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Support: Write ScaledNumber::getQuotient() and getProduct()

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llvm-svn: 211409
This commit is contained in:
Duncan P. N. Exon Smith 2014-06-20 21:47:47 +00:00
parent 6fde469206
commit db0cbc8b8a
6 changed files with 314 additions and 136 deletions
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51
include/llvm/Analysis/BlockFrequencyInfoImpl.h
View File

@ -77,9 +77,6 @@ public:
return Lg.first + (Lg.second < 0);
}
static std::pair<uint64_t, int16_t> divide64(uint64_t L, uint64_t R);
static std::pair<uint64_t, int16_t> multiply64(uint64_t L, uint64_t R);
static int compare(uint64_t L, uint64_t R, int Shift) {
assert(Shift >= 0);
assert(Shift < 64);
@ -315,8 +312,12 @@ public:
UnsignedFloat inverse() const { return UnsignedFloat(*this).invert(); }
private:
static UnsignedFloat getProduct(DigitsType L, DigitsType R);
static UnsignedFloat getQuotient(DigitsType Dividend, DigitsType Divisor);
static UnsignedFloat getProduct(DigitsType LHS, DigitsType RHS) {
return ScaledNumbers::getProduct(LHS, RHS);
}
static UnsignedFloat getQuotient(DigitsType Dividend, DigitsType Divisor) {
return ScaledNumbers::getQuotient(Dividend, Divisor);
}
std::pair<int32_t, int> lgImpl() const;
static int countLeadingZerosWidth(DigitsType Digits) {
@ -399,46 +400,6 @@ uint64_t UnsignedFloat<DigitsT>::scale(uint64_t N) const {
return UnsignedFloat<uint64_t>(Digits, Exponent).scale(N);
}
template <class DigitsT>
UnsignedFloat<DigitsT> UnsignedFloat<DigitsT>::getProduct(DigitsType L,
DigitsType R) {
// Check for zero.
if (!L || !R)
return getZero();
// Check for numbers that we can compute with 64-bit math.
if (Width <= 32 || (L <= UINT32_MAX && R <= UINT32_MAX))
return adjustToWidth(uint64_t(L) * uint64_t(R), 0);
// Do the full thing.
return UnsignedFloat(multiply64(L, R));
}
template <class DigitsT>
UnsignedFloat<DigitsT> UnsignedFloat<DigitsT>::getQuotient(DigitsType Dividend,
DigitsType Divisor) {
// Check for zero.
if (!Dividend)
return getZero();
if (!Divisor)
return getLargest();
if (Width == 64)
return UnsignedFloat(divide64(Dividend, Divisor));
// We can compute this with 64-bit math.
int Shift = countLeadingZeros64(Dividend);
uint64_t Shifted = uint64_t(Dividend) << Shift;
uint64_t Quotient = Shifted / Divisor;
// If Quotient needs to be shifted, then adjustToWidth will round.
if (Quotient > DigitsLimits::max())
return adjustToWidth(Quotient, -Shift);
// Round based on the value of the next bit.
return getRounded(UnsignedFloat(Quotient, -Shift),
Shifted % Divisor >= getHalf(Divisor));
}
template <class DigitsT>
template <class IntT>
IntT UnsignedFloat<DigitsT>::toInt() const {

76
include/llvm/Support/ScaledNumber.h
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@ -95,6 +95,82 @@ inline std::pair<uint64_t, int16_t> getAdjusted64(uint64_t Digits,
return getAdjusted<uint64_t>(Digits, Scale);
}
/// \brief Multiply two 64-bit integers to create a 64-bit scaled number.
///
/// Implemented with four 64-bit integer multiplies.
std::pair<uint64_t, int16_t> multiply64(uint64_t LHS, uint64_t RHS);
/// \brief Multiply two 32-bit integers to create a 32-bit scaled number.
