Source file lang_stdlib.ml
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(** Plompiler standard library. *)
open Lang_core
module type Limb_list = sig
(** Input for a Plompiler program. *)
type 'a input
(** Element of the native scalar field. *)
type scalar
(** Representation of values. *)
type 'a repr
(** Plompiler program. *)
type 'a t
(** Representation of elements. *)
type tl
(** [input_bytes ~le b] returns the representation of [b]
that Plompiler expects as input.
[le] can be used to set the endianness. *)
val input_bytes : le:bool -> bytes -> tl input
(** [constant ~le b] returns the constant [b] as a Plompiler value.
[le] can be used to set the endianness. *)
val constant : le:bool -> bytes -> tl repr t
(** [of_scalar ~total_nb_bits b] converts the scalar [b] of size
[total_nb_bits] in bits into the [tl] representation. *)
val of_scalar : total_nb_bits:int -> scalar repr -> tl repr t
(** [to_scalar b] return the scalar representing the value [b]. *)
val to_scalar : tl repr -> scalar repr t
(** [of_bool_list b] converts the list of bits in little-endian
order into the [tl] representation. *)
val of_bool_list : bool list repr -> tl repr t
(** [to_bool_list b] returns the list of bits in little-endian
order, representing the value [b]. *)
val to_bool_list : tl repr -> bool list repr t
(** [xor a b] returns the exclusive disjunction of [a] and [b]. *)
val xor : tl repr -> tl repr -> tl repr t
(** [band a b] returns the conjunction of [a] and [b]. *)
val band : tl repr -> tl repr -> tl repr t
(** [not b] returns the negation of [b]. *)
val not : tl repr -> tl repr t
(** [rotate_right b n] shifts the bits right by n positions,
so that each bit is less significant.
The least significant bit becomes the most significant
i.e. it is "rotated".
[rotate_right bs (length bl) = bl] *)
val rotate_right : tl repr -> int -> tl repr t
(** [shift_right b n] shifts all bits right by n positions,
so that each bit is less significant.
The least signigicant bit is lost and the most significant bit is
set to zero.
More precisely, if we interpret the [b] as an integer,
[shift_right b n = b / 2^n] *)
val shift_right : tl repr -> int -> tl repr t
end
(** The {!LIB} module type extends the core language defined in {!Lang_core.COMMON}
by adding functions that build upon those primitives.
*)
module type LIB = sig
include COMMON
(** [foldiM] is the monadic version of a fold over a natural number. *)
val foldiM : ('a -> int -> 'a t) -> 'a -> int -> 'a t
(** [fold2M] is the monadic version of [List.fold_left2]. *)
val fold2M : ('a -> 'b -> 'c -> 'a t) -> 'a -> 'b list -> 'c list -> 'a t
(** [mapM] is the monadic version of [List.map]. *)
val mapM : ('a -> 'b t) -> 'a list -> 'b list t
(** [map2M] is the monadic version of [List.map2]. *)
val map2M : ('a -> 'b -> 'c t) -> 'a list -> 'b list -> 'c list t
(** [iterM] is the monadic version of [List.iter]. *)
val iterM : ('a -> unit repr t) -> 'a list -> unit repr t
(** [iter2M] is the monadic version of [List.iter2]. *)
val iter2M : ('a -> 'b -> unit repr t) -> 'a list -> 'b list -> unit repr t
module Bool : sig
include BOOL
(** Returns the pair (s, c_out), as per
https://en.wikipedia.org/wiki/Adder_(electronics)#Full_adder *)
val full_adder : bool repr -> bool repr -> bool repr -> (bool * bool) repr t
end
with type scalar = scalar
and type 'a repr = 'a repr
and type 'a t = 'a t
module Num : sig
include NUM
(** [square a] returns the value [a^2]. *)
val square : scalar repr -> scalar repr t
(** [pow b e_bits] returns the value [b^e] where [e] is the
number represented by the binary decomposition [e_bits]. *)
val pow : scalar repr -> bool repr list -> scalar repr t
(** [add_list ~qc ~coeffs l] returns the sum of the elements of [l]
weighted by [coeffs].
Note: if [coeffs] is defined, it should be of the same length
as [l].
