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Chapter: Compilers - Principles, Techniques, & Tools : Instruction-Level Parallelism

Code-Scheduling Constraints

1 Data Dependence 2 Finding Dependences Among Memory Accesses 3 Tradeoff Between Register Usage and Parallelism 4 Phase Ordering Between Register Allocation and Code Scheduling 5 Control Dependence 6 Speculative Execution Support 7 A Basic Machine Model 8 Exercises for Section 10.2

Code-Scheduling Constraints

 

1 Data Dependence

2 Finding Dependences Among Memory Accesses

3 Tradeoff Between Register Usage and Parallelism

4 Phase Ordering Between Register Allocation and Code Scheduling

5 Control Dependence

6 Speculative Execution Support

7 A Basic Machine Model

8 Exercises for Section 10.2

 

Code scheduling is a form of program optimization that applies to the machine code that is produced by the code generator. Code scheduling is subject to three kinds of constraints:

2. Data-dependence constraints. The operations in the optimized program must produce the same results as the corresponding ones in the original program.

3. Resource constraints. The schedule must not oversubscribe the resources on the machine.

These scheduling constraints guarantee that the optimized program pro-duces the same results as the original. However, because code scheduling changes the order in which the operations execute, the state of the memory at any one point may not match any of the memory states in a sequential ex-ecution. This situation is a problem if a program's execution is interrupted by, for example, a thrown exception or a user-inserted breakpoint. Optimized programs are therefore harder to debug. Note that this problem is not specific to code scheduling but applies to all other optimizations, including partial-redundancy elimination (Section 9.5) and register allocation (Section 8.8).

 

1. Data Dependence

 

It is easy to see that if we change the execution order of two operations that do not touch any of the same variables, we cannot possibly affect their results. In fact, even if these two operations read the same variable, we can still permute their execution. Only if an operation writes to a variable read or written by another can changing their execution order alter their results. Such pairs of operations are said to share a data dependence, and their relative execution order must be preserved. There are three flavors of data dependence:

 

 

1.                 True dependence: read after write. If a write is followed by a read of the same location, the read depends on the value written; such a dependence is known as a true dependence.

 

2.                 Antidependence: write after read. If a read is followed by a write to the same location, we say that there is an antidependence from the read to the write. The write does not depend on the read per se, but if the write happens before the read, then the read operation will pick up the wrong value. Antidependence is a byproduct of imperative programming, where the same memory locations are used to store different values. It is not a "true" dependence and potentially can be eliminated by storing the values in different locations.

 

 

3.                 Output dependence: write after write. Two writes to the same location share an output dependence. If the dependence is violated, the value of the memory location written will have the wrong value after both operations are performed. 

 

Antidependence and output dependences are referred to as storage-related de-pendences. These are not "true" dependences and can be eliminated by using different locations to store different values. Note that data dependences apply to both memory accesses and register accesses.

 

2. Finding Dependences Among Memory Accesses

 

To check if two memory accesses share a data dependence, we only need to tell if they can refer to the same location; we do not need to know which location is being accessed. For example, we can tell that the two accesses *p and O p ) + 4 cannot refer to the same location, even though we may not know what p points to. Data dependence is generally undecidable at compile time. The compiler must assume that operations may refer to the same location unless it can prove otherwise.


unless the compiler knows that p cannot possibly point to a, it must conclude that the three operations need to execute serially. There is an output depen-dence flowing from statement (1) to statement (2), and there are two true dependences flowing from statements (1) and (2) to statement (3). •

 

Data-dependence analysis is highly sensitive to the programming language used in the program. For type-unsafe languages like C and C + + , where a pointer can be cast to point to any kind of object, sophisticated analysis is necessary to prove independence between any pair of pointer-based memory ac-cesses. Even local or global scalar variables can be accessed indirectly unless we can prove that their addresses have not been stored anywhere by any instruc-tion in the program. In type-safe languages like Java, objects of different types are necessarily distinct from each other. Similarly, local primitive variables on the stack cannot be aliased with accesses through other names.

 

A correct discovery of data dependences requires a number of different forms of analysis. We shall focus on the major questions that must be resolved if the compiler is to detect all the dependences that exist in a program, and how to use this information in code scheduling. Later chapters show how these analyses are performed.

 

 

Array  Data - Dependence  Analysis

 

Array data dependence is the problem of disambiguating between the values of indexes in array-element accesses. For example, the loop


copies odd elements in the array A to the even elements just preceding them. Because all the read and written locations in the loop are distinct from each other, there are no dependences between the accesses, and all the iterations in the loop can execute in parallel. Array data-dependence analysis, often referred to simply as data-dependence analysis, is very important for the optimization of numerical applications. This topic will be discussed in detail in Section 11.6.