///
/// Implemented with one 64-bit integer multiply.
template <class DigitsT>
inline std::pair<DigitsT, int16_t> getProduct(DigitsT LHS, DigitsT RHS) {
static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
if (getWidth<DigitsT>() <= 32 || (LHS <= UINT32_MAX && RHS <= UINT32_MAX))
return getAdjusted<DigitsT>(uint64_t(LHS) * RHS);
return multiply64(LHS, RHS);
}
/// \brief Convenience helper for 32-bit product.
inline std::pair<uint32_t, int16_t> getProduct32(uint32_t LHS, uint32_t RHS) {
return getProduct(LHS, RHS);
}
/// \brief Convenience helper for 64-bit product.
inline std::pair<uint64_t, int16_t> getProduct64(uint64_t LHS, uint64_t RHS) {
return getProduct(LHS, RHS);
}
/// \brief Divide two 64-bit integers to create a 64-bit scaled number.
///
/// Implemented with long division.
///
/// \pre \c Dividend and \c Divisor are non-zero.
std::pair<uint64_t, int16_t> divide64(uint64_t Dividend, uint64_t Divisor);
/// \brief Divide two 32-bit integers to create a 32-bit scaled number.
///
/// Implemented with one 64-bit integer divide/remainder pair.
///
/// \pre \c Dividend and \c Divisor are non-zero.
std::pair<uint32_t, int16_t> divide32(uint32_t Dividend, uint32_t Divisor);
/// \brief Divide two 32-bit numbers to create a 32-bit scaled number.
///
/// Implemented with one 64-bit integer divide/remainder pair.
///
/// Returns \c (DigitsT_MAX, INT16_MAX) for divide-by-zero (0 for 0/0).
template <class DigitsT>
std::pair<DigitsT, int16_t> getQuotient(DigitsT Dividend, DigitsT Divisor) {
static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
static_assert(sizeof(DigitsT) == 4 || sizeof(DigitsT) == 8,
"expected 32-bit or 64-bit digits");
// Check for zero.
if (!Dividend)
return std::make_pair(0, 0);
if (!Divisor)
return std::make_pair(std::numeric_limits<DigitsT>::max(), INT16_MAX);
if (getWidth<DigitsT>() == 64)
return divide64(Dividend, Divisor);
return divide32(Dividend, Divisor);
}
/// \brief Convenience helper for 32-bit quotient.
inline std::pair<uint32_t, int16_t> getQuotient32(uint32_t Dividend,
uint32_t Divisor) {
return getQuotient(Dividend, Divisor);
}
/// \brief Convenience helper for 64-bit quotient.
inline std::pair<uint64_t, int16_t> getQuotient64(uint64_t Dividend,
uint64_t Divisor) {
return getQuotient(Dividend, Divisor);
}
} // end namespace ScaledNumbers
} // end namespace llvm

91
lib/Analysis/BlockFrequencyInfoImpl.cpp
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@ -216,97 +216,6 @@ void UnsignedFloatBase::dump(uint64_t D, int16_t E, int Width) {
<< "]";
}
static std::pair<uint64_t, int16_t>
getRoundedFloat(uint64_t N, bool ShouldRound, int64_t Shift) {
if (ShouldRound)
if (!++N)
// Rounding caused an overflow.
return std::make_pair(UINT64_C(1), Shift + 64);
return std::make_pair(N, Shift);
}
std::pair<uint64_t, int16_t> UnsignedFloatBase::divide64(uint64_t Dividend,
uint64_t Divisor) {
// Input should be sanitized.
assert(Divisor);
assert(Dividend);
// Minimize size of divisor.
int16_t Shift = 0;
if (int Zeros = countTrailingZeros(Divisor)) {
Shift -= Zeros;
Divisor >>= Zeros;
}
// Check for powers of two.
if (Divisor == 1)
return std::make_pair(Dividend, Shift);
// Maximize size of dividend.
if (int Zeros = countLeadingZeros64(Dividend)) {
Shift -= Zeros;
Dividend <<= Zeros;
}
// Start with the result of a divide.
uint64_t Quotient = Dividend / Divisor;
Dividend %= Divisor;
// Continue building the quotient with long division.
