1 //===-- IntegerDivision.cpp - Expand integer division ---------------------===//
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 // This file contains an implementation of 32bit scalar integer division for
11 // targets that don't have native support. It's largely derived from
12 // compiler-rt's implementation of __udivsi3, but hand-tuned to reduce the
13 // amount of control flow
15 //===----------------------------------------------------------------------===//
17 #define DEBUG_TYPE "integer-division"
18 #include "llvm/Function.h"
19 #include "llvm/Instructions.h"
20 #include "llvm/Intrinsics.h"
21 #include "llvm/IRBuilder.h"
22 #include "llvm/Transforms/Utils/IntegerDivision.h"
26 // Generate code to divide two signed integers. Returns the quotient, rounded
27 // towards 0. Builder's insert point should be pointing at the sdiv
28 // instruction. This will generate a udiv in the process, and Builder's insert
29 // point will be pointing at the udiv (if present, i.e. not folded), ready to be
30 // expanded if the user wishes.
31 static Value *GenerateSignedDivisionCode(Value *Dividend, Value *Divisor,
32 IRBuilder<> &Builder) {
33 // Implementation taken from compiler-rt's __divsi3
35 ConstantInt *ThirtyOne = Builder.getInt32(31);
37 // ; %tmp = ashr i32 %dividend, 31
38 // ; %tmp1 = ashr i32 %divisor, 31
39 // ; %tmp2 = xor i32 %tmp, %dividend
40 // ; %u_dvnd = sub nsw i32 %tmp2, %tmp
41 // ; %tmp3 = xor i32 %tmp1, %divisor
42 // ; %u_dvsr = sub nsw i32 %tmp3, %tmp1
43 // ; %q_sgn = xor i32 %tmp1, %tmp
44 // ; %q_mag = udiv i32 %u_dvnd, %u_dvsr
45 // ; %tmp4 = xor i32 %q_mag, %q_sgn
46 // ; %q = sub i32 %tmp4, %q_sgn
47 Value *Tmp = Builder.CreateAShr(Dividend, ThirtyOne);
48 Value *Tmp1 = Builder.CreateAShr(Divisor, ThirtyOne);
49 Value *Tmp2 = Builder.CreateXor(Tmp, Dividend);
50 Value *U_Dvnd = Builder.CreateSub(Tmp2, Tmp);
51 Value *Tmp3 = Builder.CreateXor(Tmp1, Divisor);
52 Value *U_Dvsr = Builder.CreateSub(Tmp3, Tmp1);
53 Value *Q_Sgn = Builder.CreateXor(Tmp1, Tmp);
54 Value *Q_Mag = Builder.CreateUDiv(U_Dvnd, U_Dvsr);
55 Value *Tmp4 = Builder.CreateXor(Q_Mag, Q_Sgn);
56 Value *Q = Builder.CreateSub(Tmp4, Q_Sgn);
58 if (Instruction *UDiv = dyn_cast<Instruction>(Q_Mag))
59 Builder.SetInsertPoint(UDiv);
64 // Generates code to divide two unsigned scalar 32-bit integers. Returns the
65 // quotient, rounded towards 0. Builder's insert point should be pointing at the
67 static Value *GenerateUnsignedDivisionCode(Value *Dividend, Value *Divisor,
68 IRBuilder<> &Builder) {
69 // The basic algorithm can be found in the compiler-rt project's
70 // implementation of __udivsi3.c. Here, we do a lower-level IR based approach
71 // that's been hand-tuned to lessen the amount of control flow involved.