 

Pointer - Alias  Analysis

 

We say that two pointers are aliased if they can refer to the same object. Pointer-alias analysis is difficult because there are many potentially aliased pointers in a program, and they can each point to an unbounded number of dynamic objects over time. To get any precision, pointer-alias analysis must be applied across all the functions in a program. This topic is discussed starting in Section 12.4.

 

 

Interprocedural  Analysis

 

For languages that pass parameters by reference, interprocedural analysis is needed to determine if the same variable is passed as two or more different arguments. Such aliases can create dependences between seemingly distinct parameters. Similarly, global variables can be used as parameters and thus create dependences between parameter accesses and global variable accesses. Interprocedural analysis, discussed in Chapter 12, is necessary to determine these aliases.

 

 

3. Tradeoff Between Register Usage and Parallelism

 

In this chapter we shall assume that the machine-independent intermediate rep-resentation of the source program uses an unbounded number of pseudoregisters to represent variables that can be allocated to registers. These variables include scalar variables in the source program that cannot be referred to by any other names, as well as temporary variables that are generated by the compiler to hold the partial results in expressions. Unlike memory locations, registers are uniquely named. Thus precise data-dependence constraints can be generated for register accesses easily.

 

The unbounded number of pseudoregisters used in the intermediate repre-sentation must eventually be mapped to the small number of physical registers available on the target machine. Mapping several pseudoregisters to the same physical register has the unfortunate side effect of creating artificial storage dependences that constrain instruction-level parallelism. Conversely, executing instructions in parallel creates the need for more storage to hold the values being computed simultaneously. Thus, the goal of minimizing the number of registers used conflicts directly with the goal of maximizing instruction-level parallelism. Examples 10.2 and 10.3 below illustrate this classic trade-off between storage and parallelism.

 

Hardware Register Renaming

 

Instruction-level parallelism was first used in computer architectures as a means to speed up ordinary sequential machine code. Compilers at the time were not aware of the instruction-level parallelism in the machine and were designed to optimize the use of registers. They deliberately reordered instructions to minimize the number of registers used, and as a result, also minimized the amount of parallelism available.  Example 10.3 illustrates how minimizing register usage in the computation of expression trees also limits its parallelism. 

There was so little parallelism left in the sequential code that computer architects  invented  the  concept  of  hardware register  renaming  to undo the effects of register optimization in compilers.  Hardware register renaming dynamically changes the assignment of registers as the program runs.  It interprets the machine code, stores values intended for the same register in different internal registers, and updates all their uses to refer to the right registers accordingly.

Since the artificial register-dependence constraints were introduced by the compiler in the first place, they can be eliminated by using a register-allocation algorithm that is cognizant of instruction-level paral-lelism. Hardware register renaming is still useful in the case when a ma-chine's instruction set can only refer to a small number of registers. This capability allows an implementation of the architecture to map the small number of architectural registers in the code to a much larger number of internal registers dynamically.

 

Example 10.2 :  The code below copies the values of variables in locations a and c to variables in locations b and d, respectively, using pseudoregisters tl and t2.

 

LD t l , a

ST b , t l

LD t2, c

ST d, t2

/ / t l = a

/ / b = t l

/ / t2 = c

/ / d = t2

 

If all the memory locations accessed are known to be distinct from each other, then the copies can proceed in parallel. However, if tl and t2 are assigned the same register so as to minimize the number of registers used, the copies are necessarily serialized. •

 

Example 10.3 : Traditional register-allocation techniques aim to minimize the number of registers used when performing a computation. Consider the expression


shown as a syntax tree in Fig. 10.2. It is possible to perform this computation using three registers, as illustrated by the machine code in Fig. 10.3.


The reuse of registers, however, serializes the computation. The only oper-ations allowed to execute in parallel are the loads of the values in locations a and b, and the loads of the values in locations d and e. It thus takes a total of 7 steps to complete the computation in parallel.

 

Had we used different registers for every partial sum, the expression could be evaluated in 4 steps, which is the height of the expression tree in Fig. 10.2. The parallel computation is suggested by Fig. 10.4.


 

4. Phase Ordering Between Register Allocation and Code Scheduling

 

If registers are allocated before scheduling, the resulting code tends to have many storage dependences that limit code scheduling. On the other hand, if code is scheduled before register allocation, the schedule created may require so many registers that  register spilling  (storing the  contents  of a register in a memory location, so the register can be used for some other purpose) may negate the advantages of instruction-level parallelism. Should a compiler allo-cate registers first before it schedules the code? Or should it be the other way round? Or, do we need to address these two problems at the same time?

