Setting up the new Formula System

The basics

The new formula system is designed to do a few things relative to data:

• Validate formulas at LST load instead of runtime
• Dramatically increase flexibility
• It will replace many tokens, including all the BONUS tokens
• It allows a sensible location for global modifications (things generally related to rule book type modifications that impact all objects of a given type)

Key concepts

To use the new system a few key things need to be remembered:

• It is possible to have local variables
• All variables must be defined prior to use
• Variables are not only numbers, but can be Strings, Dice, etc.
  • We call this the variable FORMAT

You will want to keep track of what these key terms mean as you learn the new formula system:

• FORMAT: The type of variable, e.g. NUMBER, BOOLEAN, ORDEREDPAIR.
• SCOPE: The part of the data in which a (local) variable is available
• MODIFIER: An argument to MODIFY* tokens, specifically the "command" of what the modification represents
• OPERATOR: A mathematical operator as you would see in a formula ("+", "-", etc.)
• GROUPING: A name for a set of objects in PCGen
• ASSOCIATION: An additional set of information attached to a MODIFY* token. This is a key-value pair of information, e.g. PRIORITY=100

Creating and Using Variables

Required Setup

Every format that needs to be used requires a default value. This value is shared throughout an entire system (it CANNOT be redefined to a different value). This is placed into a file referred to in a PCC file from the DATACONTROL: token.

The token used within that lst file is DEFAULTVARIABLEVALUE:

The format is DEFAULTVARIABLEVALUE:X|Y

• X is the format name
• Y is the default value

Example:

  DEFAULTVARIABLEVALUE:NUMBER|0

It is a best practice to always define a DEFAULTVARIABLEVALUE for every FORMAT regardless of whether the data uses that FORMAT. The internal parts of PCGen may use it, so a default value may be required.

Note: it IS safe to "redefine" a DEFAULTVARIABLEVALUE to the same value. So if multiple datasets are loaded and they all had DATACONTROL: and all defined the default value for NUMBER to be 0, they will all happily load as the system is capable of recognizing the defaults are the same

How to define a variable

To define a variable, you need to add an LST file that is referred to in a PCC file from the VARIABLE: token.

There are 2 basic tokens for the VARIABLE file: GLOBAL and LOCAL.

• GLOBAL defines a global variable, usable from anywhere within the PlayerCharacter.
• LOCAL defines a local variable, usable only within the object on which the variable exists (or its children)
  • The place where a local variable is usable is called the SCOPE. This could include a STAT (such as the stat's SCORE or STATMOD) or EQUIPMENT. The scopes possible in PCGen are hard-coded (see below for more info)

Both of those tokens can take an additional token on the line called EXPLANATION, which it is advisable to use to communicate to other data monkeys (and it is likely any future editor will also draw on this information)

The format of GLOBAL is GLOBAL:X=Y

• X is the format name
• Y is the variable name

Example:

  GLOBAL:ORDEREDPAIR=Face

The format of LOCAL is LOCAL:W|X=Y

• W is the SCOPE of the variable
• X is the format name
• Y is the variable name

Example:

  LOCAL:STAT|NUMBER=Score

Defaults

A few notes about the VARIABLE files: If you see an item without a leading token, e.g.:

  ORDEREDPAIR=Face

...then the system is using the default (GLOBAL). For now, the data standard is to avoid using this shortcut (as far as I know)

If you see an item without a leading format ("X" in both GLOBAL and LOCAL above), e.g.:

  LOCAL:STAT|Score

...then the format is a NUMBER. For now, the data standard is to avoid using this shortcut (as far as I know)

Note both defaults can be combined, so a variable name with no other information on that line is a Global NUMBER

No Overlapping

In most programming languages, it is legal to have local variable share the same name as the global variable and thus "override" it in that context (although it is considered less than ideal, and in some languages it will now produce a warning). It is not legal in PCGen.

If a Global variable called "Hands" exists, then NO local variable IN ANY SCOPE can be "Hands".

Similar restrictions exist for scopes and SubScopes. If "CritMult" is an EQUIPMENT variable, then "CritMult" can't be an EQUIPMENT.PART variable.

