Dentaku is a parser and evaluator for a mathematical and logical formula language that allows run-time binding of values to variables referenced in the formulas. It is intended to safely evaluate untrusted expressions without opening security holes.

This is probably simplest to illustrate in code:

calculator = Dentaku::Calculator.new
calculator.evaluate('10 * 2')
#=> 20

Okay, not terribly exciting. But what if you want to have a reference to a variable, and evaluate it at run-time? Here's how that would look:

calculator.evaluate('kiwi + 5', kiwi: 2)
#=> 7

To enter a case sensitive mode, just pass an option to the calculator instance:

calculator.evaluate('Kiwi + 5', Kiwi: -2, kiwi: 2)
#=> 7
calculator = Dentaku::Calculator.new(case_sensitive: true)
calculator.evaluate('Kiwi + 5', Kiwi: -2, kiwi: 2)
#=> 3

You can also store the variable values in the calculator's memory and then evaluate expressions against those stored values:

calculator.store(peaches: 15)
calculator.evaluate('peaches - 5')
#=> 10
calculator.evaluate('peaches >= 15')
#=> true

For maximum CS geekery, bind is an alias of store.

Dentaku understands precedence order and using parentheses to group expressions to ensure proper evaluation:

calculator.evaluate('5 + 3 * 2')
#=> 11
calculator.evaluate('(5 + 3) * 2')
#=> 16

The evaluate method will return nil if there is an error in the formula. If this is not the desired behavior, use evaluate!, which will raise an exception.

calculator.evaluate('10 * x')
#=> nil
calculator.evaluate!('10 * x')
Dentaku::UnboundVariableError: Dentaku::UnboundVariableError

Dentaku has built-in functions (including if, not, min, max, sum, and round) and the ability to define custom functions (see below). Functions generally work like their counterparts in Excel:

calculator.evaluate('SUM(1, 1, 2, 3, 5, 8)')
#=> 20

calculator.evaluate('if (pears < 10, 10, 20)', pears: 5)
#=> 10
calculator.evaluate('if (pears < 10, 10, 20)', pears: 15)
#=> 20

round can be called with or without the number of decimal places:

calculator.evaluate('round(8.2)')
#=> 8
calculator.evaluate('round(8.2759, 2)')
#=> 8.28

round follows rounding rules, while roundup and rounddown are ceil and floor, respectively.

If you're too lazy to be building calculator objects, there's a shortcut just for you:

Dentaku('plums * 1.5', plums: 2)
#=> 3.0

The flexibility and safety of Dentaku don't come without a price. Tokenizing a string, parsing to an AST, and then evaluating that AST are about 2 orders of magnitude slower than doing the same math in pure Ruby!

The good news is that most of the time is spent in the tokenization and parsing phases, so if performance is a concern, you can enable AST caching:

Dentaku.enable_ast_cache!

After this, Dentaku will cache the AST of each formula that it evaluates, so subsequent evaluations (even with different values for variables) will be much faster -- closer to 4x native Ruby speed. As usual, these benchmarks should be considered rough estimates, and you should measure with representative formulas from your application. Also, if new formulas are constantly introduced to your application, AST caching will consume more memory with each new formula.

Math: +, -, *, /, %, ^, |, &, <<, >>

Also, all functions from Ruby's Math module, including SIN, COS, TAN, etc.

Comparison: <, >, <=, >=, <>, !=, =,

Logic: IF, AND, OR, XOR, NOT, SWITCH

Numeric: MIN, MAX, SUM, AVG, COUNT, ROUND, ROUNDDOWN, ROUNDUP, ABS, INTERCEPT

Selections: CASE (syntax see spec)

String: LEFT, RIGHT, MID, LEN, FIND, SUBSTITUTE, CONCAT, CONTAINS

Collection: MAP, FILTER, ALL, ANY, PLUCK

If your formulas rely on one another, they may need to be resolved in a particular order. For example:

calc = Dentaku::Calculator.new
calc.store(monthly_income: 50)
need_to_compute = {
  income_taxes: "annual_income / 5",
  annual_income: "monthly_income * 12"
}

In the example, annual_income needs to be computed (and stored) before income_taxes.

Dentaku provides two methods to help resolve formulas in order:

Pass a (string) expression to Dependencies and get back a list of variables (as :symbols) that are required for the expression. Dependencies also takes into account variables already (explicitly) stored into the calculator.

calc.dependencies("monthly_income * 12")
#=> []
# (since monthly_income is in memory)

calc.dependencies("annual_income / 5")
#=> [:annual_income]

Have Dentaku figure out the order in which your formulas need to be evaluated.

Pass in a hash of {eventual_variable_name: "expression"} to solve! and have Dentaku resolve dependencies (using TSort) for you.

Raises TSort::Cyclic when a valid expression order cannot be found.

calc = Dentaku::Calculator.new
calc.store(monthly_income: 50)
need_to_compute = {
  income_taxes:  "annual_income / 5",
  annual_income: "monthly_income * 12"
}
calc.solve!(need_to_compute)
#=> {annual_income: 600, income_taxes: 120}

calc.solve!(
  make_money: "have_money",
  have_money: "make_money"
}
#=> raises TSort::Cyclic

solve! will also raise an exception if any of the formulas in the set cannot be evaluated (e.g. raise ZeroDivisionError). The non-bang solve method will find as many solutions as possible and return the symbol :undefined for the problem formulas.

If your expressions grow long or complex, you may add inline comments for future reference. This is particularly useful if you save your expressions in a model.

calculator.evaluate('kiwi + 5 /* This is a comment */', kiwi: 2)
#=> 7

Comments can be single or multi-line. The following are also valid.

/*
 * This is a multi-line comment
 */

/*
 This is another type of multi-line comment
 */

I don't know everything, so I might not have implemented all the functions you need. Please implement your favorites and send a pull request! Okay, so maybe that's not feasible because:

1. You can't be bothered to share
2. You can't wait for me to respond to a pull request, you need it NOW()
3. The formula is the secret sauce for your startup

Whatever your reasons, Dentaku supports adding functions at runtime. To add a function, you'll need to specify a name, a return type, and a lambda that accepts all function arguments and returns the result value.

Here's an example of adding a function named POW that implements exponentiation.

> c = Dentaku::Calculator.new
> c.add_function(:pow, :numeric, ->(mantissa, exponent) { mantissa ** exponent })
> c.evaluate('POW(3,2)')
#=> 9
> c.evaluate('POW(2,3)')
#=> 8

Here's an example of adding a variadic function:

> c = Dentaku::Calculator.new
> c.add_function(:max, :numeric, ->(*args) { args.max })
> c.evaluate 'MAX(8,6,7,5,3,0,9)'
#=> 9

(However both of these are already built-in -- the ^ operator and the MAX function)

Functions can be added individually using Calculator#add_function, or en masse using Calculator#add_functions.

Every function can be aliased by synonyms. For example, it can be useful if your application is multilingual.

Dentaku.aliases = {
  round: ['rrrrround!', 'округлить']
}

Dentaku('rrrrround!(8.2) + округлить(8.4)') # the same as round(8.2) + round(8.4)
# 16

Also, if you need thread-safe aliases you can pass them to Dentaku::Calculator initializer:

aliases = {
  round: ['rrrrround!', 'округлить']
}
c = Dentaku::Calculator.new(aliases: aliases)
c.evaluate('rrrrround!(8.2) + округлить(8.4)')
# 16

Big thanks to ElkStone Basements for allowing me to extract and open source this code. Thanks also to all the contributors!

(The MIT License)

Copyright © 2012-2022 Solomon White

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