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// Copyright Catch2 Authors
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.txt or copy at
// https://www.boost.org/LICENSE_1_0.txt)
// SPDX-License-Identifier: BSL-1.0
#include <catch2/catch_test_macros.hpp>
#include <catch2/internal/catch_random_integer_helpers.hpp>
#include <random>
namespace {
template <typename Int>
static void
CommutativeMultCheck( Int a, Int b, Int upper_result, Int lower_result ) {
using Catch::Detail::extendedMult;
using Catch::Detail::ExtendedMultResult;
CHECK( extendedMult( a, b ) ==
ExtendedMultResult<Int>{ upper_result, lower_result } );
CHECK( extendedMult( b, a ) ==
ExtendedMultResult<Int>{ upper_result, lower_result } );
}
// Simple (and slow) implmentation of extended multiplication for tests
constexpr Catch::Detail::ExtendedMultResult<std::uint64_t>
extendedMultNaive( std::uint64_t lhs, std::uint64_t rhs ) {
// This is a simple long multiplication, where we split lhs and rhs
// into two 32-bit "digits", so that we can do ops with carry in 64-bits.
//
// 32b 32b 32b 32b
// lhs L1 L2
// * rhs R1 R2
// ------------------------
// | R2 * L2 |
// | R2 * L1 |
// | R1 * L2 |
// | R1 * L1 |
// -------------------------
// | a | b | c | d |
#define CarryBits( x ) ( x >> 32 )
#define Digits( x ) ( x & 0xFF'FF'FF'FF )
auto r2l2 = Digits( rhs ) * Digits( lhs );
auto r2l1 = Digits( rhs ) * CarryBits( lhs );
auto r1l2 = CarryBits( rhs ) * Digits( lhs );
auto r1l1 = CarryBits( rhs ) * CarryBits( lhs );
// Sum to columns first
auto d = Digits( r2l2 );
auto c = CarryBits( r2l2 ) + Digits( r2l1 ) + Digits( r1l2 );
auto b = CarryBits( r2l1 ) + CarryBits( r1l2 ) + Digits( r1l1 );
auto a = CarryBits( r1l1 );
// Propagate carries between columns
c += CarryBits( d );
b += CarryBits( c );
a += CarryBits( b );
// Remove the used carries
c = Digits( c );
b = Digits( b );
a = Digits( a );
#undef CarryBits
#undef Digits
return {
a << 32 | b, // upper 64 bits
c << 32 | d // lower 64 bits
};
}
} // namespace
TEST_CASE( "extendedMult 64x64", "[Integer][approvals]" ) {
// a x 0 == 0
CommutativeMultCheck<uint64_t>( 0x1234'5678'9ABC'DEFF, 0, 0, 0 );
// bit carried from low half to upper half
CommutativeMultCheck<uint64_t>( uint64_t( 1 ) << 63, 2, 1, 0 );
// bits in upper half on one side, bits in lower half on other side
CommutativeMultCheck<uint64_t>( 0xcdcd'dcdc'0000'0000,
0x0000'0000'aeae'aeae,
0x0000'0000'8c6e'5a77,
0x7391'a588'0000'0000 );
// Some input numbers without interesting patterns
CommutativeMultCheck<uint64_t>( 0xaaaa'aaaa'aaaa'aaaa,
0xbbbb'bbbb'bbbb'bbbb,
0x7d27'd27d'27d2'7d26,
0xd82d'82d8'2d82'd82e );
CommutativeMultCheck<uint64_t>( 0x7d27'd27d'27d2'7d26,
0xd82d'82d8'2d82'd82e,
0x69af'd991'8256'b953,
0x8724'8909'fcb6'8cd4 );
CommutativeMultCheck<uint64_t>( 0xdead'beef'dead'beef,
0xfeed'feed'feed'feef,
0xddbf'680b'2b0c'b558,
0x7a36'b06f'2ce9'6321 );
CommutativeMultCheck<uint64_t>( 0xddbf'680b'2b0c'b558,
0x7a36'b06f'2ce9'6321,
0x69dc'96c9'294b'fc7f,
0xd038'39fa'a3dc'6858 );
CommutativeMultCheck<uint64_t>( 0x61c8'8646'80b5'83eb,
0x61c8'8646'80b5'83eb,
0x2559'92d3'8220'8bbe,
0xdf44'2d22'ce48'59b9 );
}
TEST_CASE("extendedMult 64x64 - all implementations", "[integer][approvals]") {
using Catch::Detail::extendedMult;
using Catch::Detail::extendedMultPortable;
using Catch::Detail::fillBitsFrom;
std::random_device rng;
for (size_t i = 0; i < 100; ++i) {
auto a = fillBitsFrom<std::uint64_t>( rng );
auto b = fillBitsFrom<std::uint64_t>( rng );
CAPTURE( a, b );
auto naive_ab = extendedMultNaive( a, b );
REQUIRE( naive_ab == extendedMultNaive( b, a ) );
REQUIRE( naive_ab == extendedMultPortable( a, b ) );
