<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <title>The LLVM Target-Independent Code Generator</title> <link rel="stylesheet" href="llvm.css" type="text/css"> </head> <body> <div class="doc_title"> The LLVM Target-Independent Code Generator </div> <ol> <li><a href="#introduction">Introduction</a> <ul> <li><a href="#required">Required components in the code generator</a></li> <li><a href="#high-level-design">The high-level design of the code generator</a></li> <li><a href="#tablegen">Using TableGen for target description</a></li> </ul> </li> <li><a href="#targetdesc">Target description classes</a> <ul> <li><a href="#targetmachine">The <tt>TargetMachine</tt> class</a></li> <li><a href="#targetdata">The <tt>TargetData</tt> class</a></li> <li><a href="#targetlowering">The <tt>TargetLowering</tt> class</a></li> <li><a href="#targetregisterinfo">The <tt>TargetRegisterInfo</tt> class</a></li> <li><a href="#targetinstrinfo">The <tt>TargetInstrInfo</tt> class</a></li> <li><a href="#targetframeinfo">The <tt>TargetFrameInfo</tt> class</a></li> <li><a href="#targetsubtarget">The <tt>TargetSubtarget</tt> class</a></li> <li><a href="#targetjitinfo">The <tt>TargetJITInfo</tt> class</a></li> </ul> </li> <li><a href="#codegendesc">Machine code description classes</a> <ul> <li><a href="#machineinstr">The <tt>MachineInstr</tt> class</a></li> <li><a href="#machinebasicblock">The <tt>MachineBasicBlock</tt> class</a></li> <li><a href="#machinefunction">The <tt>MachineFunction</tt> class</a></li> </ul> </li> <li><a href="#codegenalgs">Target-independent code generation algorithms</a> <ul> <li><a href="#instselect">Instruction Selection</a> <ul> <li><a href="#selectiondag_intro">Introduction to SelectionDAGs</a></li> <li><a href="#selectiondag_process">SelectionDAG Code Generation Process</a></li> <li><a href="#selectiondag_build">Initial SelectionDAG Construction</a></li> <li><a href="#selectiondag_legalize_types">SelectionDAG LegalizeTypes Phase</a></li> <li><a href="#selectiondag_legalize">SelectionDAG Legalize Phase</a></li> <li><a href="#selectiondag_optimize">SelectionDAG Optimization Phase: the DAG Combiner</a></li> <li><a href="#selectiondag_select">SelectionDAG Select Phase</a></li> <li><a href="#selectiondag_sched">SelectionDAG Scheduling and Formation Phase</a></li> <li><a href="#selectiondag_future">Future directions for the SelectionDAG</a></li> </ul></li> <li><a href="#liveintervals">Live Intervals</a> <ul> <li><a href="#livevariable_analysis">Live Variable Analysis</a></li> <li><a href="#liveintervals_analysis">Live Intervals Analysis</a></li> </ul></li> <li><a href="#regalloc">Register Allocation</a> <ul> <li><a href="#regAlloc_represent">How registers are represented in LLVM</a></li> <li><a href="#regAlloc_howTo">Mapping virtual registers to physical registers</a></li> <li><a href="#regAlloc_twoAddr">Handling two address instructions</a></li> <li><a href="#regAlloc_ssaDecon">The SSA deconstruction phase</a></li> <li><a href="#regAlloc_fold">Instruction folding</a></li> <li><a href="#regAlloc_builtIn">Built in register allocators</a></li> </ul></li> <li><a href="#codeemit">Code Emission</a> <ul> <li><a href="#codeemit_asm">Generating Assembly Code</a></li> <li><a href="#codeemit_bin">Generating Binary Machine Code</a></li> </ul></li> </ul> </li> <li><a href="#targetimpls">Target-specific Implementation Notes</a> <ul> <li><a href="#tailcallopt">Tail call optimization</a></li> <li><a href="#x86">The X86 backend</a></li> <li><a href="#ppc">The PowerPC backend</a> <ul> <li><a href="#ppc_abi">LLVM PowerPC ABI</a></li> <li><a href="#ppc_frame">Frame Layout</a></li> <li><a href="#ppc_prolog">Prolog/Epilog</a></li> <li><a href="#ppc_dynamic">Dynamic Allocation</a></li> </ul></li> </ul></li> </ol> <div class="doc_author"> <p>Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a>, <a href="mailto:isanbard@gmail.com">Bill Wendling</a>, <a href="mailto:pronesto@gmail.com">Fernando Magno Quintao Pereira</a> and <a href="mailto:jlaskey@mac.com">Jim Laskey</a></p> </div> <div class="doc_warning"> <p>Warning: This is a work in progress.</p> </div> <!-- *********************************************************************** --> <div class="doc_section"> <a name="introduction">Introduction</a> </div> <!-- *********************************************************************** --> <div class="doc_text"> <p>The LLVM target-independent code generator is a framework that provides a suite of reusable components for translating the LLVM internal representation to the machine code for a specified target—either in assembly form (suitable for a static compiler) or in binary machine code format (usable for a JIT compiler). The LLVM target-independent code generator consists of five main components:</p> <ol> <li><a href="#targetdesc">Abstract target description</a> interfaces which capture important properties about various aspects of the machine, independently of how they will be used. These interfaces are defined in <tt>include/llvm/Target/</tt>.</li> <li>Classes used to represent the <a href="#codegendesc">machine code</a> being generated for a target. These classes are intended to be abstract enough to represent the machine code for <i>any</i> target machine. These classes are defined in <tt>include/llvm/CodeGen/</tt>.</li> <li><a href="#codegenalgs">Target-independent algorithms</a> used to implement various phases of native code generation (register allocation, scheduling, stack frame representation, etc). This code lives in <tt>lib/CodeGen/</tt>.</li> <li><a href="#targetimpls">Implementations of the abstract target description interfaces</a> for particular targets. These machine descriptions make use of the components provided by LLVM, and can optionally provide custom target-specific passes, to build complete code generators for a specific target. Target descriptions live in <tt>lib/Target/</tt>.</li> <li><a href="#jit">The target-independent JIT components</a>. The LLVM JIT is completely target independent (it uses the <tt>TargetJITInfo</tt> structure to interface for target-specific issues. The code for the target-independent JIT lives in <tt>lib/ExecutionEngine/JIT</tt>.</li> </ol> <p> Depending on which part of the code generator you are interested in working on, different pieces of this will be useful to you. In any case, you should be familiar with the <a href="#targetdesc">target description</a> and <a href="#codegendesc">machine code representation</a> classes. If you want to add a backend for a new target, you will need to <a href="#targetimpls">implement the target description</a> classes for your new target and understand the <a href="LangRef.html">LLVM code representation</a>. If you are interested in implementing a new <a href="#codegenalgs">code generation algorithm</a>, it should only depend on the target-description and machine code representation classes, ensuring that it is portable. </p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="required">Required components in the code generator</a> </div> <div class="doc_text"> <p>The two pieces of the LLVM code generator are the high-level interface to the code generator and the set of reusable components that can be used to build target-specific backends. The two most important interfaces (<a href="#targetmachine"><tt>TargetMachine</tt></a> and <a href="#targetdata"><tt>TargetData</tt></a>) are the only ones that are required to be defined for a backend to fit into the LLVM system, but the others must be defined if the reusable code generator components are going to be used.</p> <p>This design has two important implications. The first is that LLVM can support completely non-traditional code generation targets. For example, the C backend does not require register allocation, instruction selection, or any of the other standard components provided by the system. As such, it only implements these two interfaces, and does its own thing. Another example of a code generator like this is a (purely hypothetical) backend that converts LLVM to the GCC RTL form and uses GCC to emit machine code for a target.</p> <p>This design also implies that it is possible to design and implement radically different code generators in the LLVM system that do not make use of any of the built-in components. Doing so is not recommended at all, but could be required for radically different targets that do not fit into the LLVM machine description model: FPGAs for example.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="high-level-design">The high-level design of the code generator</a> </div> <div class="doc_text"> <p>The LLVM target-independent code generator is designed to support efficient and quality code generation for standard register-based microprocessors. Code generation in this model is divided into the following stages:</p> <ol> <li><b><a href="#instselect">Instruction Selection</a></b> - This phase determines an efficient way to express the input LLVM code in the target instruction set. This stage produces the initial code for the program in the target instruction set, then makes use of virtual registers in SSA form and physical registers that represent any required register assignments due to target constraints or calling conventions. This step turns the LLVM code into a DAG of target instructions.</li> <li><b><a href="#selectiondag_sched">Scheduling and Formation</a></b> - This phase takes the DAG of target instructions produced by the instruction selection phase, determines an ordering of the instructions, then emits the instructions as <tt><a href="#machineinstr">MachineInstr</a></tt>s with that ordering. Note that we describe this in the <a href="#instselect">instruction selection section</a> because it operates on a <a href="#selectiondag_intro">SelectionDAG</a>. </li> <li><b><a href="#ssamco">SSA-based Machine Code Optimizations</a></b> - This optional stage consists of a series of machine-code optimizations that operate on the SSA-form produced by the instruction selector. Optimizations like modulo-scheduling or peephole optimization work here. </li> <li><b><a href="#regalloc">Register Allocation</a></b> - The target code is transformed from an infinite virtual register file in SSA form to the concrete register file used by the target. This phase introduces spill code and eliminates all virtual register references from the program.