Crate exmex[−][src]
Expand description
Exmex is a fast, simple, and extendable mathematical expression evaluator with the ability to compute partial derivatives of expressions.
use exmex;
assert!((exmex::eval_str("1.5 * ((cos(0) + 23.0) / 2.0)")? - 18.0).abs() < 1e-12);For floats, we have a list of predifined operators containing
^, *, /, +, -, sin, cos, tan, exp, log, and log2. The full list is
defined in make_default_operators.
Variables
For variables we can use strings that are not in the list of operators as shown in the following expression.
Additionally, variables should consist only of letters, numbers, and underscores. More precisely, they need to fit the
regular expression
r"^[a-zA-Z_]+[a-zA-Z_0-9]*".
Variables’ values are passed as slices to eval.
use exmex;
let to_be_parsed = "log(z) + 2* (-z^2 + sin(4*y))";
let expr = exmex::parse::<f64>(to_be_parsed, &exmex::make_default_operators::<f64>())?;
assert!((expr.eval(&[3.7, 2.5])? - 14.992794866624788 as f64).abs() < 1e-12);The n-th number in the slice corresponds to the n-th variable. Thereby, the
alphatical order of the variables is relevant. In this example, we have y=3.7 and z=2.5.
If variables are between curly brackets, they can have arbitrary names, e.g.,
{456/549*(}, {x}, and confusingly even {x+y} are valid variable names as shown in the following.
use exmex;
let x = 2.1f64;
let y = 0.1f64;
let to_be_parsed = "log({x+y})"; // {x+y} is the name of one(!) variable 😕.
let expr = exmex::parse::<f64>(to_be_parsed, &exmex::make_default_operators::<f64>())?;
assert!((expr.eval(&[x+y])? - 2.2f64.ln()).abs() < 1e-12);Extendability
Library users can define their own set of operators as shown in the following.
use exmex::{BinOp, Operator};
let ops = [
Operator {
repr: "%",
bin_op: Some(BinOp{ apply: |a: i32, b: i32| a % b, prio: 1 }),
unary_op: None,
},
Operator {
repr: "/",
bin_op: Some(BinOp{ apply: |a: i32, b: i32| a / b, prio: 1 }),
unary_op: None,
},
];
let to_be_parsed = "19 % 5 / 2 / a";
let expr = exmex::parse::<i32>(to_be_parsed, &ops)?;
assert_eq!(expr.eval(&[1])?, 2);Operators
Operators are instances of the struct
Operator that has its representation in the field
repr, a binary and a unary operator of
type Option<BinOp<T>> and
Option<fn(T) -> T>, respectively, as
members. BinOp
contains in addition to the function pointer apply of type fn(T, T) -> T an
integer prio. Operators
can be both, binary and unary. See, e.g., - defined in the list of default
operators. Note that we expect a unary operator to be always on the left of a
number.
Data Types of Numbers
You can use any type that implements Copy and
FromStr. In case the representation of your data type in the
string does not match the number regex r"\.?[0-9]+(\.[0-9]+)?", you have to pass a
suitable regex and use the function
parse_with_number_pattern instead of
parse. Here is an example for bool.
use exmex::{self, BinOp, Operator};
let ops = [
Operator {
repr: "&&",
bin_op: Some(BinOp{ apply: |a: bool, b: bool| a && b, prio: 1 }),
unary_op: None,
},
Operator {
repr: "||",
bin_op: Some(BinOp{ apply: |a: bool, b: bool| a || b, prio: 1 }),
unary_op: None,
},
Operator {
repr: "!",
bin_op: None,
unary_op: Some(|a: bool| !a),
},
];
let to_be_parsed = "!(true && false) || (!false || (true && false))";
let expr = exmex::parse_with_number_pattern::<bool>(to_be_parsed, &ops, "true|false")?;
assert_eq!(expr.eval(&[])?, true);Partial Derivatives
For default operators, expressions can be transformed into their partial derivatives again represented by expressions.
use exmex;
let expr = exmex::parse_with_default_ops::<f64>("x^2 + y^2")?;
let dexpr_dx = expr.clone().partial(0)?;
let dexpr_dy = expr.partial(1)?;
assert!((dexpr_dx.eval(&[3.0, 2.0])? - 6.0).abs() < 1e-12);
assert!((dexpr_dy.eval(&[3.0, 2.0])? - 4.0).abs() < 1e-12);Priorities and Parentheses
In Exmex-land, unary operators always have higher priority than binary operators, e.g.,
-2^2=4 instead of -2^2=-4. Moreover, we are not too strict regarding parentheses.
For instance
use exmex;
assert_eq!(exmex::eval_str("---1")?, -1.0);If you want to be on the safe side, we suggest using parentheses.
Display
An instance of FlatEx can be displayed as string. Note that this
unparsed string does not necessarily coincide with the original
string, since, e.g., curly brackets are added and expressions are compiled.
use exmex;
let flatex = exmex::parse_with_default_ops::<f64>("-sin(z)/cos(mother_of_names) + 2^7")?;
assert_eq!(format!("{}", flatex), "-(sin({z}))/cos({mother_of_names})+128.0");Serialization and Deserialization
To use serde you can activate the feature serde_support.
Currently, this only works for default operators. The implementation
un-parses and re-parses the whole expression.
Unicode
Unicode input strings are currently not supported 😕 but might be added in the future 😀.
Structs
A binary operator that consists of a function pointer and a priority.
This will be thrown at you if the parsing went wrong. Ok, obviously it is not an exception, so thrown needs to be understood figuratively.
This is the core data type representing a flattened expression and the result of
parsing a string. We use flattened expressions to make efficient evaluation possible.
Simplified, a flat expression consists of a SmallVec of nodes and a
SmallVec of operators that are applied to the nodes in an order following
operator priorities.
Operators can be custom-defined by the library-user in terms of this struct.
Functions
Parses a string, evaluates a string, and returns the resulting number.
Returns the default operators.
Parses a string and a vector of operators into an expression that can be evaluated.
Parses a string into an expression that can be evaluated using default operators.
Parses a string and a vector of operators and a regex pattern that defines the looks of a number into an expression that can be evaluated.