 

To answer the questions above, we must consider the characteristics of the programs being compiled. Many nonnumeric applications do not have that much available parallelism. It suffices to dedicate a small number of registers for holding temporary results in expressions. We can first apply a coloring algorithm, as in Section 8.8.4, to allocate registers for all the nontemporary variables, then schedule the code, and finally assign registers to the temporary variables.

 

This approach does not work for numeric applications where there are many more large expressions. We can use a hierarchical approach where code is op-timized inside out, starting with the innermost loops. Instructions are first scheduled assuming that every pseudoregister will be allocated its own physical register. Register allocation is applied after scheduling and spill code is added where necessary, and the code is then rescheduled. This process is repeated for the code in the outer loops. When several inner loops are considered together in a common outer loop, the same variable may have been assigned different registers. We can change the register assignment to avoid having to copy the values from one register to another. In Section 10.5, we shall discuss the in-teraction between register allocation and scheduling further in the context of a specific scheduling algorithm.

 

5. Control Dependence

 

Scheduling operations within a basic block is relatively easy because all the instructions are guaranteed to execute once control flow reaches the beginning of the block. Instructions in a basic block can be reordered arbitrarily, as long as all the data dependences are satisfied. Unfortunately, basic blocks, especially in nonnumeric programs, are typically very small; on average, there are only about five instructions in a basic block. In addition, operations in the same block are often highly related and thus have little parallelism. Exploiting parallelism across basic blocks is therefore crucial.

 

An optimized program must execute all the operations in the original pro-gram. It can execute more instructions than the original, as long as the extra instructions do not change what the program does. Why would executing extra instructions speed up a program's execution? If we know that an instruction is likely to be executed, and an idle resource is available to perform the opera-tion "for free," we can execute the instruction speculatively. The program runs faster when the speculation turns out to be correct.

An  instruction  n  is said  to be control-dependent on instruction i2     if the outcome of i2    determines whether h is to be executed. The notion of control dependence corresponds to the concept of nesting levels in block-structured programs. Specifically, in the if-else statement


the statements b = a*a and d = a+c have no data dependence with any other part of the fragment. The statement b = a*a depends on the comparison a > t. The statement d = a+c, however, does not depend on the comparison and can be executed any time. Assuming that the multiplication a * a does not cause any side effects, it can be performed speculatively, as long as b is written only after a is found to be greater than t. •

 

 

6. Speculative Execution Support

 

Memory loads are one type of instruction that can benefit greatly from specula-tive execution. Memory loads are quite common, of course. They have relatively long execution latencies, addresses used in the loads are commonly available in advance, and the result can be stored in a new temporary variable without destroying the value of any other variable. Unfortunately, memory loads can raise exceptions if their addresses are illegal, so speculatively accessing illegal addresses may cause a correct program to halt unexpectedly. Besides, mispre-dicted memory loads can cause extra cache misses and page faults, which are extremely costly.

 

Example 10.5 :  In the fragment

 

if  (p  !=  n u l l )

 

q =  *P;

 

dereferencing p speculatively will cause this correct program to halt in error if p is null .

 

Many high-performance processors provide special features to support spec-ulative memory accesses. We mention the most important ones next.

Prefetching

 

The prefetch instruction was invented to bring data from memory to the cache before it is used. A prefetch instruction indicates to the processor that the program is likely to use a particular memory word in the near future. If the location specified is invalid or if accessing it causes a page fault, the processor can simply ignore the operation. Otherwise, the processor will bring the data from memory to the cache if it is not already there.

 

 

Poison  Bits

 

Another architectural feature called poison bits was invented to allow specu-lative load of data from memory into the register file. Each register on the machine is augmented with a poison bit. If illegal memory is accessed or the accessed page is not in memory, the processor does not raise the exception im-mediately but instead just sets the poison bit of the destination register. An exception is raised only if the contents of the register with a marked poison bit are used.

 

 

Predicated  Execution

 

Because branches are expensive, and mispredicted branches are even more so (see Section 10.1), predicated instructions were invented to reduce the number of branches in a program. A predicated instruction is like a normal instruction but has an extra predicate operand to guard its execution; the instruction is executed only if the predicate is found to be true.

 

As an example, a conditional move instruction CMOVZ R2,R3,R1 has the semantics that the contents of register R3 are moved to register R2 only if register Rl is zero. Code such as


can be implemented with two machine instructions, assuming that a, b, c, and d are allocated to registers Rl, R2, R4, R5, respectively, as follows:


This conversion replaces a series of instructions sharing a control dependence with instructions sharing only data dependences. These instructions can then be combined with adjacent basic blocks to create a larger basic block. More importantly, with this code, the processor does not have a chance to mispredict, thus guaranteeing that the instruction pipeline will run smoothly.