</li> <li><b><a href="#proepicode">Prolog/Epilog Code Insertion</a></b> - Once the machine code has been generated for the function and the amount of stack space required is known (used for LLVM alloca's and spill slots), the prolog and epilog code for the function can be inserted and "abstract stack location references" can be eliminated. This stage is responsible for implementing optimizations like frame-pointer elimination and stack packing.</li> <li><b><a href="#latemco">Late Machine Code Optimizations</a></b> - Optimizations that operate on "final" machine code can go here, such as spill code scheduling and peephole optimizations.</li> <li><b><a href="#codeemit">Code Emission</a></b> - The final stage actually puts out the code for the current function, either in the target assembler format or in machine code.</li> </ol> <p>The code generator is based on the assumption that the instruction selector will use an optimal pattern matching selector to create high-quality sequences of native instructions. Alternative code generator designs based on pattern expansion and aggressive iterative peephole optimization are much slower. This design permits efficient compilation (important for JIT environments) and aggressive optimization (used when generating code offline) by allowing components of varying levels of sophistication to be used for any step of compilation.</p> <p>In addition to these stages, target implementations can insert arbitrary target-specific passes into the flow. For example, the X86 target uses a special pass to handle the 80x87 floating point stack architecture. Other targets with unusual requirements can be supported with custom passes as needed.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="tablegen">Using TableGen for target description</a> </div> <div class="doc_text"> <p>The target description classes require a detailed description of the target architecture. These target descriptions often have a large amount of common information (e.g., an <tt>add</tt> instruction is almost identical to a <tt>sub</tt> instruction). In order to allow the maximum amount of commonality to be factored out, the LLVM code generator uses the <a href="TableGenFundamentals.html">TableGen</a> tool to describe big chunks of the target machine, which allows the use of domain-specific and target-specific abstractions to reduce the amount of repetition.</p> <p>As LLVM continues to be developed and refined, we plan to move more and more of the target description to the <tt>.td</tt> form. Doing so gives us a number of advantages. The most important is that it makes it easier to port LLVM because it reduces the amount of C++ code that has to be written, and the surface area of the code generator that needs to be understood before someone can get something working. Second, it makes it easier to change things. In particular, if tables and other things are all emitted by <tt>tblgen</tt>, we only need a change in one place (<tt>tblgen</tt>) to update all of the targets to a new interface.</p> </div> <!-- *********************************************************************** --> <div class="doc_section"> <a name="targetdesc">Target description classes</a> </div> <!-- *********************************************************************** --> <div class="doc_text"> <p>The LLVM target description classes (located in the <tt>include/llvm/Target</tt> directory) provide an abstract description of the target machine independent of any particular client. These classes are designed to capture the <i>abstract</i> properties of the target (such as the instructions and registers it has), and do not incorporate any particular pieces of code generation algorithms.</p> <p>All of the target description classes (except the <tt><a href="#targetdata">TargetData</a></tt> class) are designed to be subclassed by the concrete target implementation, and have virtual methods implemented. To get to these implementations, the <tt><a href="#targetmachine">TargetMachine</a></tt> class provides accessors that should be implemented by the target.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetmachine">The <tt>TargetMachine</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetMachine</tt> class provides virtual methods that are used to access the target-specific implementations of the various target description classes via the <tt>get*Info</tt> methods (<tt>getInstrInfo</tt>, <tt>getRegisterInfo</tt>, <tt>getFrameInfo</tt>, etc.). This class is designed to be specialized by a concrete target implementation (e.g., <tt>X86TargetMachine</tt>) which implements the various virtual methods. The only required target description class is the <a href="#targetdata"><tt>TargetData</tt></a> class, but if the code generator components are to be used, the other interfaces should be implemented as well.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetdata">The <tt>TargetData</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetData</tt> class is the only required target description class, and it is the only class that is not extensible (you cannot derived a new class from it). <tt>TargetData</tt> specifies information about how the target lays out memory for structures, the alignment requirements for various data types, the size of pointers in the target, and whether the target is little-endian or big-endian.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetlowering">The <tt>TargetLowering</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetLowering</tt> class is used by SelectionDAG based instruction selectors primarily to describe how LLVM code should be lowered to SelectionDAG operations. Among other things, this class indicates:</p> <ul> <li>an initial register class to use for various <tt>ValueType</tt>s</li> <li>which operations are natively supported by the target machine</li> <li>the return type of <tt>setcc</tt> operations</li> <li>the type to use for shift amounts</li> <li>various high-level characteristics, like whether it is profitable to turn division by a constant into a multiplication sequence</li> </ul> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetregisterinfo">The <tt>TargetRegisterInfo</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetRegisterInfo</tt> class is used to describe the register file of the target and any interactions between the registers.</p> <p>Registers in the code generator are represented in the code generator by unsigned integers. Physical registers (those that actually exist in the target description) are unique small numbers, and virtual registers are generally large. Note that register #0 is reserved as a flag value.</p> <p>Each register in the processor description has an associated <tt>TargetRegisterDesc</tt> entry, which provides a textual name for the register (used for assembly output and debugging dumps) and a set of aliases (used to indicate whether one register overlaps with another). </p> <p>In addition to the per-register description, the <tt>TargetRegisterInfo</tt> class exposes a set of processor specific register classes (instances of the <tt>TargetRegisterClass</tt> class). Each register class contains sets of registers that have the same properties (for example, they are all 32-bit integer registers). Each SSA virtual register created by the instruction selector has an associated register class. When the register allocator runs, it replaces virtual registers with a physical register in the set.</p> <p> The target-specific implementations of these classes is auto-generated from a <a href="TableGenFundamentals.html">TableGen</a> description of the register file. </p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetinstrinfo">The <tt>TargetInstrInfo</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetInstrInfo</tt> class is used to describe the machine instructions supported by the target. It is essentially an array of <tt>TargetInstrDescriptor</tt> objects, each of which describes one instruction the target supports. Descriptors define things like the mnemonic for the opcode, the number of operands, the list of implicit register uses and defs, whether the instruction has certain target-independent properties (accesses memory, is commutable, etc), and holds any target-specific flags.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetframeinfo">The <tt>TargetFrameInfo</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetFrameInfo</tt> class is used to provide information about the stack frame layout of the target. It holds the direction of stack growth, the known stack alignment on entry to each function, and the offset to the local area. The offset to the local area is the offset from the stack pointer on function entry to the first location where function data (local variables, spill locations) can be stored.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetsubtarget">The <tt>TargetSubtarget</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetSubtarget</tt> class is used to provide information about the specific chip set being targeted. A sub-target informs code generation of which instructions are supported, instruction latencies and instruction execution itinerary; i.e., which processing units are used, in what order, and for how long.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="targetjitinfo">The <tt>TargetJITInfo</tt> class</a> </div> <div class="doc_text"> <p>The <tt>TargetJITInfo</tt> class exposes an abstract interface used by the Just-In-Time code generator to perform target-specific activities, such as emitting stubs. If a <tt>TargetMachine</tt> supports JIT code generation, it should provide one of these objects through the <tt>getJITInfo</tt> method.</p> </div> <!-- *********************************************************************** --> <div class="doc_section"> <a name="codegendesc">Machine code description classes</a> </div> <!