//==- 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 << "]"; }