d2calc

d2calc is an interpreter for the mini-language used internally by Diablo 2.

Diablo 2 uses text files containing tab-separated values to store game data. These text files contain many formulae that control how various skills operate. The syntax of the formulae is similar to the C language, with some differences. For convenience, we will refer to this language as D2F.

Installing

d2calc requires Node.js 12 or above. It should be possible to use it in Node.js 10.x, but no guarantees are given.

For use in Node.js:

npm install d2calc

For use in web browsers, minified versions are also available in UMD and ESM formats. Check out the Releases page for details.

Usage

d2calc exports a function named interpret(). It can be used like this:

const { interpret } = require('d2calc');
const result = interpret("4 * (-2 + 25)"); // 92

Or, with a custom environment object:

const { interpret } = require('d2calc');
const environment = {
  identifiers: {
    lvl: 3,
    ln12: () => { /* Do something here */ },
  },
  functions: {
    max: (a, b) => Math.max(a, b),
    min: (a, b) => Math.min(a, b),
  },
  referenceFunctions: {
    stat: (ref, code) => { /* Do something here */ },
  },
};

// Calls the stat() and max() functions in the environment
const result = interpret("min(lvl * 2560, stat('hp'.accr))", environment);

d2calc also provides a CachedInterpreter class. This class caches the intermediate result of parsing the code. When the same code is interpreted later, it skips the parsing process, speeding up the result significantly.

const { CachedInterpreter } = require('d2calc');
const interpreter = new CachedInterpreter();

const result = interpreter.interpret("-(125 + 12 * 3 - 2) / 3");

d2calc can also be imported inside ECMAScript modules:

// In Node.js >= 12.x, inside an ECMAScript module:
import { interpret } from 'd2calc';

// In Node.js <= 10.x, inside an ECMAScript module:
import d2calc from 'd2calc';
const { interpret } = d2calc;

API Reference

interpret(code[, environment]) => number

Interprets the code using the environment and returns the result.

Parameters:

code

• Type: string
• Required: Yes

D2F code to interpret.

environment

• Type: object
• Required: No

An object representing the environment to use while interpreting the code.

The object may contain the following fields:

environment.identifiers

• Type:

  {
    [name: string]: number | () => number;
  } 

• Required: No

An object that maps each identifier name to its value. Each value can be either a number, or a function that takes no arguments and returns a number.

environment.functions

• Type:

  {
    [name: string]: (a: number, b: number) => number;
  } 

• Required: No

An object that maps each numeric function name to a numeric function. Each numeric function must take two numbers as arguments and return a number.

environment.referenceFunctions

• Type:

  {
    [name: string]: (ref: string | number, code: string) => number;
  } 

• Required: No

An object that maps each function name to a single-qualifier reference function. Each reference function must take two arguments: a reference (string or number), and a qualifier code (string). It must return a number.

environment.referenceFunctions2Q

• Type:

  {
    [name: string]: (ref: string | number, code1: string, code2: string) => number;
  } 

• Required: No

An object that maps each function name to a double-qualifier reference function. Each reference function must take three arguments: a reference (string or number), and two qualifier codes (string). It must return a number.

CachedInterpreter

A class that caches the abstract syntax tree (AST) of the code it interprets. When the same code is interpreted again, it will use the cached AST instead. Note that return values of identifiers and functions in the environment are NOT cached.

To free the memory used by the cache, simply delete the interpreter object.

CachedInterpreter.interpret(code[, environment]) => number

See interpret() for details.

Exceptions

d2calc throws a family of exceptions, depending on the nature of the error. Each exception class can be imported like this:

const { D2FSyntaxError, D2FInterpreterError } = require('d2calc');

The exception hierarchy:

• D2CalcError: Base class for all exceptions thrown by this package.
  • D2FError: Base class for all exceptions caused by a D2F code error.
    • D2FInterpreterError: Thrown if the code contains no syntax errors, but cannot be interpreted because it uses an identifier or function in an incorrect way.
    • D2FSyntaxError: Thrown if the code contains a syntax error.
  • D2CalcInternalError: Used internally for catching bugs. This exception is not intended to be catched by users.

D2F Language Reference

This section is based on the Formulae Guide from the Phrozen Keep, as well as my own research.

The mini-language used by Diablo 2 (henceforth "D2F") supports only one datatype: the signed 32-bit integer (i.e. DWORD).

Tokens

D2F supports the following tokens:

(* Tokens *)
operator   = "+" | "-" | "*" | "/" | "==" | "!=" | ">" | "<" | ">=" | "<=" ;
symbol     = "(" | ")" | "?" | ":" | "," ;
identifier = letter, { letter | digit } ;
reference  = "'" , { character - "'" } , "'";
dot code   = "." , identifier ;

(* Character classes *)
character = (* All possible characters *) ;
letter = "A" | "B" | "C" | "D" | "E" | "F" | "G" | "H" | "I" | "J" | "K" | "L" | "M"
       | "N" | "O" | "P" | "Q" | "R" | "S" | "T" | "U" | "V" | "W" | "X" | "Y" | "Z"
       | "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m"
       | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z" ;
digit  = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;

An identifier is the name of a built-in function or a qualifier.

A reference is the name of a skill, missile, or stat in the text files, surrounded by single quotes ('').

A dot code is a single dot (.) immediately followed by a qualifier name.

A qualifier is an identifier associated with a skill, missile, or stat. Each qualifier represents a value in a text file, an in-game property, or a computed value.

• Qualifiers for skills are defined in SkillCalc.txt.
• Qualifiers for missiles are defined in MissCalc.txt.
• Stats have the following built-in qualifiers: base, accr, mod

Expressions

Expressions are formed by joining tokens. Each token can be preceded or followed by zero or more whitespace characters.

expression  = unary , { operator , unary } ;
unary       = [ "-" ] , conditional ;
conditional = primary , { "?" , primary , ":" , primary } ;
primary     = number
            | "(" , expression , ")"
            | identifier
            | identifier , "(" , arguments , ")" ;
arguments   = ( reference | primary ) , dot code , [ dot code ]
            | expression , "," , expression ;

Operator Precedence

Operators in D2F can be grouped by precedence, from highest to lowest:

1. Parentheses
2. Conditional expressions (a ? b : c)
3. Unary negative operator (-)
4. Multiplicative operator: *, /
5. Additive operator: +, -
6. Comparison operator: ==, !=, >, <, >=, <=

Binary operators in the same group are left-associative. Conditional expressions are also left-associative.

The production rules above can be rewritten in left-recursive form to accurately reflect associativity and operator precedence:

expression     = expression , comparison operator , additive
               | additive ;
additive       = additive , ( "+" | "-" ) , multiplicative
               | multiplicative ;
multiplicative = multiplicative , ( "*" | "/" ) , unary
               = unary ;
unary          = [ "-" ] , conditional ;
conditional    = conditional , "?" , primary , ":" , primary
               | primary ;

comparison operator = "==" | "!=" | ">" | "<" | ">=" | "<=" ;

Note that this form is unsuitable for recursive-descent parsing.

Abstract Syntax

expression = number
           | expression , binary operator , expression
           | unary operator , expression
           | expression , expression , expression   (* conditional *)
           | identifier
           | function , expression , expression
           | function , ( reference | expression ) , identifier , [ identifier ] ;

Interpreter Quirks

If Diablo 2 encounters a function that does not exist (e.g. man() instead of min()), it returns the second argument. d2calc does not implement this behavior, and instead throws a D2FInterpreterError.