-- *********************************************************************** --> <div class="doc_text"> <p>At the high-level, LLVM code is translated to a machine specific representation formed out of <a href="#machinefunction"><tt>MachineFunction</tt></a>, <a href="#machinebasicblock"><tt>MachineBasicBlock</tt></a>, and <a href="#machineinstr"><tt>MachineInstr</tt></a> instances (defined in <tt>include/llvm/CodeGen</tt>). This representation is completely target agnostic, representing instructions in their most abstract form: an opcode and a series of operands. This representation is designed to support both an SSA representation for machine code, as well as a register allocated, non-SSA form.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="machineinstr">The <tt>MachineInstr</tt> class</a> </div> <div class="doc_text"> <p>Target machine instructions are represented as instances of the <tt>MachineInstr</tt> class. This class is an extremely abstract way of representing machine instructions. In particular, it only keeps track of an opcode number and a set of operands.</p> <p>The opcode number is a simple unsigned integer that only has meaning to a specific backend. All of the instructions for a target should be defined in the <tt>*InstrInfo.td</tt> file for the target. The opcode enum values are auto-generated from this description. The <tt>MachineInstr</tt> class does not have any information about how to interpret the instruction (i.e., what the semantics of the instruction are); for that you must refer to the <tt><a href="#targetinstrinfo">TargetInstrInfo</a></tt> class.</p> <p>The operands of a machine instruction can be of several different types: a register reference, a constant integer, a basic block reference, etc. In addition, a machine operand should be marked as a def or a use of the value (though only registers are allowed to be defs).</p> <p>By convention, the LLVM code generator orders instruction operands so that all register definitions come before the register uses, even on architectures that are normally printed in other orders. For example, the SPARC add instruction: "<tt>add %i1, %i2, %i3</tt>" adds the "%i1", and "%i2" registers and stores the result into the "%i3" register. In the LLVM code generator, the operands should be stored as "<tt>%i3, %i1, %i2</tt>": with the destination first.</p> <p>Keeping destination (definition) operands at the beginning of the operand list has several advantages. In particular, the debugging printer will print the instruction like this:</p> <div class="doc_code"> <pre> %r3 = add %i1, %i2 </pre> </div> <p>Also if the first operand is a def, it is easier to <a href="#buildmi">create instructions</a> whose only def is the first operand.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="buildmi">Using the <tt>MachineInstrBuilder.h</tt> functions</a> </div> <div class="doc_text"> <p>Machine instructions are created by using the <tt>BuildMI</tt> functions, located in the <tt>include/llvm/CodeGen/MachineInstrBuilder.h</tt> file. The <tt>BuildMI</tt> functions make it easy to build arbitrary machine instructions. Usage of the <tt>BuildMI</tt> functions look like this:</p> <div class="doc_code"> <pre> // Create a 'DestReg = mov 42' (rendered in X86 assembly as 'mov DestReg, 42') // instruction. The '1' specifies how many operands will be added. MachineInstr *MI = BuildMI(X86::MOV32ri, 1, DestReg).addImm(42); // Create the same instr, but insert it at the end of a basic block. MachineBasicBlock &MBB = ... BuildMI(MBB, X86::MOV32ri, 1, DestReg).addImm(42); // Create the same instr, but insert it before a specified iterator point. MachineBasicBlock::iterator MBBI = ... BuildMI(MBB, MBBI, X86::MOV32ri, 1, DestReg).addImm(42); // Create a 'cmp Reg, 0' instruction, no destination reg. MI = BuildMI(X86::CMP32ri, 2).addReg(Reg).addImm(0); // Create an 'sahf' instruction which takes no operands and stores nothing. MI = BuildMI(X86::SAHF, 0); // Create a self looping branch instruction. BuildMI(MBB, X86::JNE, 1).addMBB(&MBB); </pre> </div> <p>The key thing to remember with the <tt>BuildMI</tt> functions is that you have to specify the number of operands that the machine instruction will take. This allows for efficient memory allocation. You also need to specify if operands default to be uses of values, not definitions. If you need to add a definition operand (other than the optional destination register), you must explicitly mark it as such:</p> <div class="doc_code"> <pre> MI.addReg(Reg, MachineOperand::Def); </pre> </div> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="fixedregs">Fixed (preassigned) registers</a> </div> <div class="doc_text"> <p>One important issue that the code generator needs to be aware of is the presence of fixed registers. In particular, there are often places in the instruction stream where the register allocator <em>must</em> arrange for a particular value to be in a particular register. This can occur due to limitations of the instruction set (e.g., the X86 can only do a 32-bit divide with the <tt>EAX</tt>/<tt>EDX</tt> registers), or external factors like calling conventions. In any case, the instruction selector should emit code that copies a virtual register into or out of a physical register when needed.</p> <p>For example, consider this simple LLVM example:</p> <div class="doc_code"> <pre> define i32 @test(i32 %X, i32 %Y) { %Z = udiv i32 %X, %Y ret i32 %Z } </pre> </div> <p>The X86 instruction selector produces this machine code for the <tt>div</tt> and <tt>ret</tt> (use "<tt>llc X.bc -march=x86 -print-machineinstrs</tt>" to get this):</p> <div class="doc_code"> <pre> ;; Start of div %EAX = mov %reg1024 ;; Copy X (in reg1024) into EAX %reg1027 = sar %reg1024, 31 %EDX = mov %reg1027 ;; Sign extend X into EDX idiv %reg1025 ;; Divide by Y (in reg1025) %reg1026 = mov %EAX ;; Read the result (Z) out of EAX ;; Start of ret %EAX = mov %reg1026 ;; 32-bit return value goes in EAX ret </pre> </div> <p>By the end of code generation, the register allocator has coalesced the registers and deleted the resultant identity moves producing the following code:</p> <div class="doc_code"> <pre> ;; X is in EAX, Y is in ECX mov %EAX, %EDX sar %EDX, 31 idiv %ECX ret </pre> </div> <p>This approach is extremely general (if it can handle the X86 architecture, it can handle anything!) and allows all of the target specific knowledge about the instruction stream to be isolated in the instruction selector. Note that physical registers should have a short lifetime for good code generation, and all physical registers are assumed dead on entry to and exit from basic blocks (before register allocation). Thus, if you need a value to be live across basic block boundaries, it <em>must</em> live in a virtual register.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="ssa">Machine code in SSA form</a> </div> <div class="doc_text"> <p><tt>MachineInstr</tt>'s are initially selected in SSA-form, and are maintained in SSA-form until register allocation happens. For the most part, this is trivially simple since LLVM is already in SSA form; LLVM PHI nodes become machine code PHI nodes, and virtual registers are only allowed to have a single definition.</p> <p>After register allocation, machine code is no longer in SSA-form because there are no virtual registers left in the code.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="machinebasicblock">The <tt>MachineBasicBlock</tt> class</a> </div> <div class="doc_text"> <p>The <tt>MachineBasicBlock</tt> class contains a list of machine instructions (<tt><a href="#machineinstr">MachineInstr</a></tt> instances). It roughly corresponds to the LLVM code input to the instruction selector, but there can be a one-to-many mapping (i.e. one LLVM basic block can map to multiple machine basic blocks). The <tt>MachineBasicBlock</tt> class has a "<tt>getBasicBlock</tt>" method, which returns the LLVM basic block that it comes from.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="machinefunction">The <tt>MachineFunction</tt> class</a> </div> <div class="doc_text"> <p>The <tt>MachineFunction</tt> class contains a list of machine basic blocks (<tt><a href="#machinebasicblock">MachineBasicBlock</a></tt> instances). It corresponds one-to-one with the LLVM function input to the instruction selector. In addition to a list of basic blocks, the <tt>MachineFunction</tt> contains a a <tt>MachineConstantPool</tt>, a <tt>MachineFrameInfo</tt>, a <tt>MachineFunctionInfo</tt>, and a <tt>MachineRegisterInfo</tt>. See <tt>include/llvm/CodeGen/MachineFunction.h</tt> for more information.</p> </div> <!-- *********************************************************************** --> <div class="doc_section"> <a name="codegenalgs">Target-independent code generation algorithms</a> </div> <!-- *********************************************************************** --> <div class="doc_text"> <p>This section documents the phases described in the <a href="#high-level-design">high-level design of the code generator</a>. It explains how they work and some of the rationale behind their design.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="instselect">Instruction Selection</a> </div> <div class="doc_text"> <p> Instruction Selection is the process of translating LLVM code presented to the code generator into target-specific machine instructions. There are several well-known ways to do this in the literature. LLVM uses a SelectionDAG based instruction selector. </p> <p>Portions of the DAG instruction selector are generated from the target description (<tt>*.td</tt>) files. Our goal is for the entire instruction selector to be generated from these <tt>.td</tt> files, though currently there are still things that require custom C++ code.