#define LLVM_SUPPORT_SCALEDNUMBER_H
#include "llvm/Support/MathExtras.h"
-
+#include <algorithm>
#include <cstdint>
#include <limits>
+#include <string>
+#include <tuple>
#include <utility>
namespace llvm {
namespace ScaledNumbers {
+/// \brief Maximum scale; same as APFloat for easy debug printing.
+const int32_t MaxScale = 16383;
+
+/// \brief Maximum scale; same as APFloat for easy debug printing.
+const int32_t MinScale = -16382;
+
/// \brief Get the width of a number.
template <class DigitsT> inline int getWidth() { return sizeof(DigitsT) * 8; }
///
/// Implemented with one 64-bit integer divide/remainder pair.
///
-/// Returns \c (DigitsT_MAX, INT16_MAX) for divide-by-zero (0 for 0/0).
+/// Returns \c (DigitsT_MAX, MaxScale) 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");
if (!Dividend)
return std::make_pair(0, 0);
if (!Divisor)
- return std::make_pair(std::numeric_limits<DigitsT>::max(), INT16_MAX);
+ return std::make_pair(std::numeric_limits<DigitsT>::max(), MaxScale);
if (getWidth<DigitsT>() == 64)
return divide64(Dividend, Divisor);
/// for greater than.
template <class DigitsT>
int compare(DigitsT LDigits, int16_t LScale, DigitsT RDigits, int16_t RScale) {
+ static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
+
// Check for zero.
if (!LDigits)
return RDigits ? -1 : 0;
return -compareImpl(RDigits, LDigits, LScale - RScale);
}
+/// \brief Match scales of two numbers.
+///
+/// Given two scaled numbers, match up their scales. Change the digits and
+/// scales in place. Shift the digits as necessary to form equivalent numbers,
+/// losing precision only when necessary.
+///
+/// If the output value of \c LDigits (\c RDigits) is \c 0, the output value of
+/// \c LScale (\c RScale) is unspecified.
+///
+/// As a convenience, returns the matching scale. If the output value of one
+/// number is zero, returns the scale of the other. If both are zero, which
+/// scale is returned is unspecifed.
+template <class DigitsT>
+int16_t matchScales(DigitsT &LDigits, int16_t &LScale, DigitsT &RDigits,
+ int16_t &RScale) {
+ static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
+
+ if (LScale < RScale)
+ // Swap arguments.
+ return matchScales(RDigits, RScale, LDigits, LScale);
+ if (!LDigits)
+ return RScale;
+ if (!RDigits || LScale == RScale)
+ return LScale;
+
+ // Now LScale > RScale. Get the difference.
+ int32_t ScaleDiff = int32_t(LScale) - RScale;
+ if (ScaleDiff >= 2 * getWidth<DigitsT>()) {
+ // Don't bother shifting. RDigits will get zero-ed out anyway.
+ RDigits = 0;
+ return LScale;
+ }
+
+ // Shift LDigits left as much as possible, then shift RDigits right.
+ int32_t ShiftL = std::min<int32_t>(countLeadingZeros(LDigits), ScaleDiff);
+ assert(ShiftL < getWidth<DigitsT>() && "can't shift more than width");
+
+ int32_t ShiftR = ScaleDiff - ShiftL;
+ if (ShiftR >= getWidth<DigitsT>()) {
+ // Don't bother shifting. RDigits will get zero-ed out anyway.
+ RDigits = 0;
+ return LScale;
+ }
+
+ LDigits <<= ShiftL;
+ RDigits >>= ShiftR;
+
+ LScale -= ShiftL;
+ RScale += ShiftR;
+ assert(LScale == RScale && "scales should match");
+ return LScale;
+}
+
+/// \brief Get the sum of two scaled numbers.
+///
+/// Get the sum of two scaled numbers with as much precision as possible.
+///
+/// \pre Adding 1 to \c LScale (or \c RScale) will not overflow INT16_MAX.
