math

Commentary

added in 0.7.3

Evaluates an infix mathematical string expression. This is handy if you have a long formula and don't want to write out nested ShadowTraffic function calls. You can access variables directly by name.

In other words, you can write this:

{
    "_gen": "math",
    "expr": "(2 + 4) * 3"
}

Instead of this:

{
    "_gen": "multiply",
    "args": [
        {
            3,
            {
                "_gen": "add",
                "args": [
                    2, 4
                ]
            }
        }
    ]
}

Expressions are parsed and compiled ahead of time, meaning performance should be similar to using the rest of ShadowTraffic's math functions directly.

An expression may contain the names of local identifiers to isolate variable usage. ¹

Available functions

• abs(x): absolute value
• acos(x): arc cosine
• asin(x): arc sine
• atan(x): arc tangent
• cbrt(x): cubic root
• ceil(x): nearest upper integer
• cos(x): cosine
• cosh(x): hyperbolic cosine
• exp(x): euler's number raised to the power (e^x)
• floor(x): nearest lower integer
• log(x): logarithmus naturalis (base e)
• log10(x): logarithm (base 10)
• log2(x): logarithm (base 2)
• max(a, b): maximum of a and b
• min(a, b): minimum of a and b
• pow(x, y): raises x to the power of y
• sin(x): sine
• sinh(x): hyperbolic sine
• sqrt(x): square root
• tan(x): tangent
• tanh(x): hyperbolic tangent
• signum(x): signum function

---

Examples

Calculating constants

Use expr to supply a math expression. Use any of the available functions listed above with arbitrary nesting.

{
    "_gen": "math",
    "expr": "2 + (log(4) * cos(10))"
}

[
    0.8367998706650697
]

Using variables

Reference variables by their name. In this example the values a and b from the vars section. Only numerically-typed variables are available for use. Non-numeric variables can't be referenced.

{
    "topic": "sandbox",
    "vars": {
        "a": {
            "_gen": "uniformDistribution",
            "bounds": [
                5,
                10
            ]
        },
        "b": {
            "_gen": "uniformDistribution",
            "bounds": [
                2,
                3
            ]
        }
    },
    "value": {
        "_gen": "math",
        "expr": "a / b"
    }
}

[
    3.6154520911368606,
    2.2044545904003754,
    2.0709688375302355
]

Returning integers

By default, math will return floating point numbers. You can trim them down, even down to integers, using the decimals function modifier.

{
    "topic": "sandbox",
    "vars": {
        "a": {
            "_gen": "normalDistribution",
            "mean": 20,
            "sd": 3
        },
        "b": {
            "_gen": "uniformDistribution",
            "bounds": [
                5,
                6
            ]
        }
    },
    "value": {
        "_gen": "math",
        "expr": "a * b",
        "decimals": 0
    }
}

[
    106,
    57,
    121
]

Referring to local names

Use names to make a map of identifiers to expressions. These identifiers can be used inside of expr and are generally useful for destructuring an object to put specific values into a string.

{
    "topic": "sandbox",
    "vars": {
        "a": {
            "b": {
                "_gen": "normalDistribution",
                "mean": 4,
                "sd": 2
            }
        }
    },
    "value": {
        "_gen": "math",
        "expr": "c * 2",
        "names": {
            "c": {
                "_gen": "var",
                "var": "a",
                "path": [
                    "b"
                ]
            }
        }
    }
}

[
    11.050660417976568,
    6.039723154354938,
    10.516769175350397
]

---

Specification

JSON schema

{
    "type": "object",
    "properties": {
        "expr": {
            "type": "string"
        },
        "names": {
            "type": "object"
        }
    },
    "required": [
        "expr"
    ]
}