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_intro">Introduction to SelectionDAGs</a> </div> <div class="doc_text"> <p>The SelectionDAG provides an abstraction for code representation in a way that is amenable to instruction selection using automatic techniques (e.g. dynamic-programming based optimal pattern matching selectors). It is also well-suited to other phases of code generation; in particular, instruction scheduling (SelectionDAG's are very close to scheduling DAGs post-selection). Additionally, the SelectionDAG provides a host representation where a large variety of very-low-level (but target-independent) <a href="#selectiondag_optimize">optimizations</a> may be performed; ones which require extensive information about the instructions efficiently supported by the target.</p> <p>The SelectionDAG is a Directed-Acyclic-Graph whose nodes are instances of the <tt>SDNode</tt> class. The primary payload of the <tt>SDNode</tt> is its operation code (Opcode) that indicates what operation the node performs and the operands to the operation. The various operation node types are described at the top of the <tt>include/llvm/CodeGen/SelectionDAGNodes.h</tt> file.</p> <p>Although most operations define a single value, each node in the graph may define multiple values. For example, a combined div/rem operation will define both the dividend and the remainder. Many other situations require multiple values as well. Each node also has some number of operands, which are edges to the node defining the used value. Because nodes may define multiple values, edges are represented by instances of the <tt>SDValue</tt> class, which is a <tt><SDNode, unsigned></tt> pair, indicating the node and result value being used, respectively. Each value produced by an <tt>SDNode</tt> has an associated <tt>MVT</tt> (Machine Value Type) indicating what the type of the value is.</p> <p>SelectionDAGs contain two different kinds of values: those that represent data flow and those that represent control flow dependencies. Data values are simple edges with an integer or floating point value type. Control edges are represented as "chain" edges which are of type <tt>MVT::Other</tt>. These edges provide an ordering between nodes that have side effects (such as loads, stores, calls, returns, etc). All nodes that have side effects should take a token chain as input and produce a new one as output. By convention, token chain inputs are always operand #0, and chain results are always the last value produced by an operation.</p> <p>A SelectionDAG has designated "Entry" and "Root" nodes. The Entry node is always a marker node with an Opcode of <tt>ISD::EntryToken</tt>. The Root node is the final side-effecting node in the token chain. For example, in a single basic block function it would be the return node.</p> <p>One important concept for SelectionDAGs is the notion of a "legal" vs. "illegal" DAG. A legal DAG for a target is one that only uses supported operations and supported types. On a 32-bit PowerPC, for example, a DAG with a value of type i1, i8, i16, or i64 would be illegal, as would a DAG that uses a SREM or UREM operation. The <a href="#selectinodag_legalize_types">legalize types</a> and <a href="#selectiondag_legalize">legalize operations</a> phases are responsible for turning an illegal DAG into a legal DAG.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_process">SelectionDAG Instruction Selection Process</a> </div> <div class="doc_text"> <p>SelectionDAG-based instruction selection consists of the following steps:</p> <ol> <li><a href="#selectiondag_build">Build initial DAG</a> - This stage performs a simple translation from the input LLVM code to an illegal SelectionDAG.</li> <li><a href="#selectiondag_optimize">Optimize SelectionDAG</a> - This stage performs simple optimizations on the SelectionDAG to simplify it, and recognize meta instructions (like rotates and <tt>div</tt>/<tt>rem</tt> pairs) for targets that support these meta operations. This makes the resultant code more efficient and the <a href="#selectiondag_select">select instructions from DAG</a> phase (below) simpler.</li> <li><a href="#selectiondag_legalize_types">Legalize SelectionDAG Types</a> - This stage transforms SelectionDAG nodes to eliminate any types that are unsupported on the target.</li> <li><a href="#selectiondag_optimize">Optimize SelectionDAG</a> - The SelectionDAG optimizer is run to clean up redundancies exposed by type legalization.</li> <li><a href="#selectiondag_legalize">Legalize SelectionDAG Types</a> - This stage transforms SelectionDAG nodes to eliminate any types that are unsupported on the target.</li> <li><a href="#selectiondag_optimize">Optimize SelectionDAG</a> - The SelectionDAG optimizer is run to eliminate inefficiencies introduced by operation legalization.</li> <li><a href="#selectiondag_select">Select instructions from DAG</a> - Finally, the target instruction selector matches the DAG operations to target instructions. This process translates the target-independent input DAG into another DAG of target instructions.</li> <li><a href="#selectiondag_sched">SelectionDAG Scheduling and Formation</a> - The last phase assigns a linear order to the instructions in the target-instruction DAG and emits them into the MachineFunction being compiled. This step uses traditional prepass scheduling techniques.</li> </ol> <p>After all of these steps are complete, the SelectionDAG is destroyed and the rest of the code generation passes are run.</p> <p>One great way to visualize what is going on here is to take advantage of a few LLC command line options. The following options pop up a window displaying the SelectionDAG at specific times (if you only get errors printed to the console while using this, you probably <a href="ProgrammersManual.html#ViewGraph">need to configure your system</a> to add support for it).</p> <ul> <li><tt>-view-dag-combine1-dags</tt> displays the DAG after being built, before the first optimization pass.</li> <li><tt>-view-legalize-dags</tt> displays the DAG before Legalization.</li> <li><tt>-view-dag-combine2-dags</tt> displays the DAG before the second optimization pass.</li> <li><tt>-view-isel-dags</tt> displays the DAG before the Select phase.</li> <li><tt>-view-sched-dags</tt> displays the DAG before Scheduling.</li> </ul> <p>The <tt>-view-sunit-dags</tt> displays the Scheduler's dependency graph. This graph is based on the final SelectionDAG, with nodes that must be scheduled together bundled into a single scheduling-unit node, and with immediate operands and other nodes that aren't relevant for scheduling omitted. </p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_build">Initial SelectionDAG Construction</a> </div> <div class="doc_text"> <p>The initial SelectionDAG is naïvely peephole expanded from the LLVM input by the <tt>SelectionDAGLowering</tt> class in the <tt>lib/CodeGen/SelectionDAG/SelectionDAGISel.cpp</tt> file. The intent of this pass is to expose as much low-level, target-specific details to the SelectionDAG as possible. This pass is mostly hard-coded (e.g. an LLVM <tt>add</tt> turns into an <tt>SDNode add</tt> while a <tt>getelementptr</tt> is expanded into the obvious arithmetic). This pass requires target-specific hooks to lower calls, returns, varargs, etc. For these features, the <tt><a href="#targetlowering">TargetLowering</a></tt> interface is used.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_legalize_types">SelectionDAG LegalizeTypes Phase</a> </div> <div class="doc_text"> <p>The Legalize phase is in charge of converting a DAG to only use the types that are natively supported by the target.</p> <p>There are two main ways of converting values of unsupported scalar types to values of supported types: converting small types to larger types ("promoting"), and breaking up large integer types into smaller ones ("expanding"). For example, a target might require that all f32 values are promoted to f64 and that all i1/i8/i16 values are promoted to i32. The same target might require that all i64 values be expanded into pairs of i32 values. These changes can insert sign and zero extensions as needed to make sure that the final code has the same behavior as the input.</p> <p>There are two main ways of converting values of unsupported vector types to value of supported types: splitting vector types, multiple times if necessary, until a legal type is found, and extending vector types by adding elements to the end to round them out to legal types ("widening"). If a vector gets split all the way down to single-element parts with no supported vector type being found, the elements are converted to scalars ("scalarizing").</p> <p>A target implementation tells the legalizer which types are supported (and which register class to use for them) by calling the <tt>addRegisterClass</tt> method in its TargetLowering constructor.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_legalize">SelectionDAG Legalize Phase</a> </div> <div class="doc_text"> <p>The Legalize phase is in charge of converting a DAG to only use the operations that are natively supported by the target.</p> <p>Targets often have weird constraints, such as not supporting every operation on every supported datatype (e.g. X86 does not support byte conditional moves and PowerPC does not support sign-extending loads from a 16-bit memory location). Legalize takes care of this by open-coding another sequence of operations to emulate the operation ("expansion"), by promoting one type to a larger type that supports the operation ("promotion"), or by using a target-specific hook to implement the legalization ("custom").</p> <p>A target implementation tells the legalizer which operations are not supported (and which of the above three actions to take) by calling the <tt>setOperationAction</tt> method in its <tt>TargetLowering</tt> constructor.</p> <p>Prior to the existence of the Legalize passes, we required that every target <a href="#selectiondag_optimize">selector</a> supported and handled every operator and type even if they are not natively supported. The introduction of the Legalize phases allows all of the canonicalization patterns to be shared across targets, and makes it very easy to optimize the canonicalized code because it is still in the form of a DAG.