477 lines
14 KiB
Nim
477 lines
14 KiB
Nim
# Constantine
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# Copyright (c) 2018-2019 Status Research & Development GmbH
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# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
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# Licensed and distributed under either of
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# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
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# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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# ############################################################
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#
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# Template tests for towered extension fields
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#
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# ############################################################
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import
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# Standard library
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std/[unittest, times],
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# Internals
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../../constantine/platforms/abstractions,
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../../constantine/math/extension_fields,
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../../constantine/math/config/curves,
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../../constantine/math/arithmetic,
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../../constantine/math/io/io_extfields,
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# Test utilities
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../../helpers/[prng_unsafe, static_for]
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export unittest # Generic sandwich
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echo "\n------------------------------------------------------\n"
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template ExtField(degree: static int, curve: static Curve): untyped =
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when degree == 2:
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Fp2[curve]
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elif degree == 4:
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Fp4[curve]
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elif degree == 6:
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Fp6[curve]
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elif degree == 12:
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Fp12[curve]
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else:
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{.error: "Unconfigured extension degree".}
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type
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RandomGen = enum
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Uniform
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HighHammingWeight
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Long01Sequence
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func random_elem(rng: var RngState, F: typedesc, gen: RandomGen): F {.inline, noInit.} =
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if gen == Uniform:
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result = rng.random_unsafe(F)
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elif gen == HighHammingWeight:
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result = rng.random_highHammingWeight(F)
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else:
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result = rng.random_long01Seq(F)
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proc runTowerTests*[N](
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ExtDegree: static int,
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Iters: static int,
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TestCurves: static array[N, Curve],
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moduleName: string,
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testSuiteDesc: string
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) =
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# Random seed for reproducibility
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var rng: RngState
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let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
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rng.seed(seed)
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echo moduleName, " xoshiro512** seed: ", seed
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suite testSuiteDesc & " [" & $WordBitWidth & "-bit mode]":
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test "Comparison sanity checks":
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proc test(Field: typedesc) =
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var z, o {.noInit.}: Field
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z.setZero()
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o.setOne()
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check: not bool(z == o)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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test "Addition, substraction negation are consistent":
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proc test(Field: typedesc, Iters: static int, gen: RandomGen) =
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# Try to exercise all code paths for in-place/out-of-place add/sum/sub/diff/double/neg
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# (1 - (-a) - b + (-a) - 2a) + (2a + 2b + (-b)) == 1
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var accum {.noInit.}, One {.noInit.}, a{.noInit.}, na{.noInit.}, b{.noInit.}, nb{.noInit.}, a2 {.noInit.}, b2 {.noInit.}: Field
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for _ in 0 ..< Iters:
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One.setOne()
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a = rng.random_elem(Field, gen)
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a2 = a
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a2.double()
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na.neg(a)
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b = rng.random_elem(Field, gen)
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b2.double(b)
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nb.neg(b)
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accum.diff(One, na)
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accum -= b
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accum += na
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accum -= a2
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var t{.noInit.}: Field
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t.sum(a2, b2)
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t += nb
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accum += t
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check: bool accum.isOne()
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Division by 2":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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var a2 = a
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a2.double()
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a2.div2()
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check: bool(a == a2)
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a2.div2()
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a2.double()
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check: bool(a == a2)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Squaring 1 returns 1":
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proc test(Field: typedesc) =
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let One = block:
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var O{.noInit.}: Field
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O.setOne()
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O
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block:
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var r{.noinit.}: Field
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r.square(One)
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check: bool(r == One)
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block:
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var r{.noinit.}: Field
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r.prod(One, One)
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check: bool(r == One)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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test "Squaring 2 returns 4":
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proc test(Field: typedesc) =
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let One = block:
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var O{.noInit.}: Field
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O.setOne()
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O
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var Two: Field
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Two.double(One)
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var Four: Field
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Four.double(Two)
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block:
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var r: Field
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r.square(Two)
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check: bool(r == Four)
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block:
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var r: Field
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r.prod(Two, Two)
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check: bool(r == Four)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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test "Squaring 3 returns 9":
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proc test(Field: typedesc) =
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let One = block:
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var O{.noInit.}: Field
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O.setOne()
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O
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var Three: Field
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for _ in 0 ..< 3:
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Three += One
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var Nine: Field
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for _ in 0 ..< 9:
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Nine += One
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block:
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var u: Field
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u.square(Three)
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check: bool(u == Nine)
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block:
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var u: Field
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u.prod(Three, Three)
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check: bool(u == Nine)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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test "Squaring -3 returns 9":
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proc test(Field: typedesc) =
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let One = block:
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var O{.noInit.}: Field
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O.setOne()
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O
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var MinusThree: Field
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for _ in 0 ..< 3:
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MinusThree -= One
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var Nine: Field
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for _ in 0 ..< 9:
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Nine += One
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block:
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var u: Field
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u.square(MinusThree)
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check: bool(u == Nine)
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block:
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var u: Field
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u.prod(MinusThree, MinusThree)
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check: bool(u == Nine)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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test "Multiplication by 0 and 1":
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template test(Field: typedesc, body: untyped) =
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block:
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proc testInstance() =
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let Z {.inject.} = block:
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var Z{.noInit.}: Field
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Z.setZero()
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Z
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let O {.inject.} = block:
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var O{.noInit.}: Field
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O.setOne()
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O
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for _ in 0 ..< Iters:
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let x {.inject.} = rng.random_unsafe(Field)
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var r{.noinit, inject.}: Field
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body
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testInstance()
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve)):
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r.prod(x, Z)
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doAssert bool(r == Z),
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"\nExpected zero but got \n(" & $ExtField(ExtDegree, curve) & "): " & x.toHex()
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test(ExtField(ExtDegree, curve)):
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r.prod(Z, x)
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doAssert bool(r == Z),
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"\nExpected zero but got \n(" & $ExtField(ExtDegree, curve) & "): " & x.toHex()
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test(ExtField(ExtDegree, curve)):
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r.prod(x, O)
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doAssert bool(r == x),
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"\n(" & $ExtField(ExtDegree, curve) & "): Expected one: " & O.toHex() & "\n" &
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"got: " & x.toHex()
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test(ExtField(ExtDegree, curve)):
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r.prod(O, x)
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doAssert bool(r == x),
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"\n(" & $ExtField(ExtDegree, curve) & "): Expected one: " & O.toHex() & "\n" &
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"got: " & x.toHex()
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test "Multiplication and Squaring are consistent":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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var rMul{.noInit.}, rSqr{.noInit.}: Field
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rMul.prod(a, a)
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rSqr.square(a)
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doAssert bool(rMul == rSqr), "Failure with a (" & $Field & "): \nInput:" & a.toHex() & "\n" &
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"Mul: " & rMul.toHex() & "\n" &
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"Sqr: " & rSqr.toHex() & "\n"
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Squaring the opposite gives the same result":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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var na{.noInit.}: Field
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na.neg(a)
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var rSqr{.noInit.}, rNegSqr{.noInit.}: Field
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rSqr.square(a)
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rNegSqr.square(na)
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doAssert bool(rSqr == rNegSqr), "Failure with a \n(" & $Field & "): " & a.toHex() & "\n" &
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"Sqr: " & rSqr.toHex() & "\n" &
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"SqrNeg: " & rNegSqr.toHex() & "\n"
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Multiplication and Addition/Substraction are consistent":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let factor = rng.random_unsafe(-30..30)
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let a = rng.random_elem(Field, gen)
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if factor == 0: continue
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var sum{.noInit.}, one{.noInit.}, f{.noInit.}: Field
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one.setOne()
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if factor < 0:
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sum.neg(a)
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f.neg(one)
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for i in 1 ..< -factor:
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sum -= a
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f -= one
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else:
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sum = a
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f = one
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for i in 1 ..< factor:
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sum += a
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f += one
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var r{.noInit.}: Field
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r.prod(a, f)
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check: bool(r == sum)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Addition is associative and commutative":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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let b = rng.random_elem(Field, gen)
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let c = rng.random_elem(Field, gen)
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var tmp1{.noInit.}, tmp2{.noInit.}: Field
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# r0 = (a + b) + c
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tmp1.sum(a, b)
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tmp2.sum(tmp1, c)
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let r0 = tmp2
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# r1 = a + (b + c)
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tmp1.sum(b, c)
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tmp2.sum(a, tmp1)
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let r1 = tmp2
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# r2 = (a + c) + b
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tmp1.sum(a, c)
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tmp2.sum(tmp1, b)
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let r2 = tmp2
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# r3 = a + (c + b)
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tmp1.sum(c, b)
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tmp2.sum(a, tmp1)
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let r3 = tmp2
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# r4 = (c + a) + b
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tmp1.sum(c, a)
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tmp2.sum(tmp1, b)
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let r4 = tmp2
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# ...
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check:
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bool(r0 == r1)
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bool(r0 == r2)
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bool(r0 == r3)
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bool(r0 == r4)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Multiplication is associative and commutative":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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let b = rng.random_elem(Field, gen)
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let c = rng.random_elem(Field, gen)
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var tmp1{.noInit.}, tmp2{.noInit.}: Field
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# r0 = (a * b) * c
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tmp1.prod(a, b)
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tmp2.prod(tmp1, c)
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let r0 = tmp2
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# r1 = a * (b * c)
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tmp1.prod(b, c)
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tmp2.prod(a, tmp1)
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let r1 = tmp2
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# r2 = (a * c) * b
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tmp1.prod(a, c)
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tmp2.prod(tmp1, b)
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let r2 = tmp2
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# r3 = a * (c * b)
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tmp1.prod(c, b)
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tmp2.prod(a, tmp1)
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let r3 = tmp2
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# r4 = (c * a) * b
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tmp1.prod(c, a)
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tmp2.prod(tmp1, b)
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let r4 = tmp2
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# ...
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check:
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bool(r0 == r1)
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bool(r0 == r2)
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bool(r0 == r3)
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bool(r0 == r4)
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "Extension field multiplicative inverse":
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proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
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var aInv, r{.noInit.}: Field
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Field, gen)
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aInv.inv(a)
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r.prod(a, aInv)
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check: bool(r.isOne())
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r.prod(aInv, a)
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check: bool(r.isOne())
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
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test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
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test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
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test "0 does not have a multiplicative inverse and should return 0 for projective/jacobian => affine coordinates conversion":
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proc test(Field: typedesc) =
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var z: Field
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z.setZero()
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var zInv{.noInit.}: Field
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zInv.inv(z)
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check: bool zInv.isZero()
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staticFor(curve, TestCurves):
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test(ExtField(ExtDegree, curve))
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