//===- llvm/Support/ScaledNumber.h - Support for scaled numbers -*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file contains functions (and a class) useful for working with scaled
// numbers -- in particular, pairs of integers where one represents digits and
// another represents a scale. The functions are helpers and live in the
// namespace ScaledNumbers. The class ScaledNumber is useful for modelling
// certain cost metrics that need simple, integer-like semantics that are easy
// to reason about.
//
// These might remind you of soft-floats. If you want one of those, you're in
// the wrong place. Look at include/llvm/ADT/APFloat.h instead.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_SUPPORT_SCALEDNUMBER_H
#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 {
/// Maximum scale; same as APFloat for easy debug printing.
const int32_t MaxScale = 16383;
/// Maximum scale; same as APFloat for easy debug printing.
const int32_t MinScale = -16382;
/// Get the width of a number.
template <class DigitsT> inline int getWidth() { return sizeof(DigitsT) * 8; }
/// Conditionally round up a scaled number.
///
/// Given \c Digits and \c Scale, round up iff \c ShouldRound is \c true.
/// Always returns \c Scale unless there's an overflow, in which case it
/// returns \c 1+Scale.
///
/// \pre adding 1 to \c Scale will not overflow INT16_MAX.
template <class DigitsT>
inline std::pair<DigitsT, int16_t> getRounded(DigitsT Digits, int16_t Scale,
bool ShouldRound) {
static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
if (ShouldRound)
if (!++Digits)
// Overflow.
return std::make_pair(DigitsT(1) << (getWidth<DigitsT>() - 1), Scale + 1);
return std::make_pair(Digits, Scale);
}
/// Convenience helper for 32-bit rounding.
inline std::pair<uint32_t, int16_t> getRounded32(uint32_t Digits, int16_t Scale,
bool ShouldRound) {
return getRounded(Digits, Scale, ShouldRound);
}
/// Convenience helper for 64-bit rounding.
inline std::pair<uint64_t, int16_t> getRounded64(uint64_t Digits, int16_t Scale,
bool ShouldRound) {
return getRounded(Digits, Scale, ShouldRound);
}
/// Adjust a 64-bit scaled number down to the appropriate width.
///
/// \pre Adding 64 to \c Scale will not overflow INT16_MAX.
template <class DigitsT>
inline std::pair<DigitsT, int16_t> getAdjusted(uint64_t Digits,
int16_t Scale = 0) {
static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
const int Width = getWidth<DigitsT>();
if (Width == 64 || Digits <= std::numeric_limits<DigitsT>::max())
return std::make_pair(Digits, Scale);
// Shift right and round.
int Shift = 64 - Width - countLeadingZeros(Digits);
return getRounded<DigitsT>(Digits >> Shift, Scale + Shift,
Digits & (UINT64_C(1) << (Shift - 1)));
}
/// Convenience helper for adjusting to 32 bits.
inline std::pair<uint32_t, int16_t> getAdjusted32(uint64_t Digits,
int16_t Scale = 0) {
return getAdjusted<uint32_t>(Digits, Scale);
}
/// Convenience helper for adjusting to 64 bits.
inline std::pair<uint64_t, int16_t> getAdjusted64(uint64_t Digits,
int16_t Scale = 0) {
return getAdjusted<uint64_t>(Digits, Scale);
}
/// 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);
/// 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);
}
/// Convenience helper for 32-bit product.
inline std::pair<uint32_t, int16_t> getProduct32(uint32_t LHS, uint32_t RHS) {
return getProduct(LHS, RHS);
}
/// Convenience helper for 64-bit product.
inline std::pair<uint64_t, int16_t> getProduct64(uint64_t LHS, uint64_t RHS) {
return getProduct(LHS, RHS);
}
/// 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);
/// 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);
/// 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, 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");
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(), MaxScale);
if (getWidth<DigitsT>() == 64)
return divide64(Dividend, Divisor);
return divide32(Dividend, Divisor);
}
/// Convenience helper for 32-bit quotient.
inline std::pair<uint32_t, int16_t> getQuotient32(uint32_t Dividend,
uint32_t Divisor) {
return getQuotient(Dividend, Divisor);
}
/// Convenience helper for 64-bit quotient.
inline std::pair<uint64_t, int16_t> getQuotient64(uint64_t Dividend,
uint64_t Divisor) {
return getQuotient(Dividend, Divisor);
}
/// Implementation of getLg() and friends.
///
/// Returns the rounded lg of \c Digits*2^Scale and an int specifying whether
/// this was rounded up (1), down (-1), or exact (0).
