balanced_ternary/

lib.rs

//! A [balanced ternary](https://en.wikipedia.org/wiki/Balanced_ternary) data structure.
//!
//! A `Ternary` object in this module represents a number in the balanced ternary numeral system.
//! Balanced ternary is a non-standard positional numeral system that uses three digits: {-1, 0, +1}
//! represented here as `Neg` for -1, `Zero` for 0, and `Pos` for +1. It is useful in some domains
//! of computer science and mathematics due to its arithmetic properties and representation
//! symmetry.
//!
//! # Data Structures
//!
//! - **`Digit` Enum**:
//!     Represents a single digit for balanced ternary values, with possible values:
//!     - `Neg` for -1
//!     - `Zero` for 0
//!     - `Pos` for +1
//!
//! - **`Ternary` Struct**:
//!     Represents a balanced ternary number as a collection of `Digit`s.
//!     Provides utility functions for conversion, parsing, and manipulation.
//!
//! # Examples
//!
//! ## Converting between representations:
//! ```rust
//! use balanced_ternary::*;
//!
//! let ternary = Ternary::from_dec(5);
//! assert_eq!(ternary.to_string(), "+--");
//! assert_eq!(ternary.to_dec(), 5);
//!
//! let parsed = Ternary::parse("+--");
//! assert_eq!(parsed.to_string(), "+--");
//! assert_eq!(parsed.to_dec(), 5);
//! ```
//!
//! ## Negative numbers:
//! ```rust
//! use balanced_ternary::*;
//!
//! let neg_five = Ternary::from_dec(-5);
//! assert_eq!(neg_five.to_string(), "-++");
//! assert_eq!(neg_five.to_dec(), -5);
//!
//! let negated = -&neg_five;
//! assert_eq!(negated.to_string(), "+--");
//! assert_eq!(negated.to_dec(), 5);
//! ```
//!
//! ## Larger numbers:
//! ```rust
//! use balanced_ternary::*;
//!
//! let big = Ternary::from_dec(121);
//! assert_eq!(big.to_string(), "+++++");
//! assert_eq!(big.to_dec(), 121);
//!
//! let neg_big = Ternary::from_dec(-121);
//! assert_eq!(neg_big.to_string(), "-----");
//! assert_eq!(neg_big.to_dec(), -121);
//! ```
//!
//! ## Operations
//! ```
//! use balanced_ternary::Ternary;
//!
//! let repr9 = Ternary::parse("+00");
//! let repr4 = Ternary::parse("++");
//! let repr13 = &repr9 + &repr4;
//! let repr17 = &repr13 + &repr4;
//! let repr34 = &repr17 + &repr17;
//!
//! assert_eq!(repr13.to_string(), "+++");
//! assert_eq!(repr17.to_string(), "+-0-");
//! assert_eq!(repr34.to_string(), "++-+");
//!
//! let repr30 = &repr34 - &repr4;
//! assert_eq!(repr30.to_dec(), 30);
//! assert_eq!(repr30.to_string(), "+0+0");
//! ```
//!
#![no_std]
extern crate alloc;

use alloc::string::{String, ToString};
use alloc::vec::Vec;
use alloc::{format, vec};
use core::fmt::{Display, Formatter};
use core::str::FromStr;

/// Provides helper functions for formatting integers in a given radix.
///
/// Used internally to convert decimal numbers into their ternary representation.
/// - `x`: The number to be formatted.
/// - `radix`: The base of the numeral system.
///
/// Returns a string representation of the number in the specified base.
fn format_radix(x: i64, radix: u32) -> String {
    let mut result = vec![];
    let sign = x.signum();
    let mut x = x.abs() as u64;
    loop {
        let m = (x % radix as u64) as u32;
        x /= radix as u64;
        result.push(core::char::from_digit(m, radix).unwrap());
        if x == 0 {
            break;
        }
    }
    format!(
        "{}{}",
        if sign == -1 { "-" } else { "" },
        result.into_iter().rev().collect::<String>()
    )
}

pub mod digit;

pub use crate::digit::{
    Digit,
    Digit::{Neg, Pos, Zero},
};

/// Converts a character into a `Digit`.
///
/// # Arguments
/// * `from` - A single character (`+`, `0`, or `-`).
/// * **Panics** if the input character is invalid.
///
/// # Returns
/// * A `Digit` enum corresponding to the character.
///
/// # Example
/// ```
/// use balanced_ternary::{trit, Digit};
///
/// let digit = trit('+');
/// assert_eq!(digit, Digit::Pos);
/// ```
pub fn trit(from: char) -> Digit {
    Digit::from_char(from)
}

