1 //===- opt.cpp - The LLVM Modular Optimizer -------------------------------===//
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 // Optimizations may be specified an arbitrary number of times on the command
11 // line, They are run in the order specified.
13 //===----------------------------------------------------------------------===//
15 #include "BreakpointPrinter.h"
16 #include "NewPMDriver.h"
17 #include "PassPrinters.h"
18 #include "llvm/ADT/Triple.h"
19 #include "llvm/Analysis/CallGraph.h"
20 #include "llvm/Analysis/CallGraphSCCPass.h"
21 #include "llvm/Analysis/LoopPass.h"
22 #include "llvm/Analysis/RegionPass.h"
23 #include "llvm/Analysis/TargetLibraryInfo.h"
24 #include "llvm/Analysis/TargetTransformInfo.h"
25 #include "llvm/Bitcode/BitcodeWriterPass.h"
26 #include "llvm/CodeGen/CommandFlags.h"
27 #include "llvm/CodeGen/TargetPassConfig.h"
28 #include "llvm/IR/DataLayout.h"
29 #include "llvm/IR/DebugInfo.h"
30 #include "llvm/IR/IRPrintingPasses.h"
31 #include "llvm/IR/LLVMContext.h"
32 #include "llvm/IR/LegacyPassManager.h"
33 #include "llvm/IR/LegacyPassNameParser.h"
34 #include "llvm/IR/Module.h"
35 #include "llvm/IR/Verifier.h"
36 #include "llvm/IRReader/IRReader.h"
37 #include "llvm/InitializePasses.h"
38 #include "llvm/LinkAllIR.h"
39 #include "llvm/LinkAllPasses.h"
40 #include "llvm/MC/SubtargetFeature.h"
41 #include "llvm/Support/Debug.h"
42 #include "llvm/Support/FileSystem.h"
43 #include "llvm/Support/Host.h"
44 #include "llvm/Support/ManagedStatic.h"
45 #include "llvm/Support/PluginLoader.h"
46 #include "llvm/Support/PrettyStackTrace.h"
47 #include "llvm/Support/Signals.h"
48 #include "llvm/Support/SourceMgr.h"
49 #include "llvm/Support/SystemUtils.h"
50 #include "llvm/Support/TargetRegistry.h"
51 #include "llvm/Support/TargetSelect.h"
52 #include "llvm/Support/ToolOutputFile.h"
53 #include "llvm/Support/YAMLTraits.h"
54 #include "llvm/Target/TargetMachine.h"
55 #include "llvm/Transforms/Coroutines.h"
56 #include "llvm/Transforms/IPO/AlwaysInliner.h"
57 #include "llvm/Transforms/IPO/PassManagerBuilder.h"
58 #include "llvm/Transforms/Utils/Cloning.h"
62 using namespace opt_tool;
64 // The OptimizationList is automatically populated with registered Passes by the
67 static cl::list<const PassInfo*, bool, PassNameParser>
68 PassList(cl::desc("Optimizations available:"));
70 // This flag specifies a textual description of the optimization pass pipeline
71 // to run over the module. This flag switches opt to use the new pass manager
72 // infrastructure, completely disabling all of the flags specific to the old
74 static cl::opt<std::string> PassPipeline(
76 cl::desc("A textual description of the pass pipeline for optimizing"),
79 // Other command line options...
