596 lines
20 KiB
Nim
596 lines
20 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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import
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# Standard library
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std/[tables, unittest, times],
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# Internals
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../../constantine/platforms/abstractions,
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../../constantine/math/arithmetic,
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../../constantine/math/extension_fields,
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../../constantine/math/config/curves,
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../../constantine/math/io/io_extfields,
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../../constantine/math/pairing/lines_eval,
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# Test utilities
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../../helpers/[prng_unsafe, static_for]
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const
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Iters = 8
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TestCurves = [
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BN254_Nogami,
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BN254_Snarks,
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BLS12_377,
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BLS12_381
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]
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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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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 "\n------------------------------------------------------\n"
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echo "test_pairing_fp12_sparse xoshiro512** seed: ", seed
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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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suite "Pairing - Sparse 𝔽p12 multiplication by line function is consistent with dense 𝔽p12 mul":
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test "Dense 𝔽p4 by Sparse 0y":
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proc test_fp4_0y(C: static Curve, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Fp4[C], gen)
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let y = rng.random_elem(Fp2[C], gen)
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let b = Fp4[C](coords: [Fp2[C](), y])
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var r, r2: Fp4[C]
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r.prod(a, b)
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r2.mul_sparse_by_0y(a, y)
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check: bool(r == r2)
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staticFor(curve, TestCurves):
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test_fp4_0y(curve, gen = Uniform)
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test_fp4_0y(curve, gen = HighHammingWeight)
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test_fp4_0y(curve, gen = Long01Sequence)
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test "Dense 𝔽p6 by Sparse 0y0":
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proc test_fp6_0y0(C: static Curve, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Fp6[C], gen)
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let y = rng.random_elem(Fp2[C], gen)
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let b = Fp6[C](coords: [Fp2[C](), y, Fp2[C]()])
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var r, r2: Fp6[C]
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r.prod(a, b)
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r2.mul_sparse_by_0y0(a, y)
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check: bool(r == r2)
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staticFor(curve, TestCurves):
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test_fp6_0y0(curve, gen = Uniform)
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test_fp6_0y0(curve, gen = HighHammingWeight)
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test_fp6_0y0(curve, gen = Long01Sequence)
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test "Dense 𝔽p6 by Sparse xy0":
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proc test_fp6_xy0(C: static Curve, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Fp6[C], gen)
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let x = rng.random_elem(Fp2[C], gen)
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let y = rng.random_elem(Fp2[C], gen)
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let b = Fp6[C](coords: [x, y, Fp2[C]()])
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var r, r2: Fp6[C]
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r.prod(a, b)
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r2.mul_sparse_by_xy0(a, x, y)
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check: bool(r == r2)
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staticFor(curve, TestCurves):
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test_fp6_xy0(curve, gen = Uniform)
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test_fp6_xy0(curve, gen = HighHammingWeight)
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test_fp6_xy0(curve, gen = Long01Sequence)
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test "Dense 𝔽p6 by Sparse 0yz":
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proc test_fp6_0yz(C: static Curve, gen: static RandomGen) =
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for _ in 0 ..< Iters:
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let a = rng.random_elem(Fp6[C], gen)
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let y = rng.random_elem(Fp2[C], gen)
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let z = rng.random_elem(Fp2[C], gen)
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let b = Fp6[C](coords: [Fp2[C](), y, z])
