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Optimize 64x64 extended multiplication implementation
Now we use intrinsics when possible, and fallback to optimized implementation in portable C++. The difference is about 4x when we can use intrinsics and about 2x when we cannot. This should speed up our Lemire's algorithm implementation nicely.
This commit is contained in:
Martin Hořeňovský
parent
f181de9df4
commit
d99eb8bec8
@ -14,6 +14,32 @@
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#include <cstdint>
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#include <type_traits>
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// Note: We use the usual enable-disable-autodetect dance here even though
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// we do not support these in CMake configuration options (yet?).
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// It is highly unlikely that we will need to make these actually
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// user-configurable, but this will make it simpler if weend up needing
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// it, and it provides an escape hatch to the users who need it.
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#if defined( __SIZEOF_INT128__ )
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# define CATCH_CONFIG_INTERNAL_UINT128
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#elif defined( _MSC_VER ) && ( defined( _WIN64 ) || defined( _M_ARM64 ) )
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# define CATCH_CONFIG_INTERNAL_MSVC_UMUL128
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#endif
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#if defined( CATCH_CONFIG_INTERNAL_UINT128 ) && \
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!defined( CATCH_CONFIG_NO_UINT128 ) && \
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!defined( CATCH_CONFIG_UINT128 )
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#define CATCH_CONFIG_UINT128
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#endif
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#if defined( CATCH_CONFIG_INTERNAL_MSVC_UMUL128 ) && \
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!defined( CATCH_CONFIG_NO_MSVC_UMUL128 ) && \
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!defined( CATCH_CONFIG_MSVC_UMUL128 )
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# define CATCH_CONFIG_MSVC_UMUL128
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# include <intrin.h>
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# pragma intrinsic( _umul128 )
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#endif
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namespace Catch {
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namespace Detail {
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@ -46,59 +72,52 @@ namespace Catch {
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}
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};
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// Returns 128 bit result of multiplying lhs and rhs
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/**
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* Returns 128 bit result of lhs * rhs using portable C++ code
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*
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* This implementation is almost twice as fast as naive long multiplication,
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* and unlike intrinsic-based approach, it supports constexpr evaluation.
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*/
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constexpr ExtendedMultResult<std::uint64_t>
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extendedMult( std::uint64_t lhs, std::uint64_t rhs ) {
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// We use the simple long multiplication approach for
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// correctness, we can use platform specific builtins
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// for performance later.
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// Split the lhs and rhs into two 32bit "digits", so that we can
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// do 64 bit arithmetic to handle carry bits.
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// 32b 32b 32b 32b
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// lhs L1 L2
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// * rhs R1 R2
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// ------------------------
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// | R2 * L2 |
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// | R2 * L1 |
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// | R1 * L2 |
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// | R1 * L1 |
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// -------------------------
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// | a | b | c | d |
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extendedMultPortable(std::uint64_t lhs, std::uint64_t rhs) {
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#define CarryBits( x ) ( x >> 32 )
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#define Digits( x ) ( x & 0xFF'FF'FF'FF )
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std::uint64_t lhs_low = Digits( lhs );
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std::uint64_t rhs_low = Digits( rhs );
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std::uint64_t low_low = ( lhs_low * rhs_low );
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std::uint64_t high_high = CarryBits( lhs ) * CarryBits( rhs );
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auto r2l2 = Digits( rhs ) * Digits( lhs );
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auto r2l1 = Digits( rhs ) * CarryBits( lhs );
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auto r1l2 = CarryBits( rhs ) * Digits( lhs );
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auto r1l1 = CarryBits( rhs ) * CarryBits( lhs );
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// Sum to columns first
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auto d = Digits( r2l2 );
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auto c = CarryBits( r2l2 ) + Digits( r2l1 ) + Digits( r1l2 );
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auto b = CarryBits( r2l1 ) + CarryBits( r1l2 ) + Digits( r1l1 );
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auto a = CarryBits( r1l1 );
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// Propagate carries between columns
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c += CarryBits( d );
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b += CarryBits( c );
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a += CarryBits( b );
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// Remove the used carries
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c = Digits( c );
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b = Digits( b );
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a = Digits( a );
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// We add in carry bits from low-low already
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std::uint64_t high_low =
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( CarryBits( lhs ) * rhs_low ) + CarryBits( low_low );
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// Note that we can add only low bits from high_low, to avoid
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// overflow with large inputs
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std::uint64_t low_high =
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( lhs_low * CarryBits( rhs ) ) + Digits( high_low );
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return { high_high + CarryBits( high_low ) + CarryBits( low_high ),
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( low_high << 32 ) | Digits( low_low ) };
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#undef CarryBits
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#undef Digits
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return {
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a << 32 | b, // upper 64 bits