+template <class DigitsT>
+std::pair<DigitsT, int16_t> getSum(DigitsT LDigits, int16_t LScale,
+ DigitsT RDigits, int16_t RScale) {
+ static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
+
+ // Check inputs up front. This is only relevent if addition overflows, but
+ // testing here should catch more bugs.
+ assert(LScale < INT16_MAX && "scale too large");
+ assert(RScale < INT16_MAX && "scale too large");
+
+ // Normalize digits to match scales.
+ int16_t Scale = matchScales(LDigits, LScale, RDigits, RScale);
+
+ // Compute sum.
+ DigitsT Sum = LDigits + RDigits;
+ if (Sum >= RDigits)
+ return std::make_pair(Sum, Scale);
+
+ // Adjust sum after arithmetic overflow.
+ DigitsT HighBit = DigitsT(1) << (getWidth<DigitsT>() - 1);
+ return std::make_pair(HighBit | Sum >> 1, Scale + 1);
+}
+
+/// \brief Convenience helper for 32-bit sum.
+inline std::pair<uint32_t, int16_t> getSum32(uint32_t LDigits, int16_t LScale,
+ uint32_t RDigits, int16_t RScale) {
+ return getSum(LDigits, LScale, RDigits, RScale);
+}
+
+/// \brief Convenience helper for 64-bit sum.
+inline std::pair<uint64_t, int16_t> getSum64(uint64_t LDigits, int16_t LScale,
+ uint64_t RDigits, int16_t RScale) {
+ return getSum(LDigits, LScale, RDigits, RScale);
+}
+
+/// \brief Get the difference of two scaled numbers.
+///
+/// Get LHS minus RHS with as much precision as possible.
+///
+/// Returns \c (0, 0) if the RHS is larger than the LHS.
+template <class DigitsT>
+std::pair<DigitsT, int16_t> getDifference(DigitsT LDigits, int16_t LScale,
+ DigitsT RDigits, int16_t RScale) {
+ static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
+
+ // Normalize digits to match scales.
+ const DigitsT SavedRDigits = RDigits;
+ const int16_t SavedRScale = RScale;
+ matchScales(LDigits, LScale, RDigits, RScale);
+
+ // Compute difference.
+ if (LDigits <= RDigits)
+ return std::make_pair(0, 0);
+ if (RDigits || !SavedRDigits)
+ return std::make_pair(LDigits - RDigits, LScale);
+
+ // Check if RDigits just barely lost its last bit. E.g., for 32-bit:
+ //
+ // 1*2^32 - 1*2^0 == 0xffffffff != 1*2^32
+ const auto RLgFloor = getLgFloor(SavedRDigits, SavedRScale);
+ if (!compare(LDigits, LScale, DigitsT(1), RLgFloor + getWidth<DigitsT>()))
+ return std::make_pair(std::numeric_limits<DigitsT>::max(), RLgFloor);
+
+ return std::make_pair(LDigits, LScale);
+}
+
+/// \brief Convenience helper for 32-bit difference.
+inline std::pair<uint32_t, int16_t> getDifference32(uint32_t LDigits,
+ int16_t LScale,
+ uint32_t RDigits,
+ int16_t RScale) {
+ return getDifference(LDigits, LScale, RDigits, RScale);
+}
+
+/// \brief Convenience helper for 64-bit difference.