81 static cl::opt<std::string>
82 InputFilename(cl::Positional, cl::desc("<input bitcode file>"),
83 cl::init("-"), cl::value_desc("filename"));
85 static cl::opt<std::string>
86 OutputFilename("o", cl::desc("Override output filename"),
87 cl::value_desc("filename"));
90 Force("f", cl::desc("Enable binary output on terminals"));
93 PrintEachXForm("p", cl::desc("Print module after each transformation"));
96 NoOutput("disable-output",
97 cl::desc("Do not write result bitcode file"), cl::Hidden);
100 OutputAssembly("S", cl::desc("Write output as LLVM assembly"));
103 OutputThinLTOBC("thinlto-bc",
104 cl::desc("Write output as ThinLTO-ready bitcode"));
106 static cl::opt<std::string> ThinLinkBitcodeFile(
107 "thin-link-bitcode-file", cl::value_desc("filename"),
109 "A file in which to write minimized bitcode for the thin link only"));
112 NoVerify("disable-verify", cl::desc("Do not run the verifier"), cl::Hidden);
115 VerifyEach("verify-each", cl::desc("Verify after each transform"));
118 DisableDITypeMap("disable-debug-info-type-map",
119 cl::desc("Don't use a uniquing type map for debug info"));
122 StripDebug("strip-debug",
123 cl::desc("Strip debugger symbol info from translation unit"));
126 DisableInline("disable-inlining", cl::desc("Do not run the inliner pass"));
129 DisableOptimizations("disable-opt",
130 cl::desc("Do not run any optimization passes"));
133 StandardLinkOpts("std-link-opts",
134 cl::desc("Include the standard link time optimizations"));
138 cl::desc("Optimization level 0. Similar to clang -O0"));
142 cl::desc("Optimization level 1. Similar to clang -O1"));
146 cl::desc("Optimization level 2. Similar to clang -O2"));
150 cl::desc("Like -O2 with extra optimizations for size. Similar to clang -Os"));
154 cl::desc("Like -Os but reduces code size further. Similar to clang -Oz"));
158 cl::desc("Optimization level 3. Similar to clang -O3"));
160 static cl::opt<unsigned>
161 CodeGenOptLevel("codegen-opt-level",
162 cl::desc("Override optimization level for codegen hooks"));
164 static cl::opt<std::string>
165 TargetTriple("mtriple", cl::desc("Override target triple for module"));
168 UnitAtATime("funit-at-a-time",
169 cl::desc("Enable IPO. This corresponds to gcc's -funit-at-a-time"),
173 DisableLoopUnrolling("disable-loop-unrolling",
174 cl::desc("Disable loop unrolling in all relevant passes"),
177 DisableLoopVectorization("disable-loop-vectorization",
178 cl::desc("Disable the loop vectorization pass"),
182 DisableSLPVectorization("disable-slp-vectorization",
183 cl::desc("Disable the slp vectorization pass"),
186 static cl::opt<bool> EmitSummaryIndex("module-summary",
187 cl::desc("Emit module summary index"),
190 static cl::opt<bool> EmitModuleHash("module-hash", cl::desc("Emit module hash"),
194 DisableSimplifyLibCalls("disable-simplify-libcalls",
195 cl::desc("Disable simplify-libcalls"));
198 Quiet("q", cl::desc("Obsolete option"), cl::Hidden);
201 QuietA("quiet", cl::desc("Alias for -q"), cl::aliasopt(Quiet));
204 AnalyzeOnly("analyze", cl::desc("Only perform analysis, no optimization"));
207 PrintBreakpoints("print-breakpoints-for-testing",
208 cl::desc("Print select breakpoints location for testing"));
210 static cl::opt<std::string> ClDataLayout("data-layout",
211 cl::desc("data layout string to use"),
212 cl::value_desc("layout-string"),
215 static cl::opt<bool> PreserveBitcodeUseListOrder(
216 "preserve-bc-uselistorder",
217 cl::desc("Preserve use-list order when writing LLVM bitcode."),
218 cl::init(true), cl::Hidden);
220 static cl::opt<bool> PreserveAssemblyUseListOrder(
221 "preserve-ll-uselistorder",
222 cl::desc("Preserve use-list order when writing LLVM assembly."),
223 cl::init(false), cl::Hidden);
226 RunTwice("run-twice",
227 cl::desc("Run all passes twice, re-using the same pass manager."),
228 cl::init(false), cl::Hidden);
230 static cl::opt<bool> DiscardValueNames(
231 "discard-value-names",
232 cl::desc("Discard names from Value (other than GlobalValue)."),
233 cl::init(false), cl::Hidden);
235 static cl::opt<bool> Coroutines(
237 cl::desc("Enable coroutine passes."),
238 cl::init(false), cl::Hidden);
240 static cl::opt<bool> PassRemarksWithHotness(
241 "pass-remarks-with-hotness",
242 cl::desc("With PGO, include profile count in optimization remarks"),
245 static cl::opt<std::string>
246 RemarksFilename("pass-remarks-output",
247 cl::desc("YAML output filename for pass remarks"),
248 cl::value_desc("filename"));
250 static inline void addPass(legacy::PassManagerBase &PM, Pass *P) {
251 // Add the pass to the pass manager...
