325 lines
9.1 KiB
C++
325 lines
9.1 KiB
C++
//==- 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/ADT/ArrayRef.h"
|
|
#include "llvm/Support/Debug.h"
|
|
#include "llvm/Support/raw_ostream.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);
|
|
assert(Shift >= 0 && Shift < 64 && "undefined behavior");
|
|
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 == -64) {
|
|
// Special case: shift by 64 bits is undefined behavior.
|
|
Below0 = D;
|
|
} 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
|
|
<< "]";
|
|
}
|