1 //==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // Implementation of some scaled number algorithms.
12 //===----------------------------------------------------------------------===//
14 #include "llvm/Support/ScaledNumber.h"
15 #include "llvm/ADT/APFloat.h"
16 #include "llvm/Support/Debug.h"
19 using namespace llvm::ScaledNumbers;
21 std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
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);
28 // Compute cross products.
29 uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
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);
41 // Check whether the upper digit is empty.
43 return std::make_pair(Lower, 0);
45 // Shift as little as possible to maximize precision.
46 unsigned LeadingZeros = countLeadingZeros(Upper);
47 int Shift = 64 - LeadingZeros;
49 Upper = Upper << LeadingZeros | Lower >> Shift;
50 return getRounded(Upper, Shift,
51 Shift && (Lower & UINT64_C(1) << (Shift - 1)));
54 static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
56 std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
58 assert(Dividend && "expected non-zero dividend");
59 assert(Divisor && "expected non-zero divisor");
61 // Use 64-bit math and canonicalize the dividend to gain precision.
62 uint64_t Dividend64 = Dividend;
64 if (int Zeros = countLeadingZeros(Dividend64)) {
68 uint64_t Quotient = Dividend64 / Divisor;
69 uint64_t Remainder = Dividend64 % Divisor;
71 // If Quotient needs to be shifted, leave the rounding to getAdjusted().
72 if (Quotient > UINT32_MAX)
73 return getAdjusted<uint32_t>(Quotient, Shift);
75 // Round based on the value of the next bit.
76 return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
79 std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
81 assert(Dividend && "expected non-zero dividend");
82 assert(Divisor && "expected non-zero divisor");
84 // Minimize size of divisor.
86 if (int Zeros = countTrailingZeros(Divisor)) {
91 // Check for powers of two.
93 return std::make_pair(Dividend, Shift);
95 // Maximize size of dividend.
96 if (int Zeros = countLeadingZeros(Dividend)) {
101 // Start with the result of a divide.
102 uint64_t Quotient = Dividend / Divisor;
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;
112 // Get the next bit of Quotient.
114 if (IsOverflow || Divisor <= Dividend) {
120 return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
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");
127 uint64_t L_adjusted = L >> ScaleDiff;
133 return L > L_adjusted << ScaleDiff ? 1 : 0;
136 static void appendDigit(std::string &Str, unsigned D) {
141 static void appendNumber(std::string &Str, uint64_t N) {
143 appendDigit(Str, N % 10);
148 static bool doesRoundUp(char Digit) {
161 static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
162 assert(E >= ScaledNumbers::MinScale);
163 assert(E <= ScaledNumbers::MaxScale);
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");
175 // Check for a denormal.
176 unsigned AdjustedE = E + 16383;
178 assert(E == ScaledNumbers::MaxScale);
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());
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");
194 if (Float[NonZero] == '.')
197 return Float.substr(0, NonZero + 1);
200 std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
201 unsigned Precision) {
205 // Canonicalize exponent and digits.
213 if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
220 } else if (E > -64) {
222 Below0 = D << (64 + E);
223 } else if (E == -64) {
224 // Special case: shift by 64 bits is undefined behavior.
226 } else if (E > -120) {
227 Below0 = D >> (-E - 64);
228 Extra = D << (128 + E);
229 ExtraShift = -64 - E;
232 // Fall back on APFloat for very small and very large numbers.
233 if (!Above0 && !Below0)
234 return toStringAPFloat(D, E, Precision);
236 // Append the digits before the decimal.
238 size_t DigitsOut = 0;
240 appendNumber(Str, Above0);
241 DigitsOut = Str.size();
244 std::reverse(Str.begin(), Str.end());
246 // Return early if there's nothing after the decimal.
250 // Append the decimal and beyond.
252 uint64_t Error = UINT64_C(1) << (64 - Width);
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);
259 size_t AfterDot = Str.size();
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')
276 } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
277 (!Precision || DigitsOut <= Precision || SinceDot < 2));
279 // Return early for maximum precision.
280 if (!Precision || DigitsOut <= Precision)
281 return stripTrailingZeros(Str);
283 // Find where to truncate.
285 std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
287 // Check if there's anything to truncate.
288 if (Truncate >= Str.size())
289 return stripTrailingZeros(Str);
291 bool Carry = doesRoundUp(Str[Truncate]);
293 return stripTrailingZeros(Str.substr(0, Truncate));
295 // Round with the first truncated digit.
296 for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
310 // Add "1" in front if we still need to carry.
311 return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
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);
319 void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
320 print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E