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//===--------- SCEVAffinator.cpp - Create Scops from LLVM IR -------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Create a polyhedral description for a SCEV value.
//
//===----------------------------------------------------------------------===//
#include "polly/Support/SCEVAffinator.h"
#include "polly/Options.h"
#include "polly/ScopInfo.h"
#include "polly/Support/GICHelper.h"
#include "polly/Support/SCEVValidator.h"
#include "polly/Support/ScopHelper.h"
#include "isl/aff.h"
#include "isl/local_space.h"
#include "isl/set.h"
#include "isl/val.h"
using namespace llvm;
using namespace polly;
static cl::opt<bool> IgnoreIntegerWrapping(
"polly-ignore-integer-wrapping",
cl::desc("Do not build run-time checks to proof absence of integer "
"wrapping"),
cl::Hidden, cl::ZeroOrMore, cl::init(false), cl::cat(PollyCategory));
// The maximal number of basic sets we allow during the construction of a
// piecewise affine function. More complex ones will result in very high
// compile time.
static int const MaxDisjunctionsInPwAff = 100;
// The maximal number of bits for which a general expression is modeled
// precisely.
static unsigned const MaxSmallBitWidth = 7;
/// Add the number of basic sets in @p Domain to @p User
static isl_stat addNumBasicSets(__isl_take isl_set *Domain,
__isl_take isl_aff *Aff, void *User) {
auto *NumBasicSets = static_cast<unsigned *>(User);
*NumBasicSets += isl_set_n_basic_set(Domain);
isl_set_free(Domain);
isl_aff_free(Aff);
return isl_stat_ok;
}
/// Determine if @p PWAC is too complex to continue.
static bool isTooComplex(PWACtx PWAC) {
unsigned NumBasicSets = 0;
isl_pw_aff_foreach_piece(PWAC.first.get(), addNumBasicSets, &NumBasicSets);
if (NumBasicSets <= MaxDisjunctionsInPwAff)
return false;
return true;
}
/// Return the flag describing the possible wrapping of @p Expr.
static SCEV::NoWrapFlags getNoWrapFlags(const SCEV *Expr) {
if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))
return NAry->getNoWrapFlags();
return SCEV::NoWrapMask;
}
static PWACtx combine(PWACtx PWAC0, PWACtx PWAC1,
__isl_give isl_pw_aff *(Fn)(__isl_take isl_pw_aff *,
__isl_take isl_pw_aff *)) {
PWAC0.first = isl::manage(Fn(PWAC0.first.release(), PWAC1.first.release()));
PWAC0.second = PWAC0.second.unite(PWAC1.second);
return PWAC0;
}
static __isl_give isl_pw_aff *getWidthExpValOnDomain(unsigned Width,
__isl_take isl_set *Dom) {
auto *Ctx = isl_set_get_ctx(Dom);
auto *WidthVal = isl_val_int_from_ui(Ctx, Width);
auto *ExpVal = isl_val_2exp(WidthVal);
return isl_pw_aff_val_on_domain(Dom, ExpVal);
}
SCEVAffinator::SCEVAffinator(Scop *S, LoopInfo &LI)
: S(S), Ctx(S->getIslCtx().get()), SE(*S->getSE()), LI(LI),
TD(S->getFunction().getParent()->getDataLayout()) {}
Loop *SCEVAffinator::getScope() { return BB ? LI.getLoopFor(BB) : nullptr; }
void SCEVAffinator::interpretAsUnsigned(PWACtx &PWAC, unsigned Width) {
auto *NonNegDom = isl_pw_aff_nonneg_set(PWAC.first.copy());
auto *NonNegPWA =
isl_pw_aff_intersect_domain(PWAC.first.copy(), isl_set_copy(NonNegDom));
auto *ExpPWA = getWidthExpValOnDomain(Width, isl_set_complement(NonNegDom));
PWAC.first = isl::manage(isl_pw_aff_union_add(
NonNegPWA, isl_pw_aff_add(PWAC.first.release(), ExpPWA)));
}
void SCEVAffinator::takeNonNegativeAssumption(PWACtx &PWAC) {
auto *NegPWA = isl_pw_aff_neg(PWAC.first.copy());
auto *NegDom = isl_pw_aff_pos_set(NegPWA);
PWAC.second =
isl::manage(isl_set_union(PWAC.second.release(), isl_set_copy(NegDom)));
auto *Restriction = BB ? NegDom : isl_set_params(NegDom);
auto DL = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
S->recordAssumption(UNSIGNED, isl::manage(Restriction), DL, AS_RESTRICTION,
BB);
}
PWACtx SCEVAffinator::getPWACtxFromPWA(isl::pw_aff PWA) {
return std::make_pair(PWA, isl::set::empty(isl::space(Ctx, 0, NumIterators)));
