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use crate::Error;
use std::{
f64::consts::{E, PI},
sync::Arc,
};
use crate::Elementary::{self, *};
impl<'a> From<&'a str> for Elementary {
fn from(value: &'a str) -> Self {
let value: String = value.split_whitespace().collect();
Self::to_elementary(&value).unwrap()
}
}
impl Elementary {
fn split_function(value: &str) -> Vec<&str> {
let mut interp_slice: Vec<&str> = value.split("").collect();
// remove the first and last element because they are just empty string slices
interp_slice.remove(0);
interp_slice.pop();
let mut chunks: Vec<&str> = Vec::new();
let mut open_parenthesis = -1;
let mut cut_index = 0;
let mut skip = 0;
for i in 0..interp_slice.len() {
// if items need to be skipped (because of the implementation of constants)
if skip > 0 {
skip -= 1;
continue;
}
if interp_slice[i] == "(" {
// this is for the first case of an opening parenthesis. Note that we cannot start
// at 0 since that would match the case for closing an outer parenthesis
if open_parenthesis == -1 {
open_parenthesis = 1;
} else {
// for all other cases, however, the number of open parentheses just goes up by
// one
open_parenthesis += 1;
}
} else if interp_slice[i] == ")" {
open_parenthesis -= 1
}
// check if outer parenthesis has been closed
if open_parenthesis == 0 {
chunks.push(&value[cut_index..=i]);
// set new cut index
cut_index = i + 1;
// reset parenthesis
open_parenthesis = -1;
}
// detect operations and constants
if open_parenthesis == -1 {
if interp_slice[i] == "+"
|| interp_slice[i] == "-"
|| interp_slice[i] == "*"
|| interp_slice[i] == "/"
|| interp_slice[i] == "^"
{
chunks.push(interp_slice[i]);
cut_index = i + 1;
} else if interp_slice[i] == "!" {
chunks.push(&value[cut_index..=i]);
cut_index = i + 1;
} else if interp_slice[i] == "x" {
chunks.push(&value[cut_index..=i]);
cut_index = i + 1;
} else if interp_slice[i] == "e" {
chunks.push(&value[cut_index..=i]);
cut_index = i + 1;
} else if interp_slice[i] == "pi" || interp_slice[i] == "π" {
chunks.push("pi");
cut_index = i + 1;
} else {
// checking for numbers
if let Ok(_) = &value[cut_index..=i].parse::<f64>() {
// find the index at which the number ends
let mut last_index = i;
'index: for j in i + 1..=interp_slice.len() {
if let Ok(_) = &value[cut_index..j].parse::<f64>() {
last_index = j - 1;
} else {
break 'index;
}
}
// push the whole number
chunks.push(&value[cut_index..=last_index]);
// the next couple of indexes must be skipped in order to avoid parsing of
// individual digits
skip = last_index - i;
// by setting skip to the number of difference between the current index
// and the index at which the number ends
cut_index = last_index + 1;
}
}
}
}
if chunks.is_empty() {
chunks.push(value);
}
chunks
}
fn to_elementary(string: &str) -> Result<Self, Error> {
let strings = Self::split_function(string);
let mut functions: Vec<ElemRef> = strings
.clone()
.iter()
.map(|s| Self::parse_function(s).unwrap())
.collect();
let mut iteration = 0;
// order of operations
while functions.len() != 1 {
if iteration >= 10000 {
return Err(Error::ParseError(String::from(format!(
"Iteration limit reached while parsing function: {string}",
))));
} else {
iteration += 1;
}
// first in the order of operations is powers (seeing as parentheses are handled as a
// separate case)
if functions.contains(&ElemRef::Pow) {
for i in (0..functions.len()).rev() {
// find the index of the last power (because we treat this case from right to
// left)
if i >= functions.len() {
continue;
}
if functions[i] == ElemRef::Pow {
let replacement_func = ElemRef::Function(Pow(
Arc::new(functions[i - 1].clone().convert()?),
Arc::new(functions[i + 1].clone().convert()?),
));
functions.remove(i + 1);
functions.remove(i);
functions.remove(i - 1);
functions.insert(i - 1, replacement_func);
}
}
continue;
}
// the factorial function (x ↦ x!) is by convention written in "postfix" notation (i.e.
