1//===-- IntegerDivision.cpp - Expand integer division ---------------------===// 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// 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 14// 15//===----------------------------------------------------------------------===// 16 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" 23 24using namespace llvm; 25 26/// Generate code to compute the remainder of two signed integers. Returns the 27/// remainder, which will have the sign of the dividend. Builder's insert point 28/// should be pointing where the caller wants code generated, e.g. at the srem 29/// instruction. This will generate a urem in the process, and Builder's insert 30/// point will be pointing at the uren (if present, i.e. not folded), ready to 31/// be expanded if the user wishes 32static Value *generateSignedRemainderCode(Value *Dividend, Value *Divisor, 33 IRBuilder<> &Builder) { 34 ConstantInt *ThirtyOne = Builder.getInt32(31); 35 36 // ; %dividend_sgn = ashr i32 %dividend, 31 37 // ; %divisor_sgn = ashr i32 %divisor, 31 38 // ; %dvd_xor = xor i32 %dividend, %dividend_sgn 39 // ; %dvs_xor = xor i32 %divisor, %divisor_sgn 40 // ; %u_dividend = sub i32 %dvd_xor, %dividend_sgn 41 // ; %u_divisor = sub i32 %dvs_xor, %divisor_sgn 42 // ; %urem = urem i32 %dividend, %divisor 43 // ; %xored = xor i32 %urem, %dividend_sgn 44 // ; %srem = sub i32 %xored, %dividend_sgn 45 Value *DividendSign = Builder.CreateAShr(Dividend, ThirtyOne); 46 Value *DivisorSign = Builder.CreateAShr(Divisor, ThirtyOne); 47 Value *DvdXor = Builder.CreateXor(Dividend, DividendSign); 48 Value *DvsXor = Builder.CreateXor(Divisor, DivisorSign); 49 Value *UDividend = Builder.CreateSub(DvdXor, DividendSign); 50 Value *UDivisor = Builder.CreateSub(DvsXor, DivisorSign); 51 Value *URem = Builder.CreateURem(UDividend, UDivisor); 52 Value *Xored = Builder.CreateXor(URem, DividendSign); 53 Value *SRem = Builder.CreateSub(Xored, DividendSign); 54 55 if (Instruction *URemInst = dyn_cast<Instruction>(URem)) 56 Builder.SetInsertPoint(URemInst); 57 58 return SRem; 59} 60 61 62/// Generate code to compute the remainder of two unsigned integers. Returns the 63/// remainder. Builder's insert point should be pointing where the caller wants 64/// code generated, e.g. at the urem instruction. This will generate a udiv in 65/// the process, and Builder's insert point will be pointing at the udiv (if 66/// present, i.e. not folded), ready to be expanded if the user wishes 67static Value *generatedUnsignedRemainderCode(Value *Dividend, Value *Divisor, 68 IRBuilder<> &Builder) { 69 // Remainder = Dividend - Quotient*Divisor 70 71 // ; %quotient = udiv i32 %dividend, %divisor 72 // ; %product = mul i32 %divisor, %quotient 73 // ; %remainder = sub i32 %dividend, %product 74 Value *Quotient = Builder.CreateUDiv(Dividend, Divisor); 75 Value *Product = Builder.CreateMul(Divisor, Quotient); 76 Value *Remainder = Builder.CreateSub(Dividend, Product); 77 78 if (Instruction *UDiv = dyn_cast<Instruction>(Quotient)) 79 Builder.SetInsertPoint(UDiv); 80 81 return Remainder; 82} 83 84/// Generate code to divide two signed integers. Returns the quotient, rounded 85/// towards 0. Builder's insert point should be pointing where the caller wants 86/// code generated, e.g. at the sdiv instruction. This will generate a udiv in 87/// the process, and Builder's insert point will be pointing at the udiv (if 88/// present, i.e. not folded), ready to be expanded if the user wishes. 