254 // If we are verifying all of the intermediate steps, add the verifier...
256 PM.add(createVerifierPass());
259 /// This routine adds optimization passes based on selected optimization level,
262 /// OptLevel - Optimization Level
263 static void AddOptimizationPasses(legacy::PassManagerBase &MPM,
264 legacy::FunctionPassManager &FPM,
265 TargetMachine *TM, unsigned OptLevel,
266 unsigned SizeLevel) {
267 if (!NoVerify || VerifyEach)
268 FPM.add(createVerifierPass()); // Verify that input is correct
270 PassManagerBuilder Builder;
271 Builder.OptLevel = OptLevel;
272 Builder.SizeLevel = SizeLevel;
276 } else if (OptLevel > 1) {
277 Builder.Inliner = createFunctionInliningPass(OptLevel, SizeLevel, false);
279 Builder.Inliner = createAlwaysInlinerLegacyPass();
281 Builder.DisableUnitAtATime = !UnitAtATime;
282 Builder.DisableUnrollLoops = (DisableLoopUnrolling.getNumOccurrences() > 0) ?
283 DisableLoopUnrolling : OptLevel == 0;
285 // This is final, unless there is a #pragma vectorize enable
286 if (DisableLoopVectorization)
287 Builder.LoopVectorize = false;
288 // If option wasn't forced via cmd line (-vectorize-loops, -loop-vectorize)
289 else if (!Builder.LoopVectorize)
290 Builder.LoopVectorize = OptLevel > 1 && SizeLevel < 2;
292 // When #pragma vectorize is on for SLP, do the same as above
293 Builder.SLPVectorize =
294 DisableSLPVectorization ? false : OptLevel > 1 && SizeLevel < 2;
297 TM->adjustPassManager(Builder);
300 addCoroutinePassesToExtensionPoints(Builder);
302 Builder.populateFunctionPassManager(FPM);
303 Builder.populateModulePassManager(MPM);
306 static void AddStandardLinkPasses(legacy::PassManagerBase &PM) {
307 PassManagerBuilder Builder;
308 Builder.VerifyInput = true;
309 if (DisableOptimizations)
310 Builder.OptLevel = 0;
313 Builder.Inliner = createFunctionInliningPass();
314 Builder.populateLTOPassManager(PM);
317 //===----------------------------------------------------------------------===//
318 // CodeGen-related helper functions.
321 static CodeGenOpt::Level GetCodeGenOptLevel() {
322 if (CodeGenOptLevel.getNumOccurrences())
323 return static_cast<CodeGenOpt::Level>(unsigned(CodeGenOptLevel));
325 return CodeGenOpt::Less;
327 return CodeGenOpt::Default;
329 return CodeGenOpt::Aggressive;
330 return CodeGenOpt::None;
333 // Returns the TargetMachine instance or zero if no triple is provided.
334 static TargetMachine* GetTargetMachine(Triple TheTriple, StringRef CPUStr,
335 StringRef FeaturesStr,
336 const TargetOptions &Options) {
338 const Target *TheTarget = TargetRegistry::lookupTarget(MArch, TheTriple,
340 // Some modules don't specify a triple, and this is okay.
345 return TheTarget->createTargetMachine(TheTriple.getTriple(), CPUStr,
346 FeaturesStr, Options, getRelocModel(),
347 CMModel, GetCodeGenOptLevel());
350 #ifdef LINK_POLLY_INTO_TOOLS
352 void initializePollyPasses(llvm::PassRegistry &Registry);
356 //===----------------------------------------------------------------------===//
359 int main(int argc, char **argv) {
360 sys::PrintStackTraceOnErrorSignal(argv[0]);
361 llvm::PrettyStackTraceProgram X(argc, argv);
363 // Enable debug stream buffering.
364 EnableDebugBuffering = true;
366 llvm_shutdown_obj Y; // Call llvm_shutdown() on exit.