//
// TODO: continue with largers digits.
while (!(Quotient >> 63) && Dividend) {
// Shift Dividend, and check for overflow.
bool IsOverflow = Dividend >> 63;
Dividend <<= 1;
--Shift;
// Divide.
bool DoesDivide = IsOverflow || Divisor <= Dividend;
Quotient = (Quotient << 1) | uint64_t(DoesDivide);
Dividend -= DoesDivide ? Divisor : 0;
}
// Round.
if (Dividend >= getHalf(Divisor))
if (!++Quotient)
// Rounding caused an overflow in Quotient.
return std::make_pair(UINT64_C(1), Shift + 64);
return getRoundedFloat(Quotient, Dividend >= getHalf(Divisor), Shift);
}
std::pair<uint64_t, int16_t> UnsignedFloatBase::multiply64(uint64_t L,
uint64_t R) {
// Separate into two 32-bit digits (U.L).
uint64_t UL = L >> 32, LL = L & UINT32_MAX, UR = R >> 32, LR = R & UINT32_MAX;
// Compute cross products.
uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
// Sum into two 64-bit digits.
uint64_t Upper = P1, Lower = P4;
auto addWithCarry = [&](uint64_t N) {
uint64_t NewLower = Lower + (N << 32);
Upper += (N >> 32) + (NewLower < Lower);
Lower = NewLower;
};
addWithCarry(P2);
addWithCarry(P3);
// Check whether the upper digit is empty.
if (!Upper)
return std::make_pair(Lower, 0);
// Shift as little as possible to maximize precision.
unsigned LeadingZeros = countLeadingZeros64(Upper);
int16_t Shift = 64 - LeadingZeros;
if (LeadingZeros)
Upper = Upper << LeadingZeros | Lower >> Shift;
bool ShouldRound = Shift && (Lower & UINT64_C(1) << (Shift - 1));
return getRoundedFloat(Upper, ShouldRound, Shift);
}
//===----------------------------------------------------------------------===//
//
// BlockMass implementation.

1
lib/Support/CMakeLists.txt
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@ -42,6 +42,7 @@ add_llvm_library(LLVMSupport
PluginLoader.cpp
PrettyStackTrace.cpp
Regex.cpp
ScaledNumber.cpp
SmallPtrSet.cpp
SmallVector.cpp
SourceMgr.cpp

119
lib/Support/ScaledNumber.cpp Normal file
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@ -0,0 +1,119 @@
//==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Implementation of some scaled number algorithms.
//
//===----------------------------------------------------------------------===//
#include "llvm/Support/ScaledNumber.h"
using namespace llvm;
using namespace llvm::ScaledNumbers;
std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
uint64_t RHS) {
// Separate into two 32-bit digits (U.L).
auto getU = [](uint64_t N) { return N >> 32; };
auto getL = [](uint64_t N) { return N & UINT32_MAX; };
uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS);
// Compute cross products.
uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
// Sum into two 64-bit digits.
uint64_t Upper = P1, Lower = P4;
auto addWithCarry = [&](uint64_t N) {
uint64_t NewLower = Lower + (getL(N) << 32);
Upper += getU(N) + (NewLower < Lower);
Lower = NewLower;
};
addWithCarry(P2);
addWithCarry(P3);
// Check whether the upper digit is empty.
if (!Upper)
return std::make_pair(Lower, 0);
// Shift as little as possible to maximize precision.
unsigned LeadingZeros = countLeadingZeros(Upper);
int Shift = 64 - LeadingZeros;
if (LeadingZeros)
Upper = Upper << LeadingZeros | Lower >> Shift;
return getRounded(Upper, Shift,
Shift && (Lower & UINT64_C(1) << (Shift - 1)));
}
static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
uint32_t Divisor) {
assert(Dividend && "expected non-zero dividend");
assert(Divisor && "expected non-zero divisor");
// Use 64-bit math and canonicalize the dividend to gain precision.
