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https://github.com/rubysolo/dentaku

math and logic formula parser and evaluator
https://github.com/rubysolo/dentaku

calculator evaluate-expressions formula safeeval

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math and logic formula parser and evaluator

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Dentaku

=======



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DESCRIPTION

-----------



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.



EXAMPLE

-------



This is probably simplest to illustrate in code:



```ruby

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:



```ruby

calculator.evaluate('kiwi + 5', kiwi: 2)

#=> 7

```



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



```ruby

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:



```ruby

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:



```ruby

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.



```ruby

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:



```ruby

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:



```ruby

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:



```ruby

Dentaku('plums * 1.5', plums: 2)

#=> 3.0

```



PERFORMANCE

-----------



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:



```ruby

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.



BUILT-IN OPERATORS AND FUNCTIONS

---------------------------------



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](https://github.com/rubysolo/dentaku/blob/master/spec/calculator_spec.rb#L593))



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



Collection: `MAP`, `FILTER`, `ALL`, `ANY`, `PLUCK`



RESOLVING DEPENDENCIES

----------------------



If your formulas rely on one another, they may need to be resolved in a

particular order. For example:



```ruby

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:



#### Calculator.dependencies

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.



```ruby

calc.dependencies("monthly_income * 12")

#=> []

# (since monthly_income is in memory)



calc.dependencies("annual_income / 5")

#=> [:annual_income]

```



#### Calculator.solve! / Calculator.solve

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.



```ruby

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.



INLINE COMMENTS

---------------------------------



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.



```ruby

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

 */

```



EXTERNAL FUNCTIONS

------------------



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

1. You can't wait for me to respond to a pull request, you need it `NOW()`

1. 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.



```ruby

> 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:



```ruby

> 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.



FUNCTION ALIASES

----------------



Every function can be aliased by synonyms. For example, it can be useful if

your application is multilingual.



```ruby

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:



```ruby

aliases = {

  round: ['rrrrround!', 'округлить']

}

c = Dentaku::Calculator.new(aliases: aliases)

c.evaluate('rrrrround!(8.2) + округлить(8.4)')

# 16

```



THANKS

------



Big thanks to [ElkStone Basements](http://www.elkstonebasements.com/) for

allowing me to extract and open source this code.  Thanks also to all the

[contributors](https://github.com/rubysolo/dentaku/graphs/contributors)!



LICENSE

-------



(The MIT License)



Copyright © 2012-2022 Solomon White



Permission is hereby granted, free of charge, to any person obtaining a copy of

this software and associated documentation files (the ‘Software’), to deal in

the Software without restriction, including without limitation the rights to

use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of

the Software, and to permit persons to whom the Software is furnished to do so,

subject to the following conditions:



The above copyright notice and this permission notice shall be included in all

copies or substantial portions of the Software.



THE SOFTWARE IS PROVIDED ‘AS IS’, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS

FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR

COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER

IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN

CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.