89static Value *generateSignedDivisionCode(Value *Dividend, Value *Divisor, 90 IRBuilder<> &Builder) { 91 // Implementation taken from compiler-rt's __divsi3 92 93 ConstantInt *ThirtyOne = Builder.getInt32(31); 94 95 // ; %tmp = ashr i32 %dividend, 31 96 // ; %tmp1 = ashr i32 %divisor, 31 97 // ; %tmp2 = xor i32 %tmp, %dividend 98 // ; %u_dvnd = sub nsw i32 %tmp2, %tmp 99 // ; %tmp3 = xor i32 %tmp1, %divisor 100 // ; %u_dvsr = sub nsw i32 %tmp3, %tmp1 101 // ; %q_sgn = xor i32 %tmp1, %tmp 102 // ; %q_mag = udiv i32 %u_dvnd, %u_dvsr 103 // ; %tmp4 = xor i32 %q_mag, %q_sgn 104 // ; %q = sub i32 %tmp4, %q_sgn 105 Value *Tmp = Builder.CreateAShr(Dividend, ThirtyOne); 106 Value *Tmp1 = Builder.CreateAShr(Divisor, ThirtyOne); 107 Value *Tmp2 = Builder.CreateXor(Tmp, Dividend); 108 Value *U_Dvnd = Builder.CreateSub(Tmp2, Tmp); 109 Value *Tmp3 = Builder.CreateXor(Tmp1, Divisor); 110 Value *U_Dvsr = Builder.CreateSub(Tmp3, Tmp1); 111 Value *Q_Sgn = Builder.CreateXor(Tmp1, Tmp); 112 Value *Q_Mag = Builder.CreateUDiv(U_Dvnd, U_Dvsr); 113 Value *Tmp4 = Builder.CreateXor(Q_Mag, Q_Sgn); 114 Value *Q = Builder.CreateSub(Tmp4, Q_Sgn); 115 116 if (Instruction *UDiv = dyn_cast<Instruction>(Q_Mag)) 117 Builder.SetInsertPoint(UDiv); 118 119 return Q; 120} 121 122/// Generates code to divide two unsigned scalar 32-bit integers. Returns the 123/// quotient, rounded towards 0. Builder's insert point should be pointing where 124/// the caller wants code generated, e.g. at the udiv instruction. 125static Value *generateUnsignedDivisionCode(Value *Dividend, Value *Divisor, 126 IRBuilder<> &Builder) { 127 // The basic algorithm can be found in the compiler-rt project's 128 // implementation of __udivsi3.c. Here, we do a lower-level IR based approach 129 // that's been hand-tuned to lessen the amount of control flow involved. 130 131 // Some helper values 132 IntegerType *I32Ty = Builder.getInt32Ty(); 133 134 ConstantInt *Zero = Builder.getInt32(0); 135 ConstantInt *One = Builder.getInt32(1); 136 ConstantInt *ThirtyOne = Builder.getInt32(31); 137 ConstantInt *NegOne = ConstantInt::getSigned(I32Ty, -1); 138 ConstantInt *True = Builder.getTrue(); 139 140 BasicBlock *IBB = Builder.GetInsertBlock(); 141 Function *F = IBB->getParent(); 142 Function *CTLZi32 = Intrinsic::getDeclaration(F->getParent(), Intrinsic::ctlz, 143 I32Ty); 144 145 // Our CFG is going to look like: 146 // +---------------------+ 147 // | special-cases | 148 // | ... | 149 // +---------------------+ 150 // | | 151 // | +----------+ 152 // | | bb1 | 153 // | | ... | 154 // | +----------+ 155 // | | | 156 // | | +------------+ 157 // | | | preheader | 158 // | | | ... | 159 // | | +------------+ 160 // | | | 161 // | | | +---+ 162 // | | | | | 163 // | | +------------+ | 164 // | | | do-while | | 165 // | | | ... | | 166 // | | +------------+ | 167 // | | | | | 168 // | +-----------+ +---+ 169 // | | loop-exit | 170 // | | ... | 171 // | +-----------+ 172 // | | 173 // +-------+ 174 // | ... | 175 // | end | 176 // +-------+ 177 BasicBlock *SpecialCases = Builder.GetInsertBlock(); 178 SpecialCases->setName(Twine(SpecialCases->getName(), "_udiv-special-cases")); 179 BasicBlock *End = SpecialCases->splitBasicBlock(Builder.GetInsertPoint(), 180 "udiv-end"); 181 BasicBlock *LoopExit = BasicBlock::Create(Builder.getContext(), 182 "udiv-loop-exit", F, End); 183 BasicBlock *DoWhile = BasicBlock::Create(Builder.getContext(), 184 "udiv-do-while", F, End); 185 BasicBlock *Preheader = BasicBlock::Create(Builder.getContext(), 186 "udiv-preheader", F, End); 187 BasicBlock *BB1 = BasicBlock::Create(Builder.getContext(), 188 "udiv-bb1", F, End); 189 190 // We'll be overwriting the terminator to insert our extra blocks 191 SpecialCases->getTerminator()->eraseFromParent(); 192 193 // First off, check for special cases: dividend or divisor is zero, divisor 194 // is greater than dividend, and divisor is 1. 195 // ; special-cases: 196 // ; %ret0_1 = icmp eq i32 %divisor, 0 197 // ; %ret0_2 = icmp eq i32 %dividend, 0 198 // ; %ret0_3 = or i1 %ret0_1, %ret0_2 199 // ; %tmp0 = tail call i32 @llvm.ctlz.i32(i32 %divisor, i1 true) 200 // ; %tmp1 = tail call i32 @llvm.ctlz.i32(i32 %dividend, i1 true) 201 // ; %sr = sub nsw i32 %tmp0, %tmp1 202 // ; %ret0_4 = icmp ugt i32 %sr, 31 203 // ; %ret0 = or i1 %ret0_3, %ret0_4 204 // ; %retDividend = icmp eq i32 %sr, 31 205 // ; %retVal = select i1 %ret0, i32 0, i32 %dividend 206 // ; %earlyRet = or i1 %ret0, %retDividend 207 // ; br i1 %earlyRet, label %end, label %bb1 208 Builder.SetInsertPoint(SpecialCases); 209 Value *Ret0_1 = Builder.CreateICmpEQ(Divisor, Zero); 210 Value *Ret0_2 = Builder.CreateICmpEQ(Dividend, Zero); 211 Value *Ret0_3 = Builder.CreateOr(Ret0_1, Ret0_2); 212 Value *Tmp0 = Builder.CreateCall2(CTLZi32, Divisor, True); 213 Value *Tmp1 = Builder.CreateCall2(CTLZi32, Dividend, True); 214 Value *SR = Builder.CreateSub(Tmp0, Tmp1); 215 Value *Ret0_4 = Builder.CreateICmpUGT(SR, ThirtyOne); 216 Value *Ret0 = Builder.CreateOr(Ret0_3, Ret0_4); 217 Value *RetDividend = Builder.CreateICmpEQ(SR, ThirtyOne); 218 Value *RetVal = Builder.CreateSelect(Ret0, Zero, Dividend); 219 Value *EarlyRet = Builder.CreateOr(Ret0, RetDividend); 220 Builder.CreateCondBr(EarlyRet, End, BB1); 221 222 // ; bb1: ; preds = %special-cases 223 // ; %sr_1 = add i32 %sr, 1 224 // ; %tmp2 = sub i32 31, %sr 225 // ; %q = shl i32 %dividend, %tmp2 226 // ; %skipLoop = icmp eq i32 %sr_1, 0 227 // ; br i1 %skipLoop, label %loop-exit, label %preheader 228 Builder.SetInsertPoint(BB1); 229 Value *SR_1 = Builder.CreateAdd(SR, One); 230 Value *Tmp2 = Builder.CreateSub(ThirtyOne, SR); 231 Value *Q = Builder.CreateShl(Dividend, Tmp2); 232 Value *SkipLoop = Builder.CreateICmpEQ(SR_1, Zero); 233 Builder.CreateCondBr(SkipLoop, LoopExit, Preheader); 234 235 // ; preheader: ; preds = %bb1 236 // ; %tmp3 = lshr i32 %dividend, %sr_1 237 // ; %tmp4 = add i32 %divisor, -1 238 // ; br label %do-while 239 Builder.SetInsertPoint(Preheader); 240 Value *Tmp3 = Builder.CreateLShr(Dividend, SR_1); 241 Value *Tmp4 = Builder.CreateAdd(Divisor, NegOne); 242 Builder.CreateBr(DoWhile); 243 244 // ; do-while: ; preds = %do-while, %preheader 245 // ; %carry_1 = phi i32 [ 0, %preheader ], [ %carry, %do-while ] 246 // ; %sr_3 = phi i32 [ %sr_1, %preheader ], [ %sr_2, %do-while ] 247 // ; %r_1 = phi i32 [ %tmp3, %preheader ], [ %r, %do-while ] 248 // ; %q_2 = phi i32 [ %q, %preheader ], [ %q_1, %do-while ] 249 // ; %tmp5 = shl i32 %r_1, 1 250 // ; %tmp6 = lshr i32 %q_2, 31 251 // ; %tmp7 = or