Compilation

The explicit-control evaluator of section 5.4 is a register machine whose controller interprets Scheme programs. In this section we will see how to run Scheme programs on a register machine whose controller is not a Scheme interpreter.

The explicit-control evaluator machine is universal---it can carry out any computational process that can be described in Scheme. The evaluator's controller orchestrates the use of its data paths to perform the desired computation. Thus, the evaluator's data paths are universal: They are sufficient to perform any computation we desire, given an appropriate controller.@footnote{This is a theoretical statement. We are not claiming that the evaluator's data paths are a particularly convenient or efficient set of data paths for a general-purpose computer. For example, they are not very good for implementing high-performance floating-point calculations or calculations that intensively manipulate bit vectors.}

Commercial general-purpose computers are register machines organized around a collection of registers and operations that constitute an efficient and convenient universal set of data paths. The controller for a general-purpose machine is an interpreter for a register-machine language like the one we have been using. This language is called the native language of the machine, or simply machine language . Programs written in machine language are sequences of instructions that use the machine's data paths. For example, the explicit-control evaluator's instruction sequence can be thought of as a machine-language program for a general-purpose computer rather than as the controller for a specialized interpreter machine.

There are two common strategies for bridging the gap between higher-level languages and register-machine languages. The explicit-control evaluator illustrates the strategy of interpretation. An interpreter written in the native language of a machine configures the machine to execute programs written in a language (called the source language ) that may differ from the native language of the machine performing the evaluation. The primitive procedures of the source language are implemented as a library of subroutines written in the native language of the given machine. A program to be interpreted (called the source program ) is represented as a data structure. The interpreter traverses this data structure, analyzing the source program. As it does so, it simulates the intended behavior of the source program by calling appropriate primitive subroutines from the library.

In this section, we explore the alternative strategy of compilation . A compiler for a given source language and machine translates a source program into an equivalent program (called the object program ) written in the machine's native language. The compiler that we implement in this section translates programs written in Scheme into sequences of instructions to be executed using the explicit-control evaluator machine's data paths.@footnote{Actually, the machine that runs compiled code can be simpler than the interpreter machine, because we won't use the exp and unev registers. The interpreter used these to hold pieces of unevaluated expressions. With the compiler, however, these expressions get built into the compiled code that the register machine will run. For the same reason, we don't need the machine operations that deal with expression syntax. But compiled code will use a few additional machine operations (to represent compiled procedure objects) that didn't appear in the explicit-control evaluator machine.}

Compared with interpretation, compilation can provide a great increase in the efficiency of program execution, as we will explain below in the overview of the compiler. On the other hand, an interpreter provides a more powerful environment for interactive program development and debugging, because the source program being executed is available at run time to be examined and modified. In addition, because the entire library of primitives is present, new programs can be constructed and added to the system during debugging.

In view of the complementary advantages of compilation and interpretation, modern program-development environments pursue a mixed strategy. Lisp interpreters are generally organized so that interpreted procedures and compiled procedures can call each other. This enables a programmer to compile those parts of a program that are assumed to be debugged, thus gaining the efficiency advantage of compilation, while retaining the interpretive mode of execution for those parts of the program that are in the flux of interactive development and debugging. In section 5.5.7, after we have implemented the compiler, we will show how to interface it with our interpreter to produce an integrated interpreter-compiler development system.

An overview of the compiler

Our compiler is much like our interpreter, both in its structure and in the function it performs. Accordingly, the mechanisms used by the compiler for analyzing expressions will be similar to those used by the interpreter. Moreover, to make it easy to interface compiled and interpreted code, we will design the compiler to generate code that obeys the same conventions of register usage as the interpreter: The environment will be kept in the env register, argument lists will be accumulated in argl, a procedure to be applied will be in proc, procedures will return their answers in val, and the location to which a procedure should return will be kept in continue. In general, the compiler translates a source program into an object program that performs essentially the same register operations as would the interpreter in evaluating the same source program.

This description suggests a strategy for implementing a rudimentary compiler: We traverse the expression in the same way the interpreter does. When we encounter a register instruction that the interpreter would perform in evaluating the expression, we do not execute the instruction but instead accumulate it into a sequence. The resulting sequence of instructions will be the object code. Observe the efficiency advantage of compilation over interpretation. Each time the interpreter evaluates an expression---for example, (f 84 96)---it performs the work of classifying the expression (discovering that this is a procedure application) and testing for the end of the operand list (discovering that there are two operands). With a compiler, the expression is analyzed only once, when the instruction sequence is generated at compile time. The object code produced by the compiler contains only the instructions that evaluate the operator and the two operands, assemble the argument list, and apply the procedure (in proc) to the arguments (in argl).

This is the same kind of optimization we implemented in the analyzing evaluator of section 4.1.7. But there are further opportunities to gain efficiency in compiled code. As the interpreter runs, it follows a process that must be applicable to any expression in the language. In contrast, a given segment of compiled code is meant to execute some particular expression. This can make a big difference, for example in the use of the stack to save registers. When the interpreter evaluates an expression, it must be prepared for any contingency. Before evaluating a subexpression, the interpreter saves all registers that will be needed later, because the subexpression might require an arbitrary evaluation. A compiler, on the other hand, can exploit the structure of the particular expression it is processing to generate code that avoids unnecessary stack operations.

As a case in point, consider the combination (f 84 96). Before the interpreter evaluates the operator of the combination, it prepares for this evaluation by saving the registers containing the operands and the environment, whose values will be needed later. The interpreter then evaluates the operator to obtain the result in val, restores the saved registers, and finally moves the result from val to proc. However, in the particular expression we are dealing with, the operator is the symbol f, whose evaluation is accomplished by the machine operation lookup-variable-value, which does not alter any registers. The compiler that we implement in this section will take advantage of this fact and generate code that evaluates the operator using the instruction

(assign proc (op lookup-variable-value) (const f) (reg env))

This code not only avoids the unnecessary saves and restores but also assigns the value of the lookup directly to proc, whereas the interpreter would obtain the result in val and then move this to proc.

A compiler can also optimize access to the environment. Having analyzed the code, the compiler can in many cases know in which frame a particular variable will be located and access that frame directly, rather than performing the lookup-variable-value search. We will discuss how to implement such variable access in section 5.5.6. Until then, however, we will focus on the kind of register and stack optimizations described above. There are many other optimizations that can be performed by a compiler, such as coding primitive operations ``in line'' instead of using a general apply mechanism (see Exercise 5-38); but we will not emphasize these here. Our main goal in this section is to illustrate the compilation process in a simplified (but still interesting) context.

5.5.1 Structure of the Compiler

In section 4.1.7 we modified our original metacircular interpreter to separate analysis from execution. We analyzed each expression to produce an execution procedure that took an environment as argument and performed the required operations. In our compiler, we will do essentially the same analysis. Instead of producing execution procedures, however, we will generate sequences of instructions to be run by our register machine.

The procedure compile is the top-level dispatch in the compiler. It corresponds to the eval procedure of section 4.1.1, the analyze procedure of section 4.1.7, and the eval-dispatch entry point of the explicit-control-evaluator in section 5.4.1. The compiler, like the interpreters, uses the expression-syntax procedures defined in section 4.1.2.@footnote{Notice, however, that our compiler is a Scheme program, and the syntax procedures that it uses to manipulate expressions are the actual Scheme procedures used with the metacircular evaluator. For the explicit-control evaluator, in contrast, we assumed that equivalent syntax operations were available as operations for the register machine. (Of course, when we simulated the register machine in Scheme, we used the actual Scheme procedures in our register machine simulation.)} Compile performs a case analysis on the syntactic type of the expression to be compiled. For each type of expression, it dispatches to a specialized code generator :

(define (compile exp target linkage) (cond ((self-evaluating? exp) (compile-self-evaluating exp target linkage)) ((quoted? exp) (compile-quoted exp target linkage)) ((variable? exp) (compile-variable exp target linkage)) ((assignment? exp) (compile-assignment exp target linkage)) ((definition? exp) (compile-definition exp target linkage)) ((if? exp) (compile-if exp target linkage)) ((lambda? exp) (compile-lambda exp target linkage)) ((begin? exp) (compile-sequence (begin-actions exp) target linkage)) ((cond? exp) (compile (cond->if exp) target linkage)) ((application? exp) (compile-application exp target linkage)) (else (error "Unknown expression type -- COMPILE" exp))))

Targets and linkages

Compile and the code generators that it calls take two arguments in addition to the expression to compile. There is a target , which specifies the register in which the compiled code is to return the value of the expression. There is also a linkage descriptor , which describes how the code resulting from the compilation of the expression should proceed when it has finished its execution. The linkage descriptor can require that the code do one of the following three things:

For example, compiling the expression 5 (which is self-evaluating) with a target of the val register and a linkage of next should produce the instruction

(assign val (const 5))

Compiling the same expression with a linkage of return should produce the instructions

(assign val (const 5)) (goto (reg continue))

In the first case, execution will continue with the next instruction in the sequence. In the second case, we will return from a procedure call. In both cases, the value of the expression will be placed into the target val register.

Instruction sequences and stack usage

Each code generator returns an instruction sequence containing the object code it has generated for the expression. Code generation for a compound expression is accomplished by combining the output from simpler code generators for component expressions, just as evaluation of a compound expression is accomplished by evaluating the component expressions.

The simplest method for combining instruction sequences is a procedure called append-instruction-sequences. It takes as arguments any number of instruction sequences that are to be executed sequentially; it appends them and returns the combined sequence. That is, if and are sequences of instructions, then evaluating

(append-instruction-sequences )

produces the sequence

Whenever registers might need to be saved, the compiler's code generators use preserving, which is a more subtle method for combining instruction sequences. Preserving takes three arguments: a set of registers and two instruction sequences that are to be executed sequentially. It appends the sequences in such a way that the contents of each register in the set is preserved over the execution of the first sequence, if this is needed for the execution of the second sequence. That is, if the first sequence modifies the register and the second sequence actually needs the register's original contents, then preserving wraps a save and a restore of the register around the first sequence before appending the sequences. Otherwise, preserving simply returns the appended instruction sequences. Thus, for example,

(preserving (list <reg_1> <reg_2>) <seq_1> <seq_2>)

produces one of the following four sequences of instructions, depending on how and use and :

<seq_1> | (save <reg_1>)    | (save <reg_2>)    | (save <reg_2>)
<seq_2> | <seq_1>           | <seq_1>           | (save <reg_1>)
              | (restore <reg_1>) | (restore <reg_2>) | <seq_1>
              | <seq_2>           | <seq_2>           | (restore <reg_1>)
              |                         |                   | (restore <reg_2>)
              |                         |                   | <seq_2>

By using preserving to combine instruction sequences the compiler avoids unnecessary stack operations. This also isolates the details of whether or not to generate save and restore instructions within the preserving procedure, separating them from the concerns that arise in writing each of the individual code generators. In fact no save or restore instructions are explicitly produced by the code generators.

In principle, we could represent an instruction sequence simply as a list of instructions. Append-instruction-sequences could then combine instruction sequences by performing an ordinary list append. However, preserving would then be a complex operation, because it would have to analyze each instruction sequence to determine how the sequence uses its registers. Preserving would be inefficient as well as complex, because it would have to analyze each of its instruction sequence arguments, even though these sequences might themselves have been constructed by calls to preserving, in which case their parts would have already been analyzed. To avoid such repetitious analysis we will associate with each instruction sequence some information about its register use. When we construct a basic instruction sequence we will provide this information explicitly, and the procedures that combine instruction sequences will derive register-use information for the combined sequence from the information associated with the component sequences.

An instruction sequence will contain three pieces of information:

We will represent an instruction sequence as a list of its three parts. The constructor for instruction sequences is thus

(define (make-instruction-sequence needs modifies statements) (list needs modifies statements))

For example, the two-instruction sequence that looks up the value of the variable x in the current environment, assigns the result to val, and then returns, requires registers env and continue to have been initialized, and modifies register val. This sequence would therefore be constructed as

(make-instruction-sequence '(env continue) '(val) '((assign val (op lookup-variable-value) (const x) (reg env)) (goto (reg continue))))

We sometimes need to construct an instruction sequence with no statements:

(define (empty-instruction-sequence) (make-instruction-sequence '() '() '()))

The procedures for combining instruction sequences are shown in section 5.5.4.

Exercise 5.31: In evaluating a procedure application, the explicit-control evaluator always saves and restores the env register around the evaluation of the operator, saves and restores env around the evaluation of each operand (except the final one), saves and restores argl around the evaluation of each operand, and saves and restores proc around the evaluation of the operand sequence. For each of the following combinations, say which of these save and restore operations are superfluous and thus could be eliminated by the compiler's preserving mechanism:

(f 'x 'y) ((f) 'x 'y) (f (g 'x) y) (f (g 'x) 'y)

Exercise 5.32: Using the preserving mechanism, the compiler will avoid saving and restoring env around the evaluation of the operator of a combination in the case where the operator is a symbol. We could also build such optimizations into the evaluator. Indeed, the explicit-control evaluator of section 5.4 already performs a similar optimization, by treating combinations with no operands as a special case.

5.5.2 Compiling Expressions

In this section and the next we implement the code generators to which the compile procedure dispatches.

Compiling linkage code

In general, the output of each code generator will end with instructions---generated by the procedure compile-linkage---that implement the required linkage. If the linkage is return then we must generate the instruction (goto (reg continue)). This needs the continue register and does not modify any registers. If the linkage is next, then we needn't include any additional instructions. Otherwise, the linkage is a label, and we generate a goto to that label, an instruction that does not need or modify any registers.@footnote{This procedure uses a feature of Lisp called backquote (or quasiquote ) that is handy for constructing lists. Preceding a list with a backquote symbol is much like quoting it, except that anything in the list that is flagged with a comma is evaluated.

For example, if the value of linkage is the symbol@* branch25, then the expression@* `((goto (label ,linkage)))@* evaluates to the list@* ((goto (label branch25))).@* Similarly, if the value of x is the list (a b c), then@* `(1 2 ,(car x))@* evaluates to the list@* (1 2 a).}

(define (compile-linkage linkage) (cond ((eq? linkage 'return) (make-instruction-sequence '(continue) '() '((goto (reg continue))))) ((eq? linkage 'next) (empty-instruction-sequence)) (else (make-instruction-sequence '() '() `((goto (label ,linkage)))))))

The linkage code is appended to an instruction sequence by preserving the continue register, since a return linkage will require the continue register: If the given instruction sequence modifies continue and the linkage code needs it, continue will be saved and restored.

(define (end-with-linkage linkage instruction-sequence) (preserving '(continue) instruction-sequence (compile-linkage linkage)))

Compiling simple expressions

The code generators for self-evaluating expressions, quotations, and variables construct instruction sequences that assign the required value to the target register and then proceed as specified by the linkage descriptor.

(define (compile-self-evaluating exp target linkage) (end-with-linkage linkage (make-instruction-sequence '() (list target) `((assign ,target (const ,exp)))))) (define (compile-quoted exp target linkage) (end-with-linkage linkage (make-instruction-sequence '() (list target) `((assign ,target (const ,(text-of-quotation exp))))))) (define (compile-variable exp target linkage) (end-with-linkage linkage (make-instruction-sequence '(env) (list target) `((assign ,target (op lookup-variable-value) (const ,exp) (reg env))))))

All these assignment instructions modify the target register, and the one that looks up a variable needs the env register.

Assignments and definitions are handled much as they are in the interpreter. We recursively generate code that computes the value to be assigned to the variable, and append to it a two-instruction sequence that actually sets or defines the variable and assigns the value of the whole expression (the symbol ok) to the target register. The recursive compilation has target val and linkage next so that the code will put its result into val and continue with the code that is appended after it. The appending is done preserving env, since the environment is needed for setting or defining the variable and the code for the variable value could be the compilation of a complex expression that might modify the registers in arbitrary ways.

(define (compile-assignment exp target linkage) (let ((var (assignment-variable exp)) (get-value-code (compile (assignment-value exp) 'val 'next))) (end-with-linkage linkage (preserving '(env) get-value-code (make-instruction-sequence '(env val) (list target) `((perform (op set-variable-value!) (const ,var) (reg val) (reg env)) (assign ,target (const ok)))))))) (define (compile-definition exp target linkage) (let ((var (definition-variable exp)) (get-value-code (compile (definition-value exp) 'val 'next))) (end-with-linkage linkage (preserving '(env) get-value-code (make-instruction-sequence '(env val) (list target) `((perform (op define-variable!) (const ,var) (reg val) (reg env)) (assign ,target (const ok))))))))

The appended two-instruction sequence requires env and val and modifies the target. Note that although we preserve env for this sequence, we do not preserve val, because the get-value-code is designed to explicitly place its result in val for use by this sequence. (In fact, if we did preserve val, we would have a bug, because this would cause the previous contents of val to be restored right after the get-value-code is run.)

