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operations.cpp
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/* kitty: C++ truth table library
* Copyright (C) 2017-2018 EPFL
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
#include <gtest/gtest.h>
#include <algorithm>
#include <kitty/dynamic_truth_table.hpp>
#include <kitty/operations.hpp>
#include <kitty/static_truth_table.hpp>
#include "utility.hpp"
using namespace kitty;
class OperationsTest : public kitty::testing::Test
{
};
TEST_F( OperationsTest, unary_for_small )
{
EXPECT_EQ( unary_not( from_hex<2>( "8" ) ), from_hex<2>( "7" ) );
EXPECT_EQ( unary_not( from_hex<2>( "6" ) ), from_hex<2>( "9" ) );
EXPECT_EQ( unary_not_if( from_hex<2>( "8" ), true ), from_hex<2>( "7" ) );
EXPECT_EQ( unary_not_if( from_hex<2>( "6" ), true ), from_hex<2>( "9" ) );
EXPECT_EQ( unary_not_if( from_hex<2>( "8" ), false ), from_hex<2>( "8" ) );
EXPECT_EQ( unary_not_if( from_hex<2>( "6" ), false ), from_hex<2>( "6" ) );
}
TEST_F( OperationsTest, binary_for_small )
{
EXPECT_EQ( binary_and( nth<2>( 0 ), nth<2>( 1 ) ), from_hex<2>( "8" ) );
EXPECT_EQ( binary_or( nth<2>( 0 ), nth<2>( 1 ) ), from_hex<2>( "e" ) );
EXPECT_EQ( unary_not( binary_and( nth<2>( 0 ), nth<2>( 1 ) ) ), from_hex<2>( "7" ) );
EXPECT_EQ( unary_not( binary_or( nth<2>( 0 ), nth<2>( 1 ) ) ), from_hex<2>( "1" ) );
EXPECT_EQ( binary_and( nth( 2, 0 ), nth( 2, 1 ) ), from_hex( 2, "8" ) );
EXPECT_EQ( binary_or( nth( 2, 0 ), nth( 2, 1 ) ), from_hex( 2, "e" ) );
EXPECT_EQ( unary_not( binary_and( nth( 2, 0 ), nth( 2, 1 ) ) ), from_hex( 2, "7" ) );
EXPECT_EQ( unary_not( binary_or( nth( 2, 0 ), nth( 2, 1 ) ) ), from_hex( 2, "1" ) );
}
TEST_F( OperationsTest, ternary_for_small )
{
{
const auto t1 = nth<3>( 0 ), t2 = nth<3>( 1 ), t3 = nth<3>( 2 );
const auto maj_expr = binary_or( binary_or( binary_and( t1, t2 ), binary_and( t1, t3 ) ), binary_and( t2, t3 ) );
const auto maj_direct = ternary_majority( t1, t2, t3 );
EXPECT_EQ( maj_expr, from_hex<3>( "e8" ) );
EXPECT_EQ( maj_expr, maj_direct );
const auto ite_expr = binary_or( binary_and( t1, t2 ), binary_and( unary_not( t1 ), t3 ) );
const auto ite_direct = ternary_ite( t1, t2, t3 );
EXPECT_EQ( ite_expr, from_hex<3>( "d8" ) );
EXPECT_EQ( ite_expr, ite_direct );
}
{
const auto t1 = nth( 3, 0 ), t2 = nth( 3, 1 ), t3 = nth( 3, 2 );
const auto maj_expr = binary_or( binary_or( binary_and( t1, t2 ), binary_and( t1, t3 ) ), binary_and( t2, t3 ) );
const auto maj_direct = ternary_majority( t1, t2, t3 );
EXPECT_EQ( maj_expr, from_hex( 3, "e8" ) );
EXPECT_EQ( maj_expr, maj_direct );
const auto ite_expr = binary_or( binary_and( t1, t2 ), binary_and( unary_not( t1 ), t3 ) );
const auto ite_direct = ternary_ite( t1, t2, t3 );
EXPECT_EQ( ite_expr, from_hex( 3, "d8" ) );
EXPECT_EQ( ite_expr, ite_direct );
}
}
TEST_F( OperationsTest, unary_for_large )
{
EXPECT_EQ( unary_not( from_hex<7>( "80000000000000000000000000000000" ) ), from_hex<7>( "7fffffffffffffffffffffffffffffff" ) );
EXPECT_EQ( unary_not( from_hex<7>( "66666666666666666666666666666666" ) ), from_hex<7>( "99999999999999999999999999999999" ) );
EXPECT_EQ( unary_not_if( from_hex<7>( "80000000000000000000000000000000" ), true ), from_hex<7>( "7fffffffffffffffffffffffffffffff" ) );
EXPECT_EQ( unary_not_if( from_hex<7>( "66666666666666666666666666666666" ), true ), from_hex<7>( "99999999999999999999999999999999" ) );
EXPECT_EQ( unary_not_if( from_hex<7>( "80000000000000000000000000000000" ), false ), from_hex<7>( "80000000000000000000000000000000" ) );
EXPECT_EQ( unary_not_if( from_hex<7>( "66666666666666666666666666666666" ), false ), from_hex<7>( "66666666666666666666666666666666" ) );
}
TEST_F( OperationsTest, binary_for_large )
{
{
auto tt = nth<7>( 0 );
for ( auto i = 1; i < 7; ++i )
{
tt = binary_and( tt, nth<7>( i ) );
}
EXPECT_EQ( tt, from_hex<7>( "80000000000000000000000000000000" ) );