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_optimize">SelectionDAG Optimization Phase: the DAG Combiner</a> </div> <div class="doc_text"> <p>The SelectionDAG optimization phase is run multiple times for code generation, immediately after the DAG is built and once after each legalization. The first run of the pass allows the initial code to be cleaned up (e.g. performing optimizations that depend on knowing that the operators have restricted type inputs). Subsequent runs of the pass clean up the messy code generated by the Legalize passes, which allows Legalize to be very simple (it can focus on making code legal instead of focusing on generating <em>good</em> and legal code).</p> <p>One important class of optimizations performed is optimizing inserted sign and zero extension instructions. We currently use ad-hoc techniques, but could move to more rigorous techniques in the future. Here are some good papers on the subject:</p> <p> "<a href="http://www.eecs.harvard.edu/~nr/pubs/widen-abstract.html">Widening integer arithmetic</a>"<br> Kevin Redwine and Norman Ramsey<br> International Conference on Compiler Construction (CC) 2004 </p> <p> "<a href="http://portal.acm.org/citation.cfm?doid=512529.512552">Effective sign extension elimination</a>"<br> Motohiro Kawahito, Hideaki Komatsu, and Toshio Nakatani<br> Proceedings of the ACM SIGPLAN 2002 Conference on Programming Language Design and Implementation. </p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_select">SelectionDAG Select Phase</a> </div> <div class="doc_text"> <p>The Select phase is the bulk of the target-specific code for instruction selection. This phase takes a legal SelectionDAG as input, pattern matches the instructions supported by the target to this DAG, and produces a new DAG of target code. For example, consider the following LLVM fragment:</p> <div class="doc_code"> <pre> %t1 = add float %W, %X %t2 = mul float %t1, %Y %t3 = add float %t2, %Z </pre> </div> <p>This LLVM code corresponds to a SelectionDAG that looks basically like this:</p> <div class="doc_code"> <pre> (fadd:f32 (fmul:f32 (fadd:f32 W, X), Y), Z) </pre> </div> <p>If a target supports floating point multiply-and-add (FMA) operations, one of the adds can be merged with the multiply. On the PowerPC, for example, the output of the instruction selector might look like this DAG:</p> <div class="doc_code"> <pre> (FMADDS (FADDS W, X), Y, Z) </pre> </div> <p>The <tt>FMADDS</tt> instruction is a ternary instruction that multiplies its first two operands and adds the third (as single-precision floating-point numbers). The <tt>FADDS</tt> instruction is a simple binary single-precision add instruction. To perform this pattern match, the PowerPC backend includes the following instruction definitions:</p> <div class="doc_code"> <pre> def FMADDS : AForm_1<59, 29, (ops F4RC:$FRT, F4RC:$FRA, F4RC:$FRC, F4RC:$FRB), "fmadds $FRT, $FRA, $FRC, $FRB", [<b>(set F4RC:$FRT, (fadd (fmul F4RC:$FRA, F4RC:$FRC), F4RC:$FRB))</b>]>; def FADDS : AForm_2<59, 21, (ops F4RC:$FRT, F4RC:$FRA, F4RC:$FRB), "fadds $FRT, $FRA, $FRB", [<b>(set F4RC:$FRT, (fadd F4RC:$FRA, F4RC:$FRB))</b>]>; </pre> </div> <p>The portion of the instruction definition in bold indicates the pattern used to match the instruction. The DAG operators (like <tt>fmul</tt>/<tt>fadd</tt>) are defined in the <tt>lib/Target/TargetSelectionDAG.td</tt> file. "<tt>F4RC</tt>" is the register class of the input and result values.</p> <p>The TableGen DAG instruction selector generator reads the instruction patterns in the <tt>.td</tt> file and automatically builds parts of the pattern matching code for your target. It has the following strengths:</p> <ul> <li>At compiler-compiler time, it analyzes your instruction patterns and tells you if your patterns make sense or not.</li> <li>It can handle arbitrary constraints on operands for the pattern match. In particular, it is straight-forward to say things like "match any immediate that is a 13-bit sign-extended value". For examples, see the <tt>immSExt16</tt> and related <tt>tblgen</tt> classes in the PowerPC backend.</li> <li>It knows several important identities for the patterns defined. For example, it knows that addition is commutative, so it allows the <tt>FMADDS</tt> pattern above to match "<tt>(fadd X, (fmul Y, Z))</tt>" as well as "<tt>(fadd (fmul X, Y), Z)</tt>", without the target author having to specially handle this case.</li> <li>It has a full-featured type-inferencing system. In particular, you should rarely have to explicitly tell the system what type parts of your patterns are. In the <tt>FMADDS</tt> case above, we didn't have to tell <tt>tblgen</tt> that all of the nodes in the pattern are of type 'f32'. It was able to infer and propagate this knowledge from the fact that <tt>F4RC</tt> has type 'f32'.</li> <li>Targets can define their own (and rely on built-in) "pattern fragments". Pattern fragments are chunks of reusable patterns that get inlined into your patterns during compiler-compiler time. For example, the integer "<tt>(not x)</tt>" operation is actually defined as a pattern fragment that expands as "<tt>(xor x, -1)</tt>", since the SelectionDAG does not have a native '<tt>not</tt>' operation. Targets can define their own short-hand fragments as they see fit. See the definition of '<tt>not</tt>' and '<tt>ineg</tt>' for examples.</li> <li>In addition to instructions, targets can specify arbitrary patterns that map to one or more instructions using the 'Pat' class. For example, the PowerPC has no way to load an arbitrary integer immediate into a register in one instruction. To tell tblgen how to do this, it defines: <br> <br> <div class="doc_code"> <pre> // Arbitrary immediate support. Implement in terms of LIS/ORI. def : Pat<(i32 imm:$imm), (ORI (LIS (HI16 imm:$imm)), (LO16 imm:$imm))>; </pre> </div> <br> If none of the single-instruction patterns for loading an immediate into a register match, this will be used. This rule says "match an arbitrary i32 immediate, turning it into an <tt>ORI</tt> ('or a 16-bit immediate') and an <tt>LIS</tt> ('load 16-bit immediate, where the immediate is shifted to the left 16 bits') instruction". To make this work, the <tt>LO16</tt>/<tt>HI16</tt> node transformations are used to manipulate the input immediate (in this case, take the high or low 16-bits of the immediate).</li> <li>While the system does automate a lot, it still allows you to write custom C++ code to match special cases if there is something that is hard to express.</li> </ul> <p>While it has many strengths, the system currently has some limitations, primarily because it is a work in progress and is not yet finished:</p> <ul> <li>Overall, there is no way to define or match SelectionDAG nodes that define multiple values (e.g. <tt>ADD_PARTS</tt>, <tt>LOAD</tt>, <tt>CALL</tt>, etc). This is the biggest reason that you currently still <em>have to</em> write custom C++ code for your instruction selector.</li> <li>There is no great way to support matching complex addressing modes yet. In the future, we will extend pattern fragments to allow them to define multiple values (e.g. the four operands of the <a href="#x86_memory">X86 addressing mode</a>, which are currently matched with custom C++ code). In addition, we'll extend fragments so that a fragment can match multiple different patterns.</li> <li>We don't automatically infer flags like isStore/isLoad yet.</li> <li>We don't automatically generate the set of supported registers and operations for the <a href="#selectiondag_legalize">Legalizer</a> yet.</li> <li>We don't have a way of tying in custom legalized nodes yet.</li> </ul> <p>Despite these limitations, the instruction selector generator is still quite useful for most of the binary and logical operations in typical instruction sets. If you run into any problems or can't figure out how to do something, please let Chris know!</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_sched">SelectionDAG Scheduling and Formation Phase</a> </div> <div class="doc_text"> <p>The scheduling phase takes the DAG of target instructions from the selection phase and assigns an order. The scheduler can pick an order depending on various constraints of the machines (i.e. order for minimal register pressure or try to cover instruction latencies). Once an order is established, the DAG is converted to a list of <tt><a href="#machineinstr">MachineInstr</a></tt>s and the SelectionDAG is destroyed.</p> <p>Note that this phase is logically separate from the instruction selection phase, but is tied to it closely in the code because it operates on SelectionDAGs.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="selectiondag_future">Future directions for the SelectionDAG</a> </div> <div class="doc_text"> <ol> <li>Optional function-at-a-time selection.</li> <li>Auto-generate entire selector from <tt>.td</tt> file.</li> </ol> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="ssamco">SSA-based Machine Code Optimizations</a> </div> <div class="doc_text"><p>To Be Written</p></div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="liveintervals">Live Intervals</a> </div> <div class="doc_text"> <p>Live Intervals are the ranges (intervals) where a variable is <i>live</i>. They are used by some <a href="#regalloc">register allocator</a> passes to determine if two or more virtual registers which require the same physical register are live at the same point in the program (i.e., they conflict). When this situation occurs, one virtual register must be <i>spilled</i>.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="livevariable_analysis">Live Variable Analysis</a> </div> <div class="doc_text"> <p>The first step in determining the live intervals of variables is to calculate the set of registers that are immediately dead after the instruction (i.e., the instruction calculates the value, but it is never used) and the set of registers that are used by the instruction, but are never used after the instruction (i.e., they are killed). Live variable information is computed for each <i>virtual</i> register and <i>register allocatable</i> physical register in the function. This is done in a very efficient manner because it uses SSA to sparsely compute lifetime information for virtual registers (which are in SSA form) and only has to track physical registers within a block. Before register allocation, LLVM can assume that physical registers are only live within a single basic block. This allows it to do a single, local analysis to resolve physical register lifetimes within each basic block. If a physical register is not register allocatable (e.g., a stack pointer or condition codes), it is not tracked.