Compiling conditional expressions

The code for an if expression compiled with a given target and linkage has the form

<compilation of predicate, target val, linkage next> (test (op false?) (reg val)) (branch (label false-branch)) true-branch <compilation of consequent with given target and given linkage or after-if> false-branch <compilation of alternative with given target and linkage> after-if

To generate this code, we compile the predicate, consequent, and alternative, and combine the resulting code with instructions to test the predicate result and with newly generated labels to mark the true and false branches and the end of the conditional.@footnote{We can't just use the labels true-branch, false-branch, and after-if as shown above, because there might be more than one if in the program. The compiler uses the procedure make-label to generate labels. Make-label takes a symbol as argument and returns a new symbol that begins with the given symbol. For example, successive calls to (make-label 'a) would return a1, a2, and so on. Make-label can be implemented similarly to the generation of unique variable names in the query language, as follows:

(define label-counter 0) (define (new-label-number) (set! label-counter (+ 1 label-counter)) label-counter) (define (make-label name) (string->symbol (string-append (symbol->string name) (number->string (new-label-number)))))

} In this arrangement of code, we must branch around the true branch if the test is false. The only slight complication is in how the linkage for the true branch should be handled. If the linkage for the conditional is return or a label, then the true and false branches will both use this same linkage. If the linkage is next, the true branch ends with a jump around the code for the false branch to the label at the end of the conditional.

(define (compile-if exp target linkage) (let ((t-branch (make-label 'true-branch)) (f-branch (make-label 'false-branch)) (after-if (make-label 'after-if))) (let ((consequent-linkage (if (eq? linkage 'next) after-if linkage))) (let ((p-code (compile (if-predicate exp) 'val 'next)) (c-code (compile (if-consequent exp) target consequent-linkage)) (a-code (compile (if-alternative exp) target linkage))) (preserving '(env continue) p-code (append-instruction-sequences (make-instruction-sequence '(val) '() `((test (op false?) (reg val)) (branch (label ,f-branch)))) (parallel-instruction-sequences (append-instruction-sequences t-branch c-code) (append-instruction-sequences f-branch a-code)) after-if))))))

Env is preserved around the predicate code because it could be needed by the true and false branches, and continue is preserved because it could be needed by the linkage code in those branches. The code for the true and false branches (which are not executed sequentially) is appended using a special combiner parallel-instruction-sequences described in section 5.5.4.

Note that cond is a derived expression, so all that the compiler needs to do handle it is to apply the cond->if transformer (from section 4.1.2) and compile the resulting if expression.

Compiling sequences

The compilation of sequences (from procedure bodies or explicit begin expressions) parallels their evaluation. Each expression of the sequence is compiled---the last expression with the linkage specified for the sequence, and the other expressions with linkage next (to execute the rest of the sequence). The instruction sequences for the individual expressions are appended to form a single instruction sequence, such that env (needed for the rest of the sequence) and continue (possibly needed for the linkage at the end of the sequence) are preserved.

(define (compile-sequence seq target linkage) (if (last-exp? seq) (compile (first-exp seq) target linkage) (preserving '(env continue) (compile (first-exp seq) target 'next) (compile-sequence (rest-exps seq) target linkage))))

Compiling lambda expressions

Lambda expressions construct procedures. The object code for a lambda expression must have the form construct procedure object and assign it to target register <linkage<

When we compile the lambda expression, we also generate the code for the procedure body. Although the body won't be executed at the time of procedure construction, it is convenient to insert it into the object code right after the code for the lambda. If the linkage for the lambda expression is a label or return, this is fine. But if the linkage is next, we will need to skip around the code for the procedure body by using a linkage that jumps to a label that is inserted after the body. The object code thus has the form construct procedure object and assign it to target register code for given linkage> or (goto (label after-lambda)) compilation of procedure body after-lambda

Compile-lambda generates the code for constructing the procedure object followed by the code for the procedure body. The procedure object will be constructed at run time by combining the current environment (the environment at the point of definition) with the entry point to the compiled procedure body (a newly generated label).@footnote{[Footnote 38] We need machine operations to implement a data structure for representing compiled procedures, analogous to the structure for compound procedures described in section 4.1.3:

(define (make-compiled-procedure entry env) (list 'compiled-procedure entry env)) (define (compiled-procedure? proc) (tagged-list? proc 'compiled-procedure)) (define (compiled-procedure-entry c-proc) (cadr c-proc)) (define (compiled-procedure-env c-proc) (caddr c-proc))
}
(define (compile-lambda exp target linkage) (let ((proc-entry (make-label 'entry)) (after-lambda (make-label 'after-lambda))) (let ((lambda-linkage (if (eq? linkage 'next) after-lambda linkage))) (append-instruction-sequences (tack-on-instruction-sequence (end-with-linkage lambda-linkage (make-instruction-sequence '(env) (list target) `((assign ,target (op make-compiled-procedure) (label ,proc-entry) (reg env))))) (compile-lambda-body exp proc-entry)) after-lambda))))

Compile-lambda uses the special combiner tack-on-instruction-sequence (section 5.5.4) rather than append-instruction-sequences to append the procedure body to the lambda expression code, because the body is not part of the sequence of instructions that will be executed when the combined sequence is entered; rather, it is in the sequence only because that was a convenient place to put it.

Compile-lambda-body constructs the code for the body of the procedure. This code begins with a label for the entry point. Next come instructions that will cause the run-time evaluation environment to switch to the correct environment for evaluating the procedure body---namely, the definition environment of the procedure, extended to include the bindings of the formal parameters to the arguments with which the procedure is called. After this comes the code for the sequence of expressions that makes up the procedure body. The sequence is compiled with linkage return and target val so that it will end by returning from the procedure with the procedure result in val.

(define (compile-lambda-body exp proc-entry) (let ((formals (lambda-parameters exp))) (append-instruction-sequences (make-instruction-sequence '(env proc argl) '(env) `(,proc-entry (assign env (op compiled-procedure-env) (reg proc)) (assign env (op extend-environment) (const ,formals) (reg argl) (reg env)))) (compile-sequence (lambda-body exp) 'val 'return))))

5.5.3 Compiling Combinations

The essence of the compilation process is the compilation of procedure applications. The code for a combination compiled with a given target and linkage has the form compilation of operator, target proc, linkage next evaluate operands and construct argument list in argl compilation of procedure call with given target and linkage

The registers env, proc, and argl may have to be saved and restored during evaluation of the operator and operands. Note that this is the only place in the compiler where a target other than val is specified.

The required code is generated by compile-application. This recursively compiles the operator, to produce code that puts the procedure to be applied into proc, and compiles the operands, to produce code that evaluates the individual operands of the application. The instruction sequences for the operands are combined (by construct-arglist) with code that constructs the list of arguments in argl, and the resulting argument-list code is combined with the procedure code and the code that performs the procedure call (produced by compile-procedure-call). In appending the code sequences, the env register must be preserved around the evaluation of the operator (since evaluating the operator might modify env, which will be needed to evaluate the operands), and the proc register must be preserved around the construction of the argument list (since evaluating the operands might modify proc, which will be needed for the actual procedure application). Continue must also be preserved throughout, since it is needed for the linkage in the procedure call.

(define (compile-application exp target linkage) (let ((proc-code (compile (operator exp) 'proc 'next)) (operand-codes (map (lambda (operand) (compile operand 'val 'next)) (operands exp)))) (preserving '(env continue) proc-code (preserving '(proc continue) (construct-arglist operand-codes) (compile-procedure-call target linkage)))))

The code to construct the argument list will evaluate each operand into val and then cons that value onto the argument list being accumulated in argl. Since we cons the arguments onto argl in sequence, we must start with the last argument and end with the first, so that the arguments will appear in order from first to last in the resulting list. Rather than waste an instruction by initializing argl to the empty list to set up for this sequence of evaluations, we make the first code sequence construct the initial argl. The general form of the argument-list construction is thus as follows: compilation of last operand, targeted to val (assign argl (op list) (reg val)) compilation of next operand, targeted to val (assign argl (op cons) (reg val) (reg argl)) ... compilation of first operand, targeted to val (assign argl (op cons) (reg val) (reg argl))

Argl must be preserved around each operand evaluation except the first (so that arguments accumulated so far won't be lost), and env must be preserved around each operand evaluation except the last (for use by subsequent operand evaluations).

Compiling this argument code is a bit tricky, because of the special treatment of the first operand to be evaluated and the need to preserve argl and env in different places. The construct-arglist procedure takes as arguments the code that evaluates the individual operands. If there are no operands at all, it simply emits the instruction

(assign argl (const ()))

Otherwise, construct-arglist creates code that initializes argl with the last argument, and appends code that evaluates the rest of the arguments and adjoins them to argl in succession. In order to process the arguments from last to first, we must reverse the list of operand code sequences from the order supplied by compile-application.

