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compiler.rkt
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;; Project 5
;; Compiler from IfArith |--> x86-64
#lang racket
(provide (all-defined-out))
(define verbose-mode (make-parameter #t))
(define i-am-a-mac (make-parameter #f))
;;
;; Our compiler will have several layers
;;
;; Stage 1: IfArith <-- Surface level
;; | (ifarith?)
;; Stage 2: IfArithTiny <-- Subsurface level, desugars IfArith
;; | (ifarith-tiny?)
;; Stage 3: ANF <-- Administrative Normal Form
;; | (functions have "simple" arguments)
;; Stage 4: IR-Virtual <-- Assembly with virtual registers
;; | (linearized assembly w/ virtual registers)
;; Stage 5: x86 <-- x86, with stack allocation
;; | (ir-x86?)
;; Stage 6: NASM <-- Assembly file
;;
;; Once we have assembly code (in this case NASM assembly), we then
;; use a standard assembler / linker.
;; Stage 1: High-level language: IfArith
;;
;; Our high-level language will be IfArith--it has the obvious
;; semantics we have written several times before; the interpretation
;; is not the interesting part here. The only interesting thing to
;; note is that true is "anything but zero," and false is "exactly
;; zero."
;; Here are our primitive operators--notice that we don't include
;; =. Our notion of true will be "anything except for 0." Our notion
;; of false will be "exactly zero." We can get here by using
;; subtracts, etc...
(define (bop? op) (member op '(+ * - << >>)))
(define (uop? op) (member op '(- not)))
;; literals are either integer literals or true / false
(define (lit? l)
(match l
[(? integer? i) #:when (and (>= i (- (expt 2 63))) (< i (expt 2 63))) #t]
['true #t]
['false #t]
[_ #f]))
;; IfArith is a tiny (sub-Turing) language we've seen several times
;; throughout the course. We will compile IfArith to x86, by way of
;; several steps. Our language is intentionally tiny: project 4 showed
;; us we can compile to the lambda calculus, now we show how to
;; compile a (much less expressive) language all the way down to
;; assembly code.
(define (ifarith? e)
(match e
;; literals
[(? integer? i) #:when (and (>= i (- (expt 2 63))) (< i (expt 2 63))) #t]
['true #t]
['false #t]
;; applications of primitives, our language has no lambdas
[`(,(? bop? bop) ,(? ifarith? e0) ,(? ifarith? e1)) #t]
[`(,(? uop? bop) ,(? ifarith? e0)) #t]
;; let* works in the usual way
[`(let* ([,(? symbol? xs) ,(? ifarith? es)] ...) ,(? ifarith? e-body)) #t]
;; print an arbitrary expression (must be a number at runtime)
[`(print ,(? ifarith? e)) #t]
;; and/or, with short-circuiting semantics
[`(and ,(? ifarith? e0) ,(? ifarith? es) ...) #t]
[`(or ,(? ifarith? e0) ,(? ifarith? es) ...) #t]
;; if argument is 0, false, otherwise true
[`(if ,(? ifarith? e0) ,(? ifarith? e1) ,(? ifarith? e2)) #t]
;; cond where the last case is else
[`(cond [,(? ifarith? conditions) ,(? ifarith? bodies)]
...
[else ,(? ifarith? else-body)]) #t]
[_ #f]))
;; Stage 2: IfArith-Tiny
;;
;; Now we'll observe that many of the forms in ifarith? can be written
;; in terms of other forms. This is like the desugaring we did in p4:
;; we just eliminate some forms by using existing forms. For example,
;; let* can be written as a sequence of single-binding lets (notice we
;; change let* to let). Similarly, forms for and/or/cond can be
;; compiled to usages of `if`.
;; (Stage 2) Language spec
(define (ifarith-tiny? e)
(match e
;; literals
[(? integer? i) #:when (and (>= i (- (expt 2 63))) (< i (expt 2 63))) #t]
['true #t]
['false #t]
;; variables, bound in let
[(? symbol? x) #t]
;; applications of primitives, our language has no lambdas
[`(,(? bop? bop) ,(? ifarith? e0) ,(? ifarith? e1)) #t]
[`(,(? uop? bop) ,(? ifarith? e0)) #t]
;; let* works in the usual way
[`(let ([,(? symbol? x) ,(? ifarith? e)]) ,(? ifarith? e-body)) #t]
;; print an arbitrary expression (must be a number at runtime)
[`(print ,(? ifarith? e)) #t]
;; if argument is 0, false, otherwise true
[`(if ,(? ifarith? e0) ,(? ifarith? e1) ,(? ifarith? e2)) #t]
[_ #f]))
;; TODO TODO TODO
;;
;; This is the *only* programming part, and mostly a way to get the
;; team on the same page.
;;
;; Translator: IfArith |--> IfArith-Tiny
;;
;; You will implement a translator from IfArith to IfArithTiny,
;; sketched up above. Specifically, you will convert everything to
;; direct-style applications of builtins, along with let, print, and
;; if.
(define (ifarith->ifarith-tiny e)
(match e
;; literals
[(? integer? i) i]
['true 'todo]
['false 'todo]
[(? symbol? x) 'todo]
[`(,(? bop? bop) ,e0 ,e1) 'todo]
[`(,(? uop? uop) ,e) 'todo]
;; 0-binding case
[`(let* () ,e) 'todo]
;; 1+-binding case
[`(let* ([,(? symbol? x0) ,e0]) ,e-body)
'todo]
[`(let* ([,(? symbol? x0) ,e0] ,rest-binding-pairs ...) ,e-body)
'todo]
;; print an arbitrary expression (must be a number at runtime)
[`(print ,_)
'todo]
;; and/or, with short-circuiting semantics
[`(and ,e0) 'todo]
[`(and ,e0 ,es ...) 'todo]
[`(or ,e0) 'todo]
[`(or ,e0 ,es ...) 'todo]
;; if argument is 0, false, otherwise true
[`(if ,e0 ,e1 ,e2) 'todo]
;; cond where the last case is else
[`(cond [else ,(? ifarith? else-body)])
'todo]
[`(cond [,c0 ,e0] ,rest ...)
'todo]))
;; Stage 3: Administrative Normal Form (ANF)
;;
;; In administrative normal form (or A-normal form) breaks up complex
;; instructions into simple instructions by introducing extra
;; "administrative" bindings. For example, (+ 1 (* 2 3)) may be
;; decomposed as (let ([v (* 2 3)]) (+ 1 v)). We want to do this
;; because, in assembly, we must do one single operation at a time.
;; Translator: IfArith-Tiny |--> ANF
;;
;; Conversion into A-Normal form. