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"
16 #include "llvm/ADT/APFloat.h"
17 #include "llvm/Support/Debug.h"
20 using namespace llvm::ScaledNumbers;
22 std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
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);
29 // Compute cross products.
30 uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
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);
42 // Check whether the upper digit is empty.
44 return std::make_pair(Lower, 0);
46 // Shift as little as possible to maximize precision.
47 unsigned LeadingZeros = countLeadingZeros(Upper);
48 int Shift = 64 - LeadingZeros;
50 Upper = Upper << LeadingZeros | Lower >> Shift;
51 return getRounded(Upper, Shift,
52 Shift && (Lower & UINT64_C(1) << (Shift - 1)));
55 static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
57 std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
59 assert(Dividend && "expected non-zero dividend");
60 assert(Divisor && "expected non-zero divisor");
62 // Use 64-bit math and canonicalize the dividend to gain precision.
63 uint64_t Dividend64 = Dividend;
65 if (int Zeros = countLeadingZeros(Dividend64)) {
69 uint64_t Quotient = Dividend64 / Divisor;
70 uint64_t Remainder = Dividend64 % Divisor;
72 // If Quotient needs to be shifted, leave the rounding to getAdjusted().
73 if (Quotient > UINT32_MAX)
74 return getAdjusted<uint32_t>(Quotient, Shift);
76 // Round based on the value of the next bit.
77 return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
80 std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
82 assert(Dividend && "expected non-zero dividend");
83 assert(Divisor && "expected non-zero divisor");
85 // Minimize size of divisor.
87 if (int Zeros = countTrailingZeros(Divisor)) {
92 // Check for powers of two.
94 return std::make_pair(Dividend, Shift);
96 // Maximize size of dividend.
97 if (int Zeros = countLeadingZeros(Dividend)) {
102 // Start with the result of a divide.
103 uint64_t Quotient = Dividend / Divisor;
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;
113 // Get the next bit of Quotient.
115 if (IsOverflow || Divisor <= Dividend) {
121 return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
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");
128 uint64_t L_adjusted = L >> ScaleDiff;
134 return L > L_adjusted << ScaleDiff ? 1 : 0;
137 static void appendDigit(std::string &Str, unsigned D) {
142 static void appendNumber(std::string &Str, uint64_t N) {
144 appendDigit(Str, N % 10);
149 static bool doesRoundUp(char Digit) {
162 static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
163 assert(E >= ScaledNumbers::MinScale);
164 assert(E <= ScaledNumbers::MaxScale);
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 & (1u << std::numeric_limits<int>::digits)) == 0 &&
173 "undefined behavior");
177 // Check for a denormal.
178 unsigned AdjustedE = E + 16383;
180 assert(E == ScaledNumbers::MaxScale);
184 // Build the float and print it.
185 uint64_t RawBits[2] = {D, AdjustedE};
186 APFloat Float(APFloat::x87DoubleExtended, APInt(80, RawBits));
187 SmallVector<char, 24> Chars;
188 Float.toString(Chars, Precision, 0);
189 return std::string(Chars.begin(), Chars.end());
192 static std::string stripTrailingZeros(const std::string &Float) {
193 size_t NonZero = Float.find_last_not_of('0');
194 assert(NonZero != std::string::npos && "no . in floating point string");
196 if (Float[NonZero] == '.')
199 return Float.substr(0, NonZero + 1);
202 std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
203 unsigned Precision) {
207 // Canonicalize exponent and digits.
215 if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
222 } else if (E > -64) {
224 Below0 = D << (64 + E);
225 } else if (E == -64) {
226 // Special case: shift by 64 bits is undefined behavior.
228 } else if (E > -120) {
229 Below0 = D >> (-E - 64);
230 Extra = D << (128 + E);
231 ExtraShift = -64 - E;
234 // Fall back on APFloat for very small and very large numbers.
235 if (!Above0 && !Below0)
236 return toStringAPFloat(D, E, Precision);
238 // Append the digits before the decimal.
240 size_t DigitsOut = 0;
242 appendNumber(Str, Above0);
243 DigitsOut = Str.size();
246 std::reverse(Str.begin(), Str.end());
248 // Return early if there's nothing after the decimal.
252 // Append the decimal and beyond.
254 uint64_t Error = UINT64_C(1) << (64 - Width);
256 // We need to shift Below0 to the right to make space for calculating
257 // digits. Save the precision we're losing in Extra.
258 Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
261 size_t AfterDot = Str.size();
271 Below0 += (Extra >> 60);
272 Extra = Extra & (UINT64_MAX >> 4);
273 appendDigit(Str, Below0 >> 60);
274 Below0 = Below0 & (UINT64_MAX >> 4);
275 if (DigitsOut || Str.back() != '0')
278 } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
279 (!Precision || DigitsOut <= Precision || SinceDot < 2));
281 // Return early for maximum precision.
282 if (!Precision || DigitsOut <= Precision)
283 return stripTrailingZeros(Str);
285 // Find where to truncate.
287 std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
289 // Check if there's anything to truncate.
290 if (Truncate >= Str.size())
291 return stripTrailingZeros(Str);
293 bool Carry = doesRoundUp(Str[Truncate]);
295 return stripTrailingZeros(Str.substr(0, Truncate));
297 // Round with the first truncated digit.
298 for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
312 // Add "1" in front if we still need to carry.
313 return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
316 raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
317 int Width, unsigned Precision) {
318 return OS << toString(D, E, Width, Precision);
321 void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
322 print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E