(define (construct-arglist operand-codes) (let ((operand-codes (reverse operand-codes))) (if (null? operand-codes) (make-instruction-sequence '() '(argl) '((assign argl (const ())))) (let ((code-to-get-last-arg (append-instruction-sequences (car operand-codes) (make-instruction-sequence '(val) '(argl) '((assign argl (op list) (reg val))))))) (if (null? (cdr operand-codes)) code-to-get-last-arg (preserving '(env) code-to-get-last-arg (code-to-get-rest-args (cdr operand-codes)))))))) (define (code-to-get-rest-args operand-codes) (let ((code-for-next-arg (preserving '(argl) (car operand-codes) (make-instruction-sequence '(val argl) '(argl) '((assign argl (op cons) (reg val) (reg argl))))))) (if (null? (cdr operand-codes)) code-for-next-arg (preserving '(env) code-for-next-arg (code-to-get-rest-args (cdr operand-codes))))))

Applying procedures

After evaluating the elements of a combination, the compiled code must apply the procedure in proc to the arguments in argl. The code performs essentially the same dispatch as the apply procedure in the metacircular evaluator of section 4.1.1 or the apply-dispatch entry point in the explicit-control evaluator of section 5.4.1. It checks whether the procedure to be applied is a primitive procedure or a compiled procedure. For a primitive procedure, it uses apply-primitive-procedure; we will see shortly how it handles compiled procedures. The procedure-application code has the following form:

(test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch)) compiled-branch <code to apply compiled procedure with given target and appropriate linkage> primitive-branch (assign (op apply-primitive-procedure) (reg proc) (reg argl)) after-call

Observe that the compiled branch must skip around the primitive branch. Therefore, if the linkage for the original procedure call was next, the compound branch must use a linkage that jumps to a label that is inserted after the primitive branch. (This is similar to the linkage used for the true branch in compile-if.)

(define (compile-procedure-call target linkage) (let ((primitive-branch (make-label 'primitive-branch)) (compiled-branch (make-label 'compiled-branch)) (after-call (make-label 'after-call))) (let ((compiled-linkage (if (eq? linkage 'next) after-call linkage))) (append-instruction-sequences (make-instruction-sequence '(proc) '() `((test (op primitive-procedure?) (reg proc)) (branch (label ,primitive-branch)))) (parallel-instruction-sequences (append-instruction-sequences compiled-branch (compile-proc-appl target compiled-linkage)) (append-instruction-sequences primitive-branch (end-with-linkage linkage (make-instruction-sequence '(proc argl) (list target) `((assign ,target (op apply-primitive-procedure) (reg proc) (reg argl))))))) after-call))))

The primitive and compound branches, like the true and false branches in compile-if, are appended using parallel-instruction-sequences rather than the ordinary append-instruction-sequences, because they will not be executed sequentially.

Applying compiled procedures

The code that handles procedure application is the most subtle part of the compiler, even though the instruction sequences it generates are very short. A compiled procedure (as constructed by compile-lambda) has an entry point, which is a label that designates where the code for the procedure starts. The code at this entry point computes a result in val and returns by executing the instruction (goto (reg continue)). Thus, we might expect the code for a compiled-procedure application (to be generated by compile-proc-appl) with a given target and linkage to look like this if the linkage is a label

(assign continue (label proc-return)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) proc-return (assign (reg val)) ; included if target is not val (goto (label )) ; linkage code

or like this if the linkage is return.

(save continue) (assign continue (label proc-return)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) proc-return (assign (reg val)) ; included if target is not val (restore continue) (goto (reg continue)) ; linkage code

This code sets up continue so that the procedure will return to a label proc-return and jumps to the procedure's entry point. The code at proc-return transfers the procedure's result from val to the target register (if necessary) and then jumps to the location specified by the linkage. (The linkage is always return or a label, because compile-procedure-call replaces a next linkage for the compound-procedure branch by an after-call label.)

In fact, if the target is not val, that is exactly the code our compiler will generate.@footnote{Actually, we signal an error when the target is not val and the linkage is return, since the only place we request return linkages is in compiling procedures, and our convention is that procedures return their values in val.} Usually, however, the target is val (the only time the compiler specifies a different register is when targeting the evaluation of an operator to proc), so the procedure result is put directly into the target register and there is no need to return to a special location that copies it. Instead, we simplify the code by setting up continue so that the procedure will ``return'' directly to the place specified by the caller's linkage: set up continue for linkage (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))

If the linkage is a label, we set up continue so that the procedure will return to that label. (That is, the (goto (reg continue)) the procedure ends with becomes equivalent to the (goto (label >)) at proc-return above.)

(assign continue (label )) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))

If the linkage is return, we don't need to set up continue at all: It already holds the desired location. (That is, the (goto (reg continue)) the procedure ends with goes directly to the place where the (goto (reg continue)) at proc-return would have gone.)

(assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))

With this implementation of the return linkage, the compiler generates tail-recursive code. Calling a procedure as the final step in a procedure body does a direct transfer, without saving any information on the stack.

Suppose instead that we had handled the case of a procedure call with a linkage of return and a target of val as shown above for a non-val target. This would destroy tail recursion. Our system would still give the same value for any expression. But each time we called a procedure, we would save continue and return after the call to undo the (useless) save. These extra saves would accumulate during a nest of procedure calls.@footnote{Making a compiler generate tail-recursive code might seem like a straightforward idea. But most compilers for common languages, including C and Pascal, do not do this, and therefore these languages cannot represent iterative processes in terms of procedure call alone. The difficulty with tail recursion in these languages is that their implementations use the stack to store procedure arguments and local variables as well as return addresses. The Scheme implementations described in this book store arguments and variables in memory to be garbage-collected. The reason for using the stack for variables and arguments is that it avoids the need for garbage collection in languages that would not otherwise require it, and is generally believed to be more efficient. Sophisticated Lisp compilers can, in fact, use the stack for arguments without destroying tail recursion. (See Hanson 1990 for a description.) There is also some debate about whether stack allocation is actually more efficient than garbage collection in the first place, but the details seem to hinge on fine points of computer architecture. (See Appel 1987 and Miller and Rozas 1994 for opposing views on this issue.)}

Compile-proc-appl generates the above procedure-application code by considering four cases, depending on whether the target for the call is val and whether the linkage is return. Observe that the instruction sequences are declared to modify all the registers, since executing the procedure body can change the registers in arbitrary ways.@footnote{The variable all-regs is bound to the list of names of all the registers:

(define all-regs '(env proc val argl continue))
}

Also note that the code sequence for the case with target val and linkage return is declared to need continue: Even though continue is not explicitly used in the two-instruction sequence, we must be sure that continue will have the correct value when we enter the compiled procedure.

(define (compile-proc-appl target linkage) (cond ((and (eq? target 'val) (not (eq? linkage 'return))) (make-instruction-sequence '(proc) all-regs `((assign continue (label ,linkage)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))))) ((and (not (eq? target 'val)) (not (eq? linkage 'return))) (let ((proc-return (make-label 'proc-return))) (make-instruction-sequence '(proc) all-regs `((assign continue (label ,proc-return)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) ,proc-return (assign ,target (reg val)) (goto (label ,linkage)))))) ((and (eq? target 'val) (eq? linkage 'return)) (make-instruction-sequence '(proc continue) all-regs '((assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))))) ((and (not (eq? target 'val)) (eq? linkage 'return)) (error "return linkage, target not val -- COMPILE" target))))

5.5.4 Combining Instruction Sequences

This section describes the details on how instruction sequences are represented and combined. Recall from section 5.5.1 that an instruction sequence is represented as a list of the registers needed, the registers modified, and the actual instructions. We will also consider a label (symbol) to be a degenerate case of an instruction sequence, which doesn't need or modify any registers. So to determine the registers needed and modified by instruction sequences we use the selectors

(define (registers-needed s) (if (symbol? s) '() (car s))) (define (registers-modified s) (if (symbol? s) '() (cadr s))) (define (statements s) (if (symbol? s) (list s) (caddr s)))

and to determine whether a given sequence needs or modifies a given register we use the predicates

(define (needs-register? seq reg) (memq reg (registers-needed seq))) (define (modifies-register? seq reg) (memq reg (registers-modified seq)))

In terms of these predicates and selectors, we can implement the various instruction sequence combiners used throughout the compiler.

The basic combiner is append-instruction-sequences. This takes as arguments an arbitrary number of instruction sequences that are to be executed sequentially and returns an instruction sequence whose statements are the statements of all the sequences appended together. The subtle point is to determine the registers that are needed and modified by the resulting sequence. It modifies those registers that are modified by any of the sequences; it needs those registers that must be initialized before the first sequence can be run (the registers needed by the first sequence), together with those registers needed by any of the other sequences that are not initialized (modified) by sequences preceding it.