369 InitializeAllTargets();
370 InitializeAllTargetMCs();
371 InitializeAllAsmPrinters();
372 InitializeAllAsmParsers();
375 PassRegistry &Registry = *PassRegistry::getPassRegistry();
376 initializeCore(Registry);
377 initializeCoroutines(Registry);
378 initializeScalarOpts(Registry);
379 initializeObjCARCOpts(Registry);
380 initializeVectorization(Registry);
381 initializeIPO(Registry);
382 initializeAnalysis(Registry);
383 initializeTransformUtils(Registry);
384 initializeInstCombine(Registry);
385 initializeInstrumentation(Registry);
386 initializeTarget(Registry);
387 // For codegen passes, only passes that do IR to IR transformation are
389 initializeScalarizeMaskedMemIntrinPass(Registry);
390 initializeCodeGenPreparePass(Registry);
391 initializeAtomicExpandPass(Registry);
392 initializeRewriteSymbolsLegacyPassPass(Registry);
393 initializeWinEHPreparePass(Registry);
394 initializeDwarfEHPreparePass(Registry);
395 initializeSafeStackLegacyPassPass(Registry);
396 initializeSjLjEHPreparePass(Registry);
397 initializePreISelIntrinsicLoweringLegacyPassPass(Registry);
398 initializeGlobalMergePass(Registry);
399 initializeInterleavedAccessPass(Registry);
400 initializeCountingFunctionInserterPass(Registry);
401 initializeUnreachableBlockElimLegacyPassPass(Registry);
402 initializeExpandReductionsPass(Registry);
404 #ifdef LINK_POLLY_INTO_TOOLS
405 polly::initializePollyPasses(Registry);
408 cl::ParseCommandLineOptions(argc, argv,
409 "llvm .bc -> .bc modular optimizer and analysis printer\n");
411 if (AnalyzeOnly && NoOutput) {
412 errs() << argv[0] << ": analyze mode conflicts with no-output mode.\n";
418 Context.setDiscardValueNames(DiscardValueNames);
419 if (!DisableDITypeMap)
420 Context.enableDebugTypeODRUniquing();
422 if (PassRemarksWithHotness)
423 Context.setDiagnosticHotnessRequested(true);
425 std::unique_ptr<tool_output_file> YamlFile;
426 if (RemarksFilename != "") {
428 YamlFile = llvm::make_unique<tool_output_file>(RemarksFilename, EC,
431 errs() << EC.message() << '\n';
434 Context.setDiagnosticsOutputFile(
435 llvm::make_unique<yaml::Output>(YamlFile->os()));
438 // Load the input module...
439 std::unique_ptr<Module> M = parseIRFile(InputFilename, Err, Context);
442 Err.print(argv[0], errs());
446 // Strip debug info before running the verifier.
450 // Immediately run the verifier to catch any problems before starting up the
451 // pass pipelines. Otherwise we can crash on broken code during
452 // doInitialization().
453 if (!NoVerify && verifyModule(*M, &errs())) {
454 errs() << argv[0] << ": " << InputFilename
455 << ": error: input module is broken!\n";
459 // If we are supposed to override the target triple or data layout, do so now.
460 if (!TargetTriple.empty())
461 M->setTargetTriple(Triple::normalize(TargetTriple));
462 if (!ClDataLayout.empty())
463 M->setDataLayout(ClDataLayout);
465 // Figure out what stream we are supposed to write to...
466 std::unique_ptr<tool_output_file> Out;
467 std::unique_ptr<tool_output_file> ThinLinkOut;
469 if (!OutputFilename.empty())
470 errs() << "WARNING: The -o (output filename) option is ignored when\n"
471 "the --disable-output option is used.\n";
473 // Default to standard output.
474 if (OutputFilename.empty())
475 OutputFilename = "-";
478 Out.reset(new tool_output_file(OutputFilename, EC, sys::fs::F_None));
480 errs() << EC.message() << '\n';
484 if (!ThinLinkBitcodeFile.empty()) {
486 new tool_output_file(ThinLinkBitcodeFile, EC, sys::fs::F_None));
488 errs() << EC.message() << '\n';
494 Triple ModuleTriple(M->getTargetTriple());
495 std::string CPUStr, FeaturesStr;
496 TargetMachine *Machine = nullptr;
497 const TargetOptions Options = InitTargetOptionsFromCodeGenFlags();
499 if (ModuleTriple.getArch()) {
500 CPUStr = getCPUStr();
501 FeaturesStr = getFeaturesStr();
502 Machine = GetTargetMachine(ModuleTriple, CPUStr, FeaturesStr, Options);
505 std::unique_ptr<TargetMachine> TM(Machine);
507 // Override function attributes based on CPUStr, FeaturesStr, and command line
509 setFunctionAttributes(CPUStr, FeaturesStr, *M);
511 // If the output is set to be emitted to standard out, and standard out is a
512 // console, print out a warning message and refuse to do it. We don't
513 // impress anyone by spewing tons of binary goo to a terminal.