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var r, r2: Fp6[C]
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r.prod(a, b)
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r2.mul_sparse_by_0yz(a, y, z)
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check: bool(r == r2)
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staticFor(curve, TestCurves):
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test_fp6_0yz(curve, gen = Uniform)
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test_fp6_0yz(curve, gen = HighHammingWeight)
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test_fp6_0yz(curve, gen = Long01Sequence)
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when Fp12[BN254_Snarks]().c0.typeof is Fp6:
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# =========== Towering 𝔽p12/𝔽p6 ======================================
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test "Sparse 𝔽p12/𝔽p6 resulting from a00bc0 line function":
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proc test_fp12_a00bc0(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == D_Twist:
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for _ in 0 ..< Iters:
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var a = rng.random_elem(Fp12[C], gen)
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var a2 = a
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var x = rng.random_elem(Fp2[C], gen)
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var y = rng.random_elem(Fp2[C], gen)
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var z = rng.random_elem(Fp2[C], gen)
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let line = Line[Fp2[C]](a: x, b: y, c: z)
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let b = Fp12[C]( coords: [
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Fp6[C](coords: [ x, Fp2[C](), Fp2[C]()]),
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Fp6[C](coords: [ y, z, Fp2[C]()])
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])
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a *= b
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a2.mul_sparse_by_line_a00bc0(line)
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check: bool(a == a2)
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staticFor(curve, TestCurves):
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test_fp12_a00bc0(curve, gen = Uniform)
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test_fp12_a00bc0(curve, gen = HighHammingWeight)
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test_fp12_a00bc0(curve, gen = Long01Sequence)
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test "Sparse 𝔽p12/𝔽p6 resulting from cb00a0 line function":
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proc test_fp12_cb00a0(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == M_Twist:
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for _ in 0 ..< Iters:
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var a = rng.random_elem(Fp12[C], gen)
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var a2 = a
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var x = rng.random_elem(Fp2[C], gen)
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var y = rng.random_elem(Fp2[C], gen)
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var z = rng.random_elem(Fp2[C], gen)
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let line = Line[Fp2[C]](a: x, b: y, c: z)
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let b = Fp12[C](coords: [
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Fp6[C](coords: [ z, y, Fp2[C]()]),
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Fp6[C](coords: [Fp2[C](), x, Fp2[C]()])
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])
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a *= b
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a2.mul_sparse_by_line_cb00a0(line)
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check: bool(a == a2)
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staticFor(curve, TestCurves):
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test_fp12_cb00a0(curve, gen = Uniform)
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test_fp12_cb00a0(curve, gen = HighHammingWeight)
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test_fp12_cb00a0(curve, gen = Long01Sequence)
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test "Somewhat-sparse 𝔽p12/𝔽p6 resulting from a00bc0*a00bc0 line functions (D-twist only)":
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proc test_fp12_a00bc0_a00bc0(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == D_Twist:
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for _ in 0 ..< Iters:
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var x0 = rng.random_elem(Fp2[C], gen)
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var y0 = rng.random_elem(Fp2[C], gen)
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var z0 = rng.random_elem(Fp2[C], gen)
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let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
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let f0 = Fp12[C]( coords: [
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Fp6[C](coords: [ x0, Fp2[C](), Fp2[C]()]),
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Fp6[C](coords: [ y0, z0, Fp2[C]()])
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])
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var x1 = rng.random_elem(Fp2[C], gen)
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var y1 = rng.random_elem(Fp2[C], gen)
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var z1 = rng.random_elem(Fp2[C], gen)
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let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
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let f1 = Fp12[C]( coords: [
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Fp6[C](coords: [ x1, Fp2[C](), Fp2[C]()]),
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Fp6[C](coords: [ y1, z1, Fp2[C]()])