+inline std::pair<uint64_t, int16_t> getDifference64(uint64_t LDigits,
+ int16_t LScale,
+ uint64_t RDigits,
+ int16_t RScale) {
+ return getDifference(LDigits, LScale, RDigits, RScale);
+}
+
} // end namespace ScaledNumbers
} // end namespace llvm
+namespace llvm {
+
+class raw_ostream;
+class ScaledNumberBase {
+public:
+ static const int DefaultPrecision = 10;
+
+ static void dump(uint64_t D, int16_t E, int Width);
+ static raw_ostream &print(raw_ostream &OS, uint64_t D, int16_t E, int Width,
+ unsigned Precision);
+ static std::string toString(uint64_t D, int16_t E, int Width,
+ unsigned Precision);
+ static int countLeadingZeros32(uint32_t N) { return countLeadingZeros(N); }
+ static int countLeadingZeros64(uint64_t N) { return countLeadingZeros(N); }
+ static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
+
+ static std::pair<uint64_t, bool> splitSigned(int64_t N) {
+ if (N >= 0)
+ return std::make_pair(N, false);
+ uint64_t Unsigned = N == INT64_MIN ? UINT64_C(1) << 63 : uint64_t(-N);
+ return std::make_pair(Unsigned, true);
+ }
+ static int64_t joinSigned(uint64_t U, bool IsNeg) {
+ if (U > uint64_t(INT64_MAX))
+ return IsNeg ? INT64_MIN : INT64_MAX;
+ return IsNeg ? -int64_t(U) : int64_t(U);
+ }
+};
+
+/// \brief Simple representation of a scaled number.
+///
+/// ScaledNumber is a number represented by digits and a scale. It uses simple
+/// saturation arithmetic and every operation is well-defined for every value.
+/// It's somewhat similar in behaviour to a soft-float, but is *not* a
+/// replacement for one. If you're doing numerics, look at \a APFloat instead.
+/// Nevertheless, we've found these semantics useful for modelling certain cost
+/// metrics.
+///
+/// The number is split into a signed scale and unsigned digits. The number
+/// represented is \c getDigits()*2^getScale(). In this way, the digits are
+/// much like the mantissa in the x87 long double, but there is no canonical
+/// form so the same number can be represented by many bit representations.
+///
+/// ScaledNumber is templated on the underlying integer type for digits, which
+/// is expected to be unsigned.
+///
+/// Unlike APFloat, ScaledNumber does not model architecture floating point
+/// behaviour -- while this might make it a little faster and easier to reason
+/// about, it certainly makes it more dangerous for general numerics.
+///
+/// ScaledNumber is totally ordered. However, there is no canonical form, so
+/// there are multiple representations of most scalars. E.g.:
+///
+/// ScaledNumber(8u, 0) == ScaledNumber(4u, 1)
+/// ScaledNumber(4u, 1) == ScaledNumber(2u, 2)
+/// ScaledNumber(2u, 2) == ScaledNumber(1u, 3)
+///
+/// ScaledNumber implements most arithmetic operations. Precision is kept
+/// where possible. Uses simple saturation arithmetic, so that operations
+/// saturate to 0.0 or getLargest() rather than under or overflowing. It has
+/// some extra arithmetic for unit inversion. 0.0/0.0 is defined to be 0.0.
+/// Any other division by 0.0 is defined to be getLargest().
+///
+/// As a convenience for modifying the exponent, left and right shifting are
+/// both implemented, and both interpret negative shifts as positive shifts in
+/// the opposite direction.
+///
+/// Scales are limited to the range accepted by x87 long double. This makes
+/// it trivial to add functionality to convert to APFloat (this is already
+/// relied on for the implementation of printing).
+///
+/// Possible (and conflicting) future directions:
+///
+/// 1. Turn this into a wrapper around \a APFloat.
+/// 2. Share the algorithm implementations with \a APFloat.
+/// 3. Allow \a ScaledNumber to represent a signed number.