The sequences are appended two at a time by append-2-sequences. This takes two instruction sequences seq1 and seq2 and returns the instruction sequence whose statements are the statements of seq1 followed by the statements of seq2, whose modified registers are those registers that are modified by either seq1 or seq2, and whose needed registers are the registers needed by seq1 together with those registers needed by seq2 that are not modified by seq1. (In terms of set operations, the new set of needed registers is the union of the set of registers needed by seq1 with the set difference of the registers needed by seq2 and the registers modified by seq1.) Thus, append-instruction-sequences is implemented as follows:

(define (append-instruction-sequences . seqs) (define (append-2-sequences seq1 seq2) (make-instruction-sequence (list-union (registers-needed seq1) (list-difference (registers-needed seq2) (registers-modified seq1))) (list-union (registers-modified seq1) (registers-modified seq2)) (append (statements seq1) (statements seq2)))) (define (append-seq-list seqs) (if (null? seqs) (empty-instruction-sequence) (append-2-sequences (car seqs) (append-seq-list (cdr seqs))))) (append-seq-list seqs))

This procedure uses some simple operations for manipulating sets represented as lists, similar to the (unordered) set representation described in section 2.3.3:

(define (list-union s1 s2) (cond ((null? s1) s2) ((memq (car s1) s2) (list-union (cdr s1) s2)) (else (cons (car s1) (list-union (cdr s1) s2))))) (define (list-difference s1 s2) (cond ((null? s1) '()) ((memq (car s1) s2) (list-difference (cdr s1) s2)) (else (cons (car s1) (list-difference (cdr s1) s2)))))

Preserving, the second major instruction sequence combiner, takes a list of registers regs and two instruction sequences seq1 and seq2 that are to be executed sequentially. It returns an instruction sequence whose statements are the statements of seq1 followed by the statements of seq2, with appropriate save and restore instructions around seq1 to protect the registers in regs that are modified by seq1 but needed by seq2. To accomplish this, preserving first creates a sequence that has the required saves followed by the statements of seq1 followed by the required restores. This sequence needs the registers being saved and restored in addition to the registers needed by seq1, and modifies the registers modified by seq1 except for the ones being saved and restored. This augmented sequence and seq2 are then appended in the usual way. The following procedure implements this strategy recursively, walking down the list of registers to be preserved:@footnote{Note that preserving calls append with three arguments. Though the definition of append shown in this book accepts only two arguments, Scheme standardly provides an append procedure that takes an arbitrary number of arguments.}

(define (preserving regs seq1 seq2) (if (null? regs) (append-instruction-sequences seq1 seq2) (let ((first-reg (car regs))) (if (and (needs-register? seq2 first-reg) (modifies-register? seq1 first-reg)) (preserving (cdr regs) (make-instruction-sequence (list-union (list first-reg) (registers-needed seq1)) (list-difference (registers-modified seq1) (list first-reg)) (append `((save ,first-reg)) (statements seq1) `((restore ,first-reg)))) seq2) (preserving (cdr regs) seq1 seq2)))))

Another sequence combiner, tack-on-instruction-sequence, is used by compile-lambda to append a procedure body to another sequence. Because the procedure body is not ``in line'' to be executed as part of the combined sequence, its register use has no impact on the register use of the sequence in which it is embedded. We thus ignore the procedure body's sets of needed and modified registers when we tack it onto the other sequence.

(define (tack-on-instruction-sequence seq body-seq) (make-instruction-sequence (registers-needed seq) (registers-modified seq) (append (statements seq) (statements body-seq))))

Compile-if and compile-procedure-call use a special combiner called parallel-instruction-sequences to append the two alternative branches that follow a test. The two branches will never be executed sequentially; for any particular evaluation of the test, one branch or the other will be entered. Because of this, the registers needed by the second branch are still needed by the combined sequence, even if these are modified by the first branch.

(define (parallel-instruction-sequences seq1 seq2) (make-instruction-sequence (list-union (registers-needed seq1) (registers-needed seq2)) (list-union (registers-modified seq1) (registers-modified seq2)) (append (statements seq1) (statements seq2))))

5.5.5 An Example of Compiled Code

Now that we have seen all the elements of the compiler, let us examine an example of compiled code to see how things fit together. We will compile the definition of a recursive factorial procedure by calling compile:

(compile '(define (factorial n) (if (= n 1) 1 (* (factorial (- n 1)) n))) 'val 'next)

We have specified that the value of the define expression should be placed in the val register. We don't care what the compiled code does after executing the define, so our choice of next as the linkage descriptor is arbitrary.

Compile determines that the expression is a definition, so it calls compile-definition to compile code to compute the value to be assigned (targeted to val), followed by code to install the definition, followed by code to put the value of the define (which is the symbol ok) into the target register, followed finally by the linkage code. Env is preserved around the computation of the value, because it is needed in order to install the definition. Because the linkage is next, there is no linkage code in this case. The skeleton of the compiled code is thus save env if modified by code to compute value compilation of definition value, target val, linkage next restore env if saved above (perform (op define-variable!) (const factorial) (reg val) (reg env)) (assign val (const ok))

The expression that is to be compiled to produce the value for the variable factorial is a lambda expression whose value is the procedure that computes factorials. Compile handles this by calling compile-lambda, which compiles the procedure body, labels it as a new entry point, and generates the instruction that will combine the procedure body at the new entry point with the run-time environment and assign the result to val. The sequence then skips around the compiled procedure code, which is inserted at this point. The procedure code itself begins by extending the procedure's definition environment by a frame that binds the formal parameter n to the procedure argument. Then comes the actual procedure body. Since this code for the value of the variable doesn't modify the env register, the optional save and restore shown above aren't generated. (The procedure code at entry2 isn't executed at this point, so its use of env is irrelevant.) Therefore, the skeleton for the compiled code becomes

(assign val (op make-compiled-procedure) (label entry2) (reg env)) (goto (label after-lambda1)) entry2 (assign env (op compiled-procedure-env) (reg proc)) (assign env (op extend-environment) (const (n)) (reg argl) (reg env)) <compilation of procedure body> after-lambda1 (perform (op define-variable!) (const factorial) (reg val) (reg env)) (assign val (const ok))

A procedure body is always compiled (by compile-lambda-body) as a sequence with target val and linkage return. The sequence in this case consists of a single if expression:

(if (= n 1) 1 (* (factorial (- n 1)) n))

Compile-if generates code that first computes the predicate (targeted to val), then checks the result and branches around the true branch if the predicate is false. Env and continue are preserved around the predicate code, since they may be needed for the rest of the if expression. Since the if expression is the final expression (and only expression) in the sequence making up the procedure body, its target is val and its linkage is return, so the true and false branches are both compiled with target val and linkage return. (That is, the value of the conditional, which is the value computed by either of its branches, is the value of the procedure.) save continue, env if modified by predicate and needed by branches compilation of predicate, target val, linkage next restore continue, env if saved above (test (op false?) (reg val)) (branch (label false-branch4)) true-branch5 compilation of true branch, target val, linkage return false-branch4 compilation of false branch, target val, linkage return after-if3

The predicate (= n 1) is a procedure call. This looks up the operator (the symbol =) and places this value in proc. It then assembles the arguments 1 and the value of n into argl. Then it tests whether proc contains a primitive or a compound procedure, and dispatches to a primitive branch or a compound branch accordingly. Both branches resume at the after-call label. The requirements to preserve registers around the evaluation of the operator and operands don't result in any saving of registers, because in this case those evaluations don't modify the registers in question.

(assign proc (op lookup-variable-value) (const =) (reg env)) (assign val (const 1)) (assign argl (op list) (reg val)) (assign val (op lookup-variable-value) (const n) (reg env)) (assign argl (op cons) (reg val) (reg argl)) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch17)) compiled-branch16 (assign continue (label after-call15)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch17 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) after-call15

The true branch, which is the constant 1, compiles (with target val and linkage return) to

(assign val (const 1)) (goto (reg continue))

The code for the false branch is another a procedure call, where the procedure is the value of the symbol *, and the arguments are n and the result of another procedure call (a call to factorial). Each of these calls sets up proc and argl and its own primitive and compound branches. Figure 5-17 shows the complete compilation of the definition of the factorial procedure. Notice that the possible save and restore of continue and env around the predicate, shown above, are in fact generated, because these registers are modified by the procedure call in the predicate and needed for the procedure call and the return linkage in the branches.

Exercise 5.33: Consider the following definition of a factorial procedure, which is slightly different from the one given above:

(define (factorial-alt n) (if (= n 1) 1 (* n (factorial-alt (- n 1)))))

Compile this procedure and compare the resulting code with that produced for factorial. Explain any differences you find. Does either program execute more efficiently than the other?

Exercise 5.34: Compile the iterative factorial procedure

(define (factorial n) (define (iter product counter) (if (> counter n) product (iter (* counter product) (+ counter 1)))) (iter 1 1))

Annotate the resulting code, showing the essential difference between the code for iterative and recursive versions of factorial that makes one process build up stack space and the other run in constant stack space.