// it taeks precedence over normal operations)
if functions.contains(&ElemRef::Factorial) {
iterate_operation(&mut functions, ElemRef::Factorial)?;
continue;
}
// next up in the order of operations is multiplication
if functions.contains(&ElemRef::Mul) {
iterate_operation(&mut functions, ElemRef::Mul)?;
continue;
}
// we also have to handle implied multiplication. Weather this is handled before or
// after the explicit multiplication doesn't matter since multiplication is commutative
// i.e. a*b = b*a
// check if there is there are any instances of implied multiplication
for i in 0..functions.len() {
if i < functions.len() - 1 {
if let (ElemRef::Function(func1), ElemRef::Function(func2)) =
(&functions[i], &functions[i + 1])
{
// multiply the two together
let replacement_func = ElemRef::Function(Mul(
Arc::new(func1.to_owned()),
Arc::new(func2.to_owned()),
));
// remove the functions and replace them with the multiplied function
functions.remove(i + 1);
functions.remove(i);
functions.insert(i, replacement_func);
}
}
}
// next up is division
if functions.contains(&ElemRef::Div) {
iterate_operation(&mut functions, ElemRef::Div)?;
continue;
}
// then addition
if functions.contains(&ElemRef::Add) {
iterate_operation(&mut functions, ElemRef::Add)?;
continue;
}
// and lastly subtracion
if functions.contains(&ElemRef::Sub) {
iterate_operation(&mut functions, ElemRef::Sub)?;
continue;
}
}
functions
.pop()
.expect("Couldn't find a function to parse")
.convert()
}
fn parse_function(string: &str) -> Result<ElemRef, Error> {
let mut string = string.to_lowercase();
// unwrap potential parentheses
if &string[..1] == "(" {
while &string[..1] == "(" {
string = string[1..string.len() - 1].to_string();
}
return Ok(ElemRef::Function(Self::to_elementary(&string)?));
}
// check for special function (independent variable) x, and then check for constants
if string == "x" {
return Ok(ElemRef::Function(X));
} else if let Ok(number) = string.parse::<f64>() {
return Ok(ElemRef::Function(Con(number)));
}
match &string[..] {
// check in order of operations
"^" => Ok(ElemRef::Pow),
"*" => Ok(ElemRef::Mul),
"/" => Ok(ElemRef::Div),
"+" => Ok(ElemRef::Add),
"-" => Ok(ElemRef::Sub),
// also constants
"e" => Ok(ElemRef::Function(Con(E))),
"pi" => Ok(ElemRef::Function(Con(PI))),
"!" => Ok(ElemRef::Factorial),
_ => {
// if we do not have an operation, we must have a function consisting of a function
// identifier and its contents
let (func, cont) = split_first(&string, "(");
// remove outer parenthesis
let mut graphemes: Vec<&str> = cont.split("").collect();
// remove the first and last character because they should be parentheses
graphemes.remove(0);
graphemes.pop();
let cont: String = graphemes.iter().map(|x| *x).collect();
match func {
"sin" => Ok(ElemRef::Function(Sin(Arc::new(Self::to_elementary(
&cont,
)?)))),
"cos" => Ok(ElemRef::Function(Cos(Arc::new(Self::to_elementary(
&cont,
)?)))),
"tan" => Ok(ElemRef::Function(Tan(Arc::new(Self::to_elementary(
&cont,
)?)))),
"sec" => Ok(ElemRef::Function(Sec(Arc::new(Self::to_elementary(
&cont,
)?)))),
"csc" => Ok(ElemRef::Function(Csc(Arc::new(Self::to_elementary(
&cont,
)?)))),
"cot" => Ok(ElemRef::Function(Cot(Arc::new(Self::to_elementary(
&cont,
)?)))),
"asin" => Ok(ElemRef::Function(Asin(Arc::new(Self::to_elementary(
&cont,
)?)))),
"acos" => Ok(ElemRef::Function(Acos(Arc::new(Self::to_elementary(
&cont,
)?)))),
"atan" => Ok(ElemRef::Function(Atan(Arc::new(Self::to_elementary(
&cont,
)?)))),
"sinh" => Ok(ElemRef::Function(Sinh(Arc::new(Self::to_elementary(
&cont,
)?)))),
"cosh" => Ok(ElemRef::Function(Cosh(Arc::new(Self::to_elementary(
&cont,
)?)))),
"tanh" => Ok(ElemRef::Function(Tanh(Arc::new(Self::to_elementary(
&cont,
)?)))),
"ln" => Ok(ElemRef::Function(Log(
Arc::new(Con(E)), //ln is equivalent to log base e of its contents
Arc::new(Self::to_elementary(&cont)?),
))),
"abs" => Ok(ElemRef::Function(Abs(Arc::new(Self::to_elementary(
&cont,
)?)))),
"sqrt" => Ok(ElemRef::Function(Pow(
Arc::new(Self::to_elementary(&cont)?),
Arc::new(Con(0.5)),
))),
_ => Err(Error::ParseError(format!(
"Function identifier '{func}' not recognized"
))),
}
}
}
}
}
// all instances of an operation must be handled before the parsing method can move on to the next.