+template <class DigitsT> class ScaledNumber : ScaledNumberBase {
+public:
+ static_assert(!std::numeric_limits<DigitsT>::is_signed,
+ "only unsigned floats supported");
+
+ typedef DigitsT DigitsType;
+
+private:
+ typedef std::numeric_limits<DigitsType> DigitsLimits;
+
+ static const int Width = sizeof(DigitsType) * 8;
+ static_assert(Width <= 64, "invalid integer width for digits");
+
+private:
+ DigitsType Digits;
+ int16_t Scale;
+
+public:
+ ScaledNumber() : Digits(0), Scale(0) {}
+
+ ScaledNumber(DigitsType Digits, int16_t Scale)
+ : Digits(Digits), Scale(Scale) {}
+
+private:
+ ScaledNumber(const std::pair<uint64_t, int16_t> &X)
+ : Digits(X.first), Scale(X.second) {}
+
+public:
+ static ScaledNumber getZero() { return ScaledNumber(0, 0); }
+ static ScaledNumber getOne() { return ScaledNumber(1, 0); }
+ static ScaledNumber getLargest() {
+ return ScaledNumber(DigitsLimits::max(), ScaledNumbers::MaxScale);
+ }
+ static ScaledNumber get(uint64_t N) { return adjustToWidth(N, 0); }
+ static ScaledNumber getInverse(uint64_t N) {
+ return get(N).invert();
+ }
+ static ScaledNumber getFraction(DigitsType N, DigitsType D) {
+ return getQuotient(N, D);
+ }
+
+ int16_t getScale() const { return Scale; }
+ DigitsType getDigits() const { return Digits; }
+
+ /// \brief Convert to the given integer type.
+ ///
+ /// Convert to \c IntT using simple saturating arithmetic, truncating if
+ /// necessary.
+ template <class IntT> IntT toInt() const;
+
+ bool isZero() const { return !Digits; }
+ bool isLargest() const { return *this == getLargest(); }
+ bool isOne() const {
+ if (Scale > 0 || Scale <= -Width)
+ return false;
+ return Digits == DigitsType(1) << -Scale;
+ }
+
+ /// \brief The log base 2, rounded.
+ ///
+ /// Get the lg of the scalar. lg 0 is defined to be INT32_MIN.
+ int32_t lg() const { return ScaledNumbers::getLg(Digits, Scale); }
+
+ /// \brief The log base 2, rounded towards INT32_MIN.
+ ///
+ /// Get the lg floor. lg 0 is defined to be INT32_MIN.
+ int32_t lgFloor() const { return ScaledNumbers::getLgFloor(Digits, Scale); }
+
+ /// \brief The log base 2, rounded towards INT32_MAX.
+ ///
+ /// Get the lg ceiling. lg 0 is defined to be INT32_MIN.
+ int32_t lgCeiling() const {
+ return ScaledNumbers::getLgCeiling(Digits, Scale);
+ }
+
+ bool operator==(const ScaledNumber &X) const { return compare(X) == 0; }
+ bool operator<(const ScaledNumber &X) const { return compare(X) < 0; }
+ bool operator!=(const ScaledNumber &X) const { return compare(X) != 0; }
+ bool operator>(const ScaledNumber &X) const { return compare(X) > 0; }
+ bool operator<=(const ScaledNumber &X) const { return compare(X) <= 0; }
+ bool operator>=(const ScaledNumber &X) const { return compare(X) >= 0; }
+
+ bool operator!() const { return isZero(); }
+
+ /// \brief Convert to a decimal representation in a string.
+ ///
+ /// Convert to a string. Uses scientific notation for very large/small
+ /// numbers. Scientific notation is used roughly for numbers outside of the
+ /// range 2^-64 through 2^64.
+ ///
+ /// \c Precision indicates the number of decimal digits of precision to use;
+ /// 0 requests the maximum available.
+ ///
+ /// As a special case to make debugging easier, if the number is small enough
+ /// to convert without scientific notation and has more than \c Precision
+ /// digits before the decimal place, it's printed accurately to the first
+ /// digit past zero. E.g., assuming 10 digits of precision:
+ ///
+ /// 98765432198.7654... => 98765432198.8
+ /// 8765432198.7654... => 8765432198.8
+ /// 765432198.7654... => 765432198.8
+ /// 65432198.7654... => 65432198.77
+ /// 5432198.7654... => 5432198.765
+ std::string toString(unsigned Precision = DefaultPrecision) {
+ return ScaledNumberBase::toString(Digits, Scale, Width, Precision);
+ }
+
+ /// \brief Print a decimal representation.
