Arithmetic, logical, and textual operations for balanced ternary data.
From Wikipedia:
Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself.
A trit (ternary digit) is one of { -1, 0, 1 }, written here as { T, 0, 1 }. T serves as a visual approximation of a 1 with a bar over it, i.e. the negation of 1. A trit can also represent the values { false, unknown, true } for use in three-valued (Kleene) logic, or the values { less, equal, greater } for use in comparisons.
This library represents a trit as two bits using the following mapping:
| Binary | Ternary |
|---|---|
00 |
0 |
01 |
1 |
10 |
invalid |
11 |
T |
A trit holds log23 ≈ 1.58 bits of information.
A tryte is a group of 6 trits, representing the range [-364, +364].
This library represents a tryte as an unsigned 16-bit integer, packing its 6 trits into the lower 12 bits and leaving the highest 4 bits as 0.
A tryte holds log2(36) ≈ 9.51 bits of information.
Due to the nature of the balanced ternary system, there is no need for separate signed/unsigned integer types. While this library performs all of its multi-tryte operations in little-endian fashion on tryte sequences of any size, the following sizes are standardized:
| Trytes | Trits | Alias | Range |
|---|---|---|---|
| 1 | 6 | T6 |
[-364, +364] |
| 2 | 12 | T12 |
[-265,720, +265,720] |
| 4 | 24 | T24 |
[-141,214,768,240, +141,214,768,240] |
A byte can be written as two hexadecimal characters representing four bits each. Analogously, a tryte can be written as two hytes (i.e. half trytes) representing three trits each, using the following mapping:
| Hyte | Ternary | Decimal |
|---|---|---|
m |
TTT |
-13 |
l |
TT0 |
-12 |
k |
TT1 |
-11 |
j |
T0T |
-10 |
i |
T00 |
-9 |
h |
T01 |
-8 |
g |
T1T |
-7 |
f |
T10 |
-6 |
e |
T11 |
-5 |
d |
0TT |
-4 |
c |
0T0 |
-3 |
b |
0T1 |
-2 |
a |
00T |
-1 |
0 |
000 |
0 |
A |
001 |
1 |
B |
01T |
2 |
C |
010 |
3 |
D |
011 |
4 |
E |
1TT |
5 |
F |
1T0 |
6 |
G |
1T1 |
7 |
H |
10T |
8 |
I |
100 |
9 |
J |
101 |
10 |
K |
11T |
11 |
L |
110 |
12 |
M |
111 |
13 |
This library implements Unicode text handling using UTF-6T, a ternary adaptation of UTF-8. Code points are encoded in one, two, or three trytes using the following patterns:
| Code point type | Trytes |
|---|---|
| Single | 0xxxxx |
| Double | 1Txxxx Txxxxx |
| Triple | 11xxxx Txxxxx Txxxxx |