i32 %tmp5, %tmp6 252 // ; %tmp8 = shl i32 %q_2, 1 253 // ; %q_1 = or i32 %carry_1, %tmp8 254 // ; %tmp9 = sub i32 %tmp4, %tmp7 255 // ; %tmp10 = ashr i32 %tmp9, 31 256 // ; %carry = and i32 %tmp10, 1 257 // ; %tmp11 = and i32 %tmp10, %divisor 258 // ; %r = sub i32 %tmp7, %tmp11 259 // ; %sr_2 = add i32 %sr_3, -1 260 // ; %tmp12 = icmp eq i32 %sr_2, 0 261 // ; br i1 %tmp12, label %loop-exit, label %do-while 262 Builder.SetInsertPoint(DoWhile); 263 PHINode *Carry_1 = Builder.CreatePHI(I32Ty, 2); 264 PHINode *SR_3 = Builder.CreatePHI(I32Ty, 2); 265 PHINode *R_1 = Builder.CreatePHI(I32Ty, 2); 266 PHINode *Q_2 = Builder.CreatePHI(I32Ty, 2); 267 Value *Tmp5 = Builder.CreateShl(R_1, One); 268 Value *Tmp6 = Builder.CreateLShr(Q_2, ThirtyOne); 269 Value *Tmp7 = Builder.CreateOr(Tmp5, Tmp6); 270 Value *Tmp8 = Builder.CreateShl(Q_2, One); 271 Value *Q_1 = Builder.CreateOr(Carry_1, Tmp8); 272 Value *Tmp9 = Builder.CreateSub(Tmp4, Tmp7); 273 Value *Tmp10 = Builder.CreateAShr(Tmp9, 31); 274 Value *Carry = Builder.CreateAnd(Tmp10, One); 275 Value *Tmp11 = Builder.CreateAnd(Tmp10, Divisor); 276 Value *R = Builder.CreateSub(Tmp7, Tmp11); 277 Value *SR_2 = Builder.CreateAdd(SR_3, NegOne); 278 Value *Tmp12 = Builder.CreateICmpEQ(SR_2, Zero); 279 Builder.CreateCondBr(Tmp12, LoopExit, DoWhile); 280 281 // ; loop-exit: ; preds = %do-while, %bb1 282 // ; %carry_2 = phi i32 [ 0, %bb1 ], [ %carry, %do-while ] 283 // ; %q_3 = phi i32 [ %q, %bb1 ], [ %q_1, %do-while ] 284 // ; %tmp13 = shl i32 %q_3, 1 285 // ; %q_4 = or i32 %carry_2, %tmp13 286 // ; br label %end 287 Builder.SetInsertPoint(LoopExit); 288 PHINode *Carry_2 = Builder.CreatePHI(I32Ty, 2); 289 PHINode *Q_3 = Builder.CreatePHI(I32Ty, 2); 290 Value *Tmp13 = Builder.CreateShl(Q_3, One); 291 Value *Q_4 = Builder.CreateOr(Carry_2, Tmp13); 292 Builder.CreateBr(End); 293 294 // ; end: ; preds = %loop-exit, %special-cases 295 // ; %q_5 = phi i32 [ %q_4, %loop-exit ], [ %retVal, %special-cases ] 296 // ; ret i32 %q_5 297 Builder.SetInsertPoint(End, End->begin()); 298 PHINode *Q_5 = Builder.CreatePHI(I32Ty, 2); 299 300 // Populate the Phis, since all values have now been created. Our Phis were: 301 // ; %carry_1 = phi i32 [ 0, %preheader ], [ %carry, %do-while ] 302 Carry_1->addIncoming(Zero, Preheader); 303 Carry_1->addIncoming(Carry, DoWhile); 304 // ; %sr_3 = phi i32 [ %sr_1, %preheader ], [ %sr_2, %do-while ] 305 SR_3->addIncoming(SR_1, Preheader); 306 SR_3->addIncoming(SR_2, DoWhile); 307 // ; %r_1 = phi i32 [ %tmp3, %preheader ], [ %r, %do-while ] 308 R_1->addIncoming(Tmp3, Preheader); 309 R_1->addIncoming(R, DoWhile); 310 // ; %q_2 = phi i32 [ %q, %preheader ], [ %q_1, %do-while ] 311 Q_2->addIncoming(Q, Preheader); 312 Q_2->addIncoming(Q_1, DoWhile); 313 // ; %carry_2 = phi i32 [ 0, %bb1 ], [ %carry, %do-while ] 314 Carry_2->addIncoming(Zero, BB1); 315 Carry_2->addIncoming(Carry, DoWhile); 316 // ; %q_3 = phi i32 [ %q, %bb1 ], [ %q_1, %do-while ] 317 Q_3->addIncoming(Q, BB1); 318 Q_3->addIncoming(Q_1, DoWhile); 319 // ; %q_5 = phi i32 [ %q_4, %loop-exit ], [ %retVal, %special-cases ] 320 Q_5->addIncoming(Q_4, LoopExit); 321 Q_5->addIncoming(RetVal, SpecialCases); 322 323 return Q_5; 324} 325 326/// Generate code to calculate the remainder of two integers, replacing Rem with 327/// the generated code. This currently generates code using the udiv expansion, 328/// but future work includes generating more specialized code, e.g. when more 329/// information about the operands are known. Currently only implements 32bit 330/// scalar division (due to udiv's limitation), but future work is removing this 331/// limitation. 