}
{
auto tt = nth( 7, 0 );
for ( auto i = 1; i < 7; ++i )
{
tt = binary_and( tt, nth( 7, i ) );
}
EXPECT_EQ( tt, from_hex( 7, "80000000000000000000000000000000" ) );
}
}
TEST_F( OperationsTest, ternary_for_large )
{
{
const auto t1 = nth<7>( 0 ), t2 = nth<7>( 1 ), t3 = nth<7>( 2 );
const auto maj_expr = binary_or( binary_or( binary_and( t1, t2 ), binary_and( t1, t3 ) ), binary_and( t2, t3 ) );
const auto maj_direct = ternary_majority( t1, t2, t3 );
EXPECT_EQ( maj_expr, maj_direct );
const auto ite_expr = binary_or( binary_and( t1, t2 ), binary_and( unary_not( t1 ), t3 ) );
const auto ite_direct = ternary_ite( t1, t2, t3 );
EXPECT_EQ( ite_expr, ite_direct );
}
{
const auto t1 = nth( 7, 0 ), t2 = nth( 7, 1 ), t3 = nth( 7, 2 );
const auto maj_expr = binary_or( binary_or( binary_and( t1, t2 ), binary_and( t1, t3 ) ), binary_and( t2, t3 ) );
const auto maj_direct = ternary_majority( t1, t2, t3 );
EXPECT_EQ( maj_expr, maj_direct );
const auto ite_expr = binary_or( binary_and( t1, t2 ), binary_and( unary_not( t1 ), t3 ) );
const auto ite_direct = ternary_ite( t1, t2, t3 );
EXPECT_EQ( ite_expr, ite_direct );
}
}
TEST_F( OperationsTest, comparisons )
{
EXPECT_TRUE( equal( from_hex<3>( "e8" ), from_hex<3>( "e8" ) ) );
EXPECT_TRUE( equal( from_hex( 3, "e8" ), from_hex( 3, "e8" ) ) );
EXPECT_TRUE( less_than( from_hex<3>( "e5" ), from_hex<3>( "f6" ) ) );
EXPECT_TRUE( less_than( from_hex<3>( "e5" ), from_hex<3>( "f5" ) ) );
EXPECT_TRUE( less_than( from_hex<3>( "e5" ), from_hex<3>( "f4" ) ) );
EXPECT_TRUE( less_than( from_hex<3>( "e5" ), from_hex<3>( "e6" ) ) );
EXPECT_FALSE( less_than( from_hex<3>( "e5" ), from_hex<3>( "e5" ) ) );
EXPECT_FALSE( less_than( from_hex<3>( "e5" ), from_hex<3>( "e4" ) ) );
EXPECT_FALSE( less_than( from_hex<3>( "e5" ), from_hex<3>( "d6" ) ) );
EXPECT_FALSE( less_than( from_hex<3>( "e5" ), from_hex<3>( "d5" ) ) );
EXPECT_FALSE( less_than( from_hex<3>( "e5" ), from_hex<3>( "d4" ) ) );
EXPECT_TRUE( less_than( from_hex( 3, "e5" ), from_hex( 3, "f6" ) ) );
EXPECT_TRUE( less_than( from_hex( 3, "e5" ), from_hex( 3, "f5" ) ) );
EXPECT_TRUE( less_than( from_hex( 3, "e5" ), from_hex( 3, "f4" ) ) );
EXPECT_TRUE( less_than( from_hex( 3, "e5" ), from_hex( 3, "e6" ) ) );
EXPECT_FALSE( less_than( from_hex( 3, "e5" ), from_hex( 3, "e5" ) ) );
EXPECT_FALSE( less_than( from_hex( 3, "e5" ), from_hex( 3, "e4" ) ) );
EXPECT_FALSE( less_than( from_hex( 3, "e5" ), from_hex( 3, "d6" ) ) );
EXPECT_FALSE( less_than( from_hex( 3, "e5" ), from_hex( 3, "d5" ) ) );
EXPECT_FALSE( less_than( from_hex( 3, "e5" ), from_hex( 3, "d4" ) ) );
EXPECT_TRUE( equal( from_hex<7>( "e92c774439c72c8955906ef92ecefec9" ), from_hex<7>( "e92c774439c72c8955906ef92ecefec9" ) ) );
EXPECT_TRUE( equal( from_hex( 7, "e92c774439c72c8955906ef92ecefec9" ), from_hex( 7, "e92c774439c72c8955906ef92ecefec9" ) ) );
EXPECT_TRUE( less_than( from_hex<7>( "e92c774439c72c8955906ef92ecefec9" ), from_hex<7>( "e92c774439c72c8955906ef92edefec9" ) ) );
EXPECT_FALSE( less_than( from_hex<7>( "e92c774439c72c8955906ef92ecefec9" ), from_hex<7>( "e92c774439c72c8955906ef92ebefec9" ) ) );
EXPECT_TRUE( less_than( from_hex( 7, "e92c774439c72c8955906ef92ecefec9" ), from_hex( 7, "e92c774439c72c8955906ef92edefec9" ) ) );
EXPECT_FALSE( less_than( from_hex( 7, "e92c774439c72c8955906ef92ecefec9" ), from_hex( 7, "e92c774439c72c8955906ef92ebefec9" ) ) );
}
TEST_F( OperationsTest, support )
{
EXPECT_TRUE( is_const0( from_hex<0>( "0" ) ) );
EXPECT_TRUE( is_const0( from_hex<1>( "0" ) ) );
EXPECT_TRUE( is_const0( from_hex<2>( "0" ) ) );
EXPECT_TRUE( is_const0( from_hex<3>( "00" ) ) );
EXPECT_TRUE( is_const0( from_hex<4>( "0000" ) ) );
EXPECT_TRUE( is_const0( from_hex<5>( "00000000" ) ) );
EXPECT_TRUE( is_const0( from_hex<6>( "0000000000000000" ) ) );
EXPECT_TRUE( is_const0( from_hex<7>( "00000000000000000000000000000000" ) ) );
