src/llvm/lib/Support/ScaledNumber.cpp

   1 //==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
   2 //
   3 //                     The LLVM Compiler Infrastructure
   4 //
   5 // This file is distributed under the University of Illinois Open Source
   6 // License. See LICENSE.TXT for details.
   7 //
   8 //===----------------------------------------------------------------------===//
   9 //
  10 // Implementation of some scaled number algorithms.
  11 //
  12 //===----------------------------------------------------------------------===//
  13
  14 #include "llvm/Support/ScaledNumber.h"
  15 #include "llvm/ADT/APFloat.h"
  16 #include "llvm/Support/Debug.h"
  17
  18 using namespace llvm;
  19 using namespace llvm::ScaledNumbers;
  20
  21 std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
  22                                                        uint64_t RHS) {
  23   // Separate into two 32-bit digits (U.L).
  24   auto getU = [](uint64_t N) { return N >> 32; };
  25   auto getL = [](uint64_t N) { return N & UINT32_MAX; };
  26   uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS);
  27
  28   // Compute cross products.
  29   uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
  30
  31   // Sum into two 64-bit digits.
  32   uint64_t Upper = P1, Lower = P4;
  33   auto addWithCarry = [&](uint64_t N) {
  34     uint64_t NewLower = Lower + (getL(N) << 32);
  35     Upper += getU(N) + (NewLower < Lower);
  36     Lower = NewLower;
  37   };
  38   addWithCarry(P2);
  39   addWithCarry(P3);
  40
  41   // Check whether the upper digit is empty.
  42   if (!Upper)
  43     return std::make_pair(Lower, 0);
  44
  45   // Shift as little as possible to maximize precision.
  46   unsigned LeadingZeros = countLeadingZeros(Upper);
  47   int Shift = 64 - LeadingZeros;
  48   if (LeadingZeros)
  49     Upper = Upper << LeadingZeros | Lower >> Shift;
  50   return getRounded(Upper, Shift,
  51                     Shift && (Lower & UINT64_C(1) << (Shift - 1)));
  52 }
  53
  54 static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
  55
  56 std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
  57                                                      uint32_t Divisor) {
  58   assert(Dividend && "expected non-zero dividend");
  59   assert(Divisor && "expected non-zero divisor");
  60
  61   // Use 64-bit math and canonicalize the dividend to gain precision.
  62   uint64_t Dividend64 = Dividend;
  63   int Shift = 0;
  64   if (int Zeros = countLeadingZeros(Dividend64)) {
  65     Shift -= Zeros;
  66     Dividend64 <<= Zeros;
  67   }
  68   uint64_t Quotient = Dividend64 / Divisor;
  69   uint64_t Remainder = Dividend64 % Divisor;
  70
  71   // If Quotient needs to be shifted, leave the rounding to getAdjusted().
  72   if (Quotient > UINT32_MAX)
  73     return getAdjusted<uint32_t>(Quotient, Shift);
  74
  75   // Round based on the value of the next bit.
  76   return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
  77 }
  78
  79 std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
  80                                                      uint64_t Divisor) {
  81   assert(Dividend && "expected non-zero dividend");
  82   assert(Divisor && "expected non-zero divisor");
  83
  84   // Minimize size of divisor.
  85   int Shift = 0;
  86   if (int Zeros = countTrailingZeros(Divisor)) {
  87     Shift -= Zeros;
  88     Divisor >>= Zeros;
  89   }
  90
  91   // Check for powers of two.
  92   if (Divisor == 1)
  93     return std::make_pair(Dividend, Shift);
  94
  95   // Maximize size of dividend.
  96   if (int Zeros = countLeadingZeros(Dividend)) {
  97     Shift -= Zeros;
  98     Dividend <<= Zeros;
  99   }
 100
 101   // Start with the result of a divide.
 102   uint64_t Quotient = Dividend / Divisor;
 103   Dividend %= Divisor;
 104
 105   // Continue building the quotient with long division.
 106   while (!(Quotient >> 63) && Dividend) {
 107     // Shift Dividend and check for overflow.
 108     bool IsOverflow = Dividend >> 63;
 109     Dividend <<= 1;
 110     --Shift;
 111
 112     // Get the next bit of Quotient.
 113     Quotient <<= 1;
 114     if (IsOverflow || Divisor <= Dividend) {
 115       Quotient |= 1;
 116       Dividend -= Divisor;
 117     }
 118   }
 119
 120   return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
 121 }
 122
 123 int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) {
 124   assert(ScaleDiff >= 0 && "wrong argument order");
 125   assert(ScaleDiff < 64 && "numbers too far apart");
 126
 127   uint64_t L_adjusted = L >> ScaleDiff;
 128   if (L_adjusted < R)
 129     return -1;
 130   if (L_adjusted > R)
 131     return 1;
 132
 133   return L > L_adjusted << ScaleDiff ? 1 : 0;
 134 }
 135
 136 static void appendDigit(std::string &Str, unsigned D) {
 137   assert(D < 10);
 138   Str += '0' + D % 10;
 139 }
 140
 141 static void appendNumber(std::string &Str, uint64_t N) {
 142   while (N) {
 143     appendDigit(Str, N % 10);
 144     N /= 10;
 145   }
 146 }
 147
 148 static bool doesRoundUp(char Digit) {
 149   switch (Digit) {
 150   case '5':
 151   case '6':
 152   case '7':
 153   case '8':
 154   case '9':
 155     return true;
 156   default:
 157     return false;
 158   }
 159 }
 160
 161 static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
 162   assert(E >= ScaledNumbers::MinScale);
 163   assert(E <= ScaledNumbers::MaxScale);
 164
 165   // Find a new E, but don't let it increase past MaxScale.
 166   int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D);
 167   int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros);
 168   int Shift = 63 - (NewE - E);
 169   assert(Shift <= LeadingZeros);
 170   assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale);
 171   assert(Shift >= 0 && Shift < 64 && "undefined behavior");
 172   D <<= Shift;
 173   E = NewE;
 174
 175   // Check for a denormal.
 176   unsigned AdjustedE = E + 16383;
 177   if (!(D >> 63)) {
 178     assert(E == ScaledNumbers::MaxScale);
 179     AdjustedE = 0;
 180   }
 181
 182   // Build the float and print it.
 183   uint64_t RawBits[2] = {D, AdjustedE};
 184   APFloat Float(APFloat::x87DoubleExtended, APInt(80, RawBits));
 185   SmallVector<char, 24> Chars;
 186   Float.toString(Chars, Precision, 0);
 187   return std::string(Chars.begin(), Chars.end());
 188 }
 189
 190 static std::string stripTrailingZeros(const std::string &Float) {
 191   size_t NonZero = Float.find_last_not_of('0');
 192   assert(NonZero != std::string::npos && "no . in floating point string");
 193
 194   if (Float[NonZero] == '.')
 195     ++NonZero;
 196
 197   return Float.substr(0, NonZero + 1);
 198 }
 199
 200 std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
 201                                        unsigned Precision) {
 202   if (!D)
 203     return "0.0";
 204
 205   // Canonicalize exponent and digits.
 206   uint64_t Above0 = 0;
 207   uint64_t Below0 = 0;
 208   uint64_t Extra = 0;
 209   int ExtraShift = 0;
 210   if (E == 0) {
 211     Above0 = D;
 212   } else if (E > 0) {
 213     if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
 214       D <<= Shift;
 215       E -= Shift;
 216
 217       if (!E)
 218         Above0 = D;
 219     }
 220   } else if (E > -64) {
 221     Above0 = D >> -E;
 222     Below0 = D << (64 + E);
 223   } else if (E == -64) {
 224     // Special case: shift by 64 bits is undefined behavior.
 225     Below0 = D;
 226   } else if (E > -120) {
 227     Below0 = D >> (-E - 64);
 228     Extra = D << (128 + E);
 229     ExtraShift = -64 - E;
 230   }
 231
 232   // Fall back on APFloat for very small and very large numbers.
 233   if (!Above0 && !Below0)
 234     return toStringAPFloat(D, E, Precision);
 235
 236   // Append the digits before the decimal.
 237   std::string Str;
 238   size_t DigitsOut = 0;
 239   if (Above0) {
 240     appendNumber(Str, Above0);
 241     DigitsOut = Str.size();
 242   } else
 243     appendDigit(Str, 0);
 244   std::reverse(Str.begin(), Str.end());
 245
 246   // Return early if there's nothing after the decimal.
 247   if (!Below0)
 248     return Str + ".0";
 249
 250   // Append the decimal and beyond.
 251   Str += '.';
 252   uint64_t Error = UINT64_C(1) << (64 - Width);
 253
 254   // We need to shift Below0 to the right to make space for calculating
 255   // digits.  Save the precision we're losing in Extra.
 256   Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
 257   Below0 >>= 4;
 258   size_t SinceDot = 0;
 259   size_t AfterDot = Str.size();
 260   do {
 261     if (ExtraShift) {
 262       --ExtraShift;
 263       Error *= 5;
 264     } else
 265       Error *= 10;
 266
 267     Below0 *= 10;
 268     Extra *= 10;
 269     Below0 += (Extra >> 60);
 270     Extra = Extra & (UINT64_MAX >> 4);
 271     appendDigit(Str, Below0 >> 60);
 272     Below0 = Below0 & (UINT64_MAX >> 4);
 273     if (DigitsOut || Str.back() != '0')
 274       ++DigitsOut;
 275     ++SinceDot;
 276   } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
 277            (!Precision || DigitsOut <= Precision || SinceDot < 2));
 278
 279   // Return early for maximum precision.
 280   if (!Precision || DigitsOut <= Precision)
 281     return stripTrailingZeros(Str);
 282
 283   // Find where to truncate.
 284   size_t Truncate =
 285       std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
 286
 287   // Check if there's anything to truncate.
 288   if (Truncate >= Str.size())
 289     return stripTrailingZeros(Str);
 290
 291   bool Carry = doesRoundUp(Str[Truncate]);
 292   if (!Carry)
 293     return stripTrailingZeros(Str.substr(0, Truncate));
 294
 295   // Round with the first truncated digit.
 296   for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
 297        I != E; ++I) {
 298     if (*I == '.')
 299       continue;
 300     if (*I == '9') {
 301       *I = '0';
 302       continue;
 303     }
 304
 305     ++*I;
 306     Carry = false;
 307     break;
 308   }
 309
 310   // Add "1" in front if we still need to carry.
 311   return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
 312 }
 313
 314 raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
 315                                      int Width, unsigned Precision) {
 316   return OS << toString(D, E, Width, Precision);
 317 }
 318
 319 void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
 320   print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
 321                                 << "]";
 322 }