74 IntegerType *I32Ty = Builder.getInt32Ty();
76 ConstantInt *Zero = Builder.getInt32(0);
77 ConstantInt *One = Builder.getInt32(1);
78 ConstantInt *ThirtyOne = Builder.getInt32(31);
79 ConstantInt *NegOne = ConstantInt::getSigned(I32Ty, -1);
80 ConstantInt *True = Builder.getTrue();
82 BasicBlock *IBB = Builder.GetInsertBlock();
83 Function *F = IBB->getParent();
84 Function *CTLZi32 = Intrinsic::getDeclaration(F->getParent(), Intrinsic::ctlz,
87 // Our CFG is going to look like:
88 // +---------------------+
91 // +---------------------+
101 // | | +------------+
105 // | | +------------+ |
106 // | | | do-while | |
108 // | | +------------+ |
110 // | +-----------+ +---+
119 BasicBlock *SpecialCases = Builder.GetInsertBlock();
120 SpecialCases->setName(Twine(SpecialCases->getName(), "_udiv-special-cases"));
121 BasicBlock *End = SpecialCases->splitBasicBlock(Builder.GetInsertPoint(),
123 BasicBlock *LoopExit = BasicBlock::Create(Builder.getContext(),
124 "udiv-loop-exit", F, End);
125 BasicBlock *DoWhile = BasicBlock::Create(Builder.getContext(),
126 "udiv-do-while", F, End);
127 BasicBlock *Preheader = BasicBlock::Create(Builder.getContext(),
128 "udiv-preheader", F, End);
129 BasicBlock *BB1 = BasicBlock::Create(Builder.getContext(),
132 // We'll be overwriting the terminator to insert our extra blocks
133 SpecialCases->getTerminator()->eraseFromParent();
135 // First off, check for special cases: dividend or divisor is zero, divisor
136 // is greater than dividend, and divisor is 1.
138 // ; %ret0_1 = icmp eq i32 %divisor, 0
139 // ; %ret0_2 = icmp eq i32 %dividend, 0
140 // ; %ret0_3 = or i1 %ret0_1, %ret0_2
141 // ; %tmp0 = tail call i32 @llvm.ctlz.i32(i32 %divisor, i1 true)
142 // ; %tmp1 = tail call i32 @llvm.ctlz.i32(i32 %dividend, i1 true)
143 // ; %sr = sub nsw i32 %tmp0, %tmp1
144 // ; %ret0_4 = icmp ugt i32 %sr, 31
145 // ; %ret0 = or i1 %ret0_3, %ret0_4
146 // ; %retDividend = icmp eq i32 %sr, 31
147 // ; %retVal = select i1 %ret0, i32 0, i32 %dividend
148 // ; %earlyRet = or i1 %ret0, %retDividend
149 // ; br i1 %earlyRet, label %end, label %bb1
150 Builder.SetInsertPoint(SpecialCases);
151 Value *Ret0_1 = Builder.CreateICmpEQ(Divisor, Zero);
152 Value *Ret0_2 = Builder.CreateICmpEQ(Dividend, Zero);
153 Value *Ret0_3 = Builder.CreateOr(Ret0_1, Ret0_2);
154 Value *Tmp0 = Builder.CreateCall2(CTLZi32, Divisor, True);
155 Value *Tmp1 = Builder.CreateCall2(CTLZi32, Dividend, True);
156 Value *SR = Builder.CreateSub(Tmp0, Tmp1);
157 Value *Ret0_4 = Builder.CreateICmpUGT(SR, ThirtyOne);
158 Value *Ret0 = Builder.CreateOr(Ret0_3, Ret0_4);
159 Value *RetDividend = Builder.CreateICmpEQ(SR, ThirtyOne);
160 Value *RetVal = Builder.CreateSelect(Ret0, Zero, Dividend);
161 Value *EarlyRet = Builder.CreateOr(Ret0, RetDividend);