*)
val add_list :
?qc:S.t -> ?coeffs:S.t list -> scalar list repr -> scalar repr t
(** [mul_list l] returns the product of the elements of [l]. *)
val mul_list : scalar list repr -> scalar repr t
(** [mul_by_constant k a] returns the value [k * a]. *)
val mul_by_constant : S.t -> scalar repr -> scalar repr t
val scalar_of_bytes : bool list repr -> scalar repr t
(** [is_eq_const a k] returns whether [a] is equal to [k]. *)
val is_eq_const : scalar repr -> S.t -> bool repr t
(** [assert_eq_const a k] asserts that [a] is equal to [k]. *)
val assert_eq_const : scalar repr -> S.t -> unit repr t
(** [is_upper_bounded ~bound x] returns whether the scalar [x] is
strictly lower than [bound] when [x] is interpreted as an integer
from [0] to [p-1] (being [p] the scalar field order).
This circuit is total (and more expensive than our version below). *)
val is_upper_bounded : bound:Z.t -> scalar repr -> bool repr t
(** Same as [is_upper_bounded] but cheaper and partial.
[is_upper_bounded_unsafe ~bound l] is unsatisfiable if l cannot be
represented in binary with [Z.numbits bound] bits. *)
val is_upper_bounded_unsafe :
?nb_bits:int -> bound:Z.t -> scalar repr -> bool repr t
(** [geq (a, bound_a) (b, bound_b)] returns the boolean wire representing
a >= b.
Pre-condition: [a ∈ \[0, bound_a) ∧ b ∈ \[0, bound_b)] *)
val geq : scalar repr * Z.t -> scalar repr * Z.t -> bool repr t
end
with type scalar = scalar
and type 'a repr = 'a repr
and type 'a t = 'a t
(** Enumerations, represented as a list of cases. *)
module Enum (N : sig
val n : int
end) : sig
(** [switch_case k l] returns the k-th element of the list [l] if
k ∈ \[0,n) or the first element of [l] otherwise. *)
val switch_case : scalar repr -> 'a list repr -> 'a repr t
end
(** Representation of bytes. *)
module Bytes : sig
(** Little-endian representation of bytes.
First element of the list is the Least Significant Bit. *)
include
Limb_list
with type tl = bool list
and type scalar = scalar
and type 'a repr = 'a repr
and type 'a t = 'a t
and type 'a input = 'a Input.t
(** [constant_uint32 ~le n] returns a value holding the bytes correspoding
to the uint [n].
[le] can be used to set the endianness. *)
val constant_uint32 : le:bool -> Stdint.uint32 -> tl repr t
(** [length b] returns the length of [b] in bits. *)
val length : tl repr -> int
(** [concat bs] returns the concatenation of the bitlists in [bs]. *)
val concat : tl repr array -> tl repr
(** [add b1 b2] computes the addition of [b1] and [b2]. *)
val add : ?ignore_carry:bool -> tl repr -> tl repr -> tl repr t
(** [rotate_left bl n] shifts the bits left by n positions,
so that each bit is more significant.
The most significant bit becomes the least significant
i.e. it is "rotated".
[rotate_left bl (length bl) = bl] *)
val rotate_left : tl repr -> int -> tl repr t
(** [shift_left bl n] shifts all bits left by n positions,
so that each bit is more significant.
The most signigicant bit is lost and the least significant bit is
set to zero.
More precisely, if we interpret the [bl] as an integer
[shift_left bl i = bl * 2^i mod 2^{length a}] *)
val shift_left : tl repr -> int -> tl repr t
end
(** This module is a more generic version of Bytes, where each scalar
stores an [nb_bits]-bit number. *)
module Limbs (N : sig
val nb_bits : int
end) : sig
include
Limb_list
with type tl = scalar list
and type scalar = scalar
and type 'a repr = 'a repr
and type 'a t = 'a t
and type 'a input = 'a Input.t
end
(** [add2 p1 p2] returns the pair [(fst p1 + fst p2, snd p1 + snd p2)]. *)
val add2 :
(scalar * scalar) repr -> (scalar * scalar) repr -> (scalar * scalar) repr t
module Encodings : sig
(**
Encoding type for encapsulating encoding/decoding/input functions.
This type enables us to use more structured types for data
in circuits.
For that, encoding is parameterized by 3 types:
- 'oh is the type of the high-level OCaml representation
- 'u is the unpacked type, i.e. a collection of atomic reprs.
- `p is the packed type, i.e the inner type of Plompiler's repr.
For example, for the representation of a point (pair of scalars),
one might have:
{[
( {x:int; y:int},
scalar repr * scalar repr,
scalar * scalar
) encoding
]}
The first type, the record [{x:int; y:int}], represents an OCaml point,
which becomes the argument taken by the [input] function.
The second type, [scalar repr * scalar repr], is an unpacking of the
encoding. This is used for the result of [decode]. We can use any type
isomorphic to [scalar repr * scalar repr] here.
The last type must be [scalar * scalar], as an encoding of a point will be
of the type [(scalar * scalar) repr].
*)
type ('oh, 'u, 'p) encoding = {
encode : 'u -> 'p repr;
decode : 'p repr -> 'u;
input : 'oh -> 'p Input.input;
of_input : 'p Input.input -> 'oh;
}
(**
The function [conv] defines conversions for [encoding]s, by changing
the higher-level ['u] and and ['oh] types.
*)
val conv :
('u1 -> 'u0) ->
('u0 -> 'u1) ->
('o1 -> 'o0) ->
('o0 -> 'o1) ->
('o0, 'u0, 'p) encoding ->
('o1, 'u1, 'p) encoding
val with_implicit_bool_check :
('p repr -> bool repr t) -> ('o, 'u, 'p) encoding -> ('o, 'u, 'p) encoding
val with_assertion :
('p repr -> unit repr t) -> ('o, 'u, 'p) encoding -> ('o, 'u, 'p) encoding
val scalar_encoding : (Bls12_381.Fr.t, scalar repr, scalar) encoding
val bool_encoding : (bool, bool repr, bool) encoding
val list_encoding :
('a, 'b, 'c) encoding -> ('a list, 'b list, 'c list) encoding
val atomic_list_encoding :
('a, 'b repr, 'c) encoding -> ('a list, 'b list repr, 'c list) encoding
val obj2_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('a * 'd, 'b * 'e, 'c * 'f) encoding
val atomic_obj2_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('a * 'd, ('b * 'e) repr, 'c * 'f) encoding
val obj3_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('a * ('d * 'g), 'b * ('e * 'h), 'c * ('f * 'i)) encoding
val atomic_obj3_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('a * ('d * 'g), ('b * ('e * 'h)) repr, 'c * ('f * 'i)) encoding
val obj4_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
( 'a * ('d * ('g * 'j)),
'b * ('e * ('h * 'k)),
'c * ('f * ('i * 'l)) )
encoding
val atomic_obj4_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
( 'a * ('d * ('g * 'j)),
('b * ('e * ('h * 'k))) repr,
'c * ('f * ('i * 'l)) )
encoding
val obj5_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
( 'a * ('d * ('g * ('j * 'm))),
'b * ('e * ('h * ('k * 'n))),
'c * ('f * ('i * ('l * 'o))) )
encoding
val atomic_obj5_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
( 'a * ('d * ('g * ('j * 'm))),
('b * ('e * ('h * ('k * 'n)))) repr,
'c * ('f * ('i * ('l * 'o))) )
encoding
val obj6_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
('p, 'q, 'r) encoding ->
( 'a * ('d * ('g * ('j * ('m * 'p)))),
'b * ('e * ('h * ('k * ('n * 'q)))),
'c * ('f * ('i * ('l * ('o * 'r)))) )
encoding
val atomic_obj6_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
('p, 'q repr, 'r) encoding ->
( 'a * ('d * ('g * ('j * ('m * 'p)))),
('b * ('e * ('h * ('k * ('n * 'q))))) repr,
'c * ('f * ('i * ('l * ('o * 'r)))) )
encoding
val obj7_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
('p, 'q, 'r) encoding ->
('s, 't, 'u) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * 's))))),
'b * ('e * ('h * ('k * ('n * ('q * 't))))),
'c * ('f * ('i * ('l * ('o * ('r * 'u))))) )
encoding
val atomic_obj7_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
('p, 'q repr, 'r) encoding ->
('s, 't repr, 'u) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * 's))))),
('b * ('e * ('h * ('k * ('n * ('q * 't)))))) repr,
'c * ('f * ('i * ('l * ('o * ('r * 'u))))) )
encoding
val obj8_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
('p, 'q, 'r) encoding ->
('s, 't, 'u) encoding ->
('v, 'w, 'x) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * 'v)))))),
'b * ('e * ('h * ('k * ('n * ('q * ('t * 'w)))))),
'c * ('f * ('i * ('l * ('o * ('r * ('u * 'x)))))) )
encoding
val atomic_obj8_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
('p, 'q repr, 'r) encoding ->
('s, 't repr, 'u) encoding ->
('v, 'w repr, 'x) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * 'v)))))),
('b * ('e * ('h * ('k * ('n * ('q * ('t * 'w))))))) repr,
'c * ('f * ('i * ('l * ('o * ('r * ('u * 'x)))))) )
encoding
val obj9_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
('p, 'q, 'r) encoding ->
('s, 't, 'u) encoding ->
('v, 'w, 'x) encoding ->
('y, 'z, 'a1) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * ('v * 'y))))))),
'b * ('e * ('h * ('k * ('n * ('q * ('t * ('w * 'z))))))),
'c * ('f * ('i * ('l * ('o * ('r * ('u * ('x * 'a1))))))) )
encoding
val atomic_obj9_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
('p, 'q repr, 'r) encoding ->
('s, 't repr, 'u) encoding ->
('v, 'w repr, 'x) encoding ->
('y, 'z repr, 'a1) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * ('v * 'y))))))),
('b * ('e * ('h * ('k * ('n * ('q * ('t * ('w * 'z)))))))) repr,
'c * ('f * ('i * ('l * ('o * ('r * ('u * ('x * 'a1))))))) )
encoding
val obj10_encoding :
('a, 'b, 'c) encoding ->
('d, 'e, 'f) encoding ->
('g, 'h, 'i) encoding ->
('j, 'k, 'l) encoding ->
('m, 'n, 'o) encoding ->
('p, 'q, 'r) encoding ->
('s, 't, 'u) encoding ->
('v, 'w, 'x) encoding ->
('y, 'z, 'a1) encoding ->
('b1, 'c1, 'd1) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * ('v * ('y * 'b1)))))))),
'b * ('e * ('h * ('k * ('n * ('q * ('t * ('w * ('z * 'c1)))))))),
'c * ('f * ('i * ('l * ('o * ('r * ('u * ('x * ('a1 * 'd1)))))))) )
encoding
val atomic_obj10_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('g, 'h repr, 'i) encoding ->
('j, 'k repr, 'l) encoding ->
('m, 'n repr, 'o) encoding ->
('p, 'q repr, 'r) encoding ->
('s, 't repr, 'u) encoding ->
('v, 'w repr, 'x) encoding ->
('y, 'z repr, 'a1) encoding ->
('b1, 'c1 repr, 'd1) encoding ->
( 'a * ('d * ('g * ('j * ('m * ('p * ('s * ('v * ('y * 'b1)))))))),
('b * ('e * ('h * ('k * ('n * ('q * ('t * ('w * ('z * 'c1))))))))) repr,
'c * ('f * ('i * ('l * ('o * ('r * ('u * ('x * ('a1 * 'd1)))))))) )
encoding
end
end
module Lib (C : COMMON) = struct
include C
let foldiM : ('a -> int -> 'a t) -> 'a -> int -> 'a t =
fun f e n -> foldM f e (List.init n (fun i -> i))
let fold2M f acc ls rs =
foldM (fun acc (l, r) -> f acc l r) acc (List.combine ls rs)
let mapM f l =
let* l =
foldM
(fun acc e ->
let* e = f e in
ret @@ (e :: acc))
[]
l
in
ret @@ List.rev l
let map2M f ls rs = mapM (fun (l, r) -> f l r) (List.combine ls rs)
let iterM f l = foldM (fun _ a -> f a) unit l
let iter2M f l r = iterM (fun (l, r) -> f l r) (List.combine l r)
module Bool = struct
include Bool
let full_adder a b c_in =
with_label ~label:"Bool.full_adder"
@@ let* a_xor_b = xor a b in
let* a_xor_b_xor_c = xor a_xor_b c_in in
let* a_xor_b_and_c = band a_xor_b c_in in
let* a_and_b = band a b in
let* c = bor a_xor_b_and_c a_and_b in
ret (pair a_xor_b_xor_c c)
end
module Num = struct
include Num
let square l = mul l l
let pow x n_list =
let* init =
let* left = Num.one in
ret (left, x)
in
let* res, _acc =
foldM
(fun (res, acc) bool ->
let* res_true = mul res acc in
let* res = Bool.ifthenelse bool res_true res in
let* acc = mul acc acc in
ret (res, acc))
init
n_list
in
ret res
let add_list ?(qc = S.zero) ?(coeffs = []) l =
let l = of_list l in
let q =
if coeffs != [] then coeffs
else List.init (List.length l) (fun _ -> S.one)
in
assert (List.compare_lengths q l = 0) ;
match (l, q) with
| x1 :: x2 :: xs, ql :: qr :: qs ->
let* res = Num.add ~qc ~ql ~qr x1 x2 in
fold2M (fun acc x ql -> Num.add ~ql x acc) res xs qs
| [x], [ql] -> Num.add_constant ~ql qc x
| [], [] -> Num.constant qc
| _, _ -> assert false
let mul_list l =
match of_list l with [] -> assert false | x :: xs -> foldM Num.mul x xs
let mul_by_constant s x = Num.add_constant ~ql:s S.zero x
let scalar_of_bytes b =
let sb = List.map scalar_of_bool (of_list b) in
scalar_of_limbs ~nb_bits:1 (to_list sb)
let assert_eq_const l s = Num.assert_custom ~ql:S.mone ~qc:s l l l
let is_eq_const l s =
let* diff = add_constant ~ql:S.mone s l in
is_zero diff
let ignore_leading_zeros ~nb_bits ~bound xbits =
let rec shave_zeros = function
| [] ->
raise
(Invalid_argument
"is_upper_bounded cannot be satisfied on bound = 0")
| (x, true) :: tl -> (x, tl)
| (_, false) :: tl -> shave_zeros tl
in
List.combine (of_list xbits) (Utils.bool_list_of_z ~nb_bits bound)
|> shave_zeros
let is_upper_bounded_unsafe ?nb_bits ~bound x =
assert (Z.zero <= bound && bound < S.order) ;
let nb_bits =
Option.value
~default:(if Z.(equal bound zero) then 1 else Z.numbits bound)
nb_bits
in
let* xbits = bits_of_scalar ~nb_bits x in
let init, xibi = ignore_leading_zeros ~nb_bits ~bound xbits in
let* geq =
foldM
(fun acc (xi, bi) ->
let op = if bi then Bool.band else Bool.bor in
op xi acc)
init
xibi
in
Bool.bnot geq
let is_upper_bounded ~bound x =
assert (Z.zero <= bound && bound < S.order) ;
let nb_bits = Z.numbits S.order in
let bound_plus_alpha = Z.(bound + Utils.alpha) in
let* xbits = bits_of_scalar ~shift:Utils.alpha ~nb_bits x in
let init, xibi =
ignore_leading_zeros ~nb_bits ~bound:bound_plus_alpha xbits
in
let* geq =
foldM
(fun acc (xi, bi) ->
let op = if bi then Bool.band else Bool.bor in
op xi acc)
init
xibi
in
Bool.bnot geq
let geq (a, bound_a) (b, bound_b) =
let* shifted_diff =
Num.add ~qr:S.mone ~qc:(S.of_z Z.(pred bound_b)) a b
in
let nb_bits = Z.(numbits @@ pred (add bound_a bound_b)) in
let* bits = bits_of_scalar ~nb_bits shifted_diff in
let init, xibi =
ignore_leading_zeros ~nb_bits ~bound:Z.(pred bound_b) bits
in
foldM
(fun acc (xi, bi) ->
let op = if bi then Bool.band else Bool.bor in
op xi acc)
init
xibi
end
module Enum (N : sig
val n : int
end) =
struct
let switch_case k cases =
let cases = of_list cases in
assert (List.compare_length_with cases N.n = 0) ;
let indexed = List.mapi (fun i x -> (i, x)) cases in
foldM
(fun c (i, ci) ->
let* f = Num.is_eq_const k (S.of_z (Z.of_int i)) in
Bool.ifthenelse f ci c)
(snd @@ List.hd indexed)
(List.tl indexed)
end
module Bytes = struct
type 'a input = 'a Input.t
type nonrec scalar = scalar
type nonrec 'a repr = 'a repr
type nonrec 'a t = 'a t
type tl = bool list
let input_bitlist l = Input.list (List.map Input.bool l)
let input_bytes ~le b = input_bitlist @@ Utils.bitlist ~le b
let of_bool_list x = ret x
let to_bool_list x = ret x
let of_scalar ~total_nb_bits x = bits_of_scalar ~nb_bits:total_nb_bits x
let to_scalar = Num.scalar_of_bytes
let constant ~le b =
let bl = Utils.bitlist ~le b in
let* ws =
foldM
(fun ws bit ->
let* w = Bool.constant bit in
ret (w :: ws))
[]
bl
in
ret @@ to_list @@ List.rev ws
let constant_uint32 ~le u32 =
let b = Stdlib.Bytes.create 4 in
Stdint.Uint32.to_bytes_big_endian u32 b 0 ;
constant ~le b
let length b = List.length (of_list b)
let concat : tl repr array -> tl repr =
fun bs ->
let bs = Array.to_list bs in
let bs = List.rev bs in
let bs = List.map of_list bs in
let bs = List.concat bs in
to_list bs
let check_args_length name a b =
let la = length a in
let lb = length b in
if la != lb then
raise
(Invalid_argument
(Format.sprintf
"%s arguments of different lengths %i %i"
name
la
lb))
let add ?(ignore_carry = true) a b =
check_args_length "Bytes.add" a b ;
with_label ~label:"Bytes.add"
@@
let ha, ta = (List.hd (of_list a), List.tl (of_list a)) in
let hb, tb = (List.hd (of_list b), List.tl (of_list b)) in
let* a_xor_b = Bool.xor ha hb in
let* a_and_b = Bool.band ha hb in
let* res, carry =
fold2M
(fun (res, c) a b ->
let* p = Bool.full_adder a b c in
let s, c = of_pair p in
ret (s :: res, c))
([a_xor_b], a_and_b)
ta
tb
in
ret @@ to_list @@ List.rev (if ignore_carry then res else carry :: res)
let xor a b =
check_args_length "Bytes.xor" a b ;
let* l = map2M Bool.xor (of_list a) (of_list b) in
ret @@ to_list l
let not a =
let* l = mapM Bool.bnot (of_list a) in
ret @@ to_list l
let band a b =
check_args_length "Bytes.band" a b ;
let* l = map2M Bool.band (of_list a) (of_list b) in
ret @@ to_list l
let rotate_right a i =
let split_n n l =
let rec aux acc k l =
if k = n then (List.rev acc, l)
else
match l with
| h :: t -> aux (h :: acc) (k + 1) t
| [] ->
raise
(Invalid_argument
(Printf.sprintf "split_n: n=%d >= List.length l=%d" n k))
in
aux [] 0 l
in
let head, tail = split_n i (of_list a) in
ret @@ to_list @@ tail @ head
let rotate_left a i = rotate_right a (length a - i)
let shift_left a i =
let* zero = Bool.constant false in
let l = of_list a in
let length = List.length l - i in
assert (length >= 0) ;
let res =
List.init i (fun _ -> zero) @ List.filteri (fun j _x -> j < length) l
in
ret @@ to_list res
let shift_right a i =
let* zero = Bool.constant false in
let l = of_list a in
assert (List.compare_length_with l i >= 0) ;
let res =
List.filteri (fun j _x -> j >= i) l @ List.init i (fun _ -> zero)
in
ret @@ to_list res
end
module Limbs (N : sig
val nb_bits : int
end) =
struct
type 'a input = 'a Input.t
type nonrec scalar = scalar
type nonrec 'a repr = 'a repr
type nonrec 'a t = 'a t
module LimbN = Limb (N)
type tl = scalar list
let nb_bits = N.nb_bits
let input_bytes ~le b =
let bl = Utils.bitlist ~le b in
let limbs = Utils.limbs_of_bool_list ~nb_bits bl in
let r = List.map S.of_int limbs in
Input.with_assertion
(fun x -> iterM (Num.range_check ~nb_bits) (of_list x))
(Input.list (List.map Input.scalar r))
let of_bool_list x =
let bl = Utils.split_exactly (of_list x) nb_bits in
let* r = mapM (fun x -> Num.scalar_of_bytes (to_list x)) bl in
ret @@ to_list r
let to_bool_list l =
let* lb =
mapM
(fun z ->
let* bz = bits_of_scalar ~nb_bits z in
ret @@ of_list bz)
(of_list l)
in
ret @@ to_list (List.concat lb)
let to_scalar b = scalar_of_limbs ~nb_bits b
let of_scalar ~total_nb_bits b = limbs_of_scalar ~total_nb_bits ~nb_bits b
let constant ~le b =
let bl = Utils.bitlist ~le b in
let limbs = Utils.limbs_of_bool_list ~nb_bits bl in
let* r = mapM (fun x -> Num.constant @@ S.of_int x) limbs in
ret @@ to_list r
let xor a b =
let* r = map2M LimbN.xor_lookup (of_list a) (of_list b) in
ret @@ to_list r
let band a b =
let* r = map2M LimbN.band_lookup (of_list a) (of_list b) in
ret @@ to_list r
let not b =
let* r = mapM LimbN.bnot_lookup (of_list b) in
ret @@ to_list r
let rotate_or_shift_right_rem0 ~is_shift a ind =
let a = Array.of_list (of_list a) in
let len = Array.length a in
let* zero = Num.zero in
let r =
List.init (len - ind) (fun i -> a.(i + ind))
@ List.init ind (fun i -> if is_shift then zero else a.(i))
in
ret @@ to_list r
let rotate_or_shift_right_rem ~is_shift a rem =
assert (rem < nb_bits) ;
let a = Array.of_list (of_list a) in
let len = Array.length a in
let get_i i : scalar repr t =
if i < len - 1 then LimbN.rotate_right_lookup a.(i) a.(i + 1) rem
else
let* zero = Num.zero in
let a0 = if is_shift then zero else a.(0) in
LimbN.rotate_right_lookup a.(i) a0 rem
in
let* r = mapM get_i (List.init len (fun i -> i)) in
ret @@ to_list r
let rotate_or_shift_right ~is_shift a i =
let ind = i / nb_bits in
let rem = i mod nb_bits in
let* res = rotate_or_shift_right_rem0 ~is_shift a ind in
if rem > 0 then rotate_or_shift_right_rem ~is_shift res rem else ret res
let rotate_right a i = rotate_or_shift_right ~is_shift:false a i
let shift_right a i = rotate_or_shift_right ~is_shift:true a i
end
let add2 p1 p2 =
let x1, y1 = of_pair p1 in
let x2, y2 = of_pair p2 in
let* x3 = Num.add x1 x2 in
let* y3 = Num.add y1 y2 in
ret (pair x3 y3)
module Encodings = struct
type ('oh, 'u, 'p) encoding = {
encode : 'u -> 'p repr;
decode : 'p repr -> 'u;
input : 'oh -> 'p Input.t;
of_input : 'p Input.t -> 'oh;
}
let conv :
('u1 -> 'u0) ->
('u0 -> 'u1) ->
('o1 -> 'o0) ->
('o0 -> 'o1) ->
('o0, 'u0, 'p) encoding ->
('o1, 'u1, 'p) encoding =
fun f g fi gi e ->
let encode a = e.encode @@ f a in
let decode b = g @@ e.decode b in
let input x = e.input @@ fi x in
let of_input x = gi @@ e.of_input x in
{encode; decode; input; of_input}
let with_implicit_bool_check :
('p repr -> bool repr t) ->
('o, 'u, 'p) encoding ->
('o, 'u, 'p) encoding =
fun bc e ->
{e with input = (fun x -> Input.with_implicit_bool_check bc @@ e.input x)}
let with_assertion :
('p repr -> unit repr t) ->
('o, 'u, 'p) encoding ->
('o, 'u, 'p) encoding =
fun assertion e ->
{e with input = (fun x -> Input.with_assertion assertion @@ e.input x)}
(** Encoding combinators *)
let scalar_encoding =
let encode x = x in
let decode x = x in
let input = Input.scalar in
let of_input = Input.to_scalar in
{encode; decode; input; of_input}
let bool_encoding =
let encode x = x in
let decode x = x in
let input = Input.bool in
let of_input = Input.to_bool in
{encode; decode; input; of_input}
let list_encoding (e : _ encoding) =
let encode a = to_list @@ List.map e.encode a in
let decode x = List.map e.decode (of_list x) in
let input a = Input.list @@ List.map e.input a in
let of_input x = List.map e.of_input (Input.to_list x) in
{encode; decode; input; of_input}
let atomic_list_encoding :
('a, 'b repr, 'c) encoding -> ('a list, 'b list repr, 'c list) encoding
=
fun e ->
let encode a = to_list @@ List.map e.encode (of_list a) in
let decode x = to_list @@ List.map e.decode (of_list x) in
let input a = Input.list @@ List.map e.input a in
let of_input x = List.map e.of_input (Input.to_list x) in
{encode; decode; input; of_input}
let obj2_encoding (el : _ encoding) (er : _ encoding) =
let encode (a, b) = pair (el.encode a) (er.encode b) in
let decode p =
let a, b = of_pair p in
(el.decode a, er.decode b)
in
let input (a, f) = Input.pair (el.input a) (er.input f) in
let of_input p =
let a, b = Input.to_pair p in
(el.of_input a, er.of_input b)
in
{encode; decode; input; of_input}
let atomic_obj2_encoding :
('a, 'b repr, 'c) encoding ->
('d, 'e repr, 'f) encoding ->
('a * 'd, ('b * 'e) repr, 'c * 'f) encoding =
fun el er ->
let encode p =
let a, b = of_pair p in
pair (el.encode a) (er.encode b)
in
let decode p =
let a, b = of_pair p in
pair (el.decode a) (er.decode b)
in
let input (a, f) = Input.pair (el.input a) (er.input f) in
let of_input p =
let a, b = Input.to_pair p in
(el.of_input a, er.of_input b)
in
{encode; decode; input; of_input}
let obj3_encoding e0 e1 e2 = obj2_encoding e0 (obj2_encoding e1 e2)
let atomic_obj3_encoding e0 e1 e2 =
atomic_obj2_encoding e0 (atomic_obj2_encoding e1 e2)
let obj4_encoding e0 e1 e2 e3 = obj2_encoding e0 (obj3_encoding e1 e2 e3)
let atomic_obj4_encoding e0 e1 e2 e3 =
atomic_obj2_encoding e0 (atomic_obj3_encoding e1 e2 e3)
let obj5_encoding e0 e1 e2 e3 e4 =
obj2_encoding e0 (obj4_encoding e1 e2 e3 e4)
let atomic_obj5_encoding e0 e1 e2 e3 e4 =
atomic_obj2_encoding e0 (atomic_obj4_encoding e1 e2 e3 e4)
let obj6_encoding e0 e1 e2 e3 e4 e5 =
obj2_encoding e0 (obj5_encoding e1 e2 e3 e4 e5)
let atomic_obj6_encoding e0 e1 e2 e3 e4 e5 =
atomic_obj2_encoding e0 (atomic_obj5_encoding e1 e2 e3 e4 e5)
let obj7_encoding e0 e1 e2 e3 e4 e5 e6 =
obj2_encoding e0 (obj6_encoding e1 e2 e3 e4 e5 e6)
let atomic_obj7_encoding e0 e1 e2 e3 e4 e5 e6 =
atomic_obj2_encoding e0 (atomic_obj6_encoding e1 e2 e3 e4 e5 e6)
let obj8_encoding e0 e1 e2 e3 e4 e5 e6 e7 =
obj2_encoding e0 (obj7_encoding e1 e2 e3 e4 e5 e6 e7)
let atomic_obj8_encoding e0 e1 e2 e3 e4 e5 e6 e7 =
atomic_obj2_encoding e0 (atomic_obj7_encoding e1 e2 e3 e4 e5 e6 e7)
let obj9_encoding e0 e1 e2 e3 e4 e5 e6 e7 e8 =
obj2_encoding e0 (obj8_encoding e1 e2 e3 e4 e5 e6 e7 e8)
let atomic_obj9_encoding e0 e1 e2 e3 e4 e5 e6 e7 e8 =
atomic_obj2_encoding e0 (atomic_obj8_encoding e1 e2 e3 e4 e5 e6 e7 e8)
let obj10_encoding e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 =
obj2_encoding e0 (obj9_encoding e1 e2 e3 e4 e5 e6 e7 e8 e9)
let atomic_obj10_encoding e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 =
atomic_obj2_encoding e0 (atomic_obj9_encoding e1 e2 e3 e4 e5 e6 e7 e8 e9)
end
end