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c << 32 | d // lower 64 bits
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};
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}
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//! Returns 128 bit result of lhs * rhs
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inline ExtendedMultResult<std::uint64_t>
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extendedMult( std::uint64_t lhs, std::uint64_t rhs ) {
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#if defined( CATCH_CONFIG_UINT128 )
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auto result = __uint128_t( lhs ) * __uint128_t( rhs );
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return { static_cast<std::uint64_t>( result >> 64 ),
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static_cast<std::uint64_t>( result ) };
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#elif defined( CATCH_CONFIG_MSVC_UMUL128 )
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std::uint64_t high;
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std::uint64_t low = _umul128( lhs, rhs, &high );
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return { high, low };
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#else
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return extendedMultPortable( lhs, rhs );
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#endif
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}
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template <typename UInt>
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constexpr ExtendedMultResult<UInt> extendedMult( UInt lhs, UInt rhs ) {
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static_assert( std::is_unsigned<UInt>::value,
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@ -8,6 +8,7 @@
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/internal/catch_random_integer_helpers.hpp>
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#include <random>
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namespace {
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template <typename Int>
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@ -20,6 +21,58 @@ namespace {
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CHECK( extendedMult( b, a ) ==
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ExtendedMultResult<Int>{ upper_result, lower_result } );
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}
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// Simple (and slow) implmentation of extended multiplication for tests
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constexpr Catch::Detail::ExtendedMultResult<std::uint64_t>
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extendedMultNaive( std::uint64_t lhs, std::uint64_t rhs ) {
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// This is a simple long multiplication, where we split lhs and rhs
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// into two 32-bit "digits", so that we can do ops with carry in 64-bits.
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//
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// 32b 32b 32b 32b
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// lhs L1 L2
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// * rhs R1 R2
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// ------------------------
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// | R2 * L2 |
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// | R2 * L1 |
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// | R1 * L2 |
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// | R1 * L1 |
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// -------------------------
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// | a | b | c | d |
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#define CarryBits( x ) ( x >> 32 )
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#define Digits( x ) ( x & 0xFF'FF'FF'FF )
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auto r2l2 = Digits( rhs ) * Digits( lhs );
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auto r2l1 = Digits( rhs ) * CarryBits( lhs );
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auto r1l2 = CarryBits( rhs ) * Digits( lhs );
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auto r1l1 = CarryBits( rhs ) * CarryBits( lhs );
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// Sum to columns first
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auto d = Digits( r2l2 );
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auto c = CarryBits( r2l2 ) + Digits( r2l1 ) + Digits( r1l2 );
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auto b = CarryBits( r2l1 ) + CarryBits( r1l2 ) + Digits( r1l1 );
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auto a = CarryBits( r1l1 );
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// Propagate carries between columns
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c += CarryBits( d );
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b += CarryBits( c );
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a += CarryBits( b );
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// Remove the used carries
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c = Digits( c );
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b = Digits( b );
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a = Digits( a );
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#undef CarryBits
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#undef Digits
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return {
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a << 32 | b, // upper 64 bits
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c << 32 | d // lower 64 bits
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};
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}
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} // namespace
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TEST_CASE( "extendedMult 64x64", "[Integer][approvals]" ) {
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@ -62,6 +115,27 @@ TEST_CASE( "extendedMult 64x64", "[Integer][approvals]" ) {
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0xdf44'2d22'ce48'59b9 );
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}
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TEST_CASE("extendedMult 64x64 - all implementations", "[integer][approvals]") {
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using Catch::Detail::extendedMult;
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using Catch::Detail::extendedMultPortable;
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using Catch::Detail::fillBitsFrom;
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std::random_device rng;
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for (size_t i = 0; i < 100; ++i) {
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auto a = fillBitsFrom<std::uint64_t>( rng );
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auto b = fillBitsFrom<std::uint64_t>( rng );
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CAPTURE( a, b );
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auto naive_ab = extendedMultNaive( a, b );
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REQUIRE( naive_ab == extendedMultNaive( b, a ) );
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REQUIRE( naive_ab == extendedMultPortable( a, b ) );
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REQUIRE( naive_ab == extendedMultPortable( b, a ) );
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REQUIRE( naive_ab == extendedMult( a, b ) );
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REQUIRE( naive_ab == extendedMult( b, a ) );
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}
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}
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TEST_CASE( "SizedUnsignedType helpers", "[integer][approvals]" ) {
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using Catch::Detail::SizedUnsignedType_t;
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using Catch::Detail::DoubleWidthUnsignedType_t;
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