EXPECT_TRUE( is_const0( from_hex<8>( "0000000000000000000000000000000000000000000000000000000000000000" ) ) );
EXPECT_TRUE( has_var( from_hex<3>( "77" ), 0 ) );
EXPECT_TRUE( has_var( from_hex<3>( "77" ), 1 ) );
EXPECT_TRUE( !has_var( from_hex<3>( "77" ), 2 ) );
EXPECT_TRUE( has_var( from_hex( 3, "77" ), 0 ) );
EXPECT_TRUE( has_var( from_hex( 3, "77" ), 1 ) );
EXPECT_TRUE( !has_var( from_hex( 3, "77" ), 2 ) );
for ( auto i = 0; i < 8; ++i )
{
EXPECT_EQ( has_var( from_hex<8>( "3333333333cc33cc3333333333cc33cc33cc33cccccccccc33cc33cccccccccc" ), i ), i % 2 == 1 );
}
for ( auto i = 0; i < 8; ++i )
{
EXPECT_EQ( has_var( from_hex( 8, "3333333333cc33cc3333333333cc33cc33cc33cccccccccc33cc33cccccccccc" ), i ), i % 2 == 1 );
}
}
TEST_F( OperationsTest, next )
{
EXPECT_EQ( next( from_hex<3>( "00" ) ), from_hex<3>( "01" ) );
EXPECT_EQ( next( from_hex<3>( "ab" ) ), from_hex<3>( "ac" ) );
EXPECT_EQ( next( from_hex<3>( "ff" ) ), from_hex<3>( "00" ) );
EXPECT_EQ( next( from_hex( 3, "00" ) ), from_hex( 3, "01" ) );
EXPECT_EQ( next( from_hex( 3, "ab" ) ), from_hex( 3, "ac" ) );
EXPECT_EQ( next( from_hex( 3, "ff" ) ), from_hex( 3, "00" ) );
EXPECT_EQ( next( from_hex<7>( "00000000000000000000000000000000" ) ), from_hex<7>( "00000000000000000000000000000001" ) );
EXPECT_EQ( next( from_hex<7>( "aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb" ) ), from_hex<7>( "aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbc" ) );
EXPECT_EQ( next( from_hex<7>( "ffffffffffffffffffffffffffffffff" ) ), from_hex<7>( "00000000000000000000000000000000" ) );
EXPECT_EQ( next( from_hex( 7, "00000000000000000000000000000000" ) ), from_hex( 7, "00000000000000000000000000000001" ) );
EXPECT_EQ( next( from_hex( 7, "aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb" ) ), from_hex( 7, "aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbc" ) );
EXPECT_EQ( next( from_hex( 7, "ffffffffffffffffffffffffffffffff" ) ), from_hex( 7, "00000000000000000000000000000000" ) );
}
TEST_F( OperationsTest, cofactors )
{
EXPECT_EQ( cofactor0( from_hex<3>( "e8" ), 2 ), from_hex<3>( "88" ) );
EXPECT_EQ( cofactor0( from_hex<3>( "e8" ), 1 ), from_hex<3>( "a0" ) );
EXPECT_EQ( cofactor0( from_hex<3>( "e8" ), 0 ), from_hex<3>( "c0" ) );
EXPECT_EQ( cofactor0( from_hex( 3, "e8" ), 2 ), from_hex( 3, "88" ) );
EXPECT_EQ( cofactor0( from_hex( 3, "e8" ), 1 ), from_hex( 3, "a0" ) );
EXPECT_EQ( cofactor0( from_hex( 3, "e8" ), 0 ), from_hex( 3, "c0" ) );
// Co-factors of [(<abc>d){<efg>h}]
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 0 ), from_hex<8>( "3fff3fff3fff3fff3fff3fff3fff3fff3fff3fff3fffc0003fffc000c000c000" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 1 ), from_hex<8>( "5fff5fff5fff5fff5fff5fff5fff5fff5fff5fff5fffa0005fffa000a000a000" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 2 ), from_hex<8>( "77ff77ff77ff77ff77ff77ff77ff77ff77ff77ff77ff880077ff880088008800" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 3 ), from_hex<8>( "ffffffffffffffffffffffffffffffffffffffffffff0000ffff000000000000" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 4 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800e800e800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 5 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 6 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800e80017ffe800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 7 ), from_hex<8>( "17ff17ff17ffe80017ffe800e800e80017ff17ff17ffe80017ffe800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 0 ), from_hex( 8, "3fff3fff3fff3fff3fff3fff3fff3fff3fff3fff3fffc0003fffc000c000c000" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 1 ), from_hex( 8, "5fff5fff5fff5fff5fff5fff5fff5fff5fff5fff5fffa0005fffa000a000a000" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 2 ), from_hex( 8, "77ff77ff77ff77ff77ff77ff77ff77ff77ff77ff77ff880077ff880088008800" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 3 ), from_hex( 8, "ffffffffffffffffffffffffffffffffffffffffffff0000ffff000000000000" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 4 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800e800e800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 5 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 6 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800e80017ffe800e800e800" ) );
