> Variables Used (x): STAT (Property)

> Variables Used (x): MISC (Property)

> Variables Used (x): TOTAL (Property)

> Variables Used (y): Text (Skill name)

> What it Does:

> This function returns information about the skill specified.

> - RANK returns the number of ranks the PC has in the skill not including those gained from BONUS:SKILLRANK tags.
> - TOTALRANK returns the number of ranks the PC has in the skill including those gained from BONUS:SKILLRANK tags.
> - MODIFIER returns the total bonuses the PC has in the skill.
> - STAT returns the bonus the PC has in the skill from his abilityattribute bonus.
> - MISC returns the total bonuses the PC has in the skill that do not derive from his ability bonus.
> - TOTAL returns the grand total in the skill from all ranks and bonuses.

> Examples:

> `skillinfo("RANK", "Hide")`

> Returns the number of base ranks in Hide.

> `skillinfo("TOTALRANK", "Climb")`

> Returns the number ranks in Climb including those gained from BONUS:SKILLRANK tags.

> `skillinfo("MODIFIER", "Bluff")`

> Returns the total number of bonuses in Bluff.

> `skillinfo("STAT", "Diplomacy")`

> Returns the ability bonus for Diplomacy.

> `skillinfo("MISC", "Use Magic Device")`

> Returns the total miscellaneous bonuses in Use Magic Device.

> `skillinfo("TOTAL", "Spellcraft")`

> Returns the grand total in Spellcraft.

Character Bonus Information (JEP Expression)

Formula: `charbonusto("x","y")`

> Variable Used (x): Text (Parameter 1 - Optional)

> Variable Used (x): Text (Parameter 2)

> What it Does:

> - This function returns the value of the identified parameter pair.
> - These values reflect only the bonuses applied to the parameter identified and not the total value of that parameter.
> - Valid parameter pairs (x - y) include:
>   - PCLEVEL - <class name>
>   - STAT - BASESPELLSTAT
>   - STAT - BASESPELLSTAT;CLASS.<class named>
>   - STAT - CAST.<spell type>
>   - FEAT - POOL
>   - VAR - <variable name>
>   - CHECKS - <check type>
>   - TOHIT - TOHIT
>   - DOMAIN - NUMBER
>   - CASTERLEVEL - <class name>
>   - HP - ALTHP
>   - COMBAT - BAB
>   - WEAPONPROF=<weapon name> - PCSIZE
>   - WEAPONPROF=TYPE.<weapon proficency> - PCSIZE
> - Parameter 1 (x) is optional. If it is not present, it will default to "PCLEVEL".

> Examples:

> `charbonusto("PCLEVEL","Cleric")`

> Returns the number of bonus Spellcaster Levels to the class specified, which usually come from Prestige classes.

> `charbonusto("CHECKS","Reflex")`

> Will return Reflex bonuses from a high Dexterity and other bonuses but not the full reflex save value.

*** Updated 6.01.09 - Added CAMPAIGNHISTORY property.

Count (JEP Expression)

Formula: `count(x,y)`

> Variables Used (x): Text (Object to be counted)

> Variables Used (y): Text (Matching criteria)

> What it does:

> - This token is used to obtain the number of objects matching the provided criteria.
> - The matching criteria are a comma-delimited (,) list of quotated parameters ("parameter=text") associated with the "Object" being counted.
> - "`[and]`" and "`[or]`" can be used between parameters.
> - Use of this token in conjunction with output sheet tokens `IIF` and `VAR` require a semicolon-delimited (;) list of quotated parameters instead of a comma-delimited list.
> - This token can be used in any of the OS FOR loops in place of max.
> - Valid <Object to be counted> and the associated <Matching criteria> are listed below:
>   - `ABILITIES` - Will count the abilities that satisfy the following criteria:
>     - `"CATEGORY=<text>"` - The ability category as defined in the gamemode/miscinfo.lst file or the data/abilitycategory.lst file.
>     - `"NAME=<text>"` - The name of a specific Ability which can be taken multiple times, returns the number of times it was taken. For abilities with internal choices you include the specific choices to be counted within parenthesis, i.e. Weapon Focus (Longsword).
>     - `"KEY=<text>"` - The key of a specific Ability which can be taken multiple times, returns the number of times it was taken. For abilities with internal choices you include the specific choices to be counted within parenthesis, i.e. Weapon Focus (Longsword).
>     - `"NATURE=<text>"` - "NORMAL", "VIRTUAL", or "AUTOMATIC".
>     - `"TYPE=<text>"` - The ability type as defined in the ability.lst file. (e.g. "General", "Fighter", "Metamagic", etc.)
>     - `"VISIBILITY=<text>"`
>       - "HIDDEN", includes abilities with VISIBLE:NO
>       - "DEFAULT", includes abilities with VISIBLE:YES or no VISIBLE tag at all
>       - "OUTPUT_ONLY", includes abilities with VISIBLE:EXPORT
>       - "DISPLAY_ONLY", includes abilities with VISIBLE:DISPLAY
>     - `"ASPECT=<text>"` - The aspect as defined for the ability objects in the ability.lst file.
>   - `CAMPAIGNHISTORY` - Will count the number of entries in the character's campaign history page.
>   - `CLASSES` - Not yet implemented.
>   - `DOMAINS` - Not yet implemented.
>   - `EQUIPMENT` - Not yet implemented..
>   - `FOLLOWERS` - Not yet implemented..
>   - `LANGUAGES` - Not yet implemented.
>   - `RACESUBTYPES` - Not yet implemented.
>   - `SKILLSIT` - Will count skills/situations that satisfy the stipulated criteria (y) as `"VIEW=<text>"`. Valid views are as per tag TBD.
>   - `SPELLBOOKS` - Not yet implemented.
>   - `SPELLS` - Not yet implemented.
>   - `SPELLSKNOWN` - Not yet implemented.
>   - `SPELLSINBOOK` - Not yet implemented.
>   - `TEMPLATES` - Not yet implemented.