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])
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var r: Fp12[C]
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r.prod(f0, f1)
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var rl: Fp12[C]
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rl.prod_x00yz0_x00yz0_into_abcdefghij00(line0, line1)
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check: bool(r == rl)
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staticFor(curve, TestCurves):
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test_fp12_a00bc0_a00bc0(curve, gen = Uniform)
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test_fp12_a00bc0_a00bc0(curve, gen = HighHammingWeight)
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test_fp12_a00bc0_a00bc0(curve, gen = Long01Sequence)
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test "Somewhat-sparse 𝔽p12/𝔽p6 resulting from cb00a0*cb00a0 line functions (M-twist only)":
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proc test_fp12_cb00a0_cb00a0(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == M_Twist:
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for _ in 0 ..< Iters:
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var x0 = rng.random_elem(Fp2[C], gen)
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var y0 = rng.random_elem(Fp2[C], gen)
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var z0 = rng.random_elem(Fp2[C], gen)
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let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
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let f0 = Fp12[C](coords: [
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Fp6[C](coords: [ z0, y0, Fp2[C]()]),
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Fp6[C](coords: [Fp2[C](), x0, Fp2[C]()])
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])
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var x1 = rng.random_elem(Fp2[C], gen)
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var y1 = rng.random_elem(Fp2[C], gen)
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var z1 = rng.random_elem(Fp2[C], gen)
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let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
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let f1 = Fp12[C](coords: [
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Fp6[C](coords: [ z1, y1, Fp2[C]()]),
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Fp6[C](coords: [Fp2[C](), x1, Fp2[C]()])
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])
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var r: Fp12[C]
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r.prod(f0, f1)
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var rl: Fp12[C]
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rl.prod_zy00x0_zy00x0_into_abcdef00ghij(line0, line1)
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check: bool(r == rl)
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staticFor(curve, TestCurves):
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test_fp12_cb00a0_cb00a0(curve, gen = Uniform)
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test_fp12_cb00a0_cb00a0(curve, gen = HighHammingWeight)
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test_fp12_cb00a0_cb00a0(curve, gen = Long01Sequence)
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test "Somewhat-sparse 𝔽p12/𝔽p6 mul by the product a00bc0*a00bc0 of line functions (D-twist only)":
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proc test_fp12_abcdefghij00(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == D_Twist:
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for _ in 0 ..< Iters:
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var x0 = rng.random_elem(Fp2[C], gen)
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var y0 = rng.random_elem(Fp2[C], gen)
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var z0 = rng.random_elem(Fp2[C], gen)
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let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
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let f0 = Fp12[C]( coords: [
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Fp6[C](coords: [ x0, Fp2[C](), Fp2[C]()]),
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Fp6[C](coords: [ y0, z0, Fp2[C]()])
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])
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var x1 = rng.random_elem(Fp2[C], gen)
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var y1 = rng.random_elem(Fp2[C], gen)
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var z1 = rng.random_elem(Fp2[C], gen)
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let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
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let f1 = Fp12[C]( coords: [
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Fp6[C](coords: [ x1, Fp2[C](), Fp2[C]()]),
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Fp6[C](coords: [ y1, z1, Fp2[C]()])
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])
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var r: Fp12[C]
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r.prod(f0, f1)
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var rl: Fp12[C]
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rl.prod_x00yz0_x00yz0_into_abcdefghij00(line0, line1)
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var f = rng.random_elem(Fp12[C], gen)
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var f2 = f
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f *= rl
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f2.mul_sparse_by_abcdefghij00_quad_over_cube(rl)
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check: bool(f == f2)
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staticFor(curve, TestCurves):
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test_fp12_abcdefghij00(curve, gen = Uniform)
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test_fp12_abcdefghij00(curve, gen = HighHammingWeight)