514 if (!Force && !NoOutput && !AnalyzeOnly && !OutputAssembly)
515 if (CheckBitcodeOutputToConsole(Out->os(), !Quiet))
518 if (PassPipeline.getNumOccurrences() > 0) {
519 OutputKind OK = OK_NoOutput;
521 OK = OutputAssembly ? OK_OutputAssembly : OK_OutputBitcode;
523 VerifierKind VK = VK_VerifyInAndOut;
527 VK = VK_VerifyEachPass;
529 // The user has asked to use the new pass manager and provided a pipeline
530 // string. Hand off the rest of the functionality to the new code for that
532 return runPassPipeline(argv[0], *M, TM.get(), Out.get(),
533 PassPipeline, OK, VK, PreserveAssemblyUseListOrder,
534 PreserveBitcodeUseListOrder, EmitSummaryIndex,
540 // Create a PassManager to hold and optimize the collection of passes we are
543 legacy::PassManager Passes;
545 // Add an appropriate TargetLibraryInfo pass for the module's triple.
546 TargetLibraryInfoImpl TLII(ModuleTriple);
548 // The -disable-simplify-libcalls flag actually disables all builtin optzns.
549 if (DisableSimplifyLibCalls)
550 TLII.disableAllFunctions();
551 Passes.add(new TargetLibraryInfoWrapperPass(TLII));
553 // Add internal analysis passes from the target machine.
554 Passes.add(createTargetTransformInfoWrapperPass(TM ? TM->getTargetIRAnalysis()
555 : TargetIRAnalysis()));
557 std::unique_ptr<legacy::FunctionPassManager> FPasses;
558 if (OptLevelO0 || OptLevelO1 || OptLevelO2 || OptLevelOs || OptLevelOz ||
560 FPasses.reset(new legacy::FunctionPassManager(M.get()));
561 FPasses->add(createTargetTransformInfoWrapperPass(
562 TM ? TM->getTargetIRAnalysis() : TargetIRAnalysis()));
565 if (PrintBreakpoints) {
566 // Default to standard output.
568 if (OutputFilename.empty())
569 OutputFilename = "-";
572 Out = llvm::make_unique<tool_output_file>(OutputFilename, EC,
575 errs() << EC.message() << '\n';
579 Passes.add(createBreakpointPrinter(Out->os()));
584 // FIXME: We should dyn_cast this when supported.