///
/// Returns \c INT32_MIN when \c Digits is zero.
template <class DigitsT>
inline std::pair<int32_t, int> getLgImpl(DigitsT Digits, int16_t Scale) {
static_assert(!std::numeric_limits<DigitsT>::is_signed, "expected unsigned");
if (!Digits)
return std::make_pair(INT32_MIN, 0);
// Get the floor of the lg of Digits.
int32_t LocalFloor = sizeof(Digits) * 8 - countLeadingZeros(Digits) - 1;
// Get the actual floor.
int32_t Floor = Scale + LocalFloor;
if (Digits == UINT64_C(1) << LocalFloor)
return std::make_pair(Floor, 0);
// Round based on the next digit.
assert(LocalFloor >= 1);
bool Round = Digits & UINT64_C(1) << (LocalFloor - 1);
return std::make_pair(Floor + Round, Round ? 1 : -1);
}
/// Get the lg (rounded) of a scaled number.
///
/// Get the lg of \c Digits*2^Scale.
///
/// Returns \c INT32_MIN when \c Digits is zero.
template <class DigitsT> int32_t getLg(DigitsT Digits, int16_t Scale) {
return getLgImpl(Digits, Scale).first;
}
/// Get the lg floor of a scaled number.
///
/// Get the floor of the lg of \c Digits*2^Scale.
///
/// Returns \c INT32_MIN when \c Digits is zero.
template <class DigitsT> int32_t getLgFloor(DigitsT Digits, int16_t Scale) {
auto Lg = getLgImpl(Digits, Scale);
return Lg.first - (Lg.second > 0);
}
/// Get the lg ceiling of a scaled number.
///
/// Get the ceiling of the lg of \c Digits*2^Scale.
///
/// Returns \c INT32_MIN when \c Digits is zero.
template <class DigitsT> int32_t getLgCeiling(DigitsT Digits, int16_t Scale) {
auto Lg = getLgImpl(Digits, Scale);
return Lg.first + (Lg.second < 0);
}
/// Implementation for comparing scaled numbers.
///
/// Compare two 64-bit numbers with different scales. Given that the scale of
/// \c L is higher than that of \c R by \c ScaleDiff, compare them. Return -1,
/// 1, and 0 for less than, greater than, and equal, respectively.
///
/// \pre 0 <= ScaleDiff < 64.
int compareImpl(uint64_t L, uint64_t R, int ScaleDiff);
/// Compare two scaled numbers.
///
/// Compare two scaled numbers. Returns 0 for equal, -1 for less than, and 1
/// 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;
if (!RDigits)
return 1;
// Check for the scale. Use getLgFloor to be sure that the scale difference
// is always lower than 64.
int32_t lgL = getLgFloor(LDigits, LScale), lgR = getLgFloor(RDigits, RScale);
if (lgL != lgR)
return lgL < lgR ? -1 : 1;
// Compare digits.
if (LScale < RScale)
return compareImpl(LDigits, RDigits, RScale - LScale);
return -compareImpl(RDigits, LDigits, LScale - RScale);
}
/// 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 unspecified.
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;
}
/// 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 relevant 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);
}
/// 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);
}
/// 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);
}
/// 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);
}
/// 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);
}
/// 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 constexpr 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);
}
};
/// 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 constexpr int Width = sizeof(DigitsType) * 8;
static_assert(Width <= 64, "invalid integer width for digits");
private:
DigitsType Digits = 0;
int16_t Scale = 0;
public:
ScaledNumber() = default;
constexpr ScaledNumber(DigitsType Digits, int16_t Scale)
: Digits(Digits), Scale(Scale) {}
private:
ScaledNumber(const std::pair<DigitsT, 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; }
/// 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;
}
/// 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); }
/// 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); }
/// 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(); }
/// 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);
}
/// 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);
/// 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:
/// 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 {
return ScaledNumbers::compare<uint64_t>(Digits, Scale, N, 0);
}
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;
}
/// 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(/, /= )
#undef SCALED_NUMBER_BOP
template <class DigitsT>
ScaledNumber<DigitsT> operator<<(const ScaledNumber<DigitsT> &L,
int16_t Shift) {
return ScaledNumber<DigitsT>(L) <<= Shift;
}
template <class DigitsT>
ScaledNumber<DigitsT> operator>>(const ScaledNumber<DigitsT> &L,
int16_t Shift) {
return ScaledNumber<DigitsT>(L) >>= Shift;
}
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;
}
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;
}
} // end namespace llvm
#endif // LLVM_SUPPORT_SCALEDNUMBER_H