162 Builder.CreateCondBr(EarlyRet, End, BB1);
164 // ; bb1: ; preds = %special-cases
165 // ; %sr_1 = add i32 %sr, 1
166 // ; %tmp2 = sub i32 31, %sr
167 // ; %q = shl i32 %dividend, %tmp2
168 // ; %skipLoop = icmp eq i32 %sr_1, 0
169 // ; br i1 %skipLoop, label %loop-exit, label %preheader
170 Builder.SetInsertPoint(BB1);
171 Value *SR_1 = Builder.CreateAdd(SR, One);
172 Value *Tmp2 = Builder.CreateSub(ThirtyOne, SR);
173 Value *Q = Builder.CreateShl(Dividend, Tmp2);
174 Value *SkipLoop = Builder.CreateICmpEQ(SR_1, Zero);
175 Builder.CreateCondBr(SkipLoop, LoopExit, Preheader);
177 // ; preheader: ; preds = %bb1
178 // ; %tmp3 = lshr i32 %dividend, %sr_1
179 // ; %tmp4 = add i32 %divisor, -1
180 // ; br label %do-while
181 Builder.SetInsertPoint(Preheader);
182 Value *Tmp3 = Builder.CreateLShr(Dividend, SR_1);
183 Value *Tmp4 = Builder.CreateAdd(Divisor, NegOne);
184 Builder.CreateBr(DoWhile);
186 // ; do-while: ; preds = %do-while, %preheader
187 // ; %carry_1 = phi i32 [ 0, %preheader ], [ %carry, %do-while ]
188 // ; %sr_3 = phi i32 [ %sr_1, %preheader ], [ %sr_2, %do-while ]
189 // ; %r_1 = phi i32 [ %tmp3, %preheader ], [ %r, %do-while ]
190 // ; %q_2 = phi i32 [ %q, %preheader ], [ %q_1, %do-while ]
191 // ; %tmp5 = shl i32 %r_1, 1
192 // ; %tmp6 = lshr i32 %q_2, 31
193 // ; %tmp7 = or i32 %tmp5, %tmp6
194 // ; %tmp8 = shl i32 %q_2, 1
195 // ; %q_1 = or i32 %carry_1, %tmp8
196 // ; %tmp9 = sub i32 %tmp4, %tmp7
197 // ; %tmp10 = ashr i32 %tmp9, 31
198 // ; %carry = and i32 %tmp10, 1
199 // ; %tmp11 = and i32 %tmp10, %divisor
200 // ; %r = sub i32 %tmp7, %tmp11
201 // ; %sr_2 = add i32 %sr_3, -1
202 // ; %tmp12 = icmp eq i32 %sr_2, 0
203 // ; br i1 %tmp12, label %loop-exit, label %do-while
204 Builder.SetInsertPoint(DoWhile);
205 PHINode *Carry_1 = Builder.CreatePHI(I32Ty, 2);
206 PHINode *SR_3 = Builder.CreatePHI(I32Ty, 2);
207 PHINode *R_1 = Builder.CreatePHI(I32Ty, 2);
208 PHINode *Q_2 = Builder.CreatePHI(I32Ty, 2);
209 Value *Tmp5 = Builder.CreateShl(R_1, One);
210 Value *Tmp6 = Builder.CreateLShr(Q_2, ThirtyOne);
211 Value *Tmp7 = Builder.CreateOr(Tmp5, Tmp6);
212 Value *Tmp8 = Builder.CreateShl(Q_2, One);
213 Value *Q_1 = Builder.CreateOr(Carry_1, Tmp8);
214 Value *Tmp9 = Builder.CreateSub(Tmp4, Tmp7);
215 Value *Tmp10 = Builder.CreateAShr(Tmp9, 31);
216 Value *Carry = Builder.CreateAnd(Tmp10, One);
217 Value *Tmp11 = Builder.CreateAnd(Tmp10, Divisor);
218 Value *R = Builder.CreateSub(Tmp7, Tmp11);
219 Value *SR_2 = Builder.CreateAdd(SR_3, NegOne);
220 Value *Tmp12 = Builder.CreateICmpEQ(SR_2, Zero);
221 Builder.CreateCondBr(Tmp12, LoopExit, DoWhile);
223 // ; loop-exit: ; preds = %do-while, %bb1
224 // ; %carry_2 = phi i32 [ 0, %bb1 ], [ %carry, %do-while ]
225 // ; %q_3 = phi i32 [ %q, %bb1 ], [ %q_1, %do-while ]
