Balanced Ternary

Balanced Ternary is a Rust library for manipulating * balanced ternary* numbers, a numeral system with digits -1, 0, and +1.

This system is useful in areas like computer science and mathematics due to its symmetry and unique arithmetic properties.

Features

Number Conversions: Convert between decimal and balanced ternary representations.
Arithmetic Operations: Support for addition, subtraction, multiplication, and division.
Logic Operations: Support for bitwise and, or, xor, and not.
Advanced logic: Implementation of K3, BI3, L3, RM3 and HT imply operation.
Custom Representation: Parse and display numbers using +, 0, and - symbols.
No Standard Library: Suitable for #![no_std] environments.
Provides the types:
- Digit (Neg, Zero or Pos),
- Ternary (heap allocated variable-length balanced-ternary number),
- Tryte (6 characters long copy-type ternary number).

Digits operators

These operators can be applied for Ternary with Ternary::each(operator):

Unary operators	-	0	+
possibly	-	+	+
necessary	-	-	+
contingently	-	+	-
ht_not	+	-	-
post	0	+	-
pre	+	-	0
`!` (not) / `-` (neg)	+	0	-
absolute_positive	+	0	+
positive	0	0	+
not_negative	0	+	+
not_positive	-	-	0
negative	-	0	0
absolute_negative	-	0	-

These operators can be applied for Ternary with:

Ternary::each_with(operator, with), or,
Ternary::each_zip(operator, other):

Binary operators	--	-0	-+	0-	00	0+	+-	+0	++
`+` (add)	-+	-	0	-	0	+	0	+	+-
`-` (sub)	0	-	-+	+	0	-	+-	+	0
`/` (div)	+		-	0		0	-		+
`*` (mul)	+	0	-	0	0	0	-	0	+
`&` (bitand)	-	-	-	-	0	0	-	0	+
bi3_and	-	0	-	0	0	0	-	0	+
`\|` (bitor)	-	0	+	0	0	+	+	+	+
bi3_or	-	0	+	0	0	0	+	0	+
`^` (bitxor)	-	0	+	0	0	0	+	0	-
k3_equiv	+	0	-	0	0	0	-	0	+
k3_imply	+	+	+	0	0	+	-	0	+
bi3_imply	+	0	+	0	0	0	-	0	+
l3_imply	+	+	+	0	+	+	-	0	+
rm3_imply	+	+	+	-	0	+	-	-	+
ht_imply	+	+	+	-	+	+	-	0	+

Examples

Convert between decimal and balanced ternary

use balanced_ternary::*;

fn test() {
    let ternary = Ternary::from_dec(5);
    assert_eq!(ternary.to_string(), "+--");

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

Perform arithmetic or logic operations

use balanced_ternary::*;

fn test() {
    let a = Ternary::from_dec(9);
    let b = Ternary::from_dec(4);
    let sum = &a + &b;
    assert_eq!(ternary.to_string(), "+++");
    assert_eq!(sum.to_dec(), 13);

    let bitwise = &Ternary::parse("++00") & &Ternary::parse("0000");
    assert_eq!(bitwise.to_string(), "0000");

    let bitwise = &Ternary::parse("++00") & &Ternary::parse("0+00");
    assert_eq!(bitwise.to_string(), "0+00");

    let bitwise = &Ternary::parse("+000") | &Ternary::parse("000-");
    assert_eq!(bitwise.to_string(), "+000");


    let bitwise = &Ternary::parse("+000") & &Ternary::parse("000-");
    assert_eq!(bitwise.to_string(), "000-");

    let bitwise = &Ternary::parse("+000") | &Ternary::parse("000+");
    assert_eq!(bitwise.to_string(), "+00+");
}

Handle negative numbers

use balanced_ternary::*;

fn test() {
    let negative = Ternary::from_dec(-5);
    assert_eq!(negative.to_string(), "-++");
}

Installation

Add the following to your Cargo.toml:

[dependencies]
balanced-ternary = "0.1.*"

balanced-ternary 0.2.1