Figure 5.17: Compilation of the definition of the factorial procedure @smalllisp ;; construct the procedure and skip over code for the procedure body (assign val (op make-compiled-procedure) (label entry2) (reg env)) (goto (label after-lambda1)) entry2 ; calls to factorial will enter here (assign env (op compiled-procedure-env) (reg proc)) (assign env (op extend-environment) (const (n)) (reg argl) (reg env)) ;; begin actual procedure body (save continue) (save env) ;; compute (= n 1) (assign proc (op lookup-variable-value) (const =) (reg env)) (assign val (const 1)) (assign argl (op list) (reg val)) (assign val (op lookup-variable-value) (const n) (reg env)) (assign argl (op cons) (reg val) (reg argl)) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch17)) compiled-branch16 (assign continue (label after-call15)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch17 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) after-call15 ; val now contains result of (= n 1) (restore env) (restore continue) (test (op false?) (reg val)) (branch (label false-branch4)) true-branch5 ; return 1 (assign val (const 1)) (goto (reg continue)) false-branch4 ;; compute and return (* (factorial (- n 1)) n) (assign proc (op lookup-variable-value) (const *) (reg env)) (save continue) (save proc) ; save * procedure (assign val (op lookup-variable-value) (const n) (reg env)) (assign argl (op list) (reg val)) (save argl) ; save partial argument list for * ;; compute (factorial (- n 1)), which is the other argument for * (assign proc (op lookup-variable-value) (const factorial) (reg env)) (save proc) ; save factorial procedure @end smalllisp @smalllisp ;; compute (- n 1), which is the argument for factorial (assign proc (op lookup-variable-value) (const -) (reg env)) (assign val (const 1)) (assign argl (op list) (reg val)) (assign val (op lookup-variable-value) (const n) (reg env)) (assign argl (op cons) (reg val) (reg argl)) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch8)) compiled-branch7 (assign continue (label after-call6)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch8 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) after-call6 ; val now contains result of (- n 1) (assign argl (op list) (reg val)) (restore proc) ; restore factorial ;; apply factorial (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch11)) compiled-branch10 (assign continue (label after-call9)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch11 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) after-call9 ; val now contains result of (factorial (- n 1)) (restore argl) ; restore partial argument list for * (assign argl (op cons) (reg val) (reg argl)) (restore proc) ; restore * (restore continue) ;; apply * and return its value (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch14)) compiled-branch13 ;; note that a compound procedure here is called tail-recursively (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch14 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) (goto (reg continue)) after-call12 after-if3 after-lambda1 ;; assign the procedure to the variable factorial (perform (op define-variable!) (const factorial) (reg val) (reg env)) (assign val (const ok)) @end smalllisp

Exercise 5.35: What expression was compiled to produce the code shown in Figure 5-18?

Figure 5.18: An example of compiler output. See Exercise 5-35. @smalllisp (assign val (op make-compiled-procedure) (label entry16) (reg env)) (goto (label after-lambda15)) entry16 (assign env (op compiled-procedure-env) (reg proc)) (assign env (op extend-environment) (const (x)) (reg argl) (reg env)) (assign proc (op lookup-variable-value) (const +) (reg env)) (save continue) (save proc) (save env) (assign proc (op lookup-variable-value) (const g) (reg env)) (save proc) (assign proc (op lookup-variable-value) (const +) (reg env)) (assign val (const 2)) (assign argl (op list) (reg val)) (assign val (op lookup-variable-value) (const x) (reg env)) (assign argl (op cons) (reg val) (reg argl)) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch19)) compiled-branch18 (assign continue (label after-call17)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch19 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) after-call17 (assign argl (op list) (reg val)) (restore proc) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch22)) compiled-branch21 (assign continue (label after-call20)) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch22 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) @end smalllisp @smalllisp after-call20 (assign argl (op list) (reg val)) (restore env) (assign val (op lookup-variable-value) (const x) (reg env)) (assign argl (op cons) (reg val) (reg argl)) (restore proc) (restore continue) (test (op primitive-procedure?) (reg proc)) (branch (label primitive-branch25)) compiled-branch24 (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val)) primitive-branch25 (assign val (op apply-primitive-procedure) (reg proc) (reg argl)) (goto (reg continue)) after-call23 after-lambda15 (perform (op define-variable!) (const f) (reg val) (reg env)) (assign val (const ok)) @end smalllisp

Exercise 5.37: One way to understand the compiler's preserving mechanism for optimizing stack usage is to see what extra operations would be generated if we did not use this idea. Modify preserving so that it always generates the save and restore operations. Compile some simple expressions and identify the unnecessary stack operations that are generated. Compare the code to that generated with the preserving mechanism intact.

Exercise 5.38: Our compiler is clever about avoiding unnecessary stack operations, but it is not clever at all when it comes to compiling calls to the primitive procedures of the language in terms of the primitive operations supplied by the machine. For example, consider how much code is compiled to compute (+ a 1): The code sets up an argument list in argl, puts the primitive addition procedure (which it finds by looking up the symbol + in the environment) into proc, and tests whether the procedure is primitive or compound. The compiler always generates code to perform the test, as well as code for primitive and compound branches (only one of which will be executed). We have not shown the part of the controller that implements primitives, but we presume that these instructions make use of primitive arithmetic operations in the machine's data paths. Consider how much less code would be generated if the compiler could open-code primitives---that is, if it could generate code to directly use these primitive machine operations. The expression (+ a 1) might be compiled into something as simple as @footnote{We have used the same symbol + here to denote both the source-language procedure and the machine operation. In general there will not be a one-to-one correspondence between primitives of the source language and primitives of the machine.}

(assign val (op lookup-variable-value) (const a) (reg env)) (assign val (op +) (reg val) (const 1))

In this exercise we will extend our compiler to support open coding of selected primitives. Special-purpose code will be generated for calls to these primitive procedures instead of the general procedure-application code. In order to support this, we will augment our machine with special argument registers arg1 and arg2. The primitive arithmetic operations of the machine will take their inputs from arg1 and arg2. The results may be put into val, arg1, or arg2.

The compiler must be able to recognize the application of an open-coded primitive in the source program. We will augment the dispatch in the compile procedure to recognize the names of these primitives in addition to the reserved words (the special forms) it currently recognizes.@footnote{Making the primitives into reserved words is in general a bad idea, since a user cannot then rebind these names to different procedures. Moreover, if we add reserved words to a compiler that is in use, existing programs that define procedures with these names will stop working. See Exercise 5-44 for ideas on how to avoid this problem.} For each special form our compiler has a code generator. In this exercise we will construct a family of code generators for the open-coded primitives.

  • The open-coded primitives, unlike the special forms, all need their operands evaluated. Write a code generator spread-arguments for use by all the open-coding code generators. Spread-arguments should take an operand list and compile the given operands targeted to successive argument registers. Note that an operand may contain a call to an open-coded primitive, so argument registers will have to be preserved during operand evaluation.
  • For each of the primitive procedures =, *, -, and +, write a code generator that takes a combination with that operator, together with a target and a linkage descriptor, and produces code to spread the arguments into the registers and then perform the operation targeted to the given target with the given linkage. You need only handle expressions with two operands. Make compile dispatch to these code generators.
  • Try your new compiler on the factorial example. Compare the resulting code with the result produced without open coding.
  • Extend your code generators for + and * so that they can handle expressions with arbitrary numbers of operands. An expression with more than two operands will have to be compiled into a sequence of operations, each with only two inputs.

5.5.6 Lexical Addressing

One of the most common optimizations performed by compilers is the optimization of variable lookup. Our compiler, as we have implemented it so far, generates code that uses the lookup-variable-value operation of the evaluator machine. This searches for a variable by comparing it with each variable that is currently bound, working frame by frame outward through the run-time environment. This search can be expensive if the frames are deeply nested or if there are many variables. For example, consider the problem of looking up the value of x while evaluating the expression (* x y z) in an application of the procedure that is returned by

(let ((x 3) (y 4)) (lambda (a b c d e) (let ((y (* a b x)) (z (+ c d x))) (* x y z))))

Since a let expression is just syntactic sugar for a lambda combination, this expression is equivalent to

((lambda (x y) (lambda (a b c d e) ((lambda (y z) (* x y z)) (* a b x) (+ c d x)))) 3 4)

Each time lookup-variable-value searches for x, it must determine that the symbol x is not eq? to y or z (in the first frame), nor to a, b, c, d, or e (in the second frame). We will assume, for the moment, that our programs do not use define---that variables are bound only with lambda. Because our language is lexically scoped, the run-time environment for any expression will have a structure that parallels the lexical structure of the program in which the expression appears.@footnote{This is not true if we allow internal definitions, unless we scan them out. See Exercise 5-43. } Thus, the compiler can know, when it analyzes the above expression, that each time the procedure is applied the variable x in (* x y z) will be found two frames out from the current frame and will be the first variable in that frame.