// This is to ensure that the order of operations is being upheld
fn iterate_operation(functions: &mut Vec<ElemRef>, operation: ElemRef) -> Result<(), Error> {
if functions.contains(&operation) {
for i in 0..functions.len() {
if i >= functions.len() {
continue;
}
if functions[i] == operation {
let replacement_func = match operation {
ElemRef::Mul => ElemRef::Function(Mul(
Arc::new(functions[i - 1].clone().convert()?),
Arc::new(functions[i + 1].clone().convert()?),
)),
ElemRef::Div => ElemRef::Function(Div(
Arc::new(functions[i - 1].clone().convert()?),
Arc::new(functions[i + 1].clone().convert()?),
)),
ElemRef::Add => ElemRef::Function(Add(
Arc::new(functions[i + 1].clone().convert()?),
Arc::new(functions[i - 1].clone().convert()?),
)),
ElemRef::Sub => {
if i > 0 {
ElemRef::Function(Sub(
Arc::new(functions[i - 1].clone().convert()?),
Arc::new(functions[i + 1].clone().convert()?),
))
} else {
ElemRef::Function(functions[i + 1].clone().convert()? * (-1 as f64))
}
}
ElemRef::Factorial => {
if i > 0 {
ElemRef::Function(Factorial(functions[i - 1].clone().convert()?.into()))
} else {
return Err(Error::ParseError(String::from(
"Factorial function must be applied to another function",
)));
}
}
_ => unimplemented!("No such operation"), // this point shouldn't be reached
};
if operation == ElemRef::Factorial {
println!("testing - {replacement_func:?}");
// the factorial notation is rather unique, because it always follows directly
// after the function upon which it acts.
functions.remove(i);
functions.remove(i - 1);
functions.insert(i - 1, replacement_func)
} else {
// the operation itself as well as the functions surrounding it must be removed
functions.remove(i + 1);
functions.remove(i);
if i > 0 {
functions.remove(i - 1);
// the combined new function is inserted in the place of the previous functions
functions.insert(i - 1, replacement_func);
} else {
// this is strictly for when a negative number is implied as seen above
functions.insert(i, replacement_func)
}
}
}
}
}
Ok(())
}
// enum to allow operations to be described as the same type without carrying two functions
#[derive(Debug, Clone, PartialEq)]
enum ElemRef {
Function(Elementary),
Pow,
Mul,
Div,
Add,
Sub,
Factorial,
}
impl ElemRef {
fn convert(self) -> Result<Elementary, Error> {
match self {
Self::Function(elem) => Ok(elem),
_ => Err(Error::ParseError(String::from(
"Cannot convert operation to elementary function",
))),
}
}
}
// splits the provided string at the first index where the specified identifier is found.
// if the identifier is not found, the string will be split at index 0
fn split_first<'a>(string: &'a String, indentifier: &'a str) -> (&'a str, &'a str) {
let slice: Vec<&str> = string.split("").collect();
let mut index = 0;
// find index of first insance of the identifier
for (i, s) in slice.iter().enumerate().take(string.len()) {
if *s == indentifier {
index = i;
break;
}
}
string.split_at(index - 1)
}