}
PWACtx SCEVAffinator::getPwAff(const SCEV *Expr, BasicBlock *BB) {
this->BB = BB;
if (BB) {
auto *DC = S->getDomainConditions(BB).release();
NumIterators = isl_set_n_dim(DC);
isl_set_free(DC);
} else
NumIterators = 0;
return visit(Expr);
}
PWACtx SCEVAffinator::checkForWrapping(const SCEV *Expr, PWACtx PWAC) const {
// If the SCEV flags do contain NSW (no signed wrap) then PWA already
// represents Expr in modulo semantic (it is not allowed to overflow), thus we
// are done. Otherwise, we will compute:
// PWA = ((PWA + 2^(n-1)) mod (2 ^ n)) - 2^(n-1)
// whereas n is the number of bits of the Expr, hence:
// n = bitwidth(ExprType)
if (IgnoreIntegerWrapping || (getNoWrapFlags(Expr) & SCEV::FlagNSW))
return PWAC;
isl::pw_aff PWAMod = addModuloSemantic(PWAC.first, Expr->getType());
isl::set NotEqualSet = PWAC.first.ne_set(PWAMod);
PWAC.second = PWAC.second.unite(NotEqualSet).coalesce();
const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
if (!BB)
NotEqualSet = NotEqualSet.params();
NotEqualSet = NotEqualSet.coalesce();
if (!NotEqualSet.is_empty())
S->recordAssumption(WRAPPING, NotEqualSet, Loc, AS_RESTRICTION, BB);
return PWAC;
}
isl::pw_aff SCEVAffinator::addModuloSemantic(isl::pw_aff PWA,
Type *ExprType) const {
unsigned Width = TD.getTypeSizeInBits(ExprType);
auto ModVal = isl::val::int_from_ui(Ctx, Width);
ModVal = ModVal.two_exp();
isl::set Domain = PWA.domain();
isl::pw_aff AddPW =
isl::manage(getWidthExpValOnDomain(Width - 1, Domain.release()));
return PWA.add(AddPW).mod(ModVal).sub(AddPW);
}
bool SCEVAffinator::hasNSWAddRecForLoop(Loop *L) const {
for (const auto &CachedPair : CachedExpressions) {
auto *AddRec = dyn_cast<SCEVAddRecExpr>(CachedPair.first.first);
if (!AddRec)
continue;
if (AddRec->getLoop() != L)
continue;
if (AddRec->getNoWrapFlags() & SCEV::FlagNSW)
return true;
}
return false;
}
bool SCEVAffinator::computeModuloForExpr(const SCEV *Expr) {
unsigned Width = TD.getTypeSizeInBits(Expr->getType());
// We assume nsw expressions never overflow.
if (auto *NAry = dyn_cast<SCEVNAryExpr>(Expr))
if (NAry->getNoWrapFlags() & SCEV::FlagNSW)
return false;
return Width <= MaxSmallBitWidth;
}
PWACtx SCEVAffinator::visit(const SCEV *Expr) {
auto Key = std::make_pair(Expr, BB);
PWACtx PWAC = CachedExpressions[Key];
if (PWAC.first)
return PWAC;
auto ConstantAndLeftOverPair = extractConstantFactor(Expr, SE);
auto *Factor = ConstantAndLeftOverPair.first;
Expr = ConstantAndLeftOverPair.second;
auto *Scope = getScope();
S->addParams(getParamsInAffineExpr(&S->getRegion(), Scope, Expr, SE));
// In case the scev is a valid parameter, we do not further analyze this
// expression, but create a new parameter in the isl_pw_aff. This allows us
// to treat subexpressions that we cannot translate into an piecewise affine
// expression, as constant parameters of the piecewise affine expression.
if (isl_id *Id = S->getIdForParam(Expr).release()) {
isl_space *Space = isl_space_set_alloc(Ctx.get(), 1, NumIterators);
Space = isl_space_set_dim_id(Space, isl_dim_param, 0, Id);
isl_set *Domain = isl_set_universe(isl_space_copy(Space));
isl_aff *Affine = isl_aff_zero_on_domain(isl_local_space_from_space(Space));
Affine = isl_aff_add_coefficient_si(Affine, isl_dim_param, 0, 1);
PWAC = getPWACtxFromPWA(isl::manage(isl_pw_aff_alloc(Domain, Affine)));
} else {
PWAC = SCEVVisitor<SCEVAffinator, PWACtx>::visit(Expr);
if (computeModuloForExpr(Expr))
PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());
else
PWAC = checkForWrapping(Expr, PWAC);
}
if (!Factor->getType()->isIntegerTy(1)) {
PWAC = combine(PWAC, visitConstant(Factor), isl_pw_aff_mul);
if (computeModuloForExpr(Key.first))
PWAC.first = addModuloSemantic(PWAC.first, Expr->getType());
}
// For compile time reasons we need to simplify the PWAC before we cache and
// return it.