We can exploit this fact by inventing a new kind of variable-lookup operation, lexical-address-lookup, that takes as arguments an environment and a lexical address that consists of two numbers: a frame number , which specifies how many frames to pass over, and a displacement number , which specifies how many variables to pass over in that frame. Lexical-address-lookup will produce the value of the variable stored at that lexical address relative to the current environment. If we add the lexical-address-lookup operation to our machine, we can make the compiler generate code that references variables using this operation, rather than lookup-variable-value. Similarly, our compiled code can use a new lexical-address-set! operation instead of set-variable-value!.

In order to generate such code, the compiler must be able to determine the lexical address of a variable it is about to compile a reference to. The lexical address of a variable in a program depends on where one is in the code. For example, in the following program, the address of x in expression is (2,0)---two frames back and the first variable in the frame. At that point y is at address (0,0) and c is at address (1,2). In expression , x is at (1,0), y is at (1,1), and c is at (0,2).

((lambda (x y) (lambda (a b c d e) ((lambda (y z) ) (+ c d x)))) 3 4)

One way for the compiler to produce code that uses lexical addressing is to maintain a data structure called a compile-time environment . This keeps track of which variables will be at which positions in which frames in the run-time environment when a particular variable-access operation is executed. The compile-time environment is a list of frames, each containing a list of variables. (There will of course be no values bound to the variables, since values are not computed at compile time.) The compile-time environment becomes an additional argument to compile and is passed along to each code generator. The top-level call to compile uses an empty compile-time environment. When a lambda body is compiled, compile-lambda-body extends the compile-time environment by a frame containing the procedure's parameters, so that the sequence making up the body is compiled with that extended environment. At each point in the compilation, compile-variable and compile-assignment use the compile-time environment in order to generate the appropriate lexical addresses.

Exercise 5-39 through Exercise 5-43 describe how to complete this sketch of the lexical-addressing strategy in order to incorporate lexical lookup into the compiler. Exercise 5-44 describes another use for the compile-time environment.

Exercise 5.39: Write a procedure lexical-address-lookup that implements the new lookup operation. It should take two arguments---a lexical address and a run-time environment---and return the value of the variable stored at the specified lexical address. Lexical-address-lookup should signal an error if the value of the variable is the symbol *unassigned*.@footnote{This is the modification to variable lookup required if we implement the scanning method to eliminate internal definitions (Exercise 5-43). We will need to eliminate these definitions in order for lexical addressing to work.} Also write a procedure lexical-address-set! that implements the operation that changes the value of the variable at a specified lexical address.

Exercise 5.40: Modify the compiler to maintain the compile-time environment as described above. That is, add a compile-time-environment argument to compile and the various code generators, and extend it in compile-lambda-body.

Exercise 5.41: Write a procedure find-variable that takes as arguments a variable and a compile-time environment and returns the lexical address of the variable with respect to that environment. For example, in the program fragment that is shown above, the compile-time environment during the compilation of expression is ((y z) (a b c d e) (x y)). Find-variable should produce

(find-variable 'c '((y z) (a b c d e) (x y))) (1 2) (find-variable 'x '((y z) (a b c d e) (x y))) (2 0) (find-variable 'w '((y z) (a b c d e) (x y))) not-found

Exercise 5.42: Using find-variable from Exercise 5-41, rewrite compile-variable and compile-assignment to output lexical-address instructions. In cases where find-variable returns not-found (that is, where the variable is not in the compile-time environment), you should have the code generators use the evaluator operations, as before, to search for the binding. (The only place a variable that is not found at compile time can be is in the global environment, which is part of the run-time environment but is not part of the compile-time environment.@footnote{Lexical addresses cannot be used to access variables in the global environment, because these names can be defined and redefined interactively at any time. With internal definitions scanned out, as in Exercise 5-43, the only definitions the compiler sees are those at top level, which act on the global environment. Compilation of a definition does not cause the defined name to be entered in the compile-time environment.} Thus, if you wish, you may have the evaluator operations look directly in the global environment, which can be obtained with the operation (op get-global-environment), instead of having them search the whole run-time environment found in env.) Test the modified compiler on a few simple cases, such as the nested lambda combination at the beginning of this section.

Exercise 5.43: We argued in section 4.1.6 that internal definitions for block structure should not be considered ``real''defines. Rather, a procedure body should be interpreted as if the internal variables being defined were installed as ordinary lambda variables initialized to their correct values using set!. Section 4.1.6 and Exercise 4-16 showed how to modify the metacircular interpreter to accomplish this by scanning out internal definitions. Modify the compiler to perform the same transformation before it compiles a procedure body.

Exercise 5.44: In this section we have focused on the use of the compile-time environment to produce lexical addresses. But there are other uses for compile-time environments. For instance, in Exercise 5-38 we increased the efficiency of compiled code by open-coding primitive procedures. Our implementation treated the names of open-coded procedures as reserved words. If a program were to rebind such a name, the mechanism described in Exercise 5-38 would still open-code it as a primitive, ignoring the new binding. For example, consider the procedure

(lambda (+ * a b x y) (+ (* a x) (* b y)))

which computes a linear combination of x and y. We might call it with arguments +matrix, *matrix, and four matrices, but the open-coding compiler would still open-code the + and the * in (+ (* a x) (* b y)) as primitive + and *. Modify the open-coding compiler to consult the compile-time environment in order to compile the correct code for expressions involving the names of primitive procedures. (The code will work correctly as long as the program does not define or set! these names.)

5.5.7 Interfacing Compiled Code to the Evaluator

We have not yet explained how to load compiled code into the evaluator machine or how to run it. We will assume that the explicit-control-evaluator machine has been defined as in section 5.4.4, with the additional operations specified in footnote Footnote 38. We will implement a procedure compile-and-go that compiles a Scheme expression, loads the resulting object code into the evaluator machine, and causes the machine to run the code in the evaluator global environment, print the result, and enter the evaluator's driver loop. We will also modify the evaluator so that interpreted expressions can call compiled procedures as well as interpreted ones. We can then put a compiled procedure into the machine and use the evaluator to call it:

(compile-and-go '(define (factorial n) (if (= n 1) 1 (* (factorial (- n 1)) n)))) ;;; EC-Eval value: ok ;;; EC-Eval input: (factorial 5) ;;; EC-Eval value: 120

To allow the evaluator to handle compiled procedures (for example, to evaluate the call to factorial above), we need to change the code at apply-dispatch (section 5.4.1) so that it recognizes compiled procedures (as distinct from compound or primitive procedures) and transfers control directly to the entry point of the compiled code:@footnote{Of course, compiled procedures as well as interpreted procedures are compound (nonprimitive). For compatibility with the terminology used in the explicit-control evaluator, in this section we will use ``compound'' to mean interpreted (as opposed to compiled).}

apply-dispatch (test (op primitive-procedure?) (reg proc)) (branch (label primitive-apply)) (test (op compound-procedure?) (reg proc)) (branch (label compound-apply)) (test (op compiled-procedure?) (reg proc)) (branch (label compiled-apply)) (goto (label unknown-procedure-type)) compiled-apply (restore continue) (assign val (op compiled-procedure-entry) (reg proc)) (goto (reg val))

Note the restore of continue at compiled-apply. Recall that the evaluator was arranged so that at apply-dispatch, the continuation would be at the top of the stack. The compiled code entry point, on the other hand, expects the continuation to be in continue, so continue must be restored before the compiled code is executed.

To enable us to run some compiled code when we start the evaluator machine, we add a branch instruction at the beginning of the evaluator machine, which causes the machine to go to a new entry point if the flag register is set.@footnote{Now that the evaluator machine starts with a branch, we must always initialize the flag register before starting the evaluator machine. To start the machine at its ordinary read-eval-print loop, we could use

(define (start-eceval) (set! the-global-environment (setup-environment)) (set-register-contents! eceval 'flag false) (start eceval))
}
(branch (label external-entry)) ; branches if flag is set read-eval-print-loop (perform (op initialize-stack)) ...

External-entry assumes that the machine is started with val containing the location of an instruction sequence that puts a result into val and ends with (goto (reg continue)). Starting at this entry point jumps to the location designated by val, but first assigns continue so that execution will return to print-result, which prints the value in val and then goes to the beginning of the evaluator's read-eval-print loop.@footnote{Since a compiled procedure is an object that the system may try to print, we also modify the system print operation user-print (from section 4.1.4) so that it will not attempt to print the components of a compiled procedure:

(define (user-print object) (cond ((compound-procedure? object) (display (list 'compound-procedure (procedure-parameters object) (procedure-body object) '))) ((compiled-procedure? object) (display ')) (else (display object))))
}
external-entry (perform (op initialize-stack)) (assign env (op get-global-environment)) (assign continue (label print-result)) (goto (reg val))

Now we can use the following procedure to compile a procedure definition, execute the compiled code, and run the read-eval-print loop so we can try the procedure. Because we want the compiled code to return to the location in continue with its result in val, we compile the expression with a target of val and a linkage of return. In order to transform the object code produced by the compiler into executable instructions for the evaluator register machine, we use the procedure assemble from the register-machine simulator (section 5.2.2). We then initialize the val register to point to the list of instructions, set the flag so that the evaluator will go to external-entry, and start the evaluator.