+ ///
+ /// Print a string. See toString for documentation.
+ raw_ostream &print(raw_ostream &OS,
+ unsigned Precision = DefaultPrecision) const {
+ return ScaledNumberBase::print(OS, Digits, Scale, Width, Precision);
+ }
+ void dump() const { return ScaledNumberBase::dump(Digits, Scale, Width); }
+
+ ScaledNumber &operator+=(const ScaledNumber &X) {
+ std::tie(Digits, Scale) =
+ ScaledNumbers::getSum(Digits, Scale, X.Digits, X.Scale);
+ // Check for exponent past MaxScale.
+ if (Scale > ScaledNumbers::MaxScale)
+ *this = getLargest();
+ return *this;
+ }
+ ScaledNumber &operator-=(const ScaledNumber &X) {
+ std::tie(Digits, Scale) =
+ ScaledNumbers::getDifference(Digits, Scale, X.Digits, X.Scale);
+ return *this;
+ }
+ ScaledNumber &operator*=(const ScaledNumber &X);
+ ScaledNumber &operator/=(const ScaledNumber &X);
+ ScaledNumber &operator<<=(int16_t Shift) {
+ shiftLeft(Shift);
+ return *this;
+ }
+ ScaledNumber &operator>>=(int16_t Shift) {
+ shiftRight(Shift);
+ return *this;
+ }
+
+private:
+ void shiftLeft(int32_t Shift);
+ void shiftRight(int32_t Shift);
+
+ /// \brief Adjust two floats to have matching exponents.
+ ///
+ /// Adjust \c this and \c X to have matching exponents. Returns the new \c X
+ /// by value. Does nothing if \a isZero() for either.
+ ///
+ /// The value that compares smaller will lose precision, and possibly become
+ /// \a isZero().
+ ScaledNumber matchScales(ScaledNumber X) {
+ ScaledNumbers::matchScales(Digits, Scale, X.Digits, X.Scale);
+ return X;
+ }
+
+public:
+ /// \brief Scale a large number accurately.
+ ///
+ /// Scale N (multiply it by this). Uses full precision multiplication, even
+ /// if Width is smaller than 64, so information is not lost.
+ uint64_t scale(uint64_t N) const;
+ uint64_t scaleByInverse(uint64_t N) const {
+ // TODO: implement directly, rather than relying on inverse. Inverse is
+ // expensive.
+ return inverse().scale(N);
+ }
+ int64_t scale(int64_t N) const {
+ std::pair<uint64_t, bool> Unsigned = splitSigned(N);
+ return joinSigned(scale(Unsigned.first), Unsigned.second);
+ }
+ int64_t scaleByInverse(int64_t N) const {
+ std::pair<uint64_t, bool> Unsigned = splitSigned(N);
+ return joinSigned(scaleByInverse(Unsigned.first), Unsigned.second);
+ }
+
+ int compare(const ScaledNumber &X) const {
+ return ScaledNumbers::compare(Digits, Scale, X.Digits, X.Scale);
+ }
+ int compareTo(uint64_t N) const {
+ ScaledNumber Scaled = get(N);
+ int Compare = compare(Scaled);
+ if (Width == 64 || Compare != 0)
+ return Compare;
+
+ // Check for precision loss. We know *this == RoundTrip.