PWAC.first = PWAC.first.coalesce();
if (!computeModuloForExpr(Key.first))
PWAC = checkForWrapping(Key.first, PWAC);
CachedExpressions[Key] = PWAC;
return PWAC;
}
PWACtx SCEVAffinator::visitConstant(const SCEVConstant *Expr) {
ConstantInt *Value = Expr->getValue();
isl_val *v;
// LLVM does not define if an integer value is interpreted as a signed or
// unsigned value. Hence, without further information, it is unknown how
// this value needs to be converted to GMP. At the moment, we only support
// signed operations. So we just interpret it as signed. Later, there are
// two options:
//
// 1. We always interpret any value as signed and convert the values on
// demand.
// 2. We pass down the signedness of the calculation and use it to interpret
// this constant correctly.
v = isl_valFromAPInt(Ctx.get(), Value->getValue(), /* isSigned */ true);
isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);
isl_local_space *ls = isl_local_space_from_space(Space);
return getPWACtxFromPWA(
isl::manage(isl_pw_aff_from_aff(isl_aff_val_on_domain(ls, v))));
}
PWACtx SCEVAffinator::visitTruncateExpr(const SCEVTruncateExpr *Expr) {
// Truncate operations are basically modulo operations, thus we can
// model them that way. However, for large types we assume the operand
// to fit in the new type size instead of introducing a modulo with a very
// large constant.
auto *Op = Expr->getOperand();
auto OpPWAC = visit(Op);
unsigned Width = TD.getTypeSizeInBits(Expr->getType());
if (computeModuloForExpr(Expr))
return OpPWAC;
auto *Dom = OpPWAC.first.domain().release();
auto *ExpPWA = getWidthExpValOnDomain(Width - 1, Dom);
auto *GreaterDom =
isl_pw_aff_ge_set(OpPWAC.first.copy(), isl_pw_aff_copy(ExpPWA));
auto *SmallerDom =
isl_pw_aff_lt_set(OpPWAC.first.copy(), isl_pw_aff_neg(ExpPWA));
auto *OutOfBoundsDom = isl_set_union(SmallerDom, GreaterDom);
OpPWAC.second = OpPWAC.second.unite(isl::manage_copy(OutOfBoundsDom));
if (!BB) {
assert(isl_set_dim(OutOfBoundsDom, isl_dim_set) == 0 &&
"Expected a zero dimensional set for non-basic-block domains");
OutOfBoundsDom = isl_set_params(OutOfBoundsDom);
}
S->recordAssumption(UNSIGNED, isl::manage(OutOfBoundsDom), DebugLoc(),
AS_RESTRICTION, BB);
return OpPWAC;
}
PWACtx SCEVAffinator::visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
// A zero-extended value can be interpreted as a piecewise defined signed
// value. If the value was non-negative it stays the same, otherwise it
// is the sum of the original value and 2^n where n is the bit-width of
// the original (or operand) type. Examples:
// zext i8 127 to i32 -> { [127] }
// zext i8 -1 to i32 -> { [256 + (-1)] } = { [255] }
// zext i8 %v to i32 -> [v] -> { [v] | v >= 0; [256 + v] | v < 0 }
//
// However, LLVM/Scalar Evolution uses zero-extend (potentially lead by a
// truncate) to represent some forms of modulo computation. The left-hand side
// of the condition in the code below would result in the SCEV
// "zext i1 <false, +, true>for.body" which is just another description
// of the C expression "i & 1 != 0" or, equivalently, "i % 2 != 0".
//
// for (i = 0; i < N; i++)
// if (i & 1 != 0 /* == i % 2 */)
// /* do something */
//
// If we do not make the modulo explicit but only use the mechanism described
// above we will get the very restrictive assumption "N < 3", because for all
// values of N >= 3 the SCEVAddRecExpr operand of the zero-extend would wrap.
