https://github.com/lightsing/learn_halo2

https://github.com/lightsing/learn_halo2

Last synced: about 1 month ago
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• Host: GitHub
• URL: https://github.com/lightsing/learn_halo2
• Owner: lightsing
• Created: 2022-11-14T13:25:02.000Z (about 2 years ago)
• Default Branch: master
• Last Pushed: 2022-11-16T07:34:21.000Z (about 2 years ago)
• Last Synced: 2023-06-06T15:31:07.926Z (over 1 year ago)
• Language: Rust
• Size: 28.3 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# learn halo2 by fibonacci

## Layout

|  row  |   n    |    l     |   r    | n_inv  | instance |

|:-----:|:------:|:--------:|:------:|:------:|:--------:|

|       | Advice |  Advice  | Advice | Advice | Instance |

|   0   |   n    |  fib(0)  | fib(1) |   *    |  fib(0)  |

|   1   |  n-1   |  fib(1)  | fib(2) |   *    |  fib(1)  |

|   2   |  n-2   |  fib(2)  | fib(3) |   *    |     n    |

|   3   |  n-3   |  fib(3)  | fib(4) |   *    |  fib(n)  |

|  ...  |  ...   |   ...    |  ...   |  ...   |    ...   |

|  n-1  |   1    | fib(n-1) | fib(n) |   1    |          |

|   n   |   0    |  fib(n)  | fib(n) |   0    |          |

|       |  ...   |   ...    |  ...   |  ...   |    ...   |

|  MAX  |   0    |  fib(n)  | fib(n) |   0    |          |

| MAX+1 | UNUSED |  UNUSED  | UNUSED |        |  UNUSED  |

## Constraint Design

The rows used is defined as a constant `MAX`.

### constraint equal

- `l[0] = instance[0]`

- `l[1] = instance[1]`

- `l[MAX] = instance[3]` => to minimize rows that are equality enabled

- `n[0] = instance[2]`

### gate for fibonacci

- when `n != 0`, `l' = r, r' = l + r, n' = n - 1`, which in human language: for nth row, l is fib(n) and r is fib(n + 1)

- when `n == 0`, `l' = r, r' = r, n' = 0`

### gate for zero "gadget"

`n * (1 - n * n_inv) = 0` holds for all used column (for easy to setup, n_inv = 0 when n = 0)

this is to make it easy to use the condition `n != 0`:

- when `n == 0`, `1 - n * n_inv = 1`

- when `n != 0`, `1 - n * n_inv = 0`