EXPECT_EQ( cofactor0( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 7 ), from_hex( 8, "17ff17ff17ffe80017ffe800e800e80017ff17ff17ffe80017ffe800e800e800" ) );
EXPECT_EQ( cofactor1( from_hex<3>( "e8" ), 2 ), from_hex<3>( "ee" ) );
EXPECT_EQ( cofactor1( from_hex<3>( "e8" ), 1 ), from_hex<3>( "fa" ) );
EXPECT_EQ( cofactor1( from_hex<3>( "e8" ), 0 ), from_hex<3>( "fc" ) );
EXPECT_EQ( cofactor1( from_hex( 3, "e8" ), 2 ), from_hex( 3, "ee" ) );
EXPECT_EQ( cofactor1( from_hex( 3, "e8" ), 1 ), from_hex( 3, "fa" ) );
EXPECT_EQ( cofactor1( from_hex( 3, "e8" ), 0 ), from_hex( 3, "fc" ) );
// Co-factors of [(<abc>d){<efg>h}]
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 0 ), from_hex<8>( "03ff03ff03ff03ff03ff03ff03ff03ff03ff03ff03fffc0003fffc00fc00fc00" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 1 ), from_hex<8>( "05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05fffa0005fffa00fa00fa00" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 2 ), from_hex<8>( "11ff11ff11ff11ff11ff11ff11ff11ff11ff11ff11ffee0011ffee00ee00ee00" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 3 ), from_hex<8>( "17171717171717171717171717171717171717171717e8e81717e8e8e8e8e8e8" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 4 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 5 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 6 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ff17ff17ffe800" ) );
EXPECT_EQ( cofactor1( from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 7 ), from_hex<8>( "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 0 ), from_hex( 8, "03ff03ff03ff03ff03ff03ff03ff03ff03ff03ff03fffc0003fffc00fc00fc00" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 1 ), from_hex( 8, "05ff05ff05ff05ff05ff05ff05ff05ff05ff05ff05fffa0005fffa00fa00fa00" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 2 ), from_hex( 8, "11ff11ff11ff11ff11ff11ff11ff11ff11ff11ff11ffee0011ffee00ee00ee00" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 3 ), from_hex( 8, "17171717171717171717171717171717171717171717e8e81717e8e8e8e8e8e8" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 4 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe800e800" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 5 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 6 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ff17ff17ffe800" ) );
EXPECT_EQ( cofactor1( from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ffe80017ffe800e800e800" ), 7 ), from_hex( 8, "17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff17ff" ) );
}
TEST_F( OperationsTest, swap_adjacent_inplace_small )
{
for ( const auto& p : std::vector<std::pair<unsigned, std::string>>{{0u, "bce8"}, {1u, "e6e8"}, {2u, "dea8"}} )
{
auto tt_s = from_hex<4>( "dae8" );
swap_adjacent_inplace( tt_s, p.first );
EXPECT_EQ( tt_s, from_hex<4>( p.second ) );
auto tt_d = from_hex( 4, "dae8" );
swap_adjacent_inplace( tt_d, p.first );
EXPECT_EQ( tt_d, from_hex( 4, p.second ) );
}
}
TEST_F( OperationsTest, swap_adjacent_small )
{
for ( const auto& p : std::vector<std::pair<unsigned, std::string>>{{0u, "bce8"}, {1u, "e6e8"}, {2u, "dea8"}} )
{
EXPECT_EQ( swap_adjacent( from_hex<4>( "dae8" ), p.first ), from_hex<4>( p.second ) );
EXPECT_EQ( swap_adjacent( from_hex( 4, "dae8" ), p.first ), from_hex( 4, p.second ) );
}
}