/// Converts a string representation of a balanced ternary number into a `Ternary` object.
///
/// This function is a convenient shorthand for creating `Ternary` numbers
/// from string representations. The input string must consist of balanced
/// ternary characters: `+`, `0`, and `-`.
///
/// # Arguments
///
/// * `from` - A string slice representing the balanced ternary number.
/// * **Panics** if an input character is invalid.
///
/// # Returns
///
/// A `Ternary` object created from the provided string representation.
///
/// # Example
/// ```
/// use balanced_ternary::{ter, Ternary};
///
/// let ternary = ter("+-0+");
/// assert_eq!(ternary.to_string(), "+-0+");
/// ```
pub fn ter(from: &str) -> Ternary {
    Ternary::parse(from)
}

#[cfg(feature = "tryte")]
/// Creates a `Tryte` object from a string representation of a balanced ternary number.
///
/// This function first converts the input string representation into a `Ternary` object
/// using the `ter` function, and then constructs a `Tryte` from that `Ternary`.
///
/// # Panics
///
/// This function panics if the `Ternary` contains more than 6 digits or if an input character is invalid.
///
/// # Arguments
///
/// * `from` - A string slice representing the balanced ternary number. It must contain
///   valid balanced ternary characters (`+`, `0`, or `-`) only.
/// * Panics if an input character is invalid.
///
/// # Returns
///
/// A `Tryte` object constructed from the provided balanced ternary string.
///
/// # Example
/// ```
/// use balanced_ternary::{tryte, Tryte};
///
/// let tryte_value = tryte("+0+0");
/// assert_eq!(tryte_value.to_string(), "00+0+0");
/// ```
pub fn tryte(from: &str) -> Tryte {
    Tryte::from_ternary(&ter(from))
}

/// Represents a balanced ternary number using a sequence of `Digit`s.
///
/// Provides functions for creating, parsing, converting, and manipulating balanced ternary numbers.
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub struct Ternary {
    digits: Vec<Digit>,
}

impl Ternary {
    /// Creates a new balanced ternary number from a vector of `Digit`s.
    pub fn new(digits: Vec<Digit>) -> Ternary {
        Ternary { digits }
    }

    /// Returns the number of digits (length) of the balanced ternary number.
    pub fn log(&self) -> usize {
        self.digits.len()
    }

    /// Retrieves a slice containing the digits of the `Ternary`.
    ///
    /// # Returns
    ///
    /// A slice referencing the digits vec of the `Ternary`.
    ///
    /// This function allows access to the raw representation of the
    /// balanced ternary number as a slice of `Digit` values.
    pub fn to_digit_slice(&self) -> &[Digit] {
        self.digits.as_slice()
    }

    /// Returns a reference to the [Digit] indexed by `index` if it exists.
    ///
    /// Digits are indexed **from the right**:
    /// ```
    /// use balanced_ternary::Ternary;
    ///
    /// // Indexes :
    /// //                              32
    /// //                             4||1
    /// //                            5||||0
    /// //                            ||||||
    /// //                            vvvvvv
    /// let ternary = Ternary::parse("+++--+");
    /// assert_eq!(ternary.get_digit(1).unwrap().to_char(), '-')
    /// ```
    pub fn get_digit(&self, index: usize) -> Option<&Digit> {
        self.digits.iter().rev().nth(index)
    }

    /// Parses a string representation of a balanced ternary number into a `Ternary` object.
    ///
    /// Each character in the string must be one of `+`, `0`, or `-`.
    pub fn parse(str: &str) -> Self {
        let mut repr = Ternary::new(vec![]);
        for c in str.chars() {
            repr.digits.push(Digit::from_char(c));
        }
        repr
    }

    /// Converts the `Ternary` object to its integer (decimal) representation.
    ///
    /// Calculates the sum of each digit's value multiplied by the appropriate power of 3.
    pub fn to_dec(&self) -> i64 {
        let mut dec = 0;
        for (rank, digit) in self.digits.iter().rev().enumerate() {
            dec += digit.to_i8() as i64 * 3_i64.pow(rank as u32);
        }
        dec
    }

