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/* Crate imports */
use crate::{
element::{BinOp, Element, FunctionCall, UnOp},
token::Operator,
utils::factorial::factorial,
};
/// Trait for simplifying abstract syntax tree (AST) elements.
/// Is enabled with the `compile-time-optimizations` feature (on by default).
pub trait Simplify<'a> {
/// Simplifies the element for the specified variable.
fn simplify_for(self, var: (&str, f64)) -> Element<'a>;
/// Simplifies the element.
fn simplify(self) -> Element<'a>;
}
impl<'a> Simplify<'a> for Element<'a> {
fn simplify_for(self, var: (&str, f64)) -> Self {
match self {
Self::BinOp(binop) => binop.simplify_for(var),
Self::UnOp(unop) => unop.simplify_for(var),
Self::Function(func) => func.simplify_for(var),
Self::Variable(name) if name == var.0 => Self::Number(var.1),
Self::Number(_) | Self::Variable(_) => self,
}
}
fn simplify(self) -> Self {
match self {
Self::BinOp(binop) => binop.simplify(),
Self::UnOp(unop) => unop.simplify(),
Self::Function(func) => func.simplify(),
Self::Number(_) | Self::Variable(_) => self,
}
}
}
impl<'a> Simplify<'a> for BinOp<'a> {
fn simplify_for(mut self, var: (&str, f64)) -> Element<'a> {
self.lhs = self.lhs.simplify_for(var);
self.rhs = self.rhs.simplify_for(var);
self.simplify()
}
#[allow(clippy::too_many_lines, clippy::cognitive_complexity)]
fn simplify(mut self) -> Element<'a> {
use Element::Number;
use Operator::{Divide, Factorial, Minus, Modulo, Plus, Power, Times};
self.lhs = self.lhs.simplify();
self.rhs = self.rhs.simplify();
match self {
/////////////////////////// Additions ///////////////////////////
// 0 + a => a
BinOp { op: Plus, lhs, rhs } if lhs == Number(0.0) => rhs,
// a + 0 => a
BinOp { op: Plus, lhs, rhs } if rhs == Number(0.0) => lhs,
////// NIGHTLY FEATURES //////
#[cfg(NIGHTLY)]
// (-a) + a => 0
BinOp {
op: Plus,
lhs: Element::UnOp(box UnOp { op: Minus, operand }),
rhs,
} if operand == rhs => Number(0.0),
#[cfg(NIGHTLY)]
// a + (-a) => 0
BinOp {
op: Plus,
lhs,
rhs: Element::UnOp(box UnOp { op: Minus, operand }),
} if lhs == operand => Number(0.0),
////////////////////////// Subtractions /////////////////////////
// 0 - a => -a
BinOp {
op: Minus,
lhs,
rhs,
} if lhs == Number(0.0) => UnOp::new_element(Operator::Minus, rhs),
// a - 0 => a
BinOp {
op: Minus,
lhs,
rhs,
} if rhs == Number(0.0) => lhs,
// a - a => 0
BinOp {
op: Minus,
lhs,
rhs,
} if lhs == rhs => Number(0.0),
////// NIGHTLY FEATURES //////
#[cfg(NIGHTLY)]
// a - (-b) => a + b
BinOp {
op: Minus,
lhs,
rhs: Element::UnOp(box UnOp { op: Minus, operand }),
} => BinOp::new_element(Operator::Plus, lhs, operand),
//////////////////////// Multiplications ////////////////////////
// 0 * a => 0
BinOp { op: Times, lhs, .. } if lhs == Number(0.0) => Number(0.0),
// a * 0 => 0
BinOp { op: Times, rhs, .. } if rhs == Number(0.0) => Number(0.0),
// 1 * a => a
BinOp {
op: Times,
lhs,
rhs,
} if lhs == Number(1.0) => rhs,
// a * 1 => a
BinOp {
op: Times,
lhs,
rhs,
} if rhs == Number(1.0) => lhs,
////// NIGHTLY FEATURES //////
// (-a) * (-b) => a * b
#[cfg(NIGHTLY)]
BinOp {
op: Times,
lhs:
Element::UnOp(box UnOp {
op: Minus,
operand: lhs,
}),
rhs:
Element::UnOp(box UnOp {
op: Minus,
operand: rhs,
}),
} => BinOp::new_element(Operator::Times, lhs, rhs),
/////////////////////////// Divisions ///////////////////////////
// 0/0 => NaN // special case
BinOp {
op: Divide,
lhs,
rhs,
} if lhs == Number(0.0) && rhs == Number(0.0) => Number(f64::NAN),
// 0 / a => 0
BinOp {
op: Divide, lhs, ..