class OperationsTestSwap : public OperationsTest, public ::testing::WithParamInterface<std::pair<unsigned, std::string>>
{
};
TEST_P( OperationsTestSwap, swap_adjacent_inplace_large )
{
auto tt_s = from_hex<9>( "28e3b8d62855c4b787eef391a93b33297856658b6743aa3cc7e11fde4e9cbf7c98b07f5febfff33bc7ad6f551bc4cbc440453e1bbe24f0cb4f268c6771b55eee" );
swap_adjacent_inplace( tt_s, GetParam().first );
EXPECT_EQ( tt_s, from_hex<9>( GetParam().second ) );
auto tt_d = from_hex( 9, "28e3b8d62855c4b787eef391a93b33297856658b6743aa3cc7e11fde4e9cbf7c98b07f5febfff33bc7ad6f551bc4cbc440453e1bbe24f0cb4f268c6771b55eee" );
swap_adjacent_inplace( tt_d, GetParam().first );
EXPECT_EQ( tt_d, from_hex( 9, GetParam().second ) );
}
TEST_P( OperationsTestSwap, swap_adjacent_large )
{
EXPECT_EQ( swap_adjacent( from_hex<9>( "28e3b8d62855c4b787eef391a93b33297856658b6743aa3cc7e11fde4e9cbf7c98b07f5febfff33bc7ad6f551bc4cbc440453e1bbe24f0cb4f268c6771b55eee" ),
GetParam().first ),
from_hex<9>( GetParam().second ) );
EXPECT_EQ( swap_adjacent( from_hex( 9, "28e3b8d62855c4b787eef391a93b33297856658b6743aa3cc7e11fde4e9cbf7c98b07f5febfff33bc7ad6f551bc4cbc440453e1bbe24f0cb4f268c6771b55eee" ),
GetParam().first ),
from_hex( 9, GetParam().second ) );
}
INSTANTIATE_TEST_CASE_P( OperationsTestSwapInst,
OperationsTestSwap,
::testing::Values( std::make_pair( 0u, "48e5d8b64833a2d787eef591c95d55497836638d6725cc5aa7e11fbe2e9adf7a"
"98d07f3fedfff55da7cb6f331da2ada220235e1dde42f0ad2f468a6771d33eee" ),
std::make_pair( 1u, "28cbacd62855d09f93facf85a92f0f296c5659a35b43aa3cd3c937f672b4bf7c"
"a48c7f77ebffcf2fd3b97b5527d0e3d040513e27be18cce3731ab05b4d9d76fa" ),
std::make_pair( 2u, "2e83bd862585cb478e7ef931a39b32397586685b6473a3acce711dfe49ecb7fc"
"9b8075ffefbff33bca7d65f51cb4ccb4440531ebb2e4fc0b42f686c77b155eee" ),
std::make_pair( 3u, "28b8e3d628c455b787f3ee91a9333b297865568b67aa433cc71fe1de4ebf9c7c"
"987fb05febf3ff3bc76fad551bcbc4c4403e451bbef024cb4f8c2667715eb5ee" ),
std::make_pair( 4u, "28e32855b8d6c4b787eea93bf391332978566743658baa3cc7e14e9c1fdebf7c"
"98b0ebff7f5ff33bc7ad1bc46f55cbc44045be243e1bf0cb4f2671b58c675eee" ),
std::make_pair( 5u, "28e3b8d687eef3912855c4b7a93b33297856658bc7e11fde6743aa3c4e9cbf7c"
"98b07f5fc7ad6f55ebfff33b1bc4cbc440453e1b4f268c67be24f0cb71b55eee" ),
std::make_pair( 6u, "28e3b8d62855c4b77856658b6743aa3c87eef391a93b3329c7e11fde4e9cbf7c"
"98b07f5febfff33b40453e1bbe24f0cbc7ad6f551bc4cbc44f268c6771b55eee" ),
std::make_pair( 7u, "28e3b8d62855c4b787eef391a93b332998b07f5febfff33bc7ad6f551bc4cbc4"
"7856658b6743aa3cc7e11fde4e9cbf7c40453e1bbe24f0cb4f268c6771b55eee" ) ) );
TEST_F( OperationsTest, flip_inplace_small )
{
for ( const auto& p : std::vector<std::pair<unsigned, std::string>>{{0u, "0b34"}, {1u, "0dc2"}, {2u, "7083"}, {3u, "3807"}} )
{
auto tt_s = from_hex<4>( "0738" );
flip_inplace( tt_s, p.first );
EXPECT_EQ( tt_s, from_hex<4>( p.second ) );
auto tt_d = from_hex( 4, "0738" );
flip_inplace( tt_d, p.first );
EXPECT_EQ( tt_d, from_hex( 4, p.second ) );
}
}
TEST_F( OperationsTest, flip_small )
{
for ( const auto& p : std::vector<std::pair<unsigned, std::string>>{{0u, "0b34"}, {1u, "0dc2"}, {2u, "7083"}, {3u, "3807"}} )
{
EXPECT_EQ( flip( from_hex<4>( "0738" ), p.first ), from_hex<4>( p.second ) );
EXPECT_EQ( flip( from_hex( 4, "0738" ), p.first ), from_hex( 4, p.second ) );
}
}
class OperationsTestFlip : public OperationsTest, public ::testing::WithParamInterface<std::pair<unsigned, std::string>>
{
};
TEST_P( OperationsTestFlip, flip_inplace_large )
{
auto tt_s = from_hex<9>( "8725ca41421c7bba0ca86e26347847526fc346d7f3e79e76566a9493fbef11e24f74a07643afd946195f6a372757e045f3bca58f110ef00ebf2d81e80ba5679f" );
flip_inplace( tt_s, GetParam().first );
EXPECT_EQ( tt_s, from_hex<9>( GetParam().second ) );
auto tt_d = from_hex( 9, "8725ca41421c7bba0ca86e26347847526fc346d7f3e79e76566a9493fbef11e24f74a07643afd946195f6a372757e045f3bca58f110ef00ebf2d81e80ba5679f" );