    /// Creates a balanced ternary number from a decimal integer.
    ///
    /// The input number is converted into its balanced ternary representation,
    /// with digits represented as `Digit`s.
    pub fn from_dec(dec: i64) -> Self {
        let sign = dec.signum();
        let str = format_radix(dec.abs(), 3);
        let mut carry = 0u8;
        let mut repr = Ternary::new(vec![]);
        for digit in str.chars().rev() {
            let digit = u8::from_str(&digit.to_string()).unwrap() + carry;
            if digit < 2 {
                repr.digits.push(Digit::from_i8(digit as i8));
                carry = 0;
            } else if digit == 2 {
                repr.digits.push(Digit::from_i8(-1));
                carry = 1;
            } else if digit == 3 {
                repr.digits.push(Digit::from_i8(0));
                carry = 1;
            } else {
                panic!("Ternary::from_dec(): Invalid digit: {}", digit);
            }
        }
        if carry == 1 {
            repr.digits.push(Digit::from_i8(1));
        }
        repr.digits.reverse();
        if sign == -1 {
            -&repr
        } else {
            repr
        }
    }

    /// Converts the balanced ternary number to its unbalanced representation as a string.
    ///
    /// The unbalanced representation treats the digits as standard ternary (0, 1, 2),
    /// instead of balanced ternary (-1, 0, +1). Negative digits are handled by
    /// calculating the decimal value of the balanced ternary number and converting
    /// it back to an unbalanced ternary string.
    ///
    /// Returns:
    /// * `String` - The unbalanced ternary representation of the number, where each
    /// digit is one of `0`, `1`, or `2`.
    ///
    /// Example:
    /// ```
    /// use balanced_ternary::Ternary;
    ///
    /// let repr = Ternary::parse("+--");
    /// assert_eq!(repr.to_unbalanced(), "12");
    /// assert_eq!(repr.to_dec(), 5);
    /// let repr = Ternary::parse("-++");
    /// assert_eq!(repr.to_unbalanced(), "-12");
    /// assert_eq!(repr.to_dec(), -5);
    /// ```
    pub fn to_unbalanced(&self) -> String {
        format_radix(self.to_dec(), 3)
    }

    /// Parses a string representation of an unbalanced ternary number into a `Ternary` object.
    ///
    /// The string must only contain characters valid in the unbalanced ternary numeral system (`0`, `1`, or `2`).
    /// Each character is directly converted into its decimal value and then interpreted as a balanced ternary number.
    ///
    /// # Arguments
    ///
    /// * `unbalanced` - A string slice representing the unbalanced ternary number.
    ///
    /// # Returns
    ///
    /// A `Ternary` object representing the same value as the input string in balanced ternary form.
    ///
    /// # Panics
    ///
    /// This function will panic if the string is not a valid unbalanced ternary number.
    /// For instance, if it contains characters other than `0`, `1`, or `2`.
    ///
    /// # Examples
    ///
    /// ```
    /// use balanced_ternary::Ternary;
    ///
    /// let ternary = Ternary::from_unbalanced("-12");
    /// assert_eq!(ternary.to_string(), "-++");
    /// assert_eq!(ternary.to_dec(), -5);
    /// ```
    pub fn from_unbalanced(unbalanced: &str) -> Self {
        Self::from_dec(i64::from_str_radix(unbalanced, 3).unwrap())
    }

    /// Applies a transformation function to each digit of the balanced ternary number,
    /// returning a new `Ternary` object with the transformed digits.
    ///
    /// This method keeps the order of the digits unchanged while applying the provided
    /// transformation function `f` to each digit individually.
    ///
    /// # Arguments
    ///
    /// * `f` - A closure or function that takes a `Digit` and returns a transformed `Digit`.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object containing the transformed digits.
    ///
    /// # Digit transformations
    ///
    /// These methods (unary operators) from the [Digit] type can be called directly.
    ///
    /// * Returns either `Pos` or `Neg`:
    ///     * [Digit::possibly]
    ///     * [Digit::necessary]
    ///     * [Digit::contingently]
    ///     * [Digit::ht_not]
    /// * Returns either `Zero` or `Pos` or `Neg`.
    ///     * [Digit::pre]
    ///     * [Digit::post]
    ///     * [Digit::not]
    ///     * [Digit::neg]
    ///     * [Digit::absolute_positive]
    ///     * [Digit::positive]
    ///     * [Digit::not_negative]
    ///     * [Digit::not_positive]
    ///     * [Digit::negative]
    ///     * [Digit::absolute_negative]
    ///
    /// # Examples
    /// ```
    /// use balanced_ternary::{Ternary, Digit};
    ///
    /// let orig_ternary = Ternary::parse("+0-");
    /// let transformed = orig_ternary.each(Digit::necessary);
    /// assert_eq!(transformed.to_string(), "+--");
    /// let transformed = orig_ternary.each(Digit::positive);
    /// assert_eq!(transformed.to_string(), "+00");
    /// let transformed = orig_ternary.each(Digit::not_negative);
    /// assert_eq!(transformed.to_string(), "++0");
    /// let transformed = orig_ternary.each(Digit::absolute_negative);
    /// assert_eq!(transformed.to_string(), "-0-");
    /// ```
    pub fn each(&self, f: impl Fn(Digit) -> Digit) -> Self {
        let mut repr = Ternary::new(vec![]);
        for digit in self.digits.iter() {
            repr.digits.push(f(*digit));
        }
        repr
    }

