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ethash.v
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ethash.v
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Require Import CoqOfPython.CoqOfPython.
Definition globals : Globals.t := "ethereum.ethash".
Definition locals_stack : list Locals.t := [].
Definition expr_1 : Value.t :=
Constant.str "
Ethash is a proof-of-work algorithm designed to be [ASIC] resistant through
[memory hardness][mem-hard].
To achieve memory hardness, computing Ethash requires access to subsets of a
large structure. The particular subsets chosen are based on the nonce and block
header, while the set itself is changed every [`epoch`].
At a high level, the Ethash algorithm is as follows:
1. Create a **seed** value, generated with [`generate_seed`] and based on the
preceding block numbers.
1. From the seed, compute a pseudorandom **cache** with [`generate_cache`].
1. From the cache, generate a **dataset** with [`generate_dataset`]. The
dataset grows over time based on [`DATASET_EPOCH_GROWTH_SIZE`].
1. Miners hash slices of the dataset together, which is where the memory
hardness is introduced. Verification of the proof-of-work only requires the
cache to be able to recompute a much smaller subset of the full dataset.
[`DATASET_EPOCH_GROWTH_SIZE`]: ref:ethereum.ethash.DATASET_EPOCH_GROWTH_SIZE
[`generate_dataset`]: ref:ethereum.ethash.generate_dataset
[`generate_cache`]: ref:ethereum.ethash.generate_cache
[`generate_seed`]: ref:ethereum.ethash.generate_seed
[`epoch`]: ref:ethereum.ethash.epoch
[ASIC]: https://en.wikipedia.org/wiki/Application-specific_integrated_circuit
[mem-hard]: https://en.wikipedia.org/wiki/Memory-hard_function
".
Axiom typing_imports_Callable :
IsImported globals "typing" "Callable".
Axiom typing_imports_Tuple :
IsImported globals "typing" "Tuple".
Axiom typing_imports_Union :
IsImported globals "typing" "Union".
Axiom ethereum_base_types_imports_U32 :
IsImported globals "ethereum.base_types" "U32".
Axiom ethereum_base_types_imports_Bytes8 :
IsImported globals "ethereum.base_types" "Bytes8".
Axiom ethereum_base_types_imports_Uint :
IsImported globals "ethereum.base_types" "Uint".
Axiom ethereum_crypto_hash_imports_Hash32 :
IsImported globals "ethereum.crypto.hash" "Hash32".
Axiom ethereum_crypto_hash_imports_Hash64 :
IsImported globals "ethereum.crypto.hash" "Hash64".
Axiom ethereum_crypto_hash_imports_keccak256 :
IsImported globals "ethereum.crypto.hash" "keccak256".
Axiom ethereum_crypto_hash_imports_keccak512 :
IsImported globals "ethereum.crypto.hash" "keccak512".
Axiom ethereum_utils_numeric_imports_is_prime :
IsImported globals "ethereum.utils.numeric" "is_prime".
Axiom ethereum_utils_numeric_imports_le_bytes_to_uint32_sequence :
IsImported globals "ethereum.utils.numeric" "le_bytes_to_uint32_sequence".
Axiom ethereum_utils_numeric_imports_le_uint32_sequence_to_bytes :
IsImported globals "ethereum.utils.numeric" "le_uint32_sequence_to_bytes".
Axiom ethereum_utils_numeric_imports_le_uint32_sequence_to_uint :
IsImported globals "ethereum.utils.numeric" "le_uint32_sequence_to_uint".
Definition EPOCH_SIZE : Value.t := M.run ltac:(M.monadic (
Constant.int 30000
)).
Definition expr_41 : Value.t :=
Constant.str "
Number of blocks before a dataset needs to be regenerated (known as an
""epoch"".) See [`epoch`].
[`epoch`]: ref:ethereum.ethash.epoch
".
Definition INITIAL_CACHE_SIZE : Value.t := M.run ltac:(M.monadic (
BinOp.pow (|
Constant.int 2,
Constant.int 24
|)
)).