</p> <p>Physical registers may be live in to or out of a function. Live in values are typically arguments in registers. Live out values are typically return values in registers. Live in values are marked as such, and are given a dummy "defining" instruction during live intervals analysis. If the last basic block of a function is a <tt>return</tt>, then it's marked as using all live out values in the function.</p> <p><tt>PHI</tt> nodes need to be handled specially, because the calculation of the live variable information from a depth first traversal of the CFG of the function won't guarantee that a virtual register used by the <tt>PHI</tt> node is defined before it's used. When a <tt>PHI</tt> node is encountered, only the definition is handled, because the uses will be handled in other basic blocks.</p> <p>For each <tt>PHI</tt> node of the current basic block, we simulate an assignment at the end of the current basic block and traverse the successor basic blocks. If a successor basic block has a <tt>PHI</tt> node and one of the <tt>PHI</tt> node's operands is coming from the current basic block, then the variable is marked as <i>alive</i> within the current basic block and all of its predecessor basic blocks, until the basic block with the defining instruction is encountered.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="liveintervals_analysis">Live Intervals Analysis</a> </div> <div class="doc_text"> <p>We now have the information available to perform the live intervals analysis and build the live intervals themselves. We start off by numbering the basic blocks and machine instructions. We then handle the "live-in" values. These are in physical registers, so the physical register is assumed to be killed by the end of the basic block. Live intervals for virtual registers are computed for some ordering of the machine instructions <tt>[1, N]</tt>. A live interval is an interval <tt>[i, j)</tt>, where <tt>1 <= i <= j < N</tt>, for which a variable is live.</p> <p><i><b>More to come...</b></i></p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="regalloc">Register Allocation</a> </div> <div class="doc_text"> <p>The <i>Register Allocation problem</i> consists in mapping a program <i>P<sub>v</sub></i>, that can use an unbounded number of virtual registers, to a program <i>P<sub>p</sub></i> that contains a finite (possibly small) number of physical registers. Each target architecture has a different number of physical registers. If the number of physical registers is not enough to accommodate all the virtual registers, some of them will have to be mapped into memory. These virtuals are called <i>spilled virtuals</i>.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_represent">How registers are represented in LLVM</a> </div> <div class="doc_text"> <p>In LLVM, physical registers are denoted by integer numbers that normally range from 1 to 1023. To see how this numbering is defined for a particular architecture, you can read the <tt>GenRegisterNames.inc</tt> file for that architecture. For instance, by inspecting <tt>lib/Target/X86/X86GenRegisterNames.inc</tt> we see that the 32-bit register <tt>EAX</tt> is denoted by 15, and the MMX register <tt>MM0</tt> is mapped to 48.</p> <p>Some architectures contain registers that share the same physical location. A notable example is the X86 platform. For instance, in the X86 architecture, the registers <tt>EAX</tt>, <tt>AX</tt> and <tt>AL</tt> share the first eight bits. These physical registers are marked as <i>aliased</i> in LLVM. Given a particular architecture, you can check which registers are aliased by inspecting its <tt>RegisterInfo.td</tt> file. Moreover, the method <tt>TargetRegisterInfo::getAliasSet(p_reg)</tt> returns an array containing all the physical registers aliased to the register <tt>p_reg</tt>.</p> <p>Physical registers, in LLVM, are grouped in <i>Register Classes</i>. Elements in the same register class are functionally equivalent, and can be interchangeably used. Each virtual register can only be mapped to physical registers of a particular class. For instance, in the X86 architecture, some virtuals can only be allocated to 8 bit registers. A register class is described by <tt>TargetRegisterClass</tt> objects. To discover if a virtual register is compatible with a given physical, this code can be used: </p> <div class="doc_code"> <pre> bool RegMapping_Fer::compatible_class(MachineFunction &mf, unsigned v_reg, unsigned p_reg) { assert(TargetRegisterInfo::isPhysicalRegister(p_reg) && "Target register must be physical"); const TargetRegisterClass *trc = mf.getRegInfo().getRegClass(v_reg); return trc->contains(p_reg); } </pre> </div> <p>Sometimes, mostly for debugging purposes, it is useful to change the number of physical registers available in the target architecture. This must be done statically, inside the <tt>TargetRegsterInfo.td</tt> file. Just <tt>grep</tt> for <tt>RegisterClass</tt>, the last parameter of which is a list of registers. Just commenting some out is one simple way to avoid them being used. A more polite way is to explicitly exclude some registers from the <i>allocation order</i>. See the definition of the <tt>GR</tt> register class in <tt>lib/Target/IA64/IA64RegisterInfo.td</tt> for an example of this (e.g., <tt>numReservedRegs</tt> registers are hidden.)</p> <p>Virtual registers are also denoted by integer numbers. Contrary to physical registers, different virtual registers never share the same number. The smallest virtual register is normally assigned the number 1024. This may change, so, in order to know which is the first virtual register, you should access <tt>TargetRegisterInfo::FirstVirtualRegister</tt>. Any register whose number is greater than or equal to <tt>TargetRegisterInfo::FirstVirtualRegister</tt> is considered a virtual register. Whereas physical registers are statically defined in a <tt>TargetRegisterInfo.td</tt> file and cannot be created by the application developer, that is not the case with virtual registers. In order to create new virtual registers, use the method <tt>MachineRegisterInfo::createVirtualRegister()</tt>. This method will return a virtual register with the highest code. </p> <p>Before register allocation, the operands of an instruction are mostly virtual registers, although physical registers may also be used. In order to check if a given machine operand is a register, use the boolean function <tt>MachineOperand::isRegister()</tt>. To obtain the integer code of a register, use <tt>MachineOperand::getReg()</tt>. An instruction may define or use a register. For instance, <tt>ADD reg:1026 := reg:1025 reg:1024</tt> defines the registers 1024, and uses registers 1025 and 1026. Given a register operand, the method <tt>MachineOperand::isUse()</tt> informs if that register is being used by the instruction. The method <tt>MachineOperand::isDef()</tt> informs if that registers is being defined.</p> <p>We will call physical registers present in the LLVM bitcode before register allocation <i>pre-colored registers</i>. Pre-colored registers are used in many different situations, for instance, to pass parameters of functions calls, and to store results of particular instructions. There are two types of pre-colored registers: the ones <i>implicitly</i> defined, and those <i>explicitly</i> defined. Explicitly defined registers are normal operands, and can be accessed with <tt>MachineInstr::getOperand(int)::getReg()</tt>. In order to check which registers are implicitly defined by an instruction, use the <tt>TargetInstrInfo::get(opcode)::ImplicitDefs</tt>, where <tt>opcode</tt> is the opcode of the target instruction. One important difference between explicit and implicit physical registers is that the latter are defined statically for each instruction, whereas the former may vary depending on the program being compiled. For example, an instruction that represents a function call will always implicitly define or use the same set of physical registers. To read the registers implicitly used by an instruction, use <tt>TargetInstrInfo::get(opcode)::ImplicitUses</tt>. Pre-colored registers impose constraints on any register allocation algorithm. The register allocator must make sure that none of them is been overwritten by the values of virtual registers while still alive.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_howTo">Mapping virtual registers to physical registers</a> </div> <div class="doc_text"> <p>There are two ways to map virtual registers to physical registers (or to memory slots). The first way, that we will call <i>direct mapping</i>, is based on the use of methods of the classes <tt>TargetRegisterInfo</tt>, and <tt>MachineOperand</tt>. The second way, that we will call <i>indirect mapping</i>, relies on the <tt>VirtRegMap</tt> class in order to insert loads and stores sending and getting values to and from memory.</p> <p>The direct mapping provides more flexibility to the developer of the register allocator; however, it is more error prone, and demands more implementation work. Basically, the programmer will have to specify where load and store instructions should be inserted in the target function being compiled in order to get and store values in memory. To assign a physical register to a virtual register present in a given operand, use <tt>MachineOperand::setReg(p_reg)</tt>. To insert a store instruction, use <tt>TargetRegisterInfo::storeRegToStackSlot(...)</tt>, and to insert a load instruction, use <tt>TargetRegisterInfo::loadRegFromStackSlot</tt>.