    /// Applies a transformation function to each digit of the balanced ternary number,
    /// using an additional parameter for the transformation process, returning a new `Ternary`
    /// object with the transformed digits.
    ///
    /// This method keeps the order of the digits unchanged while applying the provided
    /// transformation function `f` to each digit individually, along with the provided extra
    /// `other` digit.
    ///
    /// # Arguments
    ///
    /// * `f` - A closure or function that takes a `Digit` and an additional `Digit`,
    ///         and returns a transformed `Digit`.
    /// * `other` - An additional `Digit` to be passed to the transformation function `f`.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object containing the transformed digits.
    ///
    /// # Digit transformations
    ///
    /// These methods (binary operators) from the [Digit] type can be called directly.
    ///
    /// * [Digit::mul]
    /// * [Digit::div]
    /// * [Digit::bitand] (k3/p3 and)
    /// * [Digit::bi3_and]
    /// * [Digit::bitor]  (k3/p3 or)
    /// * [Digit::bi3_or]
    /// * [Digit::bitxor] (k3/p3 xor)
    /// * [Digit::k3_imply]
    /// * [Digit::k3_equiv]
    /// * [Digit::bi3_imply]
    /// * [Digit::l3_imply]
    /// * [Digit::rm3_imply]
    /// * [Digit::ht_imply]
    ///
    /// # Examples
    /// ```
    /// use std::ops::Mul;
    /// use balanced_ternary::{Ternary, Digit};
    ///
    /// let original = Ternary::parse("+-0");
    /// let transformed = original.each_with(Digit::mul, Digit::Neg);
    /// assert_eq!(transformed.to_string(), "-+0");
    /// ```
    pub fn each_with(&self, f: impl Fn(Digit, Digit) -> Digit, other: Digit) -> Self {
        let mut repr = Ternary::new(vec![]);
        for digit in self.digits.iter() {
            repr.digits.push(f(*digit, other));
        }
        repr
    }


    /// Applies a transformation function to each digit of the balanced ternary number,
    /// along with a corresponding digit from another `Ternary` number.
    ///
    /// This method ensures that the digits of both `Ternary` objects are aligned from the least
    /// significant to the most significant digit. If the `other` `Ternary` has fewer digits
    /// than the current one, the process is reversed to handle the shorter `Ternary` consistently.
    /// The result is a new `Ternary` object where each digit was transformed using the provided function `f`.
    ///
    /// # Arguments
    ///
    /// * `f` - A closure or function that takes two arguments:
    ///     * a `Digit` from the current `Ternary`,
    ///     * a `Digit` from the corresponding position in the `other` `Ternary`.
    ///     * The function must return a transformed `Digit`.
    /// * `other` - A `Ternary` object with digits to process alongside the digits of the current object.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object containing the transformed digits.
    ///
    /// # Examples
    ///
    /// ```
    /// use std::ops::Mul;
    /// use balanced_ternary::{Ternary, Digit};
    ///
    /// let ternary1 = Ternary::parse("-+0-+0-+0");
    /// let ternary2 = Ternary::parse("---000+++");
    ///
    /// let result = ternary1.each_zip(Digit::mul, ternary2.clone());
    /// assert_eq!(result.to_string(), "+-0000-+0");
    ///
    /// let result = ternary1.each_zip(Digit::k3_imply, ternary2.clone());
    /// assert_eq!(result.to_string(), "+-0+00+++");
    /// let result = ternary1.each_zip(Digit::bi3_imply, ternary2.clone());
    /// assert_eq!(result.to_string(), "+-0000++0");
    /// let result = ternary1.each_zip(Digit::ht_imply, ternary2.clone());
    /// assert_eq!(result.to_string(), "+--+0++++");
    /// ```
    pub fn each_zip(&self, f: impl Fn(Digit, Digit) -> Digit, other: Self) -> Self {
        if self.digits.len() < other.digits.len() {
            return other.each_zip(f, self.clone());
        }
        let mut repr = Ternary::new(vec![]);
        for (i, digit) in self.digits.iter().rev().enumerate() {
            let d_other = other.get_digit(i).unwrap();
            let res= f(*digit, *d_other);
            repr.digits.push(res);
        }
        repr.digits.reverse();
        repr
    }