REQUIRE( naive_ab == extendedMultPortable( b, a ) );
REQUIRE( naive_ab == extendedMult( a, b ) );
REQUIRE( naive_ab == extendedMult( b, a ) );
}
}
TEST_CASE( "SizedUnsignedType helpers", "[integer][approvals]" ) {
using Catch::Detail::SizedUnsignedType_t;
using Catch::Detail::DoubleWidthUnsignedType_t;
STATIC_REQUIRE( sizeof( SizedUnsignedType_t<1> ) == 1 );
STATIC_REQUIRE( sizeof( SizedUnsignedType_t<2> ) == 2 );
STATIC_REQUIRE( sizeof( SizedUnsignedType_t<4> ) == 4 );
STATIC_REQUIRE( sizeof( SizedUnsignedType_t<8> ) == 8 );
STATIC_REQUIRE( sizeof( DoubleWidthUnsignedType_t<std::uint8_t> ) == 2 );
STATIC_REQUIRE( std::is_unsigned<DoubleWidthUnsignedType_t<std::uint8_t>>::value );
STATIC_REQUIRE( sizeof( DoubleWidthUnsignedType_t<std::uint16_t> ) == 4 );
STATIC_REQUIRE( std::is_unsigned<DoubleWidthUnsignedType_t<std::uint16_t>>::value );
STATIC_REQUIRE( sizeof( DoubleWidthUnsignedType_t<std::uint32_t> ) == 8 );
STATIC_REQUIRE( std::is_unsigned<DoubleWidthUnsignedType_t<std::uint32_t>>::value );
}
TEST_CASE( "extendedMult 32x32", "[integer][approvals]" ) {
// a x 0 == 0
CommutativeMultCheck<uint32_t>( 0x1234'5678, 0, 0, 0 );
// bit carried from low half to upper half
CommutativeMultCheck<uint32_t>( uint32_t(1) << 31, 2, 1, 0 );
// bits in upper half on one side, bits in lower half on other side
CommutativeMultCheck<uint32_t>( 0xdcdc'0000, 0x0000'aabb, 0x0000'934b, 0x6cb4'0000 );
// Some input numbers without interesting patterns
CommutativeMultCheck<uint32_t>(
0xaaaa'aaaa, 0xbbbb'bbbb, 0x7d27'd27c, 0x2d82'd82e );
CommutativeMultCheck<uint32_t>(
0x7d27'd27c, 0x2d82'd82e, 0x163f'f7e8, 0xc5b8'7248 );
CommutativeMultCheck<uint32_t>(
0xdead'beef, 0xfeed'feed, 0xddbf'6809, 0x6f8d'e543 );
CommutativeMultCheck<uint32_t>(
0xddbf'6809, 0x6f8d'e543, 0x60a0'e71e, 0x751d'475b );
}
TEST_CASE( "extendedMult 8x8", "[integer][approvals]" ) {
// a x 0 == 0
CommutativeMultCheck<uint8_t>( 0xcd, 0, 0, 0 );
// bit carried from low half to upper half
CommutativeMultCheck<uint8_t>( uint8_t( 1 ) << 7, 2, 1, 0 );
// bits in upper half on one side, bits in lower half on other side
CommutativeMultCheck<uint8_t>( 0x80, 0x03, 0x01, 0x80 );
// Some input numbers without interesting patterns
CommutativeMultCheck<uint8_t>( 0xaa, 0xbb, 0x7c, 0x2e );
CommutativeMultCheck<uint8_t>( 0x7c, 0x2e, 0x16, 0x48 );
CommutativeMultCheck<uint8_t>( 0xdc, 0xcd, 0xb0, 0x2c );
CommutativeMultCheck<uint8_t>( 0xb0, 0x2c, 0x1e, 0x40 );
}
TEST_CASE( "negative and positive signed integers keep their order after transposeToNaturalOrder",
"[integer][approvals]") {
using Catch::Detail::transposeToNaturalOrder;
int32_t negative( -1 );
int32_t positive( 1 );
uint32_t adjusted_negative =
transposeToNaturalOrder<int32_t>( static_cast<uint32_t>( negative ) );
uint32_t adjusted_positive =
transposeToNaturalOrder<int32_t>( static_cast<uint32_t>( positive ) );
REQUIRE( adjusted_negative < adjusted_positive );
REQUIRE( adjusted_positive - adjusted_negative == 2 );
// Conversion has to be reversible
REQUIRE( negative == static_cast<int32_t>( transposeToNaturalOrder<int32_t>(
adjusted_negative ) ) );
REQUIRE( positive == static_cast<int32_t>( transposeToNaturalOrder<int32_t>(
adjusted_positive ) ) );
}
TEST_CASE( "unsigned integers are unchanged by transposeToNaturalOrder",
"[integer][approvals]") {
using Catch::Detail::transposeToNaturalOrder;
uint32_t max = std::numeric_limits<uint32_t>::max();
uint32_t zero = 0;
REQUIRE( max == transposeToNaturalOrder<uint32_t>( max ) );
REQUIRE( zero == transposeToNaturalOrder<uint32_t>( zero ) );
}
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