226 // ; %tmp13 = shl i32 %q_3, 1
227 // ; %q_4 = or i32 %carry_2, %tmp13
229 Builder.SetInsertPoint(LoopExit);
230 PHINode *Carry_2 = Builder.CreatePHI(I32Ty, 2);
231 PHINode *Q_3 = Builder.CreatePHI(I32Ty, 2);
232 Value *Tmp13 = Builder.CreateShl(Q_3, One);
233 Value *Q_4 = Builder.CreateOr(Carry_2, Tmp13);
234 Builder.CreateBr(End);
236 // ; end: ; preds = %loop-exit, %special-cases
237 // ; %q_5 = phi i32 [ %q_4, %loop-exit ], [ %retVal, %special-cases ]
239 Builder.SetInsertPoint(End, End->begin());
240 PHINode *Q_5 = Builder.CreatePHI(I32Ty, 2);
242 // Populate the Phis, since all values have now been created. Our Phis were:
243 // ; %carry_1 = phi i32 [ 0, %preheader ], [ %carry, %do-while ]
244 Carry_1->addIncoming(Zero, Preheader);
245 Carry_1->addIncoming(Carry, DoWhile);
246 // ; %sr_3 = phi i32 [ %sr_1, %preheader ], [ %sr_2, %do-while ]
247 SR_3->addIncoming(SR_1, Preheader);
248 SR_3->addIncoming(SR_2, DoWhile);
249 // ; %r_1 = phi i32 [ %tmp3, %preheader ], [ %r, %do-while ]
250 R_1->addIncoming(Tmp3, Preheader);
251 R_1->addIncoming(R, DoWhile);
252 // ; %q_2 = phi i32 [ %q, %preheader ], [ %q_1, %do-while ]
253 Q_2->addIncoming(Q, Preheader);
254 Q_2->addIncoming(Q_1, DoWhile);
255 // ; %carry_2 = phi i32 [ 0, %bb1 ], [ %carry, %do-while ]
256 Carry_2->addIncoming(Zero, BB1);
257 Carry_2->addIncoming(Carry, DoWhile);
258 // ; %q_3 = phi i32 [ %q, %bb1 ], [ %q_1, %do-while ]
259 Q_3->addIncoming(Q, BB1);
260 Q_3->addIncoming(Q_1, DoWhile);
261 // ; %q_5 = phi i32 [ %q_4, %loop-exit ], [ %retVal, %special-cases ]
262 Q_5->addIncoming(Q_4, LoopExit);
263 Q_5->addIncoming(RetVal, SpecialCases);
268 bool llvm::expandDivision(BinaryOperator *Div) {
269 assert((Div->getOpcode() == Instruction::SDiv ||
270 Div->getOpcode() == Instruction::UDiv) &&
271 "Trying to expand division from a non-division function");
273 IRBuilder<> Builder(Div);
275 if (Div->getType()->isVectorTy())
276 llvm_unreachable("Div over vectors not supported");
278 // First prepare the sign if it's a signed division
279 if (Div->getOpcode() == Instruction::SDiv) {
280 // Lower the code to unsigned division, and reset Div to point to the udiv.
281 Value *Quotient = GenerateSignedDivisionCode(Div->getOperand(0),
282 Div->getOperand(1), Builder);
283 Div->replaceAllUsesWith(Quotient);
284 Div->dropAllReferences();
285 Div->eraseFromParent();
287 // If we didn't actually generate a udiv instruction, we're done
288 BinaryOperator *BO = dyn_cast<BinaryOperator>(Builder.GetInsertPoint());
289 if (!BO || BO->getOpcode() != Instruction::UDiv)
295 // Insert the unsigned division code
296 Value *Quotient = GenerateUnsignedDivisionCode(Div->getOperand(0),
299 Div->replaceAllUsesWith(Quotient);
300 Div->dropAllReferences();
301 Div->eraseFromParent();