// Alternatively, we can make the modulo in the operand explicit in the
// resulting piecewise function and thereby avoid the assumption on N. For the
// example this would result in the following piecewise affine function:
// { [i0] -> [(1)] : 2*floor((-1 + i0)/2) = -1 + i0;
// [i0] -> [(0)] : 2*floor((i0)/2) = i0 }
// To this end we can first determine if the (immediate) operand of the
// zero-extend can wrap and, in case it might, we will use explicit modulo
// semantic to compute the result instead of emitting non-wrapping
// assumptions.
//
// Note that operands with large bit-widths are less likely to be negative
// because it would result in a very large access offset or loop bound after
// the zero-extend. To this end one can optimistically assume the operand to
// be positive and avoid the piecewise definition if the bit-width is bigger
// than some threshold (here MaxZextSmallBitWidth).
//
// We choose to go with a hybrid solution of all modeling techniques described
// above. For small bit-widths (up to MaxZextSmallBitWidth) we will model the
// wrapping explicitly and use a piecewise defined function. However, if the
// bit-width is bigger than MaxZextSmallBitWidth we will employ overflow
// assumptions and assume the "former negative" piece will not exist.
auto *Op = Expr->getOperand();
auto OpPWAC = visit(Op);
// If the width is to big we assume the negative part does not occur.
if (!computeModuloForExpr(Op)) {
takeNonNegativeAssumption(OpPWAC);
return OpPWAC;
}
// If the width is small build the piece for the non-negative part and
// the one for the negative part and unify them.
unsigned Width = TD.getTypeSizeInBits(Op->getType());
interpretAsUnsigned(OpPWAC, Width);
return OpPWAC;
}
PWACtx SCEVAffinator::visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
// As all values are represented as signed, a sign extension is a noop.
return visit(Expr->getOperand());
}
PWACtx SCEVAffinator::visitAddExpr(const SCEVAddExpr *Expr) {
PWACtx Sum = visit(Expr->getOperand(0));
for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
Sum = combine(Sum, visit(Expr->getOperand(i)), isl_pw_aff_add);
if (isTooComplex(Sum))
return complexityBailout();
}
return Sum;
}
PWACtx SCEVAffinator::visitMulExpr(const SCEVMulExpr *Expr) {
PWACtx Prod = visit(Expr->getOperand(0));
for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
Prod = combine(Prod, visit(Expr->getOperand(i)), isl_pw_aff_mul);
if (isTooComplex(Prod))
return complexityBailout();
}
return Prod;
}
PWACtx SCEVAffinator::visitAddRecExpr(const SCEVAddRecExpr *Expr) {
assert(Expr->isAffine() && "Only affine AddRecurrences allowed");
auto Flags = Expr->getNoWrapFlags();
// Directly generate isl_pw_aff for Expr if 'start' is zero.
if (Expr->getStart()->isZero()) {
assert(S->contains(Expr->getLoop()) &&
"Scop does not contain the loop referenced in this AddRec");
PWACtx Step = visit(Expr->getOperand(1));
isl_space *Space = isl_space_set_alloc(Ctx.get(), 0, NumIterators);
isl_local_space *LocalSpace = isl_local_space_from_space(Space);
unsigned loopDimension = S->getRelativeLoopDepth(Expr->getLoop());
isl_aff *LAff = isl_aff_set_coefficient_si(
isl_aff_zero_on_domain(LocalSpace), isl_dim_in, loopDimension, 1);
isl_pw_aff *LPwAff = isl_pw_aff_from_aff(LAff);
Step.first = Step.first.mul(isl::manage(LPwAff));
return Step;
}
// Translate AddRecExpr from '{start, +, inc}' into 'start + {0, +, inc}'
// if 'start' is not zero.
// TODO: Using the original SCEV no-wrap flags is not always safe, however
// as our code generation is reordering the expression anyway it doesn't
// really matter.
const SCEV *ZeroStartExpr =
SE.getAddRecExpr(SE.getConstant(Expr->getStart()->getType(), 0),
Expr->getStepRecurrence(SE), Expr->getLoop(), Flags);
PWACtx Result = visit(ZeroStartExpr);
PWACtx Start = visit(Expr->getStart());
Result = combine(Result, Start, isl_pw_aff_add);
return Result;
}
PWACtx SCEVAffinator::visitSMaxExpr(const SCEVSMaxExpr *Expr) {
PWACtx Max = visit(Expr->getOperand(0));
for (int i = 1, e = Expr->getNumOperands(); i < e; ++i) {
Max = combine(Max, visit(Expr->getOperand(i)), isl_pw_aff_max);
if (isTooComplex(Max))
return complexityBailout();
}
return Max;
}
PWACtx SCEVAffinator::visitUMaxExpr(const SCEVUMaxExpr *Expr) {
llvm_unreachable("SCEVUMaxExpr not yet supported");
}
PWACtx SCEVAffinator::visitUDivExpr(const SCEVUDivExpr *Expr) {
// The handling of unsigned division is basically the same as for signed
// division, except the interpretation of the operands. As the divisor
// has to be constant in both cases we can simply interpret it as an
// unsigned value without additional complexity in the representation.