Non-overlapping (when the Scopes do not interact) is legal. "Score" can be a local STAT variable and a local CHECK variable, for example.

For clarity:

• This occurs regardless of the FORMAT of the variables - tokens will infer the format from the variable name, so you can't have overlapping variables even of different FORMAT.
• Two variables of the same name but different FORMAT in the same SCOPE will cause an error as well, because that is effectively overlapping, and those variables can't be distinguished in most circumstances.

Identical Duplication Legal

It is legal for a load to include one or more PCC files that have one or more VARIABLE: files that redefine the same variables. As long as they are the same format and scope, they are not considered an error. If either the scope or format differs, then the "No Overlapping" rules above are applied.

A difference in the "Explanation" text is not considered a difference in the variables significant enough to trigger an error. (In fact, the last loaded Explanation will "win" -> it is overwritten each time it is encountered for redefined but identical variables)

Setting and Modifying a variable

The MODIFY token is used to set a variable that is accessible in the current SCOPE. (Note: It could be local to the current scope or any ancestor of the current scope... so modifying a global variable always just requires MODIFY)

The format of the token is: MODIFY:V|W|X|Y=Z|Y=Z

• V is the Variable name for which the value will be modified
  • This variable MUST be visible in the current scope. Therefore, it must be either a global variable or a local variable on the current object or its parents.
• W is the MODIFIER to be taken on the variable (e.g. SET)
  • There can be multiple actions (more below), but SET will ALWAYS be available for any format.
• X is the value related to the action. If the action is set, the variable will be set to the value in this part of the token.
  • Note: The value CAN be a formula. It is possible, for example, to SET a variable to OtherVar+4 ... the system will solve that formula. For legal OPERATORS (e.g. "+") , see below.
• Y is the name of an (optional) ASSOCIATION. For now, PRIORITY (more below) is the only available association.
• Z is the value of the association.

Note: If a PRIORITY is not set it is assumed to be ZERO.

Example: Give a Player Character 2 hands:

  MODIFY:Hands|SET|2

The MODIFYOTHER token is used to set a variable that is not accessible in the current SCOPE. Beyond what is necessary in MODIFY, this token also requires the "address" of where to go before it runs the modification. Think of it as the ability to remotely place a MODIFY on another object (but revoke that MODIFY if the current object is no longer granted to the PC)

The format of the token is: MODIFYOTHER:T|U|V|W|X|Y=Z|Y=Z

• T is the FORMAT of the object on which the resulting MODIFY (as defined by V-Z) should occur
• U is the object or GROUPING of objects on which the MODIFY (as defined by V-Z) should occur
  • Note that this does not and will not support TYPE.
• V is the Variable name for which the value will be modified
  • This variable MUST be visible in the scope of the addressed object. Therefore, it is likely to be a local variable on the remote object or its parents.
  • In rare cases, a remote modification of a global variable is useful. It effectively adds to that global variable only if both objects are granted to the PC.
• W is the MODIFIER to be taken on the variable (e.g. SET)
  • There can be multiple actions (more below), but SET will ALWAYS be available for any format.
• X is the value related to the action. If the action is set, the variable will be set to the value in this part of the token.
  • Note: The value CAN be a formula. It is possible, for example, to SET a variable to OtherVar+4 ... the system will solve that formula. For legal OPERATORS (e.g. "+") , see below.
• Y is the name of an (optional) ASSOCIATION. For now, PRIORITY (more below) is the only available association.
• Z is the value of the association.

Note: If a PRIORITY is not set it is assumed to be ZERO.

Example: Reduce the HandsRequired on all Weapons by 1:

  MODIFYOTHER:EQUIPMENT|GROUP=Weapon|HandsRequired|ADD|-1

Note this assumes GROUP:Weapon is in the LST line of every Weapon... PCGen can't guess or derive what a weapon is :)

Formulas

SET as a MODIFIER allows the use of a formula for the value. This follows many mathematical systems of using parenthesis - "(" and ")" to be precise - to group (and thus prioritize parts of the calculation). There are a number of build in OPERATORs (see below). The system can also use functions, which use parenthesis to contain their arguments. For example:

• min(this,that)

Would return the minimum of the two variables "this" and "that".

