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Updated type checkers for generalized index functions.

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vbuterin 2019-08-01 10:56:31 -04:00 committed by GitHub
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specs/light_client/merkle_proofs.md
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@ -17,12 +17,6 @@
<!-- /TOC -->
## Constants
| Name | Value |
| - | - |
| `LENGTH_FLAG` | `2**64 - 1` |
## Generalized Merkle tree index
In a binary Merkle tree, we define a "generalized index" of a node as `2**depth + index`. Visually, this looks as follows:
@ -38,7 +32,8 @@ Note that the generalized index has the convenient property that the two childre
```python
def merkle_tree(leaves: List[Bytes32]) -> List[Bytes32]:
o = [0] * len(leaves) + leaves
padded_length = next_power_of_2(len(leaves))
o = [ZERO_HASH] * padded_length + leaves + [ZERO_HASH] * (padded_length - len(leaves))
for i in range(len(leaves) - 1, 0, -1):
o[i] = hash(o[i * 2] + o[i * 2 + 1])
return o
@ -64,27 +59,24 @@ y_data_root len(y)
We can now define a concept of a "path", a way of describing a function that takes as input an SSZ object and outputs some specific (possibly deeply nested) member. For example, `foo -> foo.x` is a path, as are `foo -> len(foo.y)` and `foo -> foo.y[5].w`. We'll describe paths as lists, which can have two representations. In "human-readable form", they are `["x"]`, `["y", "__len__"]` and `["y", 5, "w"]` respectively. In "encoded form", they are lists of `uint64` values, in these cases (assuming the fields of `foo` in order are `x` then `y`, and `w` is the first field of `y[i]`) `[0]`, `[1, 2**64-1]`, `[1, 5, 0]`.
```python
def item_length(typ: Type) -> int:
def item_length(typ: SSZType) -> int:
"""
Returns the number of bytes in a basic type, or 32 (a full hash) for compound types.
"""
if typ == bool:
return 1
elif issubclass(typ, uint):
if issubclass(typ, BasicValue):
return typ.byte_len
else:
return 32
def get_elem_type(typ: Type, index: int) -> Type:
def get_elem_type(typ: ComplexType, index: int) -> Type:
"""
Returns the type of the element of an object of the given type with the given index
or member variable name (eg. `7` for `x[7]`, `"foo"` for `x.foo`)
"""
return typ.get_fields_dict()[index] if is_container_type(typ) else typ.elem_type
return typ.get_fields()[key] if issubclass(typ, Container) else typ.elem_type
def get_chunk_count(typ: Type) -> int:
def chunk_count(typ: SSZType) -> int:
"""
Returns the number of hashes needed to represent the top-level elements in the given type
(eg. `x.foo` or `x[7]` but not `x[7].bar` or `x.foo.baz`). In all cases except lists/vectors
@ -92,24 +84,28 @@ def get_chunk_count(typ: Type) -> int:
hash. For lists/vectors of basic types, it is often fewer because multiple basic elements
can be packed into one 32-byte chunk.
"""
if is_basic_type(typ):
if issubclass(typ, BasicValue):
return 1
elif issubclass(typ, (List, Vector, Bytes, BytesN)):
elif issubclass(typ, Bits):
return (typ.length + 255) // 256
elif issubclass(typ, Elements):
return (typ.length * item_length(typ.elem_type) + 31) // 32
else:
elif issubclass(typ, Container):
return len(typ.get_fields())
else:
raise Exception(f"Type not supported: {typ}")
def get_item_position(typ: Type, index: Union[int, str]) -> Tuple[int, int, int]:
def get_item_position(typ: SSZType, index: Union[int, str]) -> Tuple[int, int, int]:
"""
Returns three variables: (i) the index of the chunk in which the given element of the item is
represented, (ii) the starting byte position, (iii) the ending byte position. For example for
a 6-item list of uint64 values, index=2 will return (0, 16, 24), index=5 will return (1, 8, 16)
"""
if issubclass(typ, (List, Vector, Bytes, BytesN)):
if issubclass(typ, Elements):
start = index * item_length(typ.elem_type)
return start // 32, start % 32, start % 32 + item_length(typ.elem_type)
elif is_container_type(typ):
elif issubclass(typ, Container):
return typ.get_field_names().index(index), 0, item_length(get_elem_type(typ, index))
else:
raise Exception("Only lists/vectors/containers supported")
@ -122,12 +118,12 @@ def get_generalized_index(typ: Type, path: List[Union[int, str]]) -> Generalized
"""
root = 1
for p in path:
assert not is_basic_type(typ) # If we descend to a basic type, the path cannot continue further
assert not issubclass(typ, BasicValue) # If we descend to a basic type, the path cannot continue further
if p == '__len__':
typ, root = uint256, root * 2 + 1 if issubclass(typ, (List, Bytes)) else None
else:
pos, _, _ = get_item_position(typ, p)
root = root * (2 if issubclass(typ, (List, Bytes)) else 1) * next_power_of_two(get_chunk_count(typ)) + pos
root = root * (2 if issubclass(typ, (List, Bytes)) else 1) * next_power_of_two(chunk_count(typ)) + pos
typ = get_elem_type(typ, p)
return root
```
@ -197,7 +193,7 @@ def get_branch_indices(tree_index: int) -> List[int]:
def get_expanded_indices(indices: List[int]) -> List[int]:
"""
Get the generalized indices of all chunks in the tree needed to prove the chunks with the given
generalized indices.
generalized indices, including the leaves.
"""
branches = set()
for index in indices: