betrusted-ed25519-verified/verification/gen/CurveScalar/Funs.lean

-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
-- [curve25519_dalek]: function definitions
import Aeneas
import CurveScalar.Types
open Aeneas Aeneas.Std Result ControlFlow Error
set_option linter.dupNamespace false
set_option linter.hashCommand false
set_option linter.unusedVariables false

/- You can set the `maxHeartbeats` value with the `-max-heartbeats` CLI option -/
set_option maxHeartbeats 1000000

/- You can set the `maxRecDepth` value with the `-max-recdepth` CLI option -/
set_option maxRecDepth 2048

namespace curve25519_dalek

/-- [curve25519_dalek::backend::serial::u64::constants::L]
    Source: 'curve25519-dalek/src/backend/serial/u64/constants.rs', lines 117:0-123:3 -/
@[global_simps, irreducible]
def backend.serial.u64.constants.L : backend.serial.u64.scalar.Scalar52 :=
  Array.make 5#usize [
    671914833335277#u64, 3916664325105025#u64, 1367801#u64, 0#u64,
    17592186044416#u64
    ]

/-- [curve25519_dalek::backend::serial::u64::constants::LFACTOR]
    Source: 'curve25519-dalek/src/backend/serial/u64/constants.rs', lines 126:0-126:48 -/
@[global_simps, irreducible]
def backend.serial.u64.constants.LFACTOR : Std.U64 := 1439961107955227#u64

/-- [curve25519_dalek::backend::serial::u64::constants::RR]
    Source: 'curve25519-dalek/src/backend/serial/u64/constants.rs', lines 138:0-144:3 -/
@[global_simps, irreducible]
def backend.serial.u64.constants.RR : backend.serial.u64.scalar.Scalar52 :=
  Array.make 5#usize [
    2764609938444603#u64, 3768881411696287#u64, 1616719297148420#u64,
    1087343033131391#u64, 10175238647962#u64
    ]

/-- [curve25519_dalek::backend::serial::u64::scalar::{impl core::ops::index::Index<usize, u64> for curve25519_dalek::backend::serial::u64::scalar::Scalar52}::index]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 42:4-44:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
  (self : backend.serial.u64.scalar.Scalar52) (_index : Std.Usize) :
  Result Std.U64
  := do
  Array.index_usize self _index

/-- [curve25519_dalek::backend::serial::u64::scalar::{impl core::ops::index::IndexMut<usize, u64> for curve25519_dalek::backend::serial::u64::scalar::Scalar52}::index_mut]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 48:4-50:5
    Visibility: public -/
def
  backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexMutUsizeU64.index_mut
  (self : backend.serial.u64.scalar.Scalar52) (_index : Std.Usize) :
  Result (Std.U64 × (Std.U64 → backend.serial.u64.scalar.Scalar52))
  := do
  let (i, index_mut_back) ← Array.index_mut_usize self _index
  let back := fun i1 => let a := index_mut_back i1
                        a
  ok (i, back)

/-- [curve25519_dalek::backend::serial::u64::scalar::m]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 55:0-57:1 -/
def backend.serial.u64.scalar.m
  (x : Std.U64) (y : Std.U64) : Result Std.U128 := do
  let i ← lift (UScalar.cast .U128 x)
  let i1 ← lift (UScalar.cast .U128 y)
  i * i1

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::ZERO]
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 61:4-61:57
    Visibility: public -/
@[global_simps, irreducible]
def backend.serial.u64.scalar.Scalar52.ZERO
  : backend.serial.u64.scalar.Scalar52 :=
  let a := Array.repeat 5#usize 0#u64
  a

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::sub]: loop body 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 182:8-185:9
    Visibility: public -/
@[rust_loop_body]
def backend.serial.u64.scalar.Scalar52.sub_loop0.body
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) (mask : Std.U64)
  (iter : core.ops.range.Range Std.Usize)
  (difference : backend.serial.u64.scalar.Scalar52) (borrow : Std.U64) :
  Result (ControlFlow ((core.ops.range.Range Std.Usize) ×
    backend.serial.u64.scalar.Scalar52 × Std.U64)
    (backend.serial.u64.scalar.Scalar52 × Std.U64))
  := do
  let (o, iter1) ←
    core.iter.range.IteratorRange.next core.iter.range.StepUsize iter
  match o with
  | none => ok (done (difference, borrow))
  | some i =>
    let i1 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        a i
    let i2 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        b i
    let i3 ← borrow >>> 63#i32
    let i4 ← i2 + i3
    let borrow1 ← lift (core.num.U64.wrapping_sub i1 i4)
    let (_, index_mut_back) ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexMutUsizeU64.index_mut
        difference i
    let i5 ← lift (borrow1 &&& mask)
    let difference1 := index_mut_back i5
    ok (cont (iter1, difference1, borrow1))

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::sub]: loop 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 182:8-185:9
    Visibility: public -/
@[rust_loop]
def backend.serial.u64.scalar.Scalar52.sub_loop0
  (iter : core.ops.range.Range Std.Usize)
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52)
  (difference : backend.serial.u64.scalar.Scalar52) (mask : Std.U64)
  (borrow : Std.U64) :
  Result (backend.serial.u64.scalar.Scalar52 × Std.U64)
  := do
  loop
    (fun (iter1, difference1, borrow1) =>
      backend.serial.u64.scalar.Scalar52.sub_loop0.body a b mask iter1
      difference1 borrow1)
    (iter, difference, borrow)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::sub]: loop body 1:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 0:0-193:9
    Visibility: public -/
@[rust_loop_body]
def backend.serial.u64.scalar.Scalar52.sub_loop1.body
  (mask : Std.U64) (underflow_mask : Std.U64)
  (iter : core.ops.range.Range Std.Usize)
  (difference : backend.serial.u64.scalar.Scalar52) (carry : Std.U64) :
  Result (ControlFlow ((core.ops.range.Range Std.Usize) ×
    backend.serial.u64.scalar.Scalar52 × Std.U64)
    backend.serial.u64.scalar.Scalar52)
  := do
  let (o, iter1) ←
    core.iter.range.IteratorRange.next core.iter.range.StepUsize iter
  match o with
  | none => ok (done difference)
  | some i =>
    let i1 ← carry >>> 52#i32
    let i2 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        difference i
    let i3 ← i1 + i2
    let i4 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        backend.serial.u64.constants.L i
    let i5 ← lift (i4 &&& underflow_mask)
    let carry1 ← i3 + i5
    let (_, index_mut_back) ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexMutUsizeU64.index_mut
        difference i
    let i6 ← lift (carry1 &&& mask)
    let difference1 := index_mut_back i6
    ok (cont (iter1, difference1, carry1))

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::sub]: loop 1:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 0:0-193:9
    Visibility: public -/
@[rust_loop]
def backend.serial.u64.scalar.Scalar52.sub_loop1
  (iter : core.ops.range.Range Std.Usize)
  (difference : backend.serial.u64.scalar.Scalar52) (mask : Std.U64)
  (underflow_mask : Std.U64) (carry : Std.U64) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  loop
    (fun (iter1, difference1, carry1) =>
      backend.serial.u64.scalar.Scalar52.sub_loop1.body mask underflow_mask
      iter1 difference1 carry1)
    (iter, difference, carry)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::sub]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 176:4-196:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.sub
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let i ← 1#u64 <<< 52#i32
  let mask ← i - 1#u64
  let (difference, borrow) ←
    backend.serial.u64.scalar.Scalar52.sub_loop0
      { start := 0#usize, «end» := 5#usize } a b
      backend.serial.u64.scalar.Scalar52.ZERO mask 0#u64
  let i1 ← borrow >>> 63#i32
  let i2 ← lift (i1 ^^^ 1#u64)
  let underflow_mask ← lift (core.num.U64.wrapping_sub i2 1#u64)
  backend.serial.u64.scalar.Scalar52.sub_loop1
    { start := 0#usize, «end» := 5#usize } difference mask underflow_mask
    0#u64

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::add]: loop body 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 166:8-169:9
    Visibility: public -/
@[rust_loop_body]
def backend.serial.u64.scalar.Scalar52.add_loop.body
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) (mask : Std.U64)
  (iter : core.ops.range.Range Std.Usize)
  (sum : backend.serial.u64.scalar.Scalar52) (carry : Std.U64) :
  Result (ControlFlow ((core.ops.range.Range Std.Usize) ×
    backend.serial.u64.scalar.Scalar52 × Std.U64)
    backend.serial.u64.scalar.Scalar52)
  := do
  let (o, iter1) ←
    core.iter.range.IteratorRange.next core.iter.range.StepUsize iter
  match o with
  | none => ok (done sum)
  | some i =>
    let i1 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        a i
    let i2 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        b i
    let i3 ← i1 + i2
    let i4 ← carry >>> 52#i32
    let carry1 ← i3 + i4
    let (_, index_mut_back) ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexMutUsizeU64.index_mut
        sum i
    let i5 ← lift (carry1 &&& mask)
    let sum1 := index_mut_back i5
    ok (cont (iter1, sum1, carry1))

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::add]: loop 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 166:8-169:9
    Visibility: public -/
@[rust_loop]
def backend.serial.u64.scalar.Scalar52.add_loop
  (iter : core.ops.range.Range Std.Usize)
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52)
  (sum : backend.serial.u64.scalar.Scalar52) (mask : Std.U64) (carry : Std.U64)
  :
  Result backend.serial.u64.scalar.Scalar52
  := do
  loop
    (fun (iter1, sum1, carry1) =>
      backend.serial.u64.scalar.Scalar52.add_loop.body a b mask iter1 sum1
      carry1)
    (iter, sum, carry)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::add]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 160:4-173:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.add
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let i ← 1#u64 <<< 52#i32
  let mask ← i - 1#u64
  let sum ←
    backend.serial.u64.scalar.Scalar52.add_loop
      { start := 0#usize, «end» := 5#usize } a b
      backend.serial.u64.scalar.Scalar52.ZERO mask 0#u64
  backend.serial.u64.scalar.Scalar52.sub sum backend.serial.u64.constants.L

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::mul_internal]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 201:4-215:5 -/
def backend.serial.u64.scalar.Scalar52.mul_internal
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) :
  Result (Array Std.U128 9#usize)
  := do
  let z := Array.repeat 9#usize 0#u128
  let i ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      0#usize
  let i1 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index b
      0#usize
  let i2 ← backend.serial.u64.scalar.m i i1
  let z1 ← Array.update z 0#usize i2
  let i3 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index b
      1#usize
  let i4 ← backend.serial.u64.scalar.m i i3
  let i5 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      1#usize
  let i6 ← backend.serial.u64.scalar.m i5 i1
  let i7 ← i4 + i6
  let z2 ← Array.update z1 1#usize i7
  let i8 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index b
      2#usize
  let i9 ← backend.serial.u64.scalar.m i i8
  let i10 ← backend.serial.u64.scalar.m i5 i3
  let i11 ← i9 + i10
  let i12 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      2#usize
  let i13 ← backend.serial.u64.scalar.m i12 i1
  let i14 ← i11 + i13
  let z3 ← Array.update z2 2#usize i14
  let i15 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index b
      3#usize
  let i16 ← backend.serial.u64.scalar.m i i15
  let i17 ← backend.serial.u64.scalar.m i5 i8
  let i18 ← i16 + i17
  let i19 ← backend.serial.u64.scalar.m i12 i3
  let i20 ← i18 + i19
  let i21 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      3#usize
  let i22 ← backend.serial.u64.scalar.m i21 i1
  let i23 ← i20 + i22
  let z4 ← Array.update z3 3#usize i23
  let i24 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index b
      4#usize
  let i25 ← backend.serial.u64.scalar.m i i24
  let i26 ← backend.serial.u64.scalar.m i5 i15
  let i27 ← i25 + i26
  let i28 ← backend.serial.u64.scalar.m i12 i8
  let i29 ← i27 + i28
  let i30 ← backend.serial.u64.scalar.m i21 i3
  let i31 ← i29 + i30
  let i32 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      4#usize
  let i33 ← backend.serial.u64.scalar.m i32 i1
  let i34 ← i31 + i33
  let z5 ← Array.update z4 4#usize i34
  let i35 ← backend.serial.u64.scalar.m i5 i24
  let i36 ← backend.serial.u64.scalar.m i12 i15
  let i37 ← i35 + i36
  let i38 ← backend.serial.u64.scalar.m i21 i8
  let i39 ← i37 + i38
  let i40 ← backend.serial.u64.scalar.m i32 i3
  let i41 ← i39 + i40
  let z6 ← Array.update z5 5#usize i41
  let i42 ← backend.serial.u64.scalar.m i12 i24
  let i43 ← backend.serial.u64.scalar.m i21 i15
  let i44 ← i42 + i43
  let i45 ← backend.serial.u64.scalar.m i32 i8
  let i46 ← i44 + i45
  let z7 ← Array.update z6 6#usize i46
  let i47 ← backend.serial.u64.scalar.m i21 i24
  let i48 ← backend.serial.u64.scalar.m i32 i15
  let i49 ← i47 + i48
  let z8 ← Array.update z7 7#usize i49
  let i50 ← backend.serial.u64.scalar.m i32 i24
  Array.update z8 8#usize i50

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::square_internal]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 220:4-239:5 -/
def backend.serial.u64.scalar.Scalar52.square_internal
  (a : backend.serial.u64.scalar.Scalar52) :
  Result (Array Std.U128 9#usize)
  := do
  let i ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      0#usize
  let i1 ← i * 2#u64
  let i2 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      1#usize
  let i3 ← i2 * 2#u64
  let i4 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      2#usize
  let i5 ← i4 * 2#u64
  let i6 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      3#usize
  let i7 ← i6 * 2#u64
  let i8 ← backend.serial.u64.scalar.m i i
  let i9 ← Array.index_usize (Array.make 4#usize [ i1, i3, i5, i7 ]) 0#usize
  let i10 ← backend.serial.u64.scalar.m i9 i2
  let i11 ← backend.serial.u64.scalar.m i9 i4
  let i12 ← backend.serial.u64.scalar.m i2 i2
  let i13 ← i11 + i12
  let i14 ← backend.serial.u64.scalar.m i9 i6
  let i15 ← Array.index_usize (Array.make 4#usize [ i1, i3, i5, i7 ]) 1#usize
  let i16 ← backend.serial.u64.scalar.m i15 i4
  let i17 ← i14 + i16
  let i18 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index a
      4#usize
  let i19 ← backend.serial.u64.scalar.m i9 i18
  let i20 ← backend.serial.u64.scalar.m i15 i6
  let i21 ← i19 + i20
  let i22 ← backend.serial.u64.scalar.m i4 i4
  let i23 ← i21 + i22
  let i24 ← backend.serial.u64.scalar.m i15 i18
  let i25 ← Array.index_usize (Array.make 4#usize [ i1, i3, i5, i7 ]) 2#usize
  let i26 ← backend.serial.u64.scalar.m i25 i6
  let i27 ← i24 + i26
  let i28 ← backend.serial.u64.scalar.m i25 i18
  let i29 ← backend.serial.u64.scalar.m i6 i6
  let i30 ← i28 + i29
  let i31 ← Array.index_usize (Array.make 4#usize [ i1, i3, i5, i7 ]) 3#usize
  let i32 ← backend.serial.u64.scalar.m i31 i18
  let i33 ← backend.serial.u64.scalar.m i18 i18
  ok (Array.make 9#usize [ i8, i10, i13, i17, i23, i27, i30, i32, i33 ])

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::montgomery_reduce::part2]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 253:8-256:9 -/
def backend.serial.u64.scalar.Scalar52.montgomery_reduce.part2
  (sum : Std.U128) : Result (Std.U128 × Std.U64) := do
  let i ← lift (UScalar.cast .U64 sum)
  let i1 ← 1#u64 <<< 52#i32
  let i2 ← i1 - 1#u64
  let w ← lift (i &&& i2)
  let i3 ← sum >>> 52#i32
  ok (i3, w)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::montgomery_reduce::part1]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 247:8-250:9 -/
def backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1
  (sum : Std.U128) : Result (Std.U128 × Std.U64) := do
  let i ← lift (UScalar.cast .U64 sum)
  let i1 ←
    lift (core.num.U64.wrapping_mul i backend.serial.u64.constants.LFACTOR)
  let i2 ← 1#u64 <<< 52#i32
  let i3 ← i2 - 1#u64
  let p ← lift (i1 &&& i3)
  let i4 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
      backend.serial.u64.constants.L 0#usize
  let i5 ← backend.serial.u64.scalar.m p i4
  let i6 ← sum + i5
  let i7 ← i6 >>> 52#i32
  ok (i7, p)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::montgomery_reduce]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 244:4-277:5 -/
def backend.serial.u64.scalar.Scalar52.montgomery_reduce
  (limbs : Array Std.U128 9#usize) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let i ← Array.index_usize limbs 0#usize
  let (carry, n0) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 i
  let i1 ← Array.index_usize limbs 1#usize
  let i2 ← carry + i1
  let i3 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
      backend.serial.u64.constants.L 1#usize
  let i4 ← backend.serial.u64.scalar.m n0 i3
  let i5 ← i2 + i4
  let (carry1, n1) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 i5
  let i6 ← Array.index_usize limbs 2#usize
  let i7 ← carry1 + i6
  let i8 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
      backend.serial.u64.constants.L 2#usize
  let i9 ← backend.serial.u64.scalar.m n0 i8
  let i10 ← i7 + i9
  let i11 ← backend.serial.u64.scalar.m n1 i3
  let i12 ← i10 + i11
  let (carry2, n2) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 i12
  let i13 ← Array.index_usize limbs 3#usize
  let i14 ← carry2 + i13
  let i15 ← backend.serial.u64.scalar.m n1 i8
  let i16 ← i14 + i15
  let i17 ← backend.serial.u64.scalar.m n2 i3
  let i18 ← i16 + i17
  let (carry3, n3) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 i18
  let i19 ← Array.index_usize limbs 4#usize
  let i20 ← carry3 + i19
  let i21 ←
    backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
      backend.serial.u64.constants.L 4#usize
  let i22 ← backend.serial.u64.scalar.m n0 i21
  let i23 ← i20 + i22
  let i24 ← backend.serial.u64.scalar.m n2 i8
  let i25 ← i23 + i24
  let i26 ← backend.serial.u64.scalar.m n3 i3
  let i27 ← i25 + i26
  let (carry4, n4) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 i27
  let i28 ← Array.index_usize limbs 5#usize
  let i29 ← carry4 + i28
  let i30 ← backend.serial.u64.scalar.m n1 i21
  let i31 ← i29 + i30
  let i32 ← backend.serial.u64.scalar.m n3 i8
  let i33 ← i31 + i32
  let i34 ← backend.serial.u64.scalar.m n4 i3
  let i35 ← i33 + i34
  let (carry5, r0) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part2 i35
  let i36 ← Array.index_usize limbs 6#usize
  let i37 ← carry5 + i36
  let i38 ← backend.serial.u64.scalar.m n2 i21
  let i39 ← i37 + i38
  let i40 ← backend.serial.u64.scalar.m n4 i8
  let i41 ← i39 + i40
  let (carry6, r1) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part2 i41
  let i42 ← Array.index_usize limbs 7#usize
  let i43 ← carry6 + i42
  let i44 ← backend.serial.u64.scalar.m n3 i21
  let i45 ← i43 + i44
  let (carry7, r2) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part2 i45
  let i46 ← Array.index_usize limbs 8#usize
  let i47 ← carry7 + i46
  let i48 ← backend.serial.u64.scalar.m n4 i21
  let i49 ← i47 + i48
  let (carry8, r3) ←
    backend.serial.u64.scalar.Scalar52.montgomery_reduce.part2 i49
  let r4 ← lift (UScalar.cast .U64 carry8)
  backend.serial.u64.scalar.Scalar52.sub
    (Array.make 5#usize [ r0, r1, r2, r3, r4 ]) backend.serial.u64.constants.L

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::mul]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 281:4-284:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.mul
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let a1 ← backend.serial.u64.scalar.Scalar52.mul_internal a b
  let ab ← backend.serial.u64.scalar.Scalar52.montgomery_reduce a1
  let a2 ←
    backend.serial.u64.scalar.Scalar52.mul_internal ab
      backend.serial.u64.constants.RR
  backend.serial.u64.scalar.Scalar52.montgomery_reduce a2

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::square]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 289:4-292:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.square
  (self : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let a ← backend.serial.u64.scalar.Scalar52.square_internal self
  let aa ← backend.serial.u64.scalar.Scalar52.montgomery_reduce a
  let a1 ←
    backend.serial.u64.scalar.Scalar52.mul_internal aa
      backend.serial.u64.constants.RR
  backend.serial.u64.scalar.Scalar52.montgomery_reduce a1

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::montgomery_mul]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 296:4-298:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.montgomery_mul
  (a : backend.serial.u64.scalar.Scalar52)
  (b : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let a1 ← backend.serial.u64.scalar.Scalar52.mul_internal a b
  backend.serial.u64.scalar.Scalar52.montgomery_reduce a1

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::montgomery_square]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 302:4-304:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.montgomery_square
  (self : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let a ← backend.serial.u64.scalar.Scalar52.square_internal self
  backend.serial.u64.scalar.Scalar52.montgomery_reduce a

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::as_montgomery]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 308:4-310:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.as_montgomery
  (self : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  backend.serial.u64.scalar.Scalar52.montgomery_mul self
    backend.serial.u64.constants.RR

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::from_montgomery]: loop body 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 317:8-319:9
    Visibility: public -/
@[rust_loop_body]
def backend.serial.u64.scalar.Scalar52.from_montgomery_loop.body
  (self : backend.serial.u64.scalar.Scalar52)
  (iter : core.ops.range.Range Std.Usize) (limbs : Array Std.U128 9#usize) :
  Result (ControlFlow ((core.ops.range.Range Std.Usize) × (Array Std.U128
    9#usize)) (Array Std.U128 9#usize))
  := do
  let (o, iter1) ←
    core.iter.range.IteratorRange.next core.iter.range.StepUsize iter
  match o with
  | none => ok (done limbs)
  | some i =>
    let i1 ←
      backend.serial.u64.scalar.Scalar52.Insts.CoreOpsIndexIndexUsizeU64.index
        self i
    let i2 ← lift (UScalar.cast .U128 i1)
    let a ← Array.update limbs i i2
    ok (cont (iter1, a))

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::from_montgomery]: loop 0:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 317:8-319:9
    Visibility: public -/
@[rust_loop]
def backend.serial.u64.scalar.Scalar52.from_montgomery_loop
  (iter : core.ops.range.Range Std.Usize)
  (self : backend.serial.u64.scalar.Scalar52) (limbs : Array Std.U128 9#usize)
  :
  Result (Array Std.U128 9#usize)
  := do
  loop
    (fun (iter1, limbs1) =>
      backend.serial.u64.scalar.Scalar52.from_montgomery_loop.body self iter1
      limbs1)
    (iter, limbs)

/-- [curve25519_dalek::backend::serial::u64::scalar::{curve25519_dalek::backend::serial::u64::scalar::Scalar52}::from_montgomery]:
    Source: 'curve25519-dalek/src/backend/serial/u64/scalar.rs', lines 315:4-321:5
    Visibility: public -/
def backend.serial.u64.scalar.Scalar52.from_montgomery
  (self : backend.serial.u64.scalar.Scalar52) :
  Result backend.serial.u64.scalar.Scalar52
  := do
  let limbs := Array.repeat 9#usize 0#u128
  let limbs1 ←
    backend.serial.u64.scalar.Scalar52.from_montgomery_loop
      { start := 0#usize, «end» := 5#usize } self limbs
  backend.serial.u64.scalar.Scalar52.montgomery_reduce limbs1

end curve25519_dalek