2 releases
0.1.1 | Jul 8, 2023 |
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0.1.0 | May 21, 2023 |
#321 in Math
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Special Numeral-Analogue Fuel Units
A Rust crate and utility to deal with conversions of SNAFU values
from Advent of Code 2022, Day 25 (here).
The file AOC-22-25.md contains the full puzzle in case the
website is unavailable.
Example conversions from SNAFU:
use snafu_numbers::FromSnafu;
assert_eq!(u32::from_snafu("1=-0-2"), 1747);
assert_eq!(u32::from_snafu("20012"), 1257);
assert_eq!(u32::from_snafu("1="), 3);
... and into SNAFU:
use snafu_numbers::IntoSnafu;
assert_eq!(1747_u32.into_snafu(), "1=-0-2");
SNAFU numbers
SNAFU numbers are a power-of-5 centric base-10 system written right to left. The zero-th (i.e., right-most) place represents a multiple of 5^{0} = 0, the first represents a multiple 5^{1} = 5, the second place 5^{2} = 25, the third place 5^{3} = 625, etc.
Five different digits are used. Here is a list alongside their decimal integer representation:
SNAFU digit | Name | Decimal / ℤ |
---|---|---|
2 |
two | 2 |
1 |
one | 1 |
0 |
zero | 0 |
- |
minus | -1 |
= |
double-minus | -2 |
As a result, the individual values in each position n
is 2×5^{n-1}, so
Position | Base | = |
- |
0 |
1 |
2 |
---|---|---|---|---|---|---|
0 | 5^{0} = 1 |
-2 |
1 |
0 |
1 |
2 |
1 | 5^{1} = 5 |
-10 |
-5 |
0 |
5 |
10 |
2 | 5^{2} = 25 |
-50 |
-25 |
0 |
25 |
50 |
3 | 5^{3} = 125 |
-250 |
-125 |
0 |
125 |
250 |
4 | 5^{4} = 625 |
-1250 |
-625 |
0 |
625 |
1250 |
5 | 5^{5} = 3125 |
-6250 |
-3125 |
0 |
3125 |
6250 |
etc.
To quote the rules:
Say you have the SNAFU number
2=-01
. That's2
in the 625s place,=
(double-minus) in the 125s place,-
(minus) in the 25s place,0
in the 5s place, and 1 in the1
s place. (2 times 625) plus (-2 times 125) plus (-1 times 25) plus (0 times 5) plus (1 times 1). That's 1250 plus -250 plus -25 plus 0 plus 1. 976!"
Example conversion from decimal to SNAFU
Decimal | SNAFU |
---|---|
1 |
1 |
2 |
2 |
3 |
1= |
4 |
1- |
5 |
10 |
6 |
11 |
7 |
12 |
8 |
2= |
9 |
2- |
10 |
20 |
15 |
1=0 |
20 |
1-0 |
2022 |
1=11-2 |
12345 |
1-0---0 |
314159265 |
1121-1110-1=0 |
Example conversion from SNAFU to decimal
SNAFU | Decimal |
---|---|
1=-0-2 |
1747 |
12111 |
906 |
2=0= |
198 |
21 |
11 |
2=01 |
201 |
111 |
31 |
20012 |
1257 |
112 |
32 |
1=-1= |
353 |
1-12 |
107 |
12 |
7 |
1= |
3 |
122 |
37 |