+ uint64_t RoundTrip = Scaled.template toInt<uint64_t>();
+ return N == RoundTrip ? 0 : RoundTrip < N ? -1 : 1;
+ }
+ int compareTo(int64_t N) const { return N < 0 ? 1 : compareTo(uint64_t(N)); }
+
+ ScaledNumber &invert() { return *this = ScaledNumber::get(1) / *this; }
+ ScaledNumber inverse() const { return ScaledNumber(*this).invert(); }
+
+private:
+ static ScaledNumber getProduct(DigitsType LHS, DigitsType RHS) {
+ return ScaledNumbers::getProduct(LHS, RHS);
+ }
+ static ScaledNumber getQuotient(DigitsType Dividend, DigitsType Divisor) {
+ return ScaledNumbers::getQuotient(Dividend, Divisor);
+ }
+
+ static int countLeadingZerosWidth(DigitsType Digits) {
+ if (Width == 64)
+ return countLeadingZeros64(Digits);
+ if (Width == 32)
+ return countLeadingZeros32(Digits);
+ return countLeadingZeros32(Digits) + Width - 32;
+ }
+
+ /// \brief Adjust a number to width, rounding up if necessary.
+ ///
+ /// Should only be called for \c Shift close to zero.
+ ///
+ /// \pre Shift >= MinScale && Shift + 64 <= MaxScale.
+ static ScaledNumber adjustToWidth(uint64_t N, int32_t Shift) {
+ assert(Shift >= ScaledNumbers::MinScale && "Shift should be close to 0");
+ assert(Shift <= ScaledNumbers::MaxScale - 64 &&
+ "Shift should be close to 0");
+ auto Adjusted = ScaledNumbers::getAdjusted<DigitsT>(N, Shift);
+ return Adjusted;
+ }
+
+ static ScaledNumber getRounded(ScaledNumber P, bool Round) {
+ // Saturate.
+ if (P.isLargest())
+ return P;
+
+ return ScaledNumbers::getRounded(P.Digits, P.Scale, Round);
+ }
+};
+
+#define SCALED_NUMBER_BOP(op, base) \
+ template <class DigitsT> \
+ ScaledNumber<DigitsT> operator op(const ScaledNumber<DigitsT> &L, \
+ const ScaledNumber<DigitsT> &R) { \
+ return ScaledNumber<DigitsT>(L) base R; \
+ }
+SCALED_NUMBER_BOP(+, += )
+SCALED_NUMBER_BOP(-, -= )
+SCALED_NUMBER_BOP(*, *= )
+SCALED_NUMBER_BOP(/, /= )
+SCALED_NUMBER_BOP(<<, <<= )
+SCALED_NUMBER_BOP(>>, >>= )
+#undef SCALED_NUMBER_BOP
+
+template <class DigitsT>
+raw_ostream &operator<<(raw_ostream &OS, const ScaledNumber<DigitsT> &X) {
+ return X.print(OS, 10);
+}
+
+#define SCALED_NUMBER_COMPARE_TO_TYPE(op, T1, T2) \
+ template <class DigitsT> \
+ bool operator op(const ScaledNumber<DigitsT> &L, T1 R) { \
+ return L.compareTo(T2(R)) op 0; \
+ } \
+ template <class DigitsT> \
+ bool operator op(T1 L, const ScaledNumber<DigitsT> &R) { \
+ return 0 op R.compareTo(T2(L)); \
+ }
+#define SCALED_NUMBER_COMPARE_TO(op) \
+ SCALED_NUMBER_COMPARE_TO_TYPE(op, uint64_t, uint64_t) \
+ SCALED_NUMBER_COMPARE_TO_TYPE(op, uint32_t, uint64_t) \
+ SCALED_NUMBER_COMPARE_TO_TYPE(op, int64_t, int64_t) \
+ SCALED_NUMBER_COMPARE_TO_TYPE(op, int32_t, int64_t)
+SCALED_NUMBER_COMPARE_TO(< )
+SCALED_NUMBER_COMPARE_TO(> )
+SCALED_NUMBER_COMPARE_TO(== )
+SCALED_NUMBER_COMPARE_TO(!= )
+SCALED_NUMBER_COMPARE_TO(<= )
+SCALED_NUMBER_COMPARE_TO(>= )
+#undef SCALED_NUMBER_COMPARE_TO
+#undef SCALED_NUMBER_COMPARE_TO_TYPE
+
+template <class DigitsT>
+uint64_t ScaledNumber<DigitsT>::scale(uint64_t N) const {
+ if (Width == 64 || N <= DigitsLimits::max())
+ return (get(N) * *this).template toInt<uint64_t>();
+
+ // Defer to the 64-bit version.