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test_fp12_abcdefghij00(curve, gen = Long01Sequence)
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test "Somewhat-sparse 𝔽p12/𝔽p6 mul by the product (cb00a0*cb00a0) of line functions (M-twist only)":
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proc test_fp12_abcdef00ghij(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == M_Twist:
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for _ in 0 ..< Iters:
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var x0 = rng.random_elem(Fp2[C], gen)
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var y0 = rng.random_elem(Fp2[C], gen)
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var z0 = rng.random_elem(Fp2[C], gen)
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let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
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let f0 = Fp12[C](coords: [
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Fp6[C](coords: [ z0, y0, Fp2[C]()]),
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Fp6[C](coords: [Fp2[C](), x0, Fp2[C]()])
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])
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var x1 = rng.random_elem(Fp2[C], gen)
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var y1 = rng.random_elem(Fp2[C], gen)
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var z1 = rng.random_elem(Fp2[C], gen)
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let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
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let f1 = Fp12[C](coords: [
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Fp6[C](coords: [ z1, y1, Fp2[C]()]),
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Fp6[C](coords: [Fp2[C](), x1, Fp2[C]()])
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])
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var r: Fp12[C]
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r.prod(f0, f1)
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var rl: Fp12[C]
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rl.prod_zy00x0_zy00x0_into_abcdef00ghij(line0, line1)
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var f = rng.random_elem(Fp12[C], gen)
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var f2 = f
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f *= rl
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f2.mul_sparse_by_abcdef00ghij_quad_over_cube(rl)
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check: bool(f == f2)
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staticFor(curve, TestCurves):
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test_fp12_abcdef00ghij(curve, gen = Uniform)
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test_fp12_abcdef00ghij(curve, gen = HighHammingWeight)
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test_fp12_abcdef00ghij(curve, gen = Long01Sequence)
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else: # =========== Towering 𝔽p12/𝔽p4 ======================================
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static: doAssert Fp12[BN254_Snarks]().c0.typeof is Fp4
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test "Sparse 𝔽p12/𝔽p4 resulting from ca00b0 line function (M-twist only)":
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proc test_fp12_ca00b0(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == M_Twist:
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for _ in 0 ..< Iters:
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var a = rng.random_elem(Fp12[C], gen)
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var a2 = a
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var x = rng.random_elem(Fp2[C], gen)
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var y = rng.random_elem(Fp2[C], gen)
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var z = rng.random_elem(Fp2[C], gen)
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let line = Line[Fp2[C]](a: x, b: y, c: z)
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let b = Fp12[C](
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coords: [
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Fp4[C](coords: [z, x]),
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Fp4[C](),
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Fp4[C](coords: [y, Fp2[C]()])
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]
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)
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a *= b
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a2.mul_sparse_by_line_ca00b0(line)
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check: bool(a == a2)
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staticFor(curve, TestCurves):
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test_fp12_ca00b0(curve, gen = Uniform)
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test_fp12_ca00b0(curve, gen = HighHammingWeight)
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test_fp12_ca00b0(curve, gen = Long01Sequence)
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test "Sparse 𝔽p12/𝔽p4 resulting from xyz000 line function (D-twist only)":
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proc test_fp12_acb000(C: static Curve, gen: static RandomGen) =
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when C.getSexticTwist() == D_Twist:
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for _ in 0 ..< Iters:
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var a = rng.random_elem(Fp12[C], gen)
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var a2 = a
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var x = rng.random_elem(Fp2[C], gen)
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var y = rng.random_elem(Fp2[C], gen)
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var z = rng.random_elem(Fp2[C], gen)
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let line = Line[Fp2[C]](a: x, b: y, c: z)
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let b = Fp12[C](
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coords: [