</p> <p>The indirect mapping shields the application developer from the complexities of inserting load and store instructions. In order to map a virtual register to a physical one, use <tt>VirtRegMap::assignVirt2Phys(vreg, preg)</tt>. In order to map a certain virtual register to memory, use <tt>VirtRegMap::assignVirt2StackSlot(vreg)</tt>. This method will return the stack slot where <tt>vreg</tt>'s value will be located. If it is necessary to map another virtual register to the same stack slot, use <tt>VirtRegMap::assignVirt2StackSlot(vreg, stack_location)</tt>. One important point to consider when using the indirect mapping, is that even if a virtual register is mapped to memory, it still needs to be mapped to a physical register. This physical register is the location where the virtual register is supposed to be found before being stored or after being reloaded.</p> <p>If the indirect strategy is used, after all the virtual registers have been mapped to physical registers or stack slots, it is necessary to use a spiller object to place load and store instructions in the code. Every virtual that has been mapped to a stack slot will be stored to memory after been defined and will be loaded before being used. The implementation of the spiller tries to recycle load/store instructions, avoiding unnecessary instructions. For an example of how to invoke the spiller, see <tt>RegAllocLinearScan::runOnMachineFunction</tt> in <tt>lib/CodeGen/RegAllocLinearScan.cpp</tt>.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_twoAddr">Handling two address instructions</a> </div> <div class="doc_text"> <p>With very rare exceptions (e.g., function calls), the LLVM machine code instructions are three address instructions. That is, each instruction is expected to define at most one register, and to use at most two registers. However, some architectures use two address instructions. In this case, the defined register is also one of the used register. For instance, an instruction such as <tt>ADD %EAX, %EBX</tt>, in X86 is actually equivalent to <tt>%EAX = %EAX + %EBX</tt>.</p> <p>In order to produce correct code, LLVM must convert three address instructions that represent two address instructions into true two address instructions. LLVM provides the pass <tt>TwoAddressInstructionPass</tt> for this specific purpose. It must be run before register allocation takes place. After its execution, the resulting code may no longer be in SSA form. This happens, for instance, in situations where an instruction such as <tt>%a = ADD %b %c</tt> is converted to two instructions such as:</p> <div class="doc_code"> <pre> %a = MOVE %b %a = ADD %a %c </pre> </div> <p>Notice that, internally, the second instruction is represented as <tt>ADD %a[def/use] %c</tt>. I.e., the register operand <tt>%a</tt> is both used and defined by the instruction.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_ssaDecon">The SSA deconstruction phase</a> </div> <div class="doc_text"> <p>An important transformation that happens during register allocation is called the <i>SSA Deconstruction Phase</i>. The SSA form simplifies many analyses that are performed on the control flow graph of programs. However, traditional instruction sets do not implement PHI instructions. Thus, in order to generate executable code, compilers must replace PHI instructions with other instructions that preserve their semantics.</p> <p>There are many ways in which PHI instructions can safely be removed from the target code. The most traditional PHI deconstruction algorithm replaces PHI instructions with copy instructions. That is the strategy adopted by LLVM. The SSA deconstruction algorithm is implemented in <tt>lib/CodeGen/PHIElimination.cpp</tt>. In order to invoke this pass, the identifier <tt>PHIEliminationID</tt> must be marked as required in the code of the register allocator.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_fold">Instruction folding</a> </div> <div class="doc_text"> <p><i>Instruction folding</i> is an optimization performed during register allocation that removes unnecessary copy instructions. For instance, a sequence of instructions such as:</p> <div class="doc_code"> <pre> %EBX = LOAD %mem_address %EAX = COPY %EBX </pre> </div> <p>can be safely substituted by the single instruction:</p> <div class="doc_code"> <pre> %EAX = LOAD %mem_address </pre> </div> <p>Instructions can be folded with the <tt>TargetRegisterInfo::foldMemoryOperand(...)</tt> method. Care must be taken when folding instructions; a folded instruction can be quite different from the original instruction. See <tt>LiveIntervals::addIntervalsForSpills</tt> in <tt>lib/CodeGen/LiveIntervalAnalysis.cpp</tt> for an example of its use.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="regAlloc_builtIn">Built in register allocators</a> </div> <div class="doc_text"> <p>The LLVM infrastructure provides the application developer with three different register allocators:</p> <ul> <li><i>Simple</i> - This is a very simple implementation that does not keep values in registers across instructions. This register allocator immediately spills every value right after it is computed, and reloads all used operands from memory to temporary registers before each instruction.</li> <li><i>Local</i> - This register allocator is an improvement on the <i>Simple</i> implementation. It allocates registers on a basic block level, attempting to keep values in registers and reusing registers as appropriate.</li> <li><i>Linear Scan</i> - <i>The default allocator</i>. This is the well-know linear scan register allocator. Whereas the <i>Simple</i> and <i>Local</i> algorithms use a direct mapping implementation technique, the <i>Linear Scan</i> implementation uses a spiller in order to place load and stores.</li> </ul> <p>The type of register allocator used in <tt>llc</tt> can be chosen with the command line option <tt>-regalloc=...</tt>:</p> <div class="doc_code"> <pre> $ llc -f -regalloc=simple file.bc -o sp.s; $ llc -f -regalloc=local file.bc -o lc.s; $ llc -f -regalloc=linearscan file.bc -o ln.s; </pre> </div> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="proepicode">Prolog/Epilog Code Insertion</a> </div> <div class="doc_text"><p>To Be Written</p></div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="latemco">Late Machine Code Optimizations</a> </div> <div class="doc_text"><p>To Be Written</p></div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="codeemit">Code Emission</a> </div> <div class="doc_text"><p>To Be Written</p></div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="codeemit_asm">Generating Assembly Code</a> </div> <div class="doc_text"><p>To Be Written</p></div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="codeemit_bin">Generating Binary Machine Code</a> </div> <div class="doc_text"> <p>For the JIT or <tt>.o</tt> file writer</p> </div> <!-- *********************************************************************** --> <div class="doc_section"> <a name="targetimpls">Target-specific Implementation Notes</a> </div> <!-- *********************************************************************** --> <div class="doc_text"> <p>This section of the document explains features or design decisions that are specific to the code generator for a particular target.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="tailcallopt">Tail call optimization</a> </div> <div class="doc_text"> <p>Tail call optimization, callee reusing the stack of the caller, is currently supported on x86/x86-64 and PowerPC. It is performed if: <ul> <li>Caller and callee have the calling convention <tt>fastcc</tt>.</li> <li>The call is a tail call - in tail position (ret immediately follows call and ret uses value of call or is void).</li> <li>Option <tt>-tailcallopt</tt> is enabled.</li> <li>Platform specific constraints are met.</li> </ul> </p> <p>x86/x86-64 constraints: <ul> <li>No variable argument lists are used.</li> <li>On x86-64 when generating GOT/PIC code only module-local calls (visibility = hidden or protected) are supported.</li> </ul> </p> <p>PowerPC constraints: <ul> <li>No variable argument lists are used.</li> <li>No byval parameters are used.</li> <li>On ppc32/64 GOT/PIC only module-local calls (visibility = hidden or protected) are supported.</li> </ul> </p> <p>Example:</p> <p>Call as <tt>llc -tailcallopt test.ll</tt>. <div class="doc_code"> <pre> declare fastcc i32 @tailcallee(i32 inreg %a1, i32 inreg %a2, i32 %a3, i32 %a4) define fastcc i32 @tailcaller(i32 %in1, i32 %in2) { %l1 = add i32 %in1, %in2 %tmp = tail call fastcc i32 @tailcallee(i32 %in1 inreg, i32 %in2 inreg, i32 %in1, i32 %l1) ret i32 %tmp }</pre> </div> </p> <p>Implications of <tt>-tailcallopt</tt>:</p> <p>To support tail call optimization in situations where the callee has more arguments than the caller a 'callee pops arguments' convention is used. This currently causes each <tt>fastcc</tt> call that is not tail call optimized (because one or more of above constraints are not met) to be followed by a readjustment of the stack. So performance might be worse in such cases.</p> <p>On x86 and x86-64 one register is reserved for indirect tail calls (e.g via a function pointer). So there is one less register for integer argument passing. For x86 this means 2 registers (if <tt>inreg</tt> parameter attribute is used) and for x86-64 this means 5 register are used.</p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="x86">The X86 backend</a> </div> <div class="doc_text"> <p>The X86 code generator lives in the <tt>lib/Target/X86</tt> directory. This code generator is capable of targeting a variety of x86-32 and x86-64 processors, and includes support for ISA extensions such as MMX and SSE. </p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="x86_tt">X86 Target Triples supported</a> </div> <div class="doc_text"> <p>The following are the known target triples that are supported by the X86 backend. This is not an exhaustive list, and it would be useful to add those that people test.