The system also has a series of built-in functions that work with the NUMBER format:

• abs: calculates the absolute value of the one argument.
• ceil: calculates the next integer that is >= the value of the one argument.
• floor: calculates the next lower integer that is <= the value of the one argument
• if: conditionally performs an operation. The first argument must resolve to a BOOLEAN. If true, the second argument is evaluated; if false, the third argument is evaluated.
• max: calculates the maximum of the provided two or more comma-separated arguments
• min: calculates the minimum of the provided two or more comma-separated arguments
• round: calculates the closest integer to the value of the one argument. Exactly 0.5 is rounded up.
• value: returns the value of the calculation before the current modification was started (no arguments)

Additional functions specifically related to PCGen are available:

• get: This function takes two arguments. The first is a Object type (like "SKILL"), the second is the key of a CDOMObject (like a Skill) (also in quotes)
• getFact: This function returns the value of a FACT. The first two arguments are much like the two arguments of "get", the third argument is the name of the FACT to be returned

Legal Values

FORMATs

Currently, the following are built-in formats:

• NUMBER: This is a mathematical value. Note that integer arithmetic is done if possible, so if you have an integer 6 and an integer 3, 6/3 will be an integer 2. If the 6 or 3 is a decimal value (double), then integer arithmetic was not possible and thus rounding may occur.
• STRING: A String
• ORDEREDPAIR: An ordered pair of numbers. This could be an X,Y point (or in a game system more like a FACE)
• DICE: A value that takes the form AdB+C. A is the number of rolls of the die, B is the number of sides on the die, and C is the value to be added afterwords

OPERATORs

For NUMBER, the following modifiers are available:

• +: performs addition
• -: performs subtraction (or is the unary minus operator to make a value negative)
• *: performs multiplication
• /: performs division
•  %: performs a remainder function
• ^: performs an exponential calculation
• ==: Checks for equality (NOTE: Returns a BOOLEAN, not a NUMBER)
•  !=: Checks for inequality (NOTE: Returns a BOOLEAN, not a NUMBER)
• >: Checks for greater than (NOTE: Returns a BOOLEAN, not a NUMBER)
• <: Checks for less than (NOTE: Returns a BOOLEAN, not a NUMBER)
• >=: Checks for greater than or equal to (NOTE: Returns a BOOLEAN, not a NUMBER)
• <=: Checks for less than or equal to (NOTE: Returns a BOOLEAN, not a NUMBER)

For BOOLEAN, the following modifiers are available:

• ==: Checks for equality
•  !=: Checks for inequality
• &&: Performs a logical AND
• ||: Performs a logical OR
•  !: Negates the value

For other formats, the following operators are always available:

• ==: Checks for equality (NOTE: Returns a BOOLEAN, not the compared format)
•  !=: Checks for inequality (NOTE: Returns a BOOLEAN, not the compared format)

MODIFIERs

For NUMBER, the following modifiers are available:

• SET: This sets the variable to the value provided in the "X" parameter
• ADD: This adds the current value of the variable to the value provided in the "X" parameter
• MAX: This takes the maximum value of the current value of the variable and the value provided in the "X" parameter (i.e. min(current value, "X"))
• MIN: This takes the minimum value of the current value of the variable and the value provided in the "X" parameter (i.e. max(current value, "X"))
• MULTIPLY: This multiplies the current value of the variable and the value provided in the "X" parameter
• DIVIDE: This divides the current value of the variable by the value provided in the "X" parameter

For other Formats, the SET modifier will always be available

GROUPINGs

At present, the second argument of MODIFYOTHER supports 3 possible values:

• ALL
  • This means the MODIFYOTHER will impact ALL objects of that type. This is useful for setting a general default for that value (e.g. you could default "HandsRequired" on weapons to 1)
• GROUP=X
  • This is set by the GROUP token in LST data
• A specific object KEY

More will be added over time.