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Fp4[C](coords: [x, z]),
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Fp4[C](coords: [y, Fp2[C]()]),
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Fp4[C]()
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]
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)
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a *= b
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a2.mul_sparse_by_line_acb000(line)
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check: bool(a == a2)
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staticFor(curve, TestCurves):
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test_fp12_acb000(curve, gen = Uniform)
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test_fp12_acb000(curve, gen = HighHammingWeight)
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test_fp12_acb000(curve, gen = Long01Sequence)
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test "Somewhat-sparse 𝔽p12/𝔽p4 resulting from ca00b0*ca00b0 line functions (M-twist only)":
|
||
proc test_fp12_ca00b0_ca00b0(C: static Curve, gen: static RandomGen) =
|
||
when C.getSexticTwist() == M_Twist:
|
||
for _ in 0 ..< Iters:
|
||
var x0 = rng.random_elem(Fp2[C], gen)
|
||
var y0 = rng.random_elem(Fp2[C], gen)
|
||
var z0 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
|
||
let f0 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [z0, x0]),
|
||
Fp4[C](),
|
||
Fp4[C](coords: [y0, Fp2[C]()])
|
||
]
|
||
)
|
||
|
||
var x1 = rng.random_elem(Fp2[C], gen)
|
||
var y1 = rng.random_elem(Fp2[C], gen)
|
||
var z1 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
|
||
let f1 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [z1, x1]),
|
||
Fp4[C](),
|
||
Fp4[C](coords: [y1, Fp2[C]()])
|
||
]
|
||
)
|
||
|
||
var r: Fp12[C]
|
||
r.prod(f0, f1)
|
||
|
||
var rl: Fp12[C]
|
||
rl.prod_zx00y0_zx00y0_into_abcd00efghij(line0, line1)
|
||
|
||
check: bool(r == rl)
|
||
|
||
staticFor(curve, TestCurves):
|
||
test_fp12_ca00b0_ca00b0(curve, gen = Uniform)
|
||
test_fp12_ca00b0_ca00b0(curve, gen = HighHammingWeight)
|
||
test_fp12_ca00b0_ca00b0(curve, gen = Long01Sequence)
|
||
|
||
test "Somewhat-sparse 𝔽p12/𝔽p4 resulting from acb000*acb000 line functions (D-twist only)":
|
||
proc test_fp12_acb000_acb000(C: static Curve, gen: static RandomGen) =
|
||
when C.getSexticTwist() == D_Twist:
|
||
for _ in 0 ..< Iters:
|
||
var x0 = rng.random_elem(Fp2[C], gen)
|
||
var y0 = rng.random_elem(Fp2[C], gen)
|
||
var z0 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
|
||
let f0 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [x0, z0]),
|
||
Fp4[C](coords: [y0, Fp2[C]()]),
|
||
Fp4[C]()
|
||
]
|
||
)
|
||
|
||
var x1 = rng.random_elem(Fp2[C], gen)
|
||
var y1 = rng.random_elem(Fp2[C], gen)
|
||
var z1 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
|
||
let f1 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [x1, z1]),
|
||
Fp4[C](coords: [y1, Fp2[C]()]),
|
||
Fp4[C]()
|
||
]
|
||
)
|
||
|
||
var r: Fp12[C]
|
||
r.prod(f0, f1)
|
||
|
||
var rl: Fp12[C]
|
||
rl.prod_xzy000_xzy000_into_abcdefghij00(line0, line1)
|
||
|
||
check: bool(r == rl)
|
||
|
||
staticFor(curve, TestCurves):
|
||
test_fp12_acb000_acb000(curve, gen = Uniform)
|
||
test_fp12_acb000_acb000(curve, gen = HighHammingWeight)
|
||
test_fp12_acb000_acb000(curve, gen = Long01Sequence)
|
||
|
||
test "Somewhat-sparse 𝔽p12/𝔽p4 mul by the product (acb000*acb000) of line functions (D-twist only)":
|
||
proc test_fp12_abcdefghij00(C: static Curve, gen: static RandomGen) =
|
||
when C.getSexticTwist() == D_Twist:
|
||
for _ in 0 ..< Iters:
|
||
var x0 = rng.random_elem(Fp2[C], gen)
|
||
var y0 = rng.random_elem(Fp2[C], gen)
|
||
var z0 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
|
||
let f0 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [x0, z0]),
|
||
Fp4[C](coords: [y0, Fp2[C]()]),
|
||
Fp4[C]()
|
||
]
|
||
)
|
||
|
||
var x1 = rng.random_elem(Fp2[C], gen)
|
||
var y1 = rng.random_elem(Fp2[C], gen)
|
||
var z1 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
|
||
let f1 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [x1, z1]),
|
||
Fp4[C](coords: [y1, Fp2[C]()]),
|
||
Fp4[C]()
|
||
]
|
||
)
|
||
|
||
var r: Fp12[C]
|
||
r.prod(f0, f1)
|
||
|
||
var rl: Fp12[C]
|
||
rl.prod_xzy000_xzy000_into_abcdefghij00(line0, line1)
|
||
|
||
var f = rng.random_elem(Fp12[C], gen)
|
||
var f2 = f
|
||
|
||
f *= rl
|
||
f2.mul_sparse_by_abcdefghij00_cube_over_quad(rl)
|
||
|
||
check: bool(f == f2)
|
||
|
||
staticFor(curve, TestCurves):
|
||
test_fp12_abcdefghij00(curve, gen = Uniform)
|
||
test_fp12_abcdefghij00(curve, gen = HighHammingWeight)
|
||
test_fp12_abcdefghij00(curve, gen = Long01Sequence)
|
||
|
||
test "Somewhat-sparse 𝔽p12/𝔽p4 mul by the product (ca00b0*ca00b0) of line functions (M-twist only)":
|
||
proc test_fp12_abcdef00ghij(C: static Curve, gen: static RandomGen) =
|
||
when C.getSexticTwist() == M_Twist:
|
||
for _ in 0 ..< Iters:
|
||
var x0 = rng.random_elem(Fp2[C], gen)
|
||
var y0 = rng.random_elem(Fp2[C], gen)
|
||
var z0 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line0 = Line[Fp2[C]](a: x0, b: y0, c: z0)
|
||
let f0 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [z0, x0]),
|
||
Fp4[C](),
|
||
Fp4[C](coords: [y0, Fp2[C]()])
|
||
]
|
||
)
|
||
|
||
var x1 = rng.random_elem(Fp2[C], gen)
|
||
var y1 = rng.random_elem(Fp2[C], gen)
|
||
var z1 = rng.random_elem(Fp2[C], gen)
|
||
|
||
let line1 = Line[Fp2[C]](a: x1, b: y1, c: z1)
|
||
let f1 = Fp12[C](
|
||
coords: [
|
||
Fp4[C](coords: [z1, x1]),
|
||
Fp4[C](),
|
||
Fp4[C](coords: [y1, Fp2[C]()])
|
||
]
|
||
)
|
||
|
||
var r: Fp12[C]
|
||
r.prod(f0, f1)
|
||
|
||
var rl: Fp12[C]
|
||
rl.prod_zx00y0_zx00y0_into_abcd00efghij(line0, line1)
|
||
|
||
var f = rng.random_elem(Fp12[C], gen)
|
||
var f2 = f
|
||
|
||
f *= rl
|
||
f2.mul_sparse_by_abcd00efghij_cube_over_quad(rl)
|
||
|
||
check: bool(f == f2)
|
||
|
||
staticFor(curve, TestCurves):
|
||
test_fp12_abcdef00ghij(curve, gen = Uniform)
|
||
test_fp12_abcdef00ghij(curve, gen = HighHammingWeight)
|
||
test_fp12_abcdef00ghij(curve, gen = Long01Sequence)
|