 

Predicated execution does come with a cost. Predicated instructions are fetched and decoded, even though they may not be executed in the end. Static schedulers must reserve all the resources needed for their execution and ensure

Dynamically Scheduled Machines

 

The instruction set of a statically scheduled machine explicitly defines what can execute in parallel. However, recall from Section 10.1.2 that some ma-chine architectures allow the decision to be made at run time about what can be executed in parallel. With dynamic scheduling, the same machine code can be run on different members of the same family (machines that implement the same instruction set) that have varying amounts of parallel-execution support. In fact, machine-code compatibility is one of the major advantages of dynamically scheduled machines.

 

Static schedulers, implemented in the compiler by software, can help dynamic schedulers (implemented in the machine's hardware) better utilize machine resources. To build a static scheduler for a dynamically sched-uled machine, we can use almost the same scheduling algorithm as for statically scheduled machines except that no - op instructions left in the schedule need not be generated explicitly. The matter is discussed further in Section 10.4.7.

 

 

 

 

that all the potential data dependences are satisfied. Predicated execution should not be used aggressively unless the machine has many more resources than can possibly be used otherwise.

 

7. A Basic Machine Model

 

Many machines can be represented using the following simple model. A machine M = {R,T), consists of:

 

1.                 A set of operation types T, such as loads, stores, arithmetic operations, and so on.

 

 

2.                 A vector R = [n, r2,... ] representing hardware resources, where r« is the number of units available of the ith kind of resource. Examples of typical resource types include: memory access units, ALU's, and floating-point functional units.

 

 

Each operation has a set of input operands, a set of output operands, and a resource requirement. Associated with each input operand is an input latency indicating when the input value must be available (relative to the start of the operation). Typical input operands have zero latency, meaning that the values are needed immediately, at the clock when the operation is issued. Similarly, associated with each output operand is an output latency, which indicates when the result is available, relative to the start of the operation.

 

Resource usage for each machine operation type t is modeled by a two-dimensional resource-reservation table, RTt. The width of the table is the number of kinds of resources in the machine, and its length is the duration over which resources are used by the operation. Entry RTt[i,j] is the number of units of the j t h resource used by an operation of type t, i clocks after it is issued. For notational simplicity, we assume RTt[i,j] = 0 if i refers to a nonex-istent entry in the table (i.e., i is greater than the number of clocks it takes to execute the operation). Of course, for any t, i, and j, RTt[i,j] must be less than or equal to R[j], the number of resources of type j that the machine has.

 

Typical machine operations occupy only one unit of resource at the time an operation is issued. Some operations may use more than one functional unit. For example, a multiply-and-add operation may use a multiplier in the first clock and an adder in the second. Some operations, such as a divide, may need to occupy a resource for several clocks. Fully pipelined operations are those that can be issued every clock, even though their results are not available until some number of clocks later. We need not model the resources of every stage of a pipeline explicitly; one single unit to represent the first stage will do. Any operation occupying the first stage of a pipeline is guaranteed the right to proceed to subsequent stages in subsequent clocks.

1) a = b

2) c = d

3) b = c

4) d = a

5) c = d

6) a   =   b

Figure 10.5:  A sequence of assignments exhibiting data dependences

 

8. Exercises for Section 10.2

 

Exercise 1 0 . 2 . 1 : The assignments in Fig. 10.5 have certain dependences. For each of the following pairs of statements, classify the dependence as (i) true de-pendence, (n) antidependence, (Hi) output dependence, or (iv) no dependence (i.e., the instructions can appear in either order):

 

a)                 Statements (1) and (4).

 

b)                Statements (3) and (5).

 

c)                 Statements (1) and (6).

 

d)         Statements (3) and (6).

 

e)          Statements (4) and (6).

Exercise 10 . 2 . Evaluate the expression ((u+v) + (w+x)) + (y+z) exactly as do not 2: parenthesized (i.e., use the commutative or associative laws to reorder the additions). Give register-level machine code to provide the maximum possible parallelism.

 

 

Exercise 10 . 2 . 3 :  Repeat Exercise 10.2.2 for the following expressions:

 

a)  (u + (v + (w + x))^j  + (y + z).

 

b)  (u + (v + w)) + (x + {y + z)).

 

If instead of maximizing the parallelism, we minimized the number of registers, how many steps would the computation take? How many steps do we save by using maximal parallelism?

 

Exercise 1 0 . 2 . 4 : The expression of Exercise 10.2.2 can be executed by the sequence of instructions shown in Fig. 10.6. If we have as much parallelism as we need, how many steps are needed to execute the instructions?


Figure 10.6:  Minimal-register implementation of an arithmetic expression

 

 

Exercise 1 0 . 2 . 5 : Translate the code fragment discussed in Example 10.4, using the CM0VZ conditional copy instruction of Section 10.2.6. What are the data dependences in your machine code?


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