    /// Applies a transformation function to each digit of the balanced ternary number,
    /// along with a corresponding digit from another `Ternary` number, and a carry digit.
    ///
    /// This method processes the digits in reverse order (from the least significant to the most significant),
    /// keeping their transformed order correct by reversing the result afterward. Each digit from the
    /// current `Ternary` object is processed with the corresponding digit from another `Ternary` object
    /// and a carry digit using the provided closure or function `f`.
    ///
    /// # Arguments
    ///
    /// * `f` - A closure or function that takes three arguments:
    ///         - a `Digit` from the current `Ternary`,
    ///         - a `Digit` from the corresponding position in the `other` `Ternary`, and
    ///         - the current carry `Digit`.
    ///         The function must return a tuple containing a new carry `Digit` and a transformed `Digit`.
    /// * `other` - A `Ternary` object with digits to process alongside the digits of the current object.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object containing the transformed digits.
    ///
    /// # Notes
    ///
    /// The carry digit is initially `Zero` and is passed between each step of the transformation process.
    /// If the `other` `Ternary` has fewer digits than the current one, the missing digits in `other`
    /// are treated as `Zero`.
    ///
    /// # Examples
    ///
    /// ```
    /// use balanced_ternary::{Digit, Ternary};
    ///
    /// let ternary1 = Ternary::parse("+-0");
    /// let ternary2 = Ternary::parse("-+0");
    ///
    /// // Transformation function that adds digits with a carry digit
    /// let combine = |d1: Digit, d2: Digit, carry: Digit| -> (Digit, Digit) {
    ///     // Simple example operation: this just illustrates transforming with carry.
    ///     // Replace with meaningful logic as needed for your application.
    ///     let sum = d1.to_i8() + d2.to_i8() + carry.to_i8();
    ///     (Digit::from_i8(sum / 3), Digit::from_i8(sum % 3))
    /// };
    ///
    /// let result = ternary1.each_zip_carry(combine, ternary2.clone());
    /// assert_eq!(result.trim().to_string(), (&ternary1 + &ternary2).to_string());
    /// ```
    pub fn each_zip_carry(&self, f: impl Fn(Digit, Digit, Digit) -> (Digit, Digit), other: Self) -> Self {
        if self.digits.len() < other.digits.len() {
            return other.each_zip_carry(f, self.clone());
        }
        let mut repr = Ternary::new(vec![]);
        let mut carry = Zero;
        for (i, digit) in self.digits.iter().rev().enumerate() {
            let d_other = other.get_digit(i).unwrap();
            let (c, res) = f(*digit, *d_other, carry);
            carry = c;
            repr.digits.push(res);
        }
        repr.digits.reverse();
        repr
    }

    /// Removes leading `Zero` digits from the `Ternary` number, effectively trimming
    /// it down to its simplest representation. The resulting `Ternary` number
    /// will still represent the same value.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object, trimmed of leading zeros.
    ///
    /// # Examples
    ///
    /// ```
    /// use balanced_ternary::{ Neg, Pos, Ternary, Zero};
    ///
    /// let ternary = Ternary::new(vec![Zero, Zero, Pos, Neg]);
    /// let trimmed = ternary.trim();
    /// assert_eq!(trimmed.to_string(), "+-");
    /// ```
    ///
    /// # Notes
    ///
    /// This method does not mutate the original `Ternary` object but returns a new representation.
    pub fn trim(&self) -> Self {
        if self.to_dec() == 0 {
            return Ternary::parse("0");
        }
        let mut repr = Ternary::new(vec![]);
        let mut first_digit = false;
        for digit in self.digits.iter() {
            if !first_digit && digit != &Zero {
                first_digit = true;
            }
            if first_digit {
                repr.digits.push(*digit);
            }
        }
        repr
    }