Definition expr_49 : Value.t :=
Constant.str "
Size of the cache (in bytes) during the first epoch. Each subsequent epoch's
cache roughly grows by [`CACHE_EPOCH_GROWTH_SIZE`] bytes. See [`cache_size`].
[`CACHE_EPOCH_GROWTH_SIZE`]: ref:ethereum.ethash.CACHE_EPOCH_GROWTH_SIZE
[`cache_size`]: ref:ethereum.ethash.cache_size
".
Definition CACHE_EPOCH_GROWTH_SIZE : Value.t := M.run ltac:(M.monadic (
BinOp.pow (|
Constant.int 2,
Constant.int 17
|)
)).
Definition expr_58 : Value.t :=
Constant.str "
After the first epoch, the cache size grows by roughly this amount. See
[`cache_size`].
[`cache_size`]: ref:ethereum.ethash.cache_size
".
Definition INITIAL_DATASET_SIZE : Value.t := M.run ltac:(M.monadic (
BinOp.pow (|
Constant.int 2,
Constant.int 30
|)
)).
Definition expr_66 : Value.t :=
Constant.str "
Size of the dataset (in bytes) during the first epoch. Each subsequent epoch's
dataset roughly grows by [`DATASET_EPOCH_GROWTH_SIZE`] bytes. See
[`dataset_size`].
[`DATASET_EPOCH_GROWTH_SIZE`]: ref:ethereum.ethash.DATASET_EPOCH_GROWTH_SIZE
[`dataset_size`]: ref:ethereum.ethash.dataset_size
".
Definition DATASET_EPOCH_GROWTH_SIZE : Value.t := M.run ltac:(M.monadic (
BinOp.pow (|
Constant.int 2,
Constant.int 23
|)
)).
Definition expr_76 : Value.t :=
Constant.str "
After the first epoch, the dataset size grows by roughly this amount. See
[`dataset_size`].
[`dataset_size`]: ref:ethereum.ethash.dataset_size
".
Definition HASH_BYTES : Value.t := M.run ltac:(M.monadic (
Constant.int 64
)).
Definition expr_84 : Value.t :=
Constant.str "
Length of a hash, in bytes.
".
Definition MIX_BYTES : Value.t := M.run ltac:(M.monadic (
Constant.int 128
)).
Definition expr_89 : Value.t :=
Constant.str "
Width of mix, in bytes. See [`generate_dataset_item`].
[`generate_dataset_item`]: ref:ethereum.ethash.generate_dataset_item
".
Definition CACHE_ROUNDS : Value.t := M.run ltac:(M.monadic (
Constant.int 3
)).
Definition expr_96 : Value.t :=
Constant.str "
Number of times to repeat the [`keccak512`] step while generating the hash. See
[`generate_cache`].
[`keccak512`]: ref:ethereum.crypto.hash.keccak512
[`generate_cache`]: ref:ethereum.ethash.generate_cache
".
Definition DATASET_PARENTS : Value.t := M.run ltac:(M.monadic (
Constant.int 256
)).
Definition expr_105 : Value.t :=
Constant.str "
Number of parents of each dataset element. See [`generate_dataset_item`].
[`generate_dataset_item`]: ref:ethereum.ethash.generate_dataset_item
".
Definition HASHIMOTO_ACCESSES : Value.t := M.run ltac:(M.monadic (
Constant.int 64
)).
Definition expr_112 : Value.t :=
Constant.str "
Number of accesses in the [`hashimoto`] loop.
[`hashimoto`]: ref:ethereum.ethash.hashimoto
".
Definition epoch : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Obtain the epoch number to which the block identified by `block_number`
belongs. The first epoch is numbered zero.
An Ethash epoch is a fixed number of blocks ([`EPOCH_SIZE`]) long, during
which the dataset remains constant. At the end of each epoch, the dataset
is generated anew. See [`generate_dataset`].