flip_inplace( tt_d, GetParam().first );
EXPECT_EQ( tt_d, from_hex( 9, GetParam().second ) );
}
TEST_P( OperationsTestFlip, flip_large )
{
EXPECT_EQ( flip( from_hex<9>( "8725ca41421c7bba0ca86e26347847526fc346d7f3e79e76566a9493fbef11e24f74a07643afd946195f6a372757e045f3bca58f110ef00ebf2d81e80ba5679f" ),
GetParam().first ),
from_hex<9>( GetParam().second ) );
EXPECT_EQ( flip( from_hex( 9, "8725ca41421c7bba0ca86e26347847526fc346d7f3e79e76566a9493fbef11e24f74a07643afd946195f6a372757e045f3bca58f110ef00ebf2d81e80ba5679f" ),
GetParam().first ),
from_hex( 9, GetParam().second ) );
}
INSTANTIATE_TEST_CASE_P( OperationsTestFlipInst,
OperationsTestFlip,
::testing::Values( std::make_pair( 0u, "4b1ac582812cb7750c549d1938b48ba19fc389ebf3db6db9a9956863f7df22d1"
"8fb850b9835fe68926af953b1babd08af37c5a4f220df00d7f1e42d4075a9b6f" ),
std::make_pair( 1u, "2d853a141843deea03a29b89c1d21d589f3c197dfcbd6bd9599a616cfebf44b8"
"1fd1a0d91caf7619465f9acd8d5db015fce3a52f440bf00bef8724b20ea59d6f" ),
std::make_pair( 2u, "7852ac1424c1b7abc08ae66243877425f63c647d3f7ee96765a64939bffe112e"
"f4470a6734fa9d6491f5a67372750e543fcb5af811e00fe0fbd2188eb05a76f9" ),
std::make_pair( 3u, "258741ca1c42ba7ba80c266e78345247c36fd746e7f3769e6a569394effbe211"
"744f76a0af4346d95f19376a572745e0bcf38fa50e110ef02dbfe881a50b9f67" ),
std::make_pair( 4u, "ca4187257bba421c6e260ca84752347846d76fc39e76f3e79493566a11e2fbef"
"a0764f74d94643af6a37195fe0452757a58ff3bcf00e110e81e8bf2d679f0ba5" ),
std::make_pair( 5u, "421c7bba8725ca41347847520ca86e26f3e79e766fc346d7fbef11e2566a9493"
"43afd9464f74a0762757e045195f6a37110ef00ef3bca58f0ba5679fbf2d81e8" ),
std::make_pair( 6u, "0ca86e26347847528725ca41421c7bba566a9493fbef11e26fc346d7f3e79e76"
"195f6a372757e0454f74a07643afd946bf2d81e80ba5679ff3bca58f110ef00e" ),
std::make_pair( 7u, "6fc346d7f3e79e76566a9493fbef11e28725ca41421c7bba0ca86e2634784752"
"f3bca58f110ef00ebf2d81e80ba5679f4f74a07643afd946195f6a372757e045" ),
std::make_pair( 8u, "4f74a07643afd946195f6a372757e045f3bca58f110ef00ebf2d81e80ba5679f"
"8725ca41421c7bba0ca86e26347847526fc346d7f3e79e76566a9493fbef11e2" ) ) );
TEST_F( OperationsTest, min_base )
{
{
auto tt = from_hex<3>( "a0" ); /* (ac) */
const auto support = min_base_inplace( tt );
EXPECT_EQ( support, std::vector<uint8_t>( {0, 2} ) );
EXPECT_EQ( tt, from_hex<3>( "88" ) );
expand_inplace( tt, support );
EXPECT_EQ( tt, from_hex<3>( "a0" ) );
}
{
auto tt = from_hex<4>( "3c3c" ); /* [bc] */
const auto support = min_base_inplace( tt );
EXPECT_EQ( support, std::vector<uint8_t>( {1, 2} ) );
EXPECT_EQ( tt, from_hex<4>( "6666" ) );
expand_inplace( tt, support );
EXPECT_EQ( tt, from_hex<4>( "3c3c" ) );
}
{
auto tt = from_hex<7>( "ff55ff55ff55ff555555555555555555" ); /* {!a(dg)} */
const auto support = min_base_inplace( tt );
EXPECT_EQ( support, std::vector<uint8_t>( {0, 3, 6} ) );
EXPECT_EQ( tt, from_hex<7>( "d5d5d5d5d5d5d5d5d5d5d5d5d5d5d5d5" ) );
expand_inplace( tt, support );
EXPECT_EQ( tt, from_hex<7>( "ff55ff55ff55ff555555555555555555" ) );
}
}
TEST_F( OperationsTest, extend_to )
{
static_truth_table<9> maj, th_extend;
static_truth_table<8> th;
create_majority( maj );
create_threshold( th, 4 );
extend_to_inplace( th_extend, th );
EXPECT_EQ( cofactor0( maj, 8 ), th_extend );
EXPECT_EQ( extend_to<3>( from_hex<2>( "a" ) ), from_hex<3>( "aa" ) );
EXPECT_EQ( extend_to<3>( from_hex( 2, "a" ) ), from_hex<3>( "aa" ) );
EXPECT_EQ( extend_to( from_hex<2>( "a" ), 3 ), from_hex( 3, "aa" ) );
EXPECT_EQ( extend_to( from_hex( 2, "a" ), 3 ), from_hex( 3, "aa" ) );
}
TEST_F( OperationsTest, extend_to_same )
{
static_truth_table<9> tt1, tt2;
create_random( tt1 );
extend_to_inplace( tt2, tt1 );
EXPECT_EQ( tt1, tt2 );
}
TEST_F( OperationsTest, shrink_to )
{
EXPECT_EQ( shrink_to<2>( from_hex<3>( "aa" ) ), from_hex<2>( "a" ) );