// For the dividend we could choose from the different representation
// schemes introduced for zero-extend operations but for now we will
// simply use an assumption.
auto *Dividend = Expr->getLHS();
auto *Divisor = Expr->getRHS();
assert(isa<SCEVConstant>(Divisor) &&
"UDiv is no parameter but has a non-constant RHS.");
auto DividendPWAC = visit(Dividend);
auto DivisorPWAC = visit(Divisor);
if (SE.isKnownNegative(Divisor)) {
// Interpret negative divisors unsigned. This is a special case of the
// piece-wise defined value described for zero-extends as we already know
// the actual value of the constant divisor.
unsigned Width = TD.getTypeSizeInBits(Expr->getType());
auto *DivisorDom = DivisorPWAC.first.domain().release();
auto *WidthExpPWA = getWidthExpValOnDomain(Width, DivisorDom);
DivisorPWAC.first = DivisorPWAC.first.add(isl::manage(WidthExpPWA));
}
// TODO: One can represent the dividend as piece-wise function to be more
// precise but therefor a heuristic is needed.
// Assume a non-negative dividend.
takeNonNegativeAssumption(DividendPWAC);
DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_div);
DividendPWAC.first = DividendPWAC.first.floor();
return DividendPWAC;
}
PWACtx SCEVAffinator::visitSDivInstruction(Instruction *SDiv) {
assert(SDiv->getOpcode() == Instruction::SDiv && "Assumed SDiv instruction!");
auto *Scope = getScope();
auto *Divisor = SDiv->getOperand(1);
auto *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);
auto DivisorPWAC = visit(DivisorSCEV);
assert(isa<SCEVConstant>(DivisorSCEV) &&
"SDiv is no parameter but has a non-constant RHS.");
auto *Dividend = SDiv->getOperand(0);
auto *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);
auto DividendPWAC = visit(DividendSCEV);
DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_q);
return DividendPWAC;
}
PWACtx SCEVAffinator::visitSRemInstruction(Instruction *SRem) {
assert(SRem->getOpcode() == Instruction::SRem && "Assumed SRem instruction!");
auto *Scope = getScope();
auto *Divisor = SRem->getOperand(1);
auto *DivisorSCEV = SE.getSCEVAtScope(Divisor, Scope);
auto DivisorPWAC = visit(DivisorSCEV);
assert(isa<ConstantInt>(Divisor) &&
"SRem is no parameter but has a non-constant RHS.");
auto *Dividend = SRem->getOperand(0);
auto *DividendSCEV = SE.getSCEVAtScope(Dividend, Scope);
auto DividendPWAC = visit(DividendSCEV);
DividendPWAC = combine(DividendPWAC, DivisorPWAC, isl_pw_aff_tdiv_r);
return DividendPWAC;
}
PWACtx SCEVAffinator::visitUnknown(const SCEVUnknown *Expr) {
if (Instruction *I = dyn_cast<Instruction>(Expr->getValue())) {
switch (I->getOpcode()) {
case Instruction::IntToPtr:
return visit(SE.getSCEVAtScope(I->getOperand(0), getScope()));
case Instruction::PtrToInt:
return visit(SE.getSCEVAtScope(I->getOperand(0), getScope()));
case Instruction::SDiv:
return visitSDivInstruction(I);
case Instruction::SRem:
return visitSRemInstruction(I);
default:
break; // Fall through.
}
}
llvm_unreachable(
"Unknowns SCEV was neither parameter nor a valid instruction.");
}
PWACtx SCEVAffinator::complexityBailout() {
// We hit the complexity limit for affine expressions; invalidate the scop
// and return a constant zero.
const DebugLoc &Loc = BB ? BB->getTerminator()->getDebugLoc() : DebugLoc();
S->invalidate(COMPLEXITY, Loc);
return visit(SE.getZero(Type::getInt32Ty(S->getFunction().getContext())));
}