[`EPOCH_SIZE`]: ref:ethereum.ethash.EPOCH_SIZE
[`generate_dataset`]: ref:ethereum.ethash.generate_dataset
" in
let _ := M.return_ (|
BinOp.floor_div (|
M.get_name (| globals, locals_stack, "block_number" |),
M.get_name (| globals, locals_stack, "EPOCH_SIZE" |)
|)
|) in
M.pure Constant.None_)).
Axiom epoch_in_globals :
IsInGlobals globals "epoch" (make_function epoch).
Definition cache_size : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Obtain the cache size (in bytes) of the epoch to which `block_number`
belongs.
See [`INITIAL_CACHE_SIZE`] and [`CACHE_EPOCH_GROWTH_SIZE`] for the initial
size and linear growth rate, respectively. The cache is generated in
[`generate_cache`].
The actual cache size is smaller than simply multiplying
`CACHE_EPOCH_GROWTH_SIZE` by the epoch number to minimize the risk of
unintended cyclic behavior. It is defined as the highest prime number below
what linear growth would calculate.
[`INITIAL_CACHE_SIZE`]: ref:ethereum.ethash.INITIAL_CACHE_SIZE
[`CACHE_EPOCH_GROWTH_SIZE`]: ref:ethereum.ethash.CACHE_EPOCH_GROWTH_SIZE
[`generate_cache`]: ref:ethereum.ethash.generate_cache
" in
let _ := M.assign_local (|
"size" ,
BinOp.add (|
M.get_name (| globals, locals_stack, "INITIAL_CACHE_SIZE" |),
BinOp.mult (|
M.get_name (| globals, locals_stack, "CACHE_EPOCH_GROWTH_SIZE" |),
M.call (|
M.get_name (| globals, locals_stack, "epoch" |),
make_list [
M.get_name (| globals, locals_stack, "block_number" |)
],
make_dict []
|)
|)
|)
|) in
let _ := M.assign_op_local (|
BinOp.sub,
"size",
M.get_name (| globals, locals_stack, "HASH_BYTES" |)
|) in
let _ :=
M.while (|
UnOp.not (| M.call (|
M.get_name (| globals, locals_stack, "is_prime" |),
make_list [
BinOp.floor_div (|
M.get_name (| globals, locals_stack, "size" |),
M.get_name (| globals, locals_stack, "HASH_BYTES" |)
|)
],
make_dict []
|) |),
ltac:(M.monadic (
let _ := M.assign_op_local (|
BinOp.sub,
"size",
BinOp.mult (|
Constant.int 2,
M.get_name (| globals, locals_stack, "HASH_BYTES" |)
|)
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ := M.return_ (|
M.get_name (| globals, locals_stack, "size" |)
|) in
M.pure Constant.None_)).
Axiom cache_size_in_globals :
IsInGlobals globals "cache_size" (make_function cache_size).
Definition dataset_size : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Obtain the dataset size (in bytes) of the epoch to which `block_number`
belongs.
See [`INITIAL_DATASET_SIZE`] and [`DATASET_EPOCH_GROWTH_SIZE`][ds] for the
initial size and linear growth rate, respectively. The complete dataset is
generated in [`generate_dataset`], while the slices used in verification
are generated in [`generate_dataset_item`].
The actual dataset size is smaller than simply multiplying
`DATASET_EPOCH_GROWTH_SIZE` by the epoch number to minimize the risk of
unintended cyclic behavior. It is defined as the highest prime number below
what linear growth would calculate.