EXPECT_EQ( shrink_to<2>( from_hex<3>( "1a" ) ), from_hex<2>( "a" ) );
EXPECT_EQ( shrink_to<2>( from_hex<2>( "8" ) ), from_hex<2>( "8" ) );
EXPECT_EQ( shrink_to<5>( from_hex<7>( "cafecafecafecafecafecafecafecafe" ) ), from_hex<5>( "cafecafe") );
EXPECT_EQ( shrink_to<2>( from_hex( 3, "aa" ) ), from_hex<2>( "a" ) );
EXPECT_EQ( shrink_to<2>( from_hex( 3, "1a" ) ), from_hex<2>( "a" ) );
EXPECT_EQ( shrink_to<2>( from_hex( 2, "8" ) ), from_hex<2>( "8" ) );
EXPECT_EQ( shrink_to<5>( from_hex( 7, "cafecafecafecafecafecafecafecafe" ) ), from_hex<5>( "cafecafe") );
EXPECT_EQ( shrink_to( from_hex( 3, "aa" ), 2 ), from_hex( 2, "a" ) );
EXPECT_EQ( shrink_to( from_hex( 3, "1a" ), 2 ), from_hex( 2, "a" ) );
EXPECT_EQ( shrink_to( from_hex( 2, "8" ), 2 ), from_hex( 2, "8" ) );
EXPECT_EQ( shrink_to( from_hex( 7, "cafecafecafecafecafecafecafecafe" ), 5 ), from_hex( 5, "cafecafe") );
}
TEST_F( OperationsTest, shift_left )
{
EXPECT_EQ( shift_left( from_hex<3>( "e8"), 1 ), from_hex<3>( "d0" ) );
EXPECT_EQ( shift_left( from_hex<4>( "cafe"), 4 ), from_hex<4>( "afe0" ) );
EXPECT_EQ( shift_left( from_hex<7>( "cafeaffe12345678acabacab91837465" ), 4 ), from_hex<7>( "afeaffe12345678acabacab918374650" ) );
EXPECT_EQ( shift_left( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 8 ), from_hex( 7, "feaffe12345678acabacab9183746500" ) );
EXPECT_EQ( shift_left( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 64 ), from_hex( 7, "acabacab918374650000000000000000" ) );
EXPECT_EQ( shift_left( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 0 ), from_hex( 7, "cafeaffe12345678acabacab91837465" ) );
EXPECT_EQ( shift_left( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 128 ), from_hex( 7, "00000000000000000000000000000000" ) );
}
TEST_F( OperationsTest, shift_right )
{
EXPECT_EQ( shift_right( from_hex<3>( "e8"), 1 ), from_hex<3>( "74" ) );
EXPECT_EQ( shift_right( from_hex<4>( "cafe"), 4 ), from_hex<4>( "0caf" ) );
EXPECT_EQ( shift_right( from_hex<7>( "cafeaffe12345678acabacab91837465" ), 4 ), from_hex<7>( "0cafeaffe12345678acabacab9183746" ) );
EXPECT_EQ( shift_right( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 8 ), from_hex( 7, "00cafeaffe12345678acabacab918374" ) );
EXPECT_EQ( shift_right( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 64 ), from_hex( 7, "0000000000000000cafeaffe12345678" ) );
EXPECT_EQ( shift_right( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 0 ), from_hex( 7, "cafeaffe12345678acabacab91837465" ) );
EXPECT_EQ( shift_right( from_hex( 7, "cafeaffe12345678acabacab91837465" ), 128 ), from_hex( 7, "00000000000000000000000000000000" ) );
}
TEST_F( OperationsTest, majority7 )
{
const auto a = nth<7>( 0 );
const auto b = nth<7>( 1 );
const auto c = nth<7>( 2 );
const auto d = nth<7>( 3 );
const auto e = nth<7>( 4 );
const auto f = nth<7>( 5 );
const auto g = nth<7>( 6 );
static_truth_table<7> maj7;
create_majority( maj7 );
auto special_func = []( auto a, auto b, auto c, auto d, auto e, auto f ) {
return ternary_majority( ternary_majority( a, b, c ), d, ternary_majority( e, f, ternary_majority( a, b, c ) ) );
};
// special_func is symmetric in variables {a, b, c}
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, c, b, d, e, f ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( b, a, c, d, e, f ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( b, c, a, d, e, f ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( c, a, b, d, e, f ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( c, b, a, d, e, f ) );
// special func is symmetric in variables {d, e, f}
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, b, c, d, f, e ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, b, c, e, d, f ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, b, c, e, f, d ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, b, c, f, d, e ) );