332/// 333/// @brief Replace Rem with generated code. 334bool llvm::expandRemainder(BinaryOperator *Rem) { 335 assert((Rem->getOpcode() == Instruction::SRem || 336 Rem->getOpcode() == Instruction::URem) && 337 "Trying to expand remainder from a non-remainder function"); 338 339 IRBuilder<> Builder(Rem); 340 341 // First prepare the sign if it's a signed remainder 342 if (Rem->getOpcode() == Instruction::SRem) { 343 Value *Remainder = generateSignedRemainderCode(Rem->getOperand(0), 344 Rem->getOperand(1), Builder); 345 346 Rem->replaceAllUsesWith(Remainder); 347 Rem->dropAllReferences(); 348 Rem->eraseFromParent(); 349 350 // If we didn't actually generate a udiv instruction, we're done 351 BinaryOperator *BO = dyn_cast<BinaryOperator>(Builder.GetInsertPoint()); 352 if (!BO || BO->getOpcode() != Instruction::URem) 353 return true; 354 355 Rem = BO; 356 } 357 358 Value *Remainder = generatedUnsignedRemainderCode(Rem->getOperand(0), 359 Rem->getOperand(1), 360 Builder); 361 362 Rem->replaceAllUsesWith(Remainder); 363 Rem->dropAllReferences(); 364 Rem->eraseFromParent(); 365 366 // Expand the udiv 367 if (BinaryOperator *UDiv = dyn_cast<BinaryOperator>(Builder.GetInsertPoint())) { 368 assert(UDiv->getOpcode() == Instruction::UDiv && "Non-udiv in expansion?"); 369 expandDivision(UDiv); 370 } 371 372 return true; 373} 374 375 376/// Generate code to divide two integers, replacing Div with the generated 377/// code. This currently generates code similarly to compiler-rt's 378/// implementations, but future work includes generating more specialized code 379/// when more information about the operands are known. Currently only 380/// implements 32bit scalar division, but future work is removing this 381/// limitation. 382/// 383/// @brief Replace Div with generated code. 384bool llvm::expandDivision(BinaryOperator *Div) { 385 assert((Div->getOpcode() == Instruction::SDiv || 386 Div->getOpcode() == Instruction::UDiv) && 387 "Trying to expand division from a non-division function"); 388 389 IRBuilder<> Builder(Div); 390 391 if (Div->getType()->isVectorTy()) 392 llvm_unreachable("Div over vectors not supported"); 393 394 // First prepare the sign if it's a signed division 395 if (Div->getOpcode() == Instruction::SDiv) { 396 // Lower the code to unsigned division, and reset Div to point to the udiv. 397 Value *Quotient = generateSignedDivisionCode(Div->getOperand(0), 398 Div->getOperand(1), Builder); 399 Div->replaceAllUsesWith(Quotient); 400 Div->dropAllReferences(); 401 Div->eraseFromParent(); 402 403 // If we didn't actually generate a udiv instruction, we're done 404 BinaryOperator *BO = dyn_cast<BinaryOperator>(Builder.GetInsertPoint()); 405 if (!BO || BO->getOpcode() != Instruction::UDiv) 406 return true; 407 408 Div = BO; 409 } 410 411 // Insert the unsigned division code 412 Value *Quotient = generateUnsignedDivisionCode(Div->getOperand(0), 413 Div->getOperand(1), 414 Builder); 415 Div->replaceAllUsesWith(Quotient); 416 Div->dropAllReferences(); 417 Div->eraseFromParent(); 418 419 return true; 420} 421