[`INITIAL_DATASET_SIZE`]: ref:ethereum.ethash.INITIAL_DATASET_SIZE
[ds]: ref:ethereum.ethash.DATASET_EPOCH_GROWTH_SIZE
[`generate_dataset`]: ref:ethereum.ethash.generate_dataset
[`generate_dataset_item`]: ref:ethereum.ethash.generate_dataset_item
" in
let _ := M.assign_local (|
"size" ,
BinOp.add (|
M.get_name (| globals, locals_stack, "INITIAL_DATASET_SIZE" |),
BinOp.mult (|
M.get_name (| globals, locals_stack, "DATASET_EPOCH_GROWTH_SIZE" |),
M.call (|
M.get_name (| globals, locals_stack, "epoch" |),
make_list [
M.get_name (| globals, locals_stack, "block_number" |)
],
make_dict []
|)
|)
|)
|) in
let _ := M.assign_op_local (|
BinOp.sub,
"size",
M.get_name (| globals, locals_stack, "MIX_BYTES" |)
|) in
let _ :=
M.while (|
UnOp.not (| M.call (|
M.get_name (| globals, locals_stack, "is_prime" |),
make_list [
BinOp.floor_div (|
M.get_name (| globals, locals_stack, "size" |),
M.get_name (| globals, locals_stack, "MIX_BYTES" |)
|)
],
make_dict []
|) |),
ltac:(M.monadic (
let _ := M.assign_op_local (|
BinOp.sub,
"size",
BinOp.mult (|
Constant.int 2,
M.get_name (| globals, locals_stack, "MIX_BYTES" |)
|)
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ := M.return_ (|
M.get_name (| globals, locals_stack, "size" |)
|) in
M.pure Constant.None_)).
Axiom dataset_size_in_globals :
IsInGlobals globals "dataset_size" (make_function dataset_size).
Definition generate_seed : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Obtain the cache generation seed for the block identified by
`block_number`. See [`generate_cache`].
[`generate_cache`]: ref:ethereum.ethash.generate_cache
" in
let _ := M.assign_local (|
"epoch_number" ,
M.call (|
M.get_name (| globals, locals_stack, "epoch" |),
make_list [
M.get_name (| globals, locals_stack, "block_number" |)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"seed" ,
BinOp.mult (|
Constant.bytes "00",
Constant.int 32
|)
|) in
let _ :=
M.while (|
Compare.not_eq (|
M.get_name (| globals, locals_stack, "epoch_number" |),
Constant.int 0
|),
ltac:(M.monadic (
let _ := M.assign_local (|
"seed" ,
M.call (|
M.get_name (| globals, locals_stack, "keccak256" |),
make_list [
M.get_name (| globals, locals_stack, "seed" |)
],
make_dict []
|)
|) in
let _ := M.assign_op_local (|
BinOp.sub,
"epoch_number",
Constant.int 1
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "Hash32" |),
make_list [
M.get_name (| globals, locals_stack, "seed" |)
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom generate_seed_in_globals :
IsInGlobals globals "generate_seed" (make_function generate_seed).
Definition generate_cache : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Generate the cache for the block identified by `block_number`. See
[`generate_dataset`] for how the cache is used.
The cache is generated in two steps: filling the array with a chain of
[`keccak512`] hashes, then running two rounds of Sergio Demian Lerner's
[RandMemoHash] on those bytes.
[`keccak512`]: ref:ethereum.crypto.hash.keccak512
[`generate_dataset`]: ref:ethereum.ethash.generate_dataset
[RandMemoHash]: http://www.hashcash.org/papers/memohash.pdf
" in
let _ := M.assign_local (|
"seed" ,
M.call (|
M.get_name (| globals, locals_stack, "generate_seed" |),
make_list [
M.get_name (| globals, locals_stack, "block_number" |)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"cache_size_bytes" ,
M.call (|
M.get_name (| globals, locals_stack, "cache_size" |),
make_list [
M.get_name (| globals, locals_stack, "block_number" |)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"cache_size_words" ,
BinOp.floor_div (|
M.get_name (| globals, locals_stack, "cache_size_bytes" |),
M.get_name (| globals, locals_stack, "HASH_BYTES" |)
|)
|) in
let _ := M.assign_local (|
"cache" ,
make_list [
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
M.get_name (| globals, locals_stack, "seed" |)
],
make_dict []
|)
]
|) in
let _ :=
M.for_ (|
M.get_name (| globals, locals_stack, "index" |),
M.call (|
M.get_name (| globals, locals_stack, "range" |),
make_list [
Constant.int 1;
M.get_name (| globals, locals_stack, "cache_size_words" |)
],
make_dict []
|),
ltac:(M.monadic (
let _ := M.assign_local (|
"cache_item" ,
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
BinOp.sub (|
M.get_name (| globals, locals_stack, "index" |),
Constant.int 1
|)
|)
],
make_dict []
|)
|) in
let _ := M.call (|
M.get_field (| M.get_name (| globals, locals_stack, "cache" |), "append" |),
make_list [
M.get_name (| globals, locals_stack, "cache_item" |)
],
make_dict []
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ :=
M.for_ (|
M.get_name (| globals, locals_stack, "_" |),
M.call (|
M.get_name (| globals, locals_stack, "range" |),
make_list [
M.get_name (| globals, locals_stack, "CACHE_ROUNDS" |)
],
make_dict []
|),
ltac:(M.monadic (
let _ :=
M.for_ (|
M.get_name (| globals, locals_stack, "index" |),
M.call (|
M.get_name (| globals, locals_stack, "range" |),
make_list [
M.get_name (| globals, locals_stack, "cache_size_words" |)
],
make_dict []
|),
ltac:(M.monadic (
let _ := M.assign_local (|
"first_cache_item" ,
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
BinOp.mod_ (|
BinOp.add (|
BinOp.sub (|
M.get_name (| globals, locals_stack, "index" |),
Constant.int 1
|),
M.call (|
M.get_name (| globals, locals_stack, "int" |),
make_list [
M.get_name (| globals, locals_stack, "cache_size_words" |)
],
make_dict []
|)
|),
M.get_name (| globals, locals_stack, "cache_size_words" |)
|)
|)
|) in
let _ := M.assign_local (|
"second_cache_item" ,
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
BinOp.mod_ (|
M.call (|
M.get_field (| M.get_name (| globals, locals_stack, "U32" |), "from_le_bytes" |),
make_list [
M.slice (|
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
M.get_name (| globals, locals_stack, "index" |)
|),
Constant.int 0,
Constant.int 4,
Constant.None_
|)
],
make_dict []
|),
M.get_name (| globals, locals_stack, "cache_size_words" |)
|)
|)
|) in
let _ := M.assign_local (|
"result" ,
M.call (|
M.get_name (| globals, locals_stack, "bytes" |),
make_list [
Constant.str "(* At expr: unsupported node type: ListComp *)"
],
make_dict []
|)
|) in
let _ := M.assign (|
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
M.get_name (| globals, locals_stack, "index" |)
|),
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
M.get_name (| globals, locals_stack, "result" |)
],
make_dict []
|)
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "tuple" |),
make_list [
Constant.str "(* At expr: unsupported node type: GeneratorExp *)"
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom generate_cache_in_globals :
IsInGlobals globals "generate_cache" (make_function generate_cache).
Definition fnv : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "a"; "b" ] in
ltac:(M.monadic (
let _ := Constant.str "
A non-associative substitute for XOR, inspired by the [FNV] hash by Fowler,
Noll, and Vo. See [`fnv_hash`], [`generate_dataset_item`], and
[`hashimoto`].
Note that here we multiply the prime with the full 32-bit input, in
contrast with the [FNV-1] spec which multiplies the prime with one byte
(octet) in turn.
[`hashimoto`]: ref:ethereum.ethash.hashimoto
[`generate_dataset_item`]: ref:ethereum.ethash.generate_dataset_item
[`fnv_hash`]: ref:ethereum.ethash.fnv_hash
[FNV]: https://w.wiki/XKZ
[FNV-1]: http://www.isthe.com/chongo/tech/comp/fnv/#FNV-1
" in
let _ := M.assign_local (|
"result" ,
BinOp.bit_and (|
BinOp.bit_xor (|
BinOp.mult (|
M.call (|
M.get_name (| globals, locals_stack, "Uint" |),
make_list [
M.get_name (| globals, locals_stack, "a" |)
],
make_dict []
|),
Constant.int 16777619
|),
M.call (|
M.get_name (| globals, locals_stack, "Uint" |),
make_list [
M.get_name (| globals, locals_stack, "b" |)
],
make_dict []
|)
|),
M.get_field (| M.get_name (| globals, locals_stack, "U32" |), "MAX_VALUE" |)
|)
|) in
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "U32" |),
make_list [
M.get_name (| globals, locals_stack, "result" |)
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom fnv_in_globals :
IsInGlobals globals "fnv" (make_function fnv).
Definition fnv_hash : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "mix_integers"; "data" ] in
ltac:(M.monadic (
let _ := Constant.str "
Combines `data` into `mix_integers` using [`fnv`]. See [`hashimoto`] and
[`generate_dataset_item`].
[`hashimoto`]: ref:ethereum.ethash.hashimoto
[`generate_dataset_item`]: ref:ethereum.ethash.generate_dataset_item
[`fnv`]: ref:ethereum.ethash.fnv
" in
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "tuple" |),
make_list [
Constant.str "(* At expr: unsupported node type: GeneratorExp *)"
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom fnv_hash_in_globals :
IsInGlobals globals "fnv_hash" (make_function fnv_hash).
Definition generate_dataset_item : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "cache"; "index" ] in
ltac:(M.monadic (
let _ := Constant.str "
Generate a particular dataset item 0-indexed by `index` by hashing
pseudorandomly-selected entries from `cache` together. See [`fnv`] and
[`fnv_hash`] for the digest function, [`generate_cache`] for generating
`cache`, and [`generate_dataset`] for the full dataset generation
algorithm.
[`fnv`]: ref:ethereum.ethash.fnv
[`fnv_hash`]: ref:ethereum.ethash.fnv_hash
[`generate_dataset`]: ref:ethereum.ethash.generate_dataset
[`generate_cache`]: ref:ethereum.ethash.generate_cache
" in
let _ := M.assign_local (|
"mix" ,
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
M.call (|
M.get_field (| BinOp.bit_xor (|
M.call (|
M.get_name (| globals, locals_stack, "le_uint32_sequence_to_uint" |),
make_list [
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
BinOp.mod_ (|
M.get_name (| globals, locals_stack, "index" |),
M.call (|
M.get_name (| globals, locals_stack, "len" |),
make_list [
M.get_name (| globals, locals_stack, "cache" |)
],
make_dict []
|)
|)
|)
],
make_dict []
|),
M.get_name (| globals, locals_stack, "index" |)
|), "to_le_bytes" |),
make_list [],
make_dict []
|)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"mix_integers" ,
M.call (|
M.get_name (| globals, locals_stack, "le_bytes_to_uint32_sequence" |),
make_list [
M.get_name (| globals, locals_stack, "mix" |)
],
make_dict []
|)
|) in
let _ :=
M.for_ (|
M.get_name (| globals, locals_stack, "j" |),
M.call (|
M.get_name (| globals, locals_stack, "range" |),
make_list [
M.get_name (| globals, locals_stack, "DATASET_PARENTS" |)
],
make_dict []
|),
ltac:(M.monadic (
(* At stmt: unsupported node type: AnnAssign *)
let _ := M.assign_local (|
"cache_index" ,
BinOp.mod_ (|
M.call (|
M.get_name (| globals, locals_stack, "fnv" |),
make_list [
BinOp.bit_xor (|
M.get_name (| globals, locals_stack, "index" |),
M.get_name (| globals, locals_stack, "j" |)
|);
M.get_name (| globals, locals_stack, "mix_word" |)
],
make_dict []
|),
M.call (|
M.get_name (| globals, locals_stack, "len" |),
make_list [
M.get_name (| globals, locals_stack, "cache" |)
],
make_dict []
|)
|)
|) in
let _ := M.assign_local (|
"parent" ,
M.get_subscript (|
M.get_name (| globals, locals_stack, "cache" |),
M.get_name (| globals, locals_stack, "cache_index" |)
|)
|) in
let _ := M.assign_local (|
"mix_integers" ,
M.call (|
M.get_name (| globals, locals_stack, "fnv_hash" |),
make_list [
M.get_name (| globals, locals_stack, "mix_integers" |);
M.get_name (| globals, locals_stack, "parent" |)
],
make_dict []
|)
|) in
M.pure Constant.None_
)),
ltac:(M.monadic (
M.pure Constant.None_
))
|) in
let _ := M.assign_local (|
"mix" ,
M.call (|
M.get_name (| globals, locals_stack, "Hash64" |),
make_list [
M.call (|
M.get_name (| globals, locals_stack, "le_uint32_sequence_to_bytes" |),
make_list [
M.get_name (| globals, locals_stack, "mix_integers" |)
],
make_dict []
|)
],
make_dict []
|)
|) in
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
M.get_name (| globals, locals_stack, "mix" |)
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom generate_dataset_item_in_globals :
IsInGlobals globals "generate_dataset_item" (make_function generate_dataset_item).