+ return ScaledNumber<uint64_t>(Digits, Scale).scale(N);
+}
+
+template <class DigitsT>
+template <class IntT>
+IntT ScaledNumber<DigitsT>::toInt() const {
+ typedef std::numeric_limits<IntT> Limits;
+ if (*this < 1)
+ return 0;
+ if (*this >= Limits::max())
+ return Limits::max();
+
+ IntT N = Digits;
+ if (Scale > 0) {
+ assert(size_t(Scale) < sizeof(IntT) * 8);
+ return N << Scale;
+ }
+ if (Scale < 0) {
+ assert(size_t(-Scale) < sizeof(IntT) * 8);
+ return N >> -Scale;
+ }
+ return N;
+}
+
+template <class DigitsT>
+ScaledNumber<DigitsT> &ScaledNumber<DigitsT>::
+operator*=(const ScaledNumber &X) {
+ if (isZero())
+ return *this;
+ if (X.isZero())
+ return *this = X;
+
+ // Save the exponents.
+ int32_t Scales = int32_t(Scale) + int32_t(X.Scale);
+
+ // Get the raw product.
+ *this = getProduct(Digits, X.Digits);
+
+ // Combine with exponents.
+ return *this <<= Scales;
+}
+template <class DigitsT>
+ScaledNumber<DigitsT> &ScaledNumber<DigitsT>::
+operator/=(const ScaledNumber &X) {
+ if (isZero())
+ return *this;
+ if (X.isZero())
+ return *this = getLargest();
+
+ // Save the exponents.
+ int32_t Scales = int32_t(Scale) - int32_t(X.Scale);
+
+ // Get the raw quotient.
+ *this = getQuotient(Digits, X.Digits);
+
+ // Combine with exponents.
+ return *this <<= Scales;
+}
+template <class DigitsT> void ScaledNumber<DigitsT>::shiftLeft(int32_t Shift) {
+ if (!Shift || isZero())
+ return;
+ assert(Shift != INT32_MIN);
+ if (Shift < 0) {
+ shiftRight(-Shift);
+ return;
+ }
+
+ // Shift as much as we can in the exponent.
+ int32_t ScaleShift = std::min(Shift, ScaledNumbers::MaxScale - Scale);
+ Scale += ScaleShift;
+ if (ScaleShift == Shift)
+ return;
+
+ // Check this late, since it's rare.
+ if (isLargest())
+ return;
+
+ // Shift the digits themselves.
+ Shift -= ScaleShift;
+ if (Shift > countLeadingZerosWidth(Digits)) {
+ // Saturate.
+ *this = getLargest();
+ return;
+ }
+
+ Digits <<= Shift;
+ return;
+}
+
+template <class DigitsT> void ScaledNumber<DigitsT>::shiftRight(int32_t Shift) {
+ if (!Shift || isZero())
+ return;
+ assert(Shift != INT32_MIN);
+ if (Shift < 0) {
+ shiftLeft(-Shift);
+ return;
+ }
+
+ // Shift as much as we can in the exponent.
+ int32_t ScaleShift = std::min(Shift, Scale - ScaledNumbers::MinScale);
+ Scale -= ScaleShift;
+ if (ScaleShift == Shift)
+ return;
+
+ // Shift the digits themselves.
+ Shift -= ScaleShift;
+ if (Shift >= Width) {
+ // Saturate.
+ *this = getZero();
+ return;
+ }
+
+ Digits >>= Shift;
+ return;
+}
+
+template <typename T> struct isPodLike;
+template <typename T> struct isPodLike<ScaledNumber<T>> {
+ static const bool value = true;
+};
+
+} // end namespace llvm
+
#endif
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