uint64_t Dividend64 = Dividend;
int Shift = 0;
if (int Zeros = countLeadingZeros(Dividend64)) {
Shift -= Zeros;
Dividend64 <<= Zeros;
}
uint64_t Quotient = Dividend64 / Divisor;
uint64_t Remainder = Dividend64 % Divisor;
// If Quotient needs to be shifted, leave the rounding to getAdjusted().
if (Quotient > UINT32_MAX)
return getAdjusted<uint32_t>(Quotient, Shift);
// Round based on the value of the next bit.
return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
}
std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
uint64_t Divisor) {
assert(Dividend && "expected non-zero dividend");
assert(Divisor && "expected non-zero divisor");
// Minimize size of divisor.
int Shift = 0;
if (int Zeros = countTrailingZeros(Divisor)) {
Shift -= Zeros;
Divisor >>= Zeros;
}
// Check for powers of two.
if (Divisor == 1)
return std::make_pair(Dividend, Shift);
// Maximize size of dividend.
if (int Zeros = countLeadingZeros(Dividend)) {
Shift -= Zeros;
Dividend <<= Zeros;
}
// Start with the result of a divide.
uint64_t Quotient = Dividend / Divisor;
Dividend %= Divisor;
// Continue building the quotient with long division.
while (!(Quotient >> 63) && Dividend) {
// Shift Dividend and check for overflow.
bool IsOverflow = Dividend >> 63;
Dividend <<= 1;
--Shift;
// Get the next bit of Quotient.
Quotient <<= 1;
if (IsOverflow || Divisor <= Dividend) {
Quotient |= 1;
Dividend -= Divisor;
}
}
return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
}

112
unittests/Support/ScaledNumberTest.cpp
View File

@ -79,4 +79,116 @@ TEST(FloatsTest, getAdjusted) {
EXPECT_EQ(getAdjusted64(UINT64_MAX), SP64(UINT64_MAX, 0));
}
TEST(PositiveFloatTest, getProduct) {
// Zero.
EXPECT_EQ(SP32(0, 0), getProduct32(0, 0));
EXPECT_EQ(SP32(0, 0), getProduct32(0, 1));
EXPECT_EQ(SP32(0, 0), getProduct32(0, 33));
// Basic.
EXPECT_EQ(SP32(6, 0), getProduct32(2, 3));
EXPECT_EQ(SP32(UINT16_MAX / 3 * UINT16_MAX / 5 * 2, 0),
getProduct32(UINT16_MAX / 3, UINT16_MAX / 5 * 2));
// Overflow, no loss of precision.
// ==> 0xf00010 * 0x1001
// ==> 0xf00f00000 + 0x10010
// ==> 0xf00f10010
// ==> 0xf00f1001 * 2^4
EXPECT_EQ(SP32(0xf00f1001, 4), getProduct32(0xf00010, 0x1001));
// Overflow, loss of precision, rounds down.
// ==> 0xf000070 * 0x1001
// ==> 0xf00f000000 + 0x70070
// ==> 0xf00f070070
// ==> 0xf00f0700 * 2^8
EXPECT_EQ(SP32(0xf00f0700, 8), getProduct32(0xf000070, 0x1001));
// Overflow, loss of precision, rounds up.
// ==> 0xf000080 * 0x1001
// ==> 0xf00f000000 + 0x80080
// ==> 0xf00f080080
// ==> 0xf00f0801 * 2^8
EXPECT_EQ(SP32(0xf00f0801, 8), getProduct32(0xf000080, 0x1001));
// Reverse operand order.
EXPECT_EQ(SP32(0, 0), getProduct32(1, 0));
EXPECT_EQ(SP32(0, 0), getProduct32(33, 0));
EXPECT_EQ(SP32(6, 0), getProduct32(3, 2));
EXPECT_EQ(SP32(UINT16_MAX / 3 * UINT16_MAX / 5 * 2, 0),
getProduct32(UINT16_MAX / 5 * 2, UINT16_MAX / 3));
EXPECT_EQ(SP32(0xf00f1001, 4), getProduct32(0x1001, 0xf00010));
EXPECT_EQ(SP32(0xf00f0700, 8), getProduct32(0x1001, 0xf000070));
EXPECT_EQ(SP32(0xf00f0801, 8), getProduct32(0x1001, 0xf000080));
// Round to overflow.