SCOPEs

The following are the legal scopes (not including GLOBAL):

• EQUIPMENT: This is a variable local to equipment
  • EQUIPMENT.PART: This is a variable local to an equipment PART (or in older terms, an Equipment HEAD). Note that due to double sided weapons, Damage, CritMult and other items are generally on an equipment PART, not on the Equipment itself. Note also that this is a SUBSCOPE of the EQUIPMENT scope (so all variables in the EQUIPMENT scope can also be seen in the EQUIPMENT.PART scope)
• SAVE: This is a variable local to Save (or if you prefer, Check)
• SIZE: This is a variable local to the Size of a PC
• SKILL: This is a variable local to a Skill
• STAT: This is a variable local to a Stat

More will be added over time.

DYNAMIC can also be used to create a Scope and Object Type (see below)

Examples

Understanding SubScope in practice

To understand how local variables work in SubScopes, consider the following (note this is not all the variables we will use but a critical set to define the scope):

  GLOBAL:NUMBER=Hands
  LOCAL:EQUIPMENT|NUMBER=HandsRequired
  LOCAL:EQUIPMENT|BOOLEAN=Penalized
  LOCAL:EQUIPMENT.PART|NUMBER=CritMult

The Equipment part is what the traditional system called a "head" (so a double headed axe has two "parts" in the new system - this was done since in some game systems, an item could have more than 2)

To understand how variables are available and how they get modified consider this:

Inside of a piece of equipment it could do something like:

  MODIFY:Penalized|SET|HandsRequired>Hands

This would be "true" if HandsRequired on the Equipment were more than the Hands on the PC. The "Hands" variable is Global, so it is available anywhere. A Template of "Extra Hands" could do something like:

  MODIFY:Hands|ADD|2 

... and that adds to the Global variable "Hands".

Now consider an Equipment Modifier that was something like "Lighter Than Normal". Assume the game benefit was one less hand is required. This would look like:

  Lighter Than Normal   MODIFY:HandsRequired|ADD|-1

(This ignores for the moment any situation like "can't be reduced to below one".)

Note that the EquipmentModifier falls into EQUIPMENT.PART, so that it has access to the HandsRequired variable from the EQUIPMENT scope and can modify it. Note that this change could then impact the result of the BOOLEAN variable Penalized, since HandsRequired changed. Note also that "HandsRequired", when evaluated anywhere in that Equipment is now 1 less. Even if another EquipmentModifier evaluates HandsRequired, it is analyzing the variable from its parent scope, so that value on a variable from EQUIPMENT is the same in every EquipmentModifier (in the EQUIPMENT.PART scope) of that piece of Equipment.

Understanding SubScope on Equipment

Since variables like CritMult and Damage would be on an Equipment "part" it is important to understand how to get access to that "part" from the LST code. If a single-headed weapon wanted a larger CritMult, it would be silly to have to add a Dummy EquipmentModifier just to modify the CritMult on the part. (Much of the point of the new system is to make things more direct)

There is a token for Equipment called PART. This effectively takes 2 arguments: A number (today 1 for the primary head, 2 for the secondary head) and a full token otherwise valid on a plain object. MODIFY and MODIFYOTHER will both work in that situation, so for a piece of Equipment to set its own CritMult to 3 on its primary (and perhaps only) head, it would do:

  PART:1|MODIFY:CritMult|SET|3

Note since the MODIFY is a "real" token call it uses ":" after the MODIFY which makes PART look slightly different to most tokens which use | as an internal separator. Since PART is effectively calling a "real" token, we need to use the inner ":" in order to have it pass through the same code/parsing system.

Understanding SubScopes in relation to MODIFYOTHER

Normally MODIFYOTHER allows you to "address" another scope. For example:

  MODIFYOTHER:EQUIPMENT|Bastard Sword|HandsRequired|ADD|-1

However, since items like Damage and CritMult are actually on the EQUIPMENT.PART, that is different. If you consider how you would have to "address" the first head on "Bastard Sword", you would need something like:

  SOMEWEIRDTOKEN:EQUIPMENT|Bastard Sword|PART|1|CritMult|ADD|1

Note that this requires both a primary and secondary address. No token like this exists (or is planned). To alter items in a SubScope, you need to pass them down to the SubScope. An attempt to modify it at the Equipment level, such as:

  MyAbility   MODIFYOTHER:EQUIPMENT|ALL|CritMult|ADD|1

... will fail (at LST load) because CritMult was on EQUIPMENT.PART, so it is not visible to the EQUIPMENT scope. Said another way, you can't universally modify all EQUIPMENT.PART variables by attempting to use that variable at a higher scope.