585 auto <M = static_cast<LLVMTargetMachine &>(*TM);
586 Pass *TPC = LTM.createPassConfig(Passes);
590 // Create a new optimization pass for each one specified on the command line
591 for (unsigned i = 0; i < PassList.size(); ++i) {
592 if (StandardLinkOpts &&
593 StandardLinkOpts.getPosition() < PassList.getPosition(i)) {
594 AddStandardLinkPasses(Passes);
595 StandardLinkOpts = false;
598 if (OptLevelO0 && OptLevelO0.getPosition() < PassList.getPosition(i)) {
599 AddOptimizationPasses(Passes, *FPasses, TM.get(), 0, 0);
603 if (OptLevelO1 && OptLevelO1.getPosition() < PassList.getPosition(i)) {
604 AddOptimizationPasses(Passes, *FPasses, TM.get(), 1, 0);
608 if (OptLevelO2 && OptLevelO2.getPosition() < PassList.getPosition(i)) {
609 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 0);
613 if (OptLevelOs && OptLevelOs.getPosition() < PassList.getPosition(i)) {
614 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 1);
618 if (OptLevelOz && OptLevelOz.getPosition() < PassList.getPosition(i)) {
619 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 2);
623 if (OptLevelO3 && OptLevelO3.getPosition() < PassList.getPosition(i)) {
624 AddOptimizationPasses(Passes, *FPasses, TM.get(), 3, 0);
628 const PassInfo *PassInf = PassList[i];
630 if (PassInf->getNormalCtor())
631 P = PassInf->getNormalCtor()();
633 errs() << argv[0] << ": cannot create pass: "
634 << PassInf->getPassName() << "\n";
636 PassKind Kind = P->getPassKind();
642 Passes.add(createBasicBlockPassPrinter(PassInf, Out->os(), Quiet));
645 Passes.add(createRegionPassPrinter(PassInf, Out->os(), Quiet));
648 Passes.add(createLoopPassPrinter(PassInf, Out->os(), Quiet));
651 Passes.add(createFunctionPassPrinter(PassInf, Out->os(), Quiet));
653 case PT_CallGraphSCC:
654 Passes.add(createCallGraphPassPrinter(PassInf, Out->os(), Quiet));
657 Passes.add(createModulePassPrinter(PassInf, Out->os(), Quiet));
665 createPrintModulePass(errs(), "", PreserveAssemblyUseListOrder));
668 if (StandardLinkOpts) {
669 AddStandardLinkPasses(Passes);
670 StandardLinkOpts = false;
674 AddOptimizationPasses(Passes, *FPasses, TM.get(), 0, 0);
677 AddOptimizationPasses(Passes, *FPasses, TM.get(), 1, 0);
680 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 0);
683 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 1);
686 AddOptimizationPasses(Passes, *FPasses, TM.get(), 2, 2);
689 AddOptimizationPasses(Passes, *FPasses, TM.get(), 3, 0);
692 FPasses->doInitialization();
693 for (Function &F : *M)
695 FPasses->doFinalization();
698 // Check that the module is well formed on completion of optimization
699 if (!NoVerify && !VerifyEach)
700 Passes.add(createVerifierPass());
702 // In run twice mode, we want to make sure the output is bit-by-bit
703 // equivalent if we run the pass manager again, so setup two buffers and
704 // a stream to write to them. Note that llc does something similar and it
705 // may be worth to abstract this out in the future.
706 SmallVector<char, 0> Buffer;
707 SmallVector<char, 0> CompileTwiceBuffer;
708 std::unique_ptr<raw_svector_ostream> BOS;
709 raw_ostream *OS = nullptr;
711 // Write bitcode or assembly to the output as the last step...
712 if (!NoOutput && !AnalyzeOnly) {
716 BOS = make_unique<raw_svector_ostream>(Buffer);
719 if (OutputAssembly) {
720 if (EmitSummaryIndex)
721 report_fatal_error("Text output is incompatible with -module-summary");
723 report_fatal_error("Text output is incompatible with -module-hash");
724 Passes.add(createPrintModulePass(*OS, "", PreserveAssemblyUseListOrder));
725 } else if (OutputThinLTOBC)
726 Passes.add(createWriteThinLTOBitcodePass(
727 *OS, ThinLinkOut ? &ThinLinkOut->os() : nullptr));
729 Passes.add(createBitcodeWriterPass(*OS, PreserveBitcodeUseListOrder,
730 EmitSummaryIndex, EmitModuleHash));
733 // Before executing passes, print the final values of the LLVM options.
734 cl::PrintOptionValues();
736 // If requested, run all passes again with the same pass manager to catch
737 // bugs caused by persistent state in the passes
739 std::unique_ptr<Module> M2(CloneModule(M.get()));
741 CompileTwiceBuffer = Buffer;
745 // Now that we have all of the passes ready, run them.
748 // Compare the two outputs and make sure they're the same
751 if (Buffer.size() != CompileTwiceBuffer.size() ||
752 (memcmp(Buffer.data(), CompileTwiceBuffer.data(), Buffer.size()) !=
754 errs() << "Running the pass manager twice changed the output.\n"
755 "Writing the result of the second run to the specified output.\n"
756 "To generate the one-run comparison binary, just run without\n"
757 "the compile-twice option\n";
758 Out->os() << BOS->str();
764 Out->os() << BOS->str();
768 if (!NoOutput || PrintBreakpoints)