EXPECT_EQ(SP64(UINT64_C(1) << 63, 64),
getProduct64(UINT64_C(10376293541461622786),
UINT64_C(16397105843297379211)));
// Big number with rounding.
EXPECT_EQ(SP64(UINT64_C(9223372036854775810), 64),
getProduct64(UINT64_C(18446744073709551556),
UINT64_C(9223372036854775840)));
}
TEST(PositiveFloatTest, Divide) {
// Zero.
EXPECT_EQ(SP32(0, 0), getQuotient32(0, 0));
EXPECT_EQ(SP32(0, 0), getQuotient32(0, 1));
EXPECT_EQ(SP32(0, 0), getQuotient32(0, 73));
EXPECT_EQ(SP32(UINT32_MAX, INT16_MAX), getQuotient32(1, 0));
EXPECT_EQ(SP32(UINT32_MAX, INT16_MAX), getQuotient32(6, 0));
// Powers of two.
EXPECT_EQ(SP32(1u << 31, -31), getQuotient32(1, 1));
EXPECT_EQ(SP32(1u << 31, -30), getQuotient32(2, 1));
EXPECT_EQ(SP32(1u << 31, -33), getQuotient32(4, 16));
EXPECT_EQ(SP32(7u << 29, -29), getQuotient32(7, 1));
EXPECT_EQ(SP32(7u << 29, -30), getQuotient32(7, 2));
EXPECT_EQ(SP32(7u << 29, -33), getQuotient32(7, 16));
// Divide evenly.
EXPECT_EQ(SP32(3u << 30, -30), getQuotient32(9, 3));
EXPECT_EQ(SP32(9u << 28, -28), getQuotient32(63, 7));
// Divide unevenly.
EXPECT_EQ(SP32(0xaaaaaaab, -33), getQuotient32(1, 3));
EXPECT_EQ(SP32(0xd5555555, -31), getQuotient32(5, 3));
// 64-bit division is hard to test, since divide64 doesn't canonicalized its
// output. However, this is the algorithm the implementation uses:
//
// - Shift divisor right.
// - If we have 1 (power of 2), return early -- not canonicalized.
// - Shift dividend left.
// - 64-bit integer divide.
// - If there's a remainder, continue with long division.
//
// TODO: require less knowledge about the implementation in the test.
// Zero.
EXPECT_EQ(SP64(0, 0), getQuotient64(0, 0));
EXPECT_EQ(SP64(0, 0), getQuotient64(0, 1));
EXPECT_EQ(SP64(0, 0), getQuotient64(0, 73));
EXPECT_EQ(SP64(UINT64_MAX, INT16_MAX), getQuotient64(1, 0));
EXPECT_EQ(SP64(UINT64_MAX, INT16_MAX), getQuotient64(6, 0));
// Powers of two.
EXPECT_EQ(SP64(1, 0), getQuotient64(1, 1));
EXPECT_EQ(SP64(2, 0), getQuotient64(2, 1));
EXPECT_EQ(SP64(4, -4), getQuotient64(4, 16));
EXPECT_EQ(SP64(7, 0), getQuotient64(7, 1));
EXPECT_EQ(SP64(7, -1), getQuotient64(7, 2));
EXPECT_EQ(SP64(7, -4), getQuotient64(7, 16));
// Divide evenly.
EXPECT_EQ(SP64(UINT64_C(3) << 60, -60), getQuotient64(9, 3));
EXPECT_EQ(SP64(UINT64_C(9) << 58, -58), getQuotient64(63, 7));
// Divide unevenly.
EXPECT_EQ(SP64(0xaaaaaaaaaaaaaaab, -65), getQuotient64(1, 3));
EXPECT_EQ(SP64(0xd555555555555555, -63), getQuotient64(5, 3));
}
} // end namespace