A more appropriate method (since this is relevant to a Feat that might alter CritMult) is to add another variable at the EQUIPMENT level:

  LOCAL:EQUIPMENT|NUMBER=CritMultAdder

If all the heads then get

  MODIFY:CritMult|ADD|CritMultAdder

... you can have the Feat do a MODIFYOTHER to alter CritMultAdder and the MODIFY will "pull" that into each PART:

  SomeFeat   MODIFYOTHER:EQUIPMENT|ALL|CritMultAdd|ADD|1

So the data can be set up to only require one modification from a Feat and each Equipment Part can pull that modification down into the part. (A tangential note for those objecting that the known modifiers of CritMult select a specific weapon type: Yep, got it. That's not possible yet, so not documented yet. Suspend disbelief on the examples - Imagine a more powerful Feat for now)

Understanding PRIORITY and processing of MODIFY and MODIFYOTHER

When a PlayerCharacter has multiple items that attempt to modify a variable, they are sorted by two systems:

• First, they are sorted by their user priority. This is provided in the PRIORITY=Z association. Lower PRIORITY will be processed first.
• Second, they are sorted by their inherent priority. This is a built-in system that approximates mathematical priority rules. It ensures, for example, that a SET will occur before ADD if they both have a matching user priority.

Example: Assume we had the following items:

  MODIFY:Hands|MULTIPLY|2|PRIORITY=100
  MODIFY:Hands|SET|2|PRIORITY=50
  MODIFY:Hands|ADD|1|PRIORITY=50

The first thing is that we can tell from the PRIORITY items that the SET and ADD will both occur BEFORE the multiply (because 50 < 100). For the SET and ADD, we would need to know the inherent priority (For what it's worth, SET is 0, ADD is 3, MULTIPLY and DIVIDE are 1 and 2 since they are higher priority than ADD in traditional math). This means the SET will happen first. So the result is Hands is SET to 2, then ADD 1 to get 3, then MULTIPLY by 2 to get 6.

By controlling the PRIORITY, the data team can reorder any calculation and perform much more complicated calculations than was possible with BONUS (where movement, for example, had multiple different BONUS tokens to try to do adding before and after a multiply). This is much the same as using parenthesis in a formula in normal math, but this allows you trigger any required ordering even if the MODIFY statements are in different objects.

Using the previous value in a more complex calculation

Take a modification that, for example, wishes to perform a calculation such as: "Reduce the value by 1, but to no less than 1". We could write this as two MODIFY statements, but that is probably undesirable for a few reasons:

• If the book states it as one sentence, it would be preferable to write it as one MODIFY
• It makes the calculation a bit harder to follow as to what is going on
• If the items are different PRIORITY, there is a risk of another dataset attempting to (or accidentally) putting something in between those two steps, resulting in an incorrect calculation.

Therefore, we need a method of drawing on the current value in a formula. To do that we use the value() function. The calculation above then becomes:

  max(value()-1,1)

...and we can use it in a MODIFY as such:

  MODIFY:HandsRequired|SET|max(value()-1,1)

Note that we are using SET here - if a formula is used, it is likely to be best done as a SET, since that will be much more clear than calculating a formula and then immediately applying another MODIFICATION. Note that some modifications may also prohibit a formula depending on their underlying behavior.

Global Modifier File

There is a new file type that is defined in the PCC files with GLOBALMODIFIER. This file allows for a centralized (and clear to the data user) location for global modifications (don't hide things on stats or elsewhere anymore). This supports MODIFY for global variables (if you want to start all PCs with 2 hands for example) or MODIFYOTHER for local variables.

Advanced Topics

To be completed

• dropIntoContext
• Channels
• lookup and tables (probably refer to the separate page)
• adding custom functions (in data)
• Why to use the MODIFIERs like ADD rather than just doing value()+4
• DYNAMIC and Scope