EXPECT_EQ( special_func( a, b, c, d, e, f ), special_func( a, b, c, f, e, d ) );
const auto sf0 = special_func( a, b, c, d, e, f );
const auto sf1 = special_func( d, e, f, a, b, c );
const auto one = ~maj7.construct();
const auto th0 = cofactor0( maj7, 6 ); /* threshold-4 function (hamming weight >= 4) */
const auto th1 = cofactor1( maj7, 6 ); /* threshold-3 function (hamming weight >= 3) */
const auto te = th1 & ~th0; /* =3 function (hamming weight = 3) */
EXPECT_EQ( ~th0 | ( sf0 & sf1 ), one );
EXPECT_EQ( th0 | ( ~sf0 | ~sf1 ), one );
EXPECT_EQ( ~th1 | ( sf0 | sf1 ), one );
EXPECT_EQ( th1 | ( ~sf0 & ~sf1), one );
const auto factor1 = d ^ e ^ f;
const auto factor2 = a ^ b ^ c;
EXPECT_EQ( sf0, ( factor1 & th1 ) ^ ( ~factor1 & th0 ) );
EXPECT_EQ( sf1, ( factor1 & th0 ) ^ ( ~factor1 & th1 ) );
EXPECT_EQ( sf0, ( factor2 & th0 ) ^ ( ~factor2 & th1 ) );
EXPECT_EQ( sf1, ( factor2 & th1 ) ^ ( ~factor2 & th0 ) );
EXPECT_EQ( sf0, th0 | ( factor1 & te ) );
EXPECT_EQ( sf1, th0 | ( factor2 & te ) );
EXPECT_EQ( ternary_majority( sf0, g, sf1 ), maj7 );
}
template<typename TT>
void majority_decomposition_acw( TT& f1, TT& f2 )
{
/* num_vars is even */
ASSERT_EQ( f1.num_vars() % 2, 0 );
/* k */
auto k = f1.num_vars() >> 1;
dynamic_truth_table lhs( 2 * k - 1 );
create_majority( lhs );
extend_to_inplace( f1, lhs );
dynamic_truth_table rhs1( 2 * k - 1 );
dynamic_truth_table rhs2( 2 * k - 1 );
create_threshold( rhs1, k );
create_threshold( rhs2, k - 2 );
auto rhs1_e = f2.construct();
auto rhs2_e = f2.construct();
extend_to_inplace( rhs1_e, rhs1 );
extend_to_inplace( rhs2_e, rhs2 );
create_nth_var( f2, 2 * k - 1 );
f2 = rhs1_e | ( f2 & rhs2_e );
}
template<typename TT>
void majority_decomposition_even( TT& f1, TT& f2 )
{
/* num_vars is even */
ASSERT_EQ( f1.num_vars() % 2, 0 );
/* k is odd */
auto k = f1.num_vars() >> 1;
ASSERT_EQ( k % 2, 1 );
create_threshold( f1, k );
f2 = f1;
auto eq_k = f1.construct();
create_equals( eq_k, k );
auto factor1 = f1.construct();
auto factor2 = f2.construct();
for ( auto i = 0; i < k; ++i )
{
auto v1 = f1.construct();
create_nth_var( v1, i );
factor1 ^= v1;
auto v2 = f1.construct();
create_nth_var( v2, k + i );
factor2 ^= v2;
}
f1 |= eq_k & factor1;
f2 |= eq_k & factor2;
}
TEST_F( OperationsTest, majority_conjecture_small_acw )
{
constexpr auto k = 4;
constexpr auto n = 2 * k + 1;
static_truth_table<n> maj, f1_e, f2_e;
static_truth_table<n - 1> f1, f2;
create_majority( maj );
majority_decomposition_acw( f1, f2 );
EXPECT_EQ( ternary_majority( extend_to<n>( f1 ), nth<n>( 2 * k ), extend_to<n>( f2 ) ), maj );
}
TEST_F( OperationsTest, majority_conjecture_small )
{
constexpr auto k = 3;
constexpr auto n = 2 * k + 1;
static_truth_table<n> maj, f1_e, f2_e;
static_truth_table<n - 1> f1, f2;
create_majority( maj );
majority_decomposition_even( f1, f2 );
EXPECT_EQ( ternary_majority( extend_to<n>( f1 ), nth<n>( 2 * k ), extend_to<n>( f2 ) ), maj );
}
TEST_F( OperationsTest, majority_odd_conjecture )
{
constexpr auto k = 3;
constexpr auto n = 2 * k + 1;
static_truth_table<n> maj;
create_majority( maj );
/* create f1 */
static_truth_table<n - 2> f1_m3;
create_majority( f1_m3 );
static_truth_table<n - 1> f1;
extend_to_inplace( f1, f1_m3 );
/* create f2 */
static_truth_table<n - 1> f2, rem;
create_threshold( f2, k );
create_equals( rem, k );
f2 |= ~f1 & rem;
auto f2_alt = nth( n - 1, n - 3 );
for ( auto i = 4; i <= n; ++i )
{
f2_alt = ternary_majority( nth( n - 1, n - i ), nth( n - 1, n - 2 ), f2_alt );
}
static_truth_table<n - 1> f2_alt2_p1, f2_alt2_p2;
create_threshold( f2_alt2_p1, k );
create_equals( f2_alt2_p2, k );
auto f2_alt2 = f2_alt2_p1 | ( f2_alt2_p2 & nth<n - 1>( n - 2 ) );
EXPECT_EQ( f2, f2_alt2 );
/* create majority */
static_truth_table<n> f1_e, f2_e;
extend_to_inplace( f1_e, f1 );
extend_to_inplace( f2_e, f2 );
EXPECT_EQ( maj, ternary_majority( nth<n>( n - 1 ), f1_e, f2_e ) );
}