    /// Adjusts the representation of the `Ternary` number to have a fixed number of digits.
    ///
    /// If the current `Ternary` has fewer digits than the specified `length`, leading zero digits
    /// will be added to the `Ternary` to match the desired length. If the current `Ternary` has
    /// more digits than the specified `length`, it will be returned unmodified.
    ///
    /// # Arguments
    ///
    /// * `length` - The desired length of the `Ternary` number.
    ///
    /// # Returns
    ///
    /// * `Self` - A new `Ternary` object with the specified fixed length.
    ///
    /// # Notes
    ///
    /// If `length` is smaller than the existing number of digits, the function does not truncate
    /// the number but instead returns the original `Ternary` unchanged.
    ///
    /// # Examples
    ///
    /// ```
    /// use balanced_ternary::{Ternary, Zero, Pos};
    ///
    /// let ternary = Ternary::new(vec![Pos]);
    /// let fixed = ternary.with_length(5);
    /// assert_eq!(fixed.to_string(), "0000+");
    ///
    /// let fixed = ternary.with_length(1);
    /// assert_eq!(fixed.to_string(), "+");
    /// ```
    pub fn with_length(&self, length: usize) -> Self {
        if length < self.log() {
            return self.clone();
        }
        let zeroes = vec![Zero; length - self.log()];
        let mut repr = Ternary::new(vec![]);
        repr.digits.extend(zeroes);
        repr.digits.extend(self.digits.iter().cloned());
        repr
    }
}

impl Display for Ternary {
    fn fmt(&self, f: &mut Formatter<'_>) -> core::fmt::Result {
        let mut str = String::new();
        for digit in self.digits.iter() {
            str.push(digit.to_char());
        }
        write!(f, "{}", str)
    }
}

pub mod operations;

pub mod conversions;

#[cfg(feature = "tryte")]
pub mod tryte;

#[cfg(feature = "tryte")]
pub use crate::tryte::Tryte;

#[cfg(test)]
#[test]
fn test_ternary() {
    use crate::*;

    let repr5 = Ternary::new(vec![Pos, Neg, Neg]);
    assert_eq!(repr5.to_dec(), 5);
    let repr5 = Ternary::from_dec(5);
    assert_eq!(repr5.to_dec(), 5);

    let repr13 = Ternary::new(vec![Pos, Pos, Pos]);
    assert_eq!(repr13.to_dec(), 13);

    let repr14 = Ternary::parse("+---");
    let repr15 = Ternary::parse("+--0");
    assert_eq!(repr14.to_dec(), 14);
    assert_eq!(repr15.to_dec(), 15);
    assert_eq!(repr14.to_string(), "+---");
    assert_eq!(repr15.to_string(), "+--0");

    let repr120 = Ternary::from_dec(120);
    assert_eq!(repr120.to_dec(), 120);
    assert_eq!(repr120.to_string(), "++++0");
    let repr121 = Ternary::from_dec(121);
    assert_eq!(repr121.to_dec(), 121);
    assert_eq!(repr121.to_string(), "+++++");

    let repr_neg_5 = Ternary::parse("-++");
    assert_eq!(repr_neg_5.to_dec(), -5);
    assert_eq!(repr_neg_5.to_string(), "-++");

    let repr_neg_5 = Ternary::from_dec(-5);
    assert_eq!(repr_neg_5.to_dec(), -5);
    assert_eq!(repr_neg_5.to_string(), "-++");

    let repr_neg_121 = Ternary::from_dec(-121);
    assert_eq!(repr_neg_121.to_dec(), -121);
    assert_eq!(repr_neg_121.to_string(), "-----");

    let test = Ternary::from_dec(18887455);
    assert_eq!(test.to_dec(), 18887455);
    assert_eq!(test.to_string(), "++00--0--+-0++0+");

    let unbalanced = Ternary::from_unbalanced("12");
    assert_eq!(unbalanced.to_dec(), 5);
    assert_eq!(unbalanced.to_string(), "+--");

    let unbalanced = Ternary::from_unbalanced("-12");
    assert_eq!(unbalanced.to_dec(), -5);
    assert_eq!(unbalanced.to_string(), "-++");

    let unbalanced = Ternary::from_dec(121);
    assert_eq!(unbalanced.to_unbalanced(), "11111");
    assert_eq!(unbalanced.to_string(), "+++++");
}