//==- 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"
#include "llvm/ADT/APFloat.h"
#include "llvm/Support/Debug.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));
}
int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) {
assert(ScaleDiff >= 0 && "wrong argument order");
assert(ScaleDiff < 64 && "numbers too far apart");
uint64_t L_adjusted = L >> ScaleDiff;
if (L_adjusted < R)
return -1;
if (L_adjusted > R)
return 1;
return L > L_adjusted << ScaleDiff ? 1 : 0;
}
static void appendDigit(std::string &Str, unsigned D) {
assert(D < 10);
Str += '0' + D % 10;
}
static void appendNumber(std::string &Str, uint64_t N) {
while (N) {
appendDigit(Str, N % 10);
N /= 10;
}
}
static bool doesRoundUp(char Digit) {
switch (Digit) {
case '5':
case '6':
case '7':
case '8':
case '9':
return true;
default:
return false;
}
}
static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
assert(E >= ScaledNumbers::MinScale);
assert(E <= ScaledNumbers::MaxScale);
// Find a new E, but don't let it increase past MaxScale.
int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D);
int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros);
int Shift = 63 - (NewE - E);
assert(Shift <= LeadingZeros);
assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale);
D <<= Shift;
E = NewE;
// Check for a denormal.
unsigned AdjustedE = E + 16383;
if (!(D >> 63)) {
assert(E == ScaledNumbers::MaxScale);
AdjustedE = 0;
}
// Build the float and print it.
uint64_t RawBits[2] = {D, AdjustedE};
APFloat Float(APFloat::x87DoubleExtended, APInt(80, RawBits));
SmallVector<char, 24> Chars;
Float.toString(Chars, Precision, 0);
return std::string(Chars.begin(), Chars.end());
}
static std::string stripTrailingZeros(const std::string &Float) {
size_t NonZero = Float.find_last_not_of('0');
assert(NonZero != std::string::npos && "no . in floating point string");
if (Float[NonZero] == '.')
++NonZero;
return Float.substr(0, NonZero + 1);
}
std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
unsigned Precision) {
if (!D)
return "0.0";
// Canonicalize exponent and digits.
uint64_t Above0 = 0;
uint64_t Below0 = 0;
uint64_t Extra = 0;
int ExtraShift = 0;
if (E == 0) {
Above0 = D;
} else if (E > 0) {
if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
D <<= Shift;
E -= Shift;
if (!E)
Above0 = D;
}
} else if (E > -64) {
Above0 = D >> -E;
Below0 = D << (64 + E);
} else if (E > -120) {
Below0 = D >> (-E - 64);
Extra = D << (128 + E);
ExtraShift = -64 - E;
}
// Fall back on APFloat for very small and very large numbers.
if (!Above0 && !Below0)
return toStringAPFloat(D, E, Precision);
// Append the digits before the decimal.
std::string Str;
size_t DigitsOut = 0;
if (Above0) {
appendNumber(Str, Above0);
DigitsOut = Str.size();
} else
appendDigit(Str, 0);
std::reverse(Str.begin(), Str.end());
// Return early if there's nothing after the decimal.
if (!Below0)
return Str + ".0";
// Append the decimal and beyond.
Str += '.';
uint64_t Error = UINT64_C(1) << (64 - Width);
// We need to shift Below0 to the right to make space for calculating
// digits. Save the precision we're losing in Extra.
Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
Below0 >>= 4;
size_t SinceDot = 0;
size_t AfterDot = Str.size();
do {
if (ExtraShift) {
--ExtraShift;
Error *= 5;
} else
Error *= 10;
Below0 *= 10;
Extra *= 10;
Below0 += (Extra >> 60);
Extra = Extra & (UINT64_MAX >> 4);
appendDigit(Str, Below0 >> 60);
Below0 = Below0 & (UINT64_MAX >> 4);
if (DigitsOut || Str.back() != '0')
++DigitsOut;
++SinceDot;
} while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
(!Precision || DigitsOut <= Precision || SinceDot < 2));
// Return early for maximum precision.
if (!Precision || DigitsOut <= Precision)
return stripTrailingZeros(Str);
// Find where to truncate.
size_t Truncate =
std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
// Check if there's anything to truncate.
if (Truncate >= Str.size())
return stripTrailingZeros(Str);
bool Carry = doesRoundUp(Str[Truncate]);
if (!Carry)
return stripTrailingZeros(Str.substr(0, Truncate));
// Round with the first truncated digit.
for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
I != E; ++I) {
if (*I == '.')
continue;
if (*I == '9') {
*I = '0';
continue;
}
++*I;
Carry = false;
break;
}
// Add "1" in front if we still need to carry.
return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
}
raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
int Width, unsigned Precision) {
return OS << toString(D, E, Width, Precision);
}
void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
<< "]";
}