> Example:

> `count("ABILITIES","CATEGORY=FEAT","TYPE=Metamagic","VISIBILITY=DEFAULT[or]VISIBILITY=OUTPUT_ONLY")`

> This token returns the number of visible metamagic feats the character has.

> `count("ABILITIES","CATEGORY=FEAT","TYPE=Fighter","VISIBILITY=DEFAULT[or]VISIBILITY=OUTPUT_ONLY")`

> Returns the number of all visible Fighter type feat abilities.

> `count("ABILITIES","CATEGORY=FEAT","NAME=Toughness")`

> Returns the number of times the Toughness feat was taken.

> `count("ABILITIES","CATEGORY=FEAT","KEY=Toughness")`

> Returns the number of times the Toughness feat was taken.

> `count("ABILITIES","CATEGORY=Special Ability","NATURE=VIRTUAL[or]NATURE=AUTOMATIC")`

> Returns the number of abilities of category "Special Ability" the character has which are either virtual or automatic.

> `count("ABILITIES","CATEGORY=FEAT","VISIBILITY=HIDDEN[or]VISIBILITY=DISPLAY_ONLY")`

> Returns the number of hidden feats.

> `|VAR.count("ABILITIES","CATEGORY=Maneuver")|`

> Outputs the number of "Maneuver" abilities the character has.

> `count("CAMPAIGNHISTORY")`

> This token returns the number of campaign history chronicles marked as being for export.

> `count("CAMPAIGNHISTORY", "EXPORT=YES[or]EXPORT=NO")`

> This token returns the number of campaign history chronicles no matter how they are marked.

*** New 5.15.x

isGameMode (JEP Expression)

Formula: `isgamemode("x")`

> Variables Used (x): Text (GameMode name)

> What it Does:

> This function tests to see if the designated "gameMode" is running. It returns a "1" if the designated gameMode is running and a "0" if it is not.

> Examples:

> `isgamemode("35e")`

> Returns a "1" if the designated gameMode is running and a "0" if it is not.

*** New 6.03.x

mastervar (JEP Expression)

Formula: `mastervar("x")`

> Variables Used (x): Text (Varuable Name)

> What it Does:

> This function used by a "companion" creature and returns the value of the designated variable attached to the relevant companion's Master PC.

> Examples:

> `mastervar("BAB")`

> Returns the base attack bonus of the relevant companion's Master PC.

*** New 6.01.02

Roll Info

Formula: `xdyz`

> Variables Used (x): Integer (Number of dice)

> Variables Used (y): Integer (Number of sides)

> Variables Used (z): +Integer (Modifier)

> Variables Used (z): -Integer (Modifier)

> What it Does:

> - This formula syntax provides

> Examples:

> `4d8+5`

> Returns a number between 9 and 37.

> Where it is Used:

> `DAMAGE` and `ALTDAMAGE` tags.

## Deprecated Functions

The following operators are deprecated as of version 5.7.1. The syntax will be replaced with JEP syntax.

`((TL/3).TRUNC)*2`

Truncation - would divide TL by 3, truncate (or round down) and then multiply by 2.

Deprecated, use floor(a).

`2MIN4`

Minimum - would return 2 since it's taking the minimum of the two values (MIN is always between the values).

Deprecated, use min(a,b).

`2MAX4`

Maximum - would return 4 since it's the max of the two values (MAX is always between the values).

Deprecated, use max(a,b).