} if lhs == Number(0.0) => Number(0.0),
// a / 0 => inf
BinOp {
op: Divide, rhs, ..
} if rhs == Number(0.0) => Number(f64::INFINITY),
// a / 1 => a
BinOp {
op: Divide,
lhs,
rhs,
} if rhs == Number(1.0) => lhs,
// a / a => 1
BinOp {
op: Divide,
lhs,
rhs,
} if lhs == rhs => Number(1.0),
////// NIGHTLY FEATURES //////
// (-a) / (-b) => a / b
#[cfg(NIGHTLY)]
BinOp {
op: Divide,
lhs:
Element::UnOp(box UnOp {
op: Minus,
operand: lhs,
}),
rhs:
Element::UnOp(box UnOp {
op: Minus,
operand: rhs,
}),
} => BinOp::new_element(Operator::Divide, lhs, rhs),
///////////////////////////// Powers ////////////////////////////
// 0 ^ 0 => 1 // special case
BinOp {
op: Power,
lhs,
rhs,
} if lhs == Number(0.0) && rhs == Number(0.0) => Number(1.0),
// 0 ^ a => 0
BinOp { op: Power, lhs, .. } if lhs == Number(0.0) => Number(0.0),
// a ^ 0 => 1
BinOp {
op: Divide, rhs, ..
} if rhs == Number(0.0) => Number(1.0),
// a ^ 1 => a
BinOp {
op: Power,
lhs,
rhs,
} if rhs == Number(1.0) => lhs,
//////////////////////////// Modulos ////////////////////////////
// 0 % 0 => NaN // special case
BinOp {
op: Modulo,
lhs,
rhs,
} if lhs == Number(0.0) && rhs == Number(0.0) => Number(f64::NAN),
// 0 % a => 0
BinOp {
op: Modulo, lhs, ..
} if lhs == Number(0.0) => Number(0.0),
// a % 0 => NaN
BinOp {
op: Modulo, rhs, ..
} if rhs == Number(0.0) => Number(f64::NAN),
// a % 1 => 0
BinOp {
op: Modulo, rhs, ..
} if rhs == Number(1.0) => Number(0.0),
// a % a => 0
BinOp {
op: Modulo,
lhs,
rhs,
} if lhs == rhs => Number(0.0),
/////////////////////////// 2 Numbers ///////////////////////////
BinOp {
op,
rhs: Number(rhs),
lhs: Number(lhs),
} => {
#[allow(clippy::unreachable)]
let result = match op {
Plus => lhs + rhs,
Minus => lhs - rhs,
Times => lhs * rhs,
Divide => lhs / rhs,
Power => lhs.powf(rhs),
Modulo => lhs % rhs,
Factorial => unreachable!(),
};
Number(result)
},
_ => self.into(),
}
}
}
impl<'a> Simplify<'a> for UnOp<'a> {
fn simplify_for(mut self, var: (&str, f64)) -> Element<'a> {
self.operand = self.operand.simplify_for(var);
self.simplify()
}
fn simplify(mut self) -> Element<'a> {
self.operand = self.operand.simplify();
#[allow(clippy::unreachable)]
match self.op {
Operator::Plus => self.operand,
Operator::Factorial => match self.operand {
Element::Number(num) => Element::Number(factorial(num)),
Element::UnOp(_)
| Element::BinOp(_)
| Element::Function(_)
| Element::Variable(_) => self.into(),
},
Operator::Minus => match self.operand {
Element::Number(num) => Element::Number(-num),
Element::UnOp(_)
| Element::BinOp(_)
| Element::Function(_)
| Element::Variable(_) => self.into(),
},
Operator::Times
| Operator::Divide
| Operator::Power
| Operator::Modulo => unreachable!(),
}
}
}
impl<'a> Simplify<'a> for FunctionCall<'a> {
fn simplify_for(mut self, var: (&str, f64)) -> Element<'a> {
self.args = self
.args
.into_iter()
.map(|arg| arg.simplify_for(var))
.collect();
self.simplify()
}
fn simplify(mut self) -> Element<'a> {
// TODO: Not a big fan of the second vector.
// We need to simplify the arguments in all cases, but
// if they are all numbers, we can call the function.
let mut args_values: Vec<f64> = Vec::with_capacity(self.args.len());
self.args = self
.args
.into_iter()
.map(|arg| {
let simplified = arg.simplify();
if let Element::Number(num) = simplified {
args_values.push(num);
}
simplified
})
.collect();
if args_values.len() == self.args.len() {
self.call(&args_values).into()
} else {
self.into()
}
}
}