(define (compile-and-go expression) (let ((instructions (assemble (statements (compile expression 'val 'return)) eceval))) (set! the-global-environment (setup-environment)) (set-register-contents! eceval 'val instructions) (set-register-contents! eceval 'flag true) (start eceval)))

If we have set up stack monitoring, as at the end of section 5.4.4, we can examine the stack usage of compiled code:

(compile-and-go '(define (factorial n) (if (= n 1) 1 (* (factorial (- n 1)) n)))) (total-pushes = 0 maximum-depth = 0) ;;; EC-Eval value: ok ;;; EC-Eval input: (factorial 5) (total-pushes = 31 maximum-depth = 14) ;;; EC-Eval value: 120

Compare this example with the evaluation of (factorial 5) using the interpreted version of the same procedure, shown at the end of section 5.4.4. The interpreted version required 144 pushes and a maximum stack depth of 28. This illustrates the optimization that results from our compilation strategy.

Interpretation and compilation

With the programs in this section, we can now experiment with the alternative execution strategies of interpretation and compilation.@footnote{We can do even better by extending the compiler to allow compiled code to call interpreted procedures. See Exercise 5-47.} An interpreter raises the machine to the level of the user program; a compiler lowers the user program to the level of the machine language. We can regard the Scheme language (or any programming language) as a coherent family of abstractions erected on the machine language. Interpreters are good for interactive program development and debugging because the steps of program execution are organized in terms of these abstractions, and are therefore more intelligible to the programmer. Compiled code can execute faster, because the steps of program execution are organized in terms of the machine language, and the compiler is free to make optimizations that cut across the higher-level abstractions.@footnote{Independent of the strategy of execution, we incur significant overhead if we insist that errors encountered in execution of a user program be detected and signaled, rather than being allowed to kill the system or produce wrong answers. For example, an out-of-bounds array reference can be detected by checking the validity of the reference before performing it. The overhead of checking, however, can be many times the cost of the array reference itself, and a programmer should weigh speed against safety in determining whether such a check is desirable. A good compiler should be able to produce code with such checks, should avoid redundant checks, and should allow programmers to control the extent and type of error checking in the compiled code.

Compilers for popular languages, such as C and C++, put hardly any error-checking operations into running code, so as to make things run as fast as possible. As a result, it falls to programmers to explicitly provide error checking. Unfortunately, people often neglect to do this, even in critical applications where speed is not a constraint. Their programs lead fast and dangerous lives. For example, the notorious ``Worm'' that paralyzed the Internet in 1988 exploited the @acronym{UNIX}(tm) operating system's failure to check whether the input buffer has overflowed in the finger daemon. (See Spafford 1989.)}

The alternatives of interpretation and compilation also lead to different strategies for porting languages to new computers. Suppose that we wish to implement Lisp for a new machine. One strategy is to begin with the explicit-control evaluator of section 5.4 and translate its instructions to instructions for the new machine. A different strategy is to begin with the compiler and change the code generators so that they generate code for the new machine. The second strategy allows us to run any Lisp program on the new machine by first compiling it with the compiler running on our original Lisp system, and linking it with a compiled version of the run-time library.@footnote{Of course, with either the interpretation or the compilation strategy we must also implement for the new machine storage allocation, input and output, and all the various operations that we took as ``primitive'' in our discussion of the evaluator and compiler. One strategy for minimizing work here is to write as many of these operations as possible in Lisp and then compile them for the new machine. Ultimately, everything reduces to a small kernel (such as garbage collection and the mechanism for applying actual machine primitives) that is hand-coded for the new machine.} Better yet, we can compile the compiler itself, and run this on the new machine to compile other Lisp programs.@footnote{This strategy leads to amusing tests of correctness of the compiler, such as checking whether the compilation of a program on the new machine, using the compiled compiler, is identical with the compilation of the program on the original Lisp system. Tracking down the source of differences is fun but often frustrating, because the results are extremely sensitive to minuscule details.} Or we can compile one of the interpreters of section 4.1 to produce an interpreter that runs on the new machine.

Exercise 5.45: By comparing the stack operations used by compiled code to the stack operations used by the evaluator for the same computation, we can determine the extent to which the compiler optimizes use of the stack, both in speed (reducing the total number of stack operations) and in space (reducing the maximum stack depth). Comparing this optimized stack use to the performance of a special-purpose machine for the same computation gives some indication of the quality of the compiler.

  • Exercise 5-27 asked you to determine, as a function of n, the number of pushes and the maximum stack depth needed by the evaluator to compute n! using the recursive factorial procedure given above. Exercise 5-14 asked you to do the same measurements for the special-purpose factorial machine shown in Figure 5-11. Now perform the same analysis using the compiled factorial procedure.

    Take the ratio of the number of pushes in the compiled version to the number of pushes in the interpreted version, and do the same for the maximum stack depth. Since the number of operations and the stack depth used to compute n! are linear in n, these ratios should approach constants as n becomes large. What are these constants? Similarly, find the ratios of the stack usage in the special-purpose machine to the usage in the interpreted version.

    Compare the ratios for special-purpose versus interpreted code to the ratios for compiled versus interpreted code. You should find that the special-purpose machine does much better than the compiled code, since the hand-tailored controller code should be much better than what is produced by our rudimentary general-purpose compiler.

  • Can you suggest improvements to the compiler that would help it generate code that would come closer in performance to the hand-tailored version?

Exercise 5.46: Carry out an analysis like the one in Exercise 5-45 to determine the effectiveness of compiling the tree-recursive Fibonacci procedure

(define (fib n) (if (< n 2) n (+ (fib (- n 1)) (fib (- n 2)))))

compared to the effectiveness of using the special-purpose Fibonacci machine of Figure 5-12. (For measurement of the interpreted performance, see Exercise 5-29.) For Fibonacci, the time resource used is not linear in n; hence the ratios of stack operations will not approach a limiting value that is independent of n.

Exercise 5.47: This section described how to modify the explicit-control evaluator so that interpreted code can call compiled procedures. Show how to modify the compiler so that compiled procedures can call not only primitive procedures and compiled procedures, but interpreted procedures as well. This requires modifying compile-procedure-call to handle the case of compound (interpreted) procedures. Be sure to handle all the same target and linkage combinations as in compile-proc-appl. To do the actual procedure application, the code needs to jump to the evaluator's compound-apply entry point. This label cannot be directly referenced in object code (since the assembler requires that all labels referenced by the code it is assembling be defined there), so we will add a register called compapp to the evaluator machine to hold this entry point, and add an instruction to initialize it:

(assign compapp (label compound-apply)) (branch (label external-entry)) ; branches if flag is set read-eval-print-loop ...

To test your code, start by defining a procedure f that calls a procedure g. Use compile-and-go to compile the definition of f and start the evaluator. Now, typing at the evaluator, define g and try to call f.

Exercise 5.48: The compile-and-go interface implemented in this section is awkward, since the compiler can be called only once (when the evaluator machine is started). Augment the compiler-interpreter interface by providing a compile-and-run primitive that can be called from within the explicit-control evaluator as follows:

;;; EC-Eval input: (compile-and-run '(define (factorial n) (if (= n 1) 1 (* (factorial (- n 1)) n)))) ;;; EC-Eval value: ok ;;; EC-Eval input: (factorial 5) ;;; EC-Eval value: 120

Exercise 5.49: As an alternative to using the explicit-control evaluator's read-eval-print loop, design a register machine that performs a read-compile-execute-print loop. That is, the machine should run a loop that reads an expression, compiles it, assembles and executes the resulting code, and prints the result. This is easy to run in our simulated setup, since we can arrange to call the procedures compile and assemble as ``register-machine operations.''

Exercise 5.50: Use the compiler to compile the metacircular evaluator of section 4.1 and run this program using the register-machine simulator. (To compile more than one definition at a time, you can package the definitions in a begin.) The resulting interpreter will run very slowly because of the multiple levels of interpretation, but getting all the details to work is an instructive exercise.

Exercise 5.51: Develop a rudimentary implementation of Scheme in C (or some other low-level language of your choice) by translating the explicit-control evaluator of section 5.4 into C. In order to run this code you will need to also provide appropriate storage-allocation routines and other run-time support.

Exercise 5.52: As a counterpoint to exercise Exercise 5-51, modify the compiler so that it compiles Scheme procedures into sequences of C instructions. Compile the metacircular evaluator of section 4.1 to produce a Scheme interpreter written in C.




Notes


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Based on Structure and Interpretation of Computer Programs, a work at http://mitpress.mit.edu/sicp/.

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