</p> <ul> <li><b>i686-pc-linux-gnu</b> - Linux</li> <li><b>i386-unknown-freebsd5.3</b> - FreeBSD 5.3</li> <li><b>i686-pc-cygwin</b> - Cygwin on Win32</li> <li><b>i686-pc-mingw32</b> - MingW on Win32</li> <li><b>i386-pc-mingw32msvc</b> - MingW crosscompiler on Linux</li> <li><b>i686-apple-darwin*</b> - Apple Darwin on X86</li> </ul> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="x86_cc">X86 Calling Conventions supported</a> </div> <div class="doc_text"> <p>The following target-specific calling conventions are known to backend:</p> <ul> <li><b>x86_StdCall</b> - stdcall calling convention seen on Microsoft Windows platform (CC ID = 64).</li> <li><b>x86_FastCall</b> - fastcall calling convention seen on Microsoft Windows platform (CC ID = 65).</li> </ul> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="x86_memory">Representing X86 addressing modes in MachineInstrs</a> </div> <div class="doc_text"> <p>The x86 has a very flexible way of accessing memory. It is capable of forming memory addresses of the following expression directly in integer instructions (which use ModR/M addressing):</p> <div class="doc_code"> <pre> Base + [1,2,4,8] * IndexReg + Disp32 </pre> </div> <p>In order to represent this, LLVM tracks no less than 4 operands for each memory operand of this form. This means that the "load" form of '<tt>mov</tt>' has the following <tt>MachineOperand</tt>s in this order:</p> <pre> Index: 0 | 1 2 3 4 Meaning: DestReg, | BaseReg, Scale, IndexReg, Displacement OperandTy: VirtReg, | VirtReg, UnsImm, VirtReg, SignExtImm </pre> <p>Stores, and all other instructions, treat the four memory operands in the same way and in the same order.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="x86_memory">X86 address spaces supported</a> </div> <div class="doc_text"> <p>x86 has the ability to perform loads and stores to different address spaces via the x86 segment registers. A segment override prefix byte on an instruction causes the instruction's memory access to go to the specified segment. LLVM address space 0 is the default address space, which includes the stack, and any unqualified memory accesses in a program. Address spaces 1-255 are currently reserved for user-defined code. The GS-segment is represented by address space 256. Other x86 segments have yet to be allocated address space numbers. <p>Some operating systems use the GS-segment to implement TLS, so care should be taken when reading and writing to address space 256 on these platforms. </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="x86_names">Instruction naming</a> </div> <div class="doc_text"> <p>An instruction name consists of the base name, a default operand size, and a a character per operand with an optional special size. For example:</p> <p> <tt>ADD8rr</tt> -> add, 8-bit register, 8-bit register<br> <tt>IMUL16rmi</tt> -> imul, 16-bit register, 16-bit memory, 16-bit immediate<br> <tt>IMUL16rmi8</tt> -> imul, 16-bit register, 16-bit memory, 8-bit immediate<br> <tt>MOVSX32rm16</tt> -> movsx, 32-bit register, 16-bit memory </p> </div> <!-- ======================================================================= --> <div class="doc_subsection"> <a name="ppc">The PowerPC backend</a> </div> <div class="doc_text"> <p>The PowerPC code generator lives in the lib/Target/PowerPC directory. The code generation is retargetable to several variations or <i>subtargets</i> of the PowerPC ISA; including ppc32, ppc64 and altivec. </p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="ppc_abi">LLVM PowerPC ABI</a> </div> <div class="doc_text"> <p>LLVM follows the AIX PowerPC ABI, with two deviations. LLVM uses a PC relative (PIC) or static addressing for accessing global values, so no TOC (r2) is used. Second, r31 is used as a frame pointer to allow dynamic growth of a stack frame. LLVM takes advantage of having no TOC to provide space to save the frame pointer in the PowerPC linkage area of the caller frame. Other details of PowerPC ABI can be found at <a href= "http://developer.apple.com/documentation/DeveloperTools/Conceptual/LowLevelABI/Articles/32bitPowerPC.html" >PowerPC ABI.</a> Note: This link describes the 32 bit ABI. The 64 bit ABI is similar except space for GPRs are 8 bytes wide (not 4) and r13 is reserved for system use.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="ppc_frame">Frame Layout</a> </div> <div class="doc_text"> <p>The size of a PowerPC frame is usually fixed for the duration of a function’s invocation. Since the frame is fixed size, all references into the frame can be accessed via fixed offsets from the stack pointer. The exception to this is when dynamic alloca or variable sized arrays are present, then a base pointer (r31) is used as a proxy for the stack pointer and stack pointer is free to grow or shrink. A base pointer is also used if llvm-gcc is not passed the -fomit-frame-pointer flag. The stack pointer is always aligned to 16 bytes, so that space allocated for altivec vectors will be properly aligned.</p> <p>An invocation frame is laid out as follows (low memory at top);</p> </div> <div class="doc_text"> <table class="layout"> <tr> <td>Linkage<br><br></td> </tr> <tr> <td>Parameter area<br><br></td> </tr> <tr> <td>Dynamic area<br><br></td> </tr> <tr> <td>Locals area<br><br></td> </tr> <tr> <td>Saved registers area<br><br></td> </tr> <tr style="border-style: none hidden none hidden;"> <td><br></td> </tr> <tr> <td>Previous Frame<br><br></td> </tr> </table> </div> <div class="doc_text"> <p>The <i>linkage</i> area is used by a callee to save special registers prior to allocating its own frame. Only three entries are relevant to LLVM. The first entry is the previous stack pointer (sp), aka link. This allows probing tools like gdb or exception handlers to quickly scan the frames in the stack. A function epilog can also use the link to pop the frame from the stack. The third entry in the linkage area is used to save the return address from the lr register. Finally, as mentioned above, the last entry is used to save the previous frame pointer (r31.) The entries in the linkage area are the size of a GPR, thus the linkage area is 24 bytes long in 32 bit mode and 48 bytes in 64 bit mode.</p> </div> <div class="doc_text"> <p>32 bit linkage area</p> <table class="layout"> <tr> <td>0</td> <td>Saved SP (r1)</td> </tr> <tr> <td>4</td> <td>Saved CR</td> </tr> <tr> <td>8</td> <td>Saved LR</td> </tr> <tr> <td>12</td> <td>Reserved</td> </tr> <tr> <td>16</td> <td>Reserved</td> </tr> <tr> <td>20</td> <td>Saved FP (r31)</td> </tr> </table> </div> <div class="doc_text"> <p>64 bit linkage area</p> <table class="layout"> <tr> <td>0</td> <td>Saved SP (r1)</td> </tr> <tr> <td>8</td> <td>Saved CR</td> </tr> <tr> <td>16</td> <td>Saved LR</td> </tr> <tr> <td>24</td> <td>Reserved</td> </tr> <tr> <td>32</td> <td>Reserved</td> </tr> <tr> <td>40</td> <td>Saved FP (r31)</td> </tr> </table> </div> <div class="doc_text"> <p>The <i>parameter area</i> is used to store arguments being passed to a callee function. Following the PowerPC ABI, the first few arguments are actually passed in registers, with the space in the parameter area unused. However, if there are not enough registers or the callee is a thunk or vararg function, these register arguments can be spilled into the parameter area. Thus, the parameter area must be large enough to store all the parameters for the largest call sequence made by the caller. The size must also be minimally large enough to spill registers r3-r10. This allows callees blind to the call signature, such as thunks and vararg functions, enough space to cache the argument registers. Therefore, the parameter area is minimally 32 bytes (64 bytes in 64 bit mode.) Also note that since the parameter area is a fixed offset from the top of the frame, that a callee can access its spilt arguments using fixed offsets from the stack pointer (or base pointer.)</p> </div> <div class="doc_text"> <p>Combining the information about the linkage, parameter areas and alignment. A stack frame is minimally 64 bytes in 32 bit mode and 128 bytes in 64 bit mode.</p> </div> <div class="doc_text"> <p>The <i>dynamic area</i> starts out as size zero. If a function uses dynamic alloca then space is added to the stack, the linkage and parameter areas are shifted to top of stack, and the new space is available immediately below the linkage and parameter areas. The cost of shifting the linkage and parameter areas is minor since only the link value needs to be copied. The link value can be easily fetched by adding the original frame size to the base pointer. Note that allocations in the dynamic space need to observe 16 byte alignment.</p> </div> <div class="doc_text"> <p>The <i>locals area</i> is where the llvm compiler reserves space for local variables.</p> </div> <div class="doc_text"> <p>The <i>saved registers area</i> is where the llvm compiler spills callee saved registers on entry to the callee.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="ppc_prolog">Prolog/Epilog</a> </div> <div class="doc_text"> <p>The llvm prolog and epilog are the same as described in the PowerPC ABI, with the following exceptions. Callee saved registers are spilled after the frame is created. This allows the llvm epilog/prolog support to be common with other targets. The base pointer callee saved register r31 is saved in the TOC slot of linkage area. This simplifies allocation of space for the base pointer and makes it convenient to locate programatically and during debugging.</p> </div> <!-- _______________________________________________________________________ --> <div class="doc_subsubsection"> <a name="ppc_dynamic">Dynamic Allocation</a> </div> <div class="doc_text"> <p></p> </div> <div class="doc_text"> <p><i>TODO - More to come.</i></p> </div> <!-- *********************************************************************** --> <hr> <address> <a href="http://jigsaw.w3.org/css-validator/check/referer"><img src="http://jigsaw.w3.org/css-validator/images/vcss-blue" alt="Valid CSS"></a> <a href="http://validator.w3.org/check/referer"><img src="http://www.w3.org/Icons/valid-html401-blue" alt="Valid HTML 4.01"></a> <a href="mailto:sabre@nondot.org">Chris Lattner</a><br> <a href="http://llvm.org">The LLVM Compiler Infrastructure</a><br> Last modified: $Date$ </address> </body> </html>