lib/Support/ScaledNumber.cpp

   1 //==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // Implementation of some scaled number algorithms.
  10 //
  11 //===----------------------------------------------------------------------===//
  12
  13 #include "llvm/Support/ScaledNumber.h"
  14 #include "llvm/ADT/APFloat.h"
  15 #include "llvm/ADT/ArrayRef.h"
  16 #include "llvm/Support/Debug.h"
  17 #include "llvm/Support/raw_ostream.h"
  18
  19 using namespace llvm;
  20 using namespace llvm::ScaledNumbers;
  21
  22 std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
  23                                                        uint64_t RHS) {
  24   // Separate into two 32-bit digits (U.L).
  25   auto getU = [](uint64_t N) { return N >> 32; };
  26   auto getL = [](uint64_t N) { return N & UINT32_MAX; };
  27   uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS);
  28
  29   // Compute cross products.
  30   uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
  31
  32   // Sum into two 64-bit digits.
  33   uint64_t Upper = P1, Lower = P4;
  34   auto addWithCarry = [&](uint64_t N) {
  35     uint64_t NewLower = Lower + (getL(N) << 32);
  36     Upper += getU(N) + (NewLower < Lower);
  37     Lower = NewLower;
  38   };
  39   addWithCarry(P2);
  40   addWithCarry(P3);
  41
  42   // Check whether the upper digit is empty.
  43   if (!Upper)
  44     return std::make_pair(Lower, 0);
  45
  46   // Shift as little as possible to maximize precision.
  47   unsigned LeadingZeros = countLeadingZeros(Upper);
  48   int Shift = 64 - LeadingZeros;
  49   if (LeadingZeros)
  50     Upper = Upper << LeadingZeros | Lower >> Shift;
  51   return getRounded(Upper, Shift,
  52                     Shift && (Lower & UINT64_C(1) << (Shift - 1)));
  53 }
  54
  55 static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
  56
  57 std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
  58                                                      uint32_t Divisor) {
  59   assert(Dividend && "expected non-zero dividend");
  60   assert(Divisor && "expected non-zero divisor");
  61
  62   // Use 64-bit math and canonicalize the dividend to gain precision.
  63   uint64_t Dividend64 = Dividend;
  64   int Shift = 0;
  65   if (int Zeros = countLeadingZeros(Dividend64)) {
  66     Shift -= Zeros;
  67     Dividend64 <<= Zeros;
  68   }
  69   uint64_t Quotient = Dividend64 / Divisor;
  70   uint64_t Remainder = Dividend64 % Divisor;
  71
  72   // If Quotient needs to be shifted, leave the rounding to getAdjusted().
  73   if (Quotient > UINT32_MAX)
  74     return getAdjusted<uint32_t>(Quotient, Shift);
  75
  76   // Round based on the value of the next bit.
  77   return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
  78 }
  79
  80 std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
  81                                                      uint64_t Divisor) {
  82   assert(Dividend && "expected non-zero dividend");
  83   assert(Divisor && "expected non-zero divisor");
  84
  85   // Minimize size of divisor.
  86   int Shift = 0;
  87   if (int Zeros = countTrailingZeros(Divisor)) {
  88     Shift -= Zeros;
  89     Divisor >>= Zeros;
  90   }
  91
  92   // Check for powers of two.
  93   if (Divisor == 1)
  94     return std::make_pair(Dividend, Shift);
  95
  96   // Maximize size of dividend.
  97   if (int Zeros = countLeadingZeros(Dividend)) {
  98     Shift -= Zeros;
  99     Dividend <<= Zeros;
 100   }
 101
 102   // Start with the result of a divide.
 103   uint64_t Quotient = Dividend / Divisor;
 104   Dividend %= Divisor;
 105
 106   // Continue building the quotient with long division.
 107   while (!(Quotient >> 63) && Dividend) {
 108     // Shift Dividend and check for overflow.
 109     bool IsOverflow = Dividend >> 63;
 110     Dividend <<= 1;
 111     --Shift;
 112
 113     // Get the next bit of Quotient.
 114     Quotient <<= 1;
 115     if (IsOverflow || Divisor <= Dividend) {
 116       Quotient |= 1;
 117       Dividend -= Divisor;
 118     }
 119   }
 120
 121   return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
 122 }
 123
 124 int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) {
 125   assert(ScaleDiff >= 0 && "wrong argument order");
 126   assert(ScaleDiff < 64 && "numbers too far apart");
 127
 128   uint64_t L_adjusted = L >> ScaleDiff;
 129   if (L_adjusted < R)
 130     return -1;
 131   if (L_adjusted > R)
 132     return 1;
 133
 134   return L > L_adjusted << ScaleDiff ? 1 : 0;
 135 }
 136
 137 static void appendDigit(std::string &Str, unsigned D) {
 138   assert(D < 10);
 139   Str += '0' + D % 10;
 140 }
 141
 142 static void appendNumber(std::string &Str, uint64_t N) {
 143   while (N) {
 144     appendDigit(Str, N % 10);
 145     N /= 10;
 146   }
 147 }
 148
 149 static bool doesRoundUp(char Digit) {
 150   switch (Digit) {
 151   case '5':
 152   case '6':
 153   case '7':
 154   case '8':
 155   case '9':
 156     return true;
 157   default:
 158     return false;
 159   }
 160 }
 161
 162 static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
 163   assert(E >= ScaledNumbers::MinScale);
 164   assert(E <= ScaledNumbers::MaxScale);
 165
 166   // Find a new E, but don't let it increase past MaxScale.
 167   int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D);
 168   int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros);
 169   int Shift = 63 - (NewE - E);
 170   assert(Shift <= LeadingZeros);
 171   assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale);
 172   assert(Shift >= 0 && Shift < 64 && "undefined behavior");
 173   D <<= Shift;
 174   E = NewE;
 175
 176   // Check for a denormal.
 177   unsigned AdjustedE = E + 16383;
 178   if (!(D >> 63)) {
 179     assert(E == ScaledNumbers::MaxScale);
 180     AdjustedE = 0;
 181   }
 182
 183   // Build the float and print it.
 184   uint64_t RawBits[2] = {D, AdjustedE};
 185   APFloat Float(APFloat::x87DoubleExtended(), APInt(80, RawBits));
 186   SmallVector<char, 24> Chars;
 187   Float.toString(Chars, Precision, 0);
 188   return std::string(Chars.begin(), Chars.end());
 189 }
 190
 191 static std::string stripTrailingZeros(const std::string &Float) {
 192   size_t NonZero = Float.find_last_not_of('0');
 193   assert(NonZero != std::string::npos && "no . in floating point string");
 194
 195   if (Float[NonZero] == '.')
 196     ++NonZero;
 197
 198   return Float.substr(0, NonZero + 1);
 199 }
 200
 201 std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
 202                                        unsigned Precision) {
 203   if (!D)
 204     return "0.0";
 205
 206   // Canonicalize exponent and digits.
 207   uint64_t Above0 = 0;
 208   uint64_t Below0 = 0;
 209   uint64_t Extra = 0;
 210   int ExtraShift = 0;
 211   if (E == 0) {
 212     Above0 = D;
 213   } else if (E > 0) {
 214     if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
 215       D <<= Shift;
 216       E -= Shift;
 217
 218       if (!E)
 219         Above0 = D;
 220     }
 221   } else if (E > -64) {
 222     Above0 = D >> -E;
 223     Below0 = D << (64 + E);
 224   } else if (E == -64) {
 225     // Special case: shift by 64 bits is undefined behavior.
 226     Below0 = D;
 227   } else if (E > -120) {
 228     Below0 = D >> (-E - 64);
 229     Extra = D << (128 + E);
 230     ExtraShift = -64 - E;
 231   }
 232
 233   // Fall back on APFloat for very small and very large numbers.
 234   if (!Above0 && !Below0)
 235     return toStringAPFloat(D, E, Precision);
 236
 237   // Append the digits before the decimal.
 238   std::string Str;
 239   size_t DigitsOut = 0;
 240   if (Above0) {
 241     appendNumber(Str, Above0);
 242     DigitsOut = Str.size();
 243   } else
 244     appendDigit(Str, 0);
 245   std::reverse(Str.begin(), Str.end());
 246
 247   // Return early if there's nothing after the decimal.
 248   if (!Below0)
 249     return Str + ".0";
 250
 251   // Append the decimal and beyond.
 252   Str += '.';
 253   uint64_t Error = UINT64_C(1) << (64 - Width);
 254
 255   // We need to shift Below0 to the right to make space for calculating
 256   // digits.  Save the precision we're losing in Extra.
 257   Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
 258   Below0 >>= 4;
 259   size_t SinceDot = 0;
 260   size_t AfterDot = Str.size();
 261   do {
 262     if (ExtraShift) {
 263       --ExtraShift;
 264       Error *= 5;
 265     } else
 266       Error *= 10;
 267
 268     Below0 *= 10;
 269     Extra *= 10;
 270     Below0 += (Extra >> 60);
 271     Extra = Extra & (UINT64_MAX >> 4);
 272     appendDigit(Str, Below0 >> 60);
 273     Below0 = Below0 & (UINT64_MAX >> 4);
 274     if (DigitsOut || Str.back() != '0')
 275       ++DigitsOut;
 276     ++SinceDot;
 277   } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
 278            (!Precision || DigitsOut <= Precision || SinceDot < 2));
 279
 280   // Return early for maximum precision.
 281   if (!Precision || DigitsOut <= Precision)
 282     return stripTrailingZeros(Str);
 283
 284   // Find where to truncate.
 285   size_t Truncate =
 286       std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
 287
 288   // Check if there's anything to truncate.
 289   if (Truncate >= Str.size())
 290     return stripTrailingZeros(Str);
 291
 292   bool Carry = doesRoundUp(Str[Truncate]);
 293   if (!Carry)
 294     return stripTrailingZeros(Str.substr(0, Truncate));
 295
 296   // Round with the first truncated digit.
 297   for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
 298        I != E; ++I) {
 299     if (*I == '.')
 300       continue;
 301     if (*I == '9') {
 302       *I = '0';
 303       continue;
 304     }
 305
 306     ++*I;
 307     Carry = false;
 308     break;
 309   }
 310
 311   // Add "1" in front if we still need to carry.
 312   return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
 313 }
 314
 315 raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
 316                                      int Width, unsigned Precision) {
 317   return OS << toString(D, E, Width, Precision);
 318 }
 319
 320 void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
 321   print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
 322                                 << "]";
 323 }