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
16 #include "llvm/ADT/APFloat.h"
17 #include "llvm/Support/Debug.h"
18
19 using namespace llvm;
20 using namespace llvm::ScaledNumbers;
21
multiply64(uint64_t LHS,uint64_t RHS)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
getHalf(uint64_t N)55 static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
56
divide32(uint32_t Dividend,uint32_t Divisor)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
divide64(uint64_t Dividend,uint64_t Divisor)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
compareImpl(uint64_t L,uint64_t R,int ScaleDiff)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
appendDigit(std::string & Str,unsigned D)137 static void appendDigit(std::string &Str, unsigned D) {
138 assert(D < 10);
139 Str += '0' + D % 10;
140 }
141
appendNumber(std::string & Str,uint64_t N)142 static void appendNumber(std::string &Str, uint64_t N) {
143 while (N) {
144 appendDigit(Str, N % 10);
145 N /= 10;
146 }
147 }
148
doesRoundUp(char Digit)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
toStringAPFloat(uint64_t D,int E,unsigned Precision)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 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
stripTrailingZeros(const std::string & Float)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
toString(uint64_t D,int16_t E,int Width,unsigned Precision)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 > -120) {
224 Below0 = D >> (-E - 64);
225 Extra = D << (128 + E);
226 ExtraShift = -64 - E;
227 }
228
229 // Fall back on APFloat for very small and very large numbers.
230 if (!Above0 && !Below0)
231 return toStringAPFloat(D, E, Precision);
232
233 // Append the digits before the decimal.
234 std::string Str;
235 size_t DigitsOut = 0;
236 if (Above0) {
237 appendNumber(Str, Above0);
238 DigitsOut = Str.size();
239 } else
240 appendDigit(Str, 0);
241 std::reverse(Str.begin(), Str.end());
242
243 // Return early if there's nothing after the decimal.
244 if (!Below0)
245 return Str + ".0";
246
247 // Append the decimal and beyond.
248 Str += '.';
249 uint64_t Error = UINT64_C(1) << (64 - Width);
250
251 // We need to shift Below0 to the right to make space for calculating
252 // digits. Save the precision we're losing in Extra.
253 Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
254 Below0 >>= 4;
255 size_t SinceDot = 0;
256 size_t AfterDot = Str.size();
257 do {
258 if (ExtraShift) {
259 --ExtraShift;
260 Error *= 5;
261 } else
262 Error *= 10;
263
264 Below0 *= 10;
265 Extra *= 10;
266 Below0 += (Extra >> 60);
267 Extra = Extra & (UINT64_MAX >> 4);
268 appendDigit(Str, Below0 >> 60);
269 Below0 = Below0 & (UINT64_MAX >> 4);
270 if (DigitsOut || Str.back() != '0')
271 ++DigitsOut;
272 ++SinceDot;
273 } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
274 (!Precision || DigitsOut <= Precision || SinceDot < 2));
275
276 // Return early for maximum precision.
277 if (!Precision || DigitsOut <= Precision)
278 return stripTrailingZeros(Str);
279
280 // Find where to truncate.
281 size_t Truncate =
282 std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
283
284 // Check if there's anything to truncate.
285 if (Truncate >= Str.size())
286 return stripTrailingZeros(Str);
287
288 bool Carry = doesRoundUp(Str[Truncate]);
289 if (!Carry)
290 return stripTrailingZeros(Str.substr(0, Truncate));
291
292 // Round with the first truncated digit.
293 for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
294 I != E; ++I) {
295 if (*I == '.')
296 continue;
297 if (*I == '9') {
298 *I = '0';
299 continue;
300 }
301
302 ++*I;
303 Carry = false;
304 break;
305 }
306
307 // Add "1" in front if we still need to carry.
308 return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
309 }
310
print(raw_ostream & OS,uint64_t D,int16_t E,int Width,unsigned Precision)311 raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
312 int Width, unsigned Precision) {
313 return OS << toString(D, E, Width, Precision);
314 }
315
dump(uint64_t D,int16_t E,int Width)316 void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
317 print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
318 << "]";
319 }
320