Definition generate_dataset : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "block_number" ] in
ltac:(M.monadic (
let _ := Constant.str "
Generate the full dataset for the block identified by `block_number`.
This function is present only for demonstration purposes. It is not used
while validating blocks.
" in
(* At stmt: unsupported node type: AnnAssign *)
(* At stmt: unsupported node type: AnnAssign *)
let _ := M.return_ (|
M.call (|
M.get_name (| globals, locals_stack, "tuple" |),
make_list [
Constant.str "(* At expr: unsupported node type: GeneratorExp *)"
],
make_dict []
|)
|) in
M.pure Constant.None_)).
Axiom generate_dataset_in_globals :
IsInGlobals globals "generate_dataset" (make_function generate_dataset).
Definition hashimoto : Value.t -> Value.t -> M :=
fun (args kwargs : Value.t) =>
let- locals_stack := M.create_locals locals_stack args kwargs [ "header_hash"; "nonce"; "dataset_size"; "fetch_dataset_item" ] in
ltac:(M.monadic (
let _ := Constant.str "
Obtain the mix digest and the final value for a header, by aggregating
data from the full dataset.
#### Parameters
- `header_hash` is a valid [RLP hash] of a block header.
- `nonce` is the propagated nonce for the given block.
- `dataset_size` is the size of the dataset. See [`dataset_size`].
- `fetch_dataset_item` is a function that retrieves a specific dataset item
based on its index.
#### Returns
- The mix digest generated from the header hash and propagated nonce.
- The final result obtained which will be checked for leading zeros (in
byte representation) in correspondence with the block difficulty.
[RLP hash]: ref:ethereum.rlp.rlp_hash
[`dataset_size`]: ref:ethereum.ethash.dataset_size
" in
let _ := M.assign_local (|
"nonce_le" ,
M.call (|
M.get_name (| globals, locals_stack, "bytes" |),
make_list [
M.call (|
M.get_name (| globals, locals_stack, "reversed" |),
make_list [
M.get_name (| globals, locals_stack, "nonce" |)
],
make_dict []
|)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"seed_hash" ,
M.call (|
M.get_name (| globals, locals_stack, "keccak512" |),
make_list [
BinOp.add (|
M.get_name (| globals, locals_stack, "header_hash" |),
M.get_name (| globals, locals_stack, "nonce_le" |)
|)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"seed_head" ,
M.call (|
M.get_field (| M.get_name (| globals, locals_stack, "U32" |), "from_le_bytes" |),
make_list [
M.slice (|
M.get_name (| globals, locals_stack, "seed_hash" |),
Constant.None_,
Constant.int 4,
Constant.None_
|)
],
make_dict []
|)
|) in
let _ := M.assign_local (|
"rows" ,
BinOp.floor_div (|
M.get_name (| globals, locals_stack, "dataset_size" |),
Constant.int 128
|)
|) in
let _ := M.assign_local (|
"mix" ,
BinOp.mult (|