Double balanced ternary arithmetic

reimplementing in Nim.

Double balanced ternary is a complex number representation based on a 3x3 magic square:

6 1 8
7 5 3
2 9 4

notating with a & at head, such as &1, &12, &1.3, &.33. And &1 is the main direction, like "front".

&1   -> (0, 1)
&3   -> (1, 0)
&5   -> (0, 0)
&7   -> (-1, 0)
&9   -> (0, -1)
&2   -> (-1, -1)

&1   -> (0, 1)
&19  -> (0, 2)
&15  -> (0, 3)
&11  -> (0, 4)
&199 -> (0, 5)

&18  -> (1, 1)
&36  -> (2, 1)
&31  -> (3, 1)
&38  -> (4, 1)
&38  -> (4, 1)
&376 -> (5, 1)

similarly, it can be added, mutiplied and even divided. Notice that &1 is the main direction for &1 * &1 == &1 and &5 is zero point for &5 + &5 = &5.

Usage

requires "https://github.com/dual-balanced-ternary/dual-balanced-ternary.nim#v0.0.2"

import dual_balanced_ternary

echo "&1.1".parseTernary() # gets &1.1
echo "&1.1".ternary # alias

"&.3".ternary + "&45".ternary
"&.3".ternary - "&45".ternary
"&.3".ternary * "&45".ternary
"&.3".ternary / "&45".ternary

"&.3".ternary.isZero # false
"&.3".ternary.conjugate

createDualBalancedTernary(1.1, 1.2) # create from float
"&36".ternary.toFloat # (2.0, 1.0)
"&36".ternary.hash

"&3.33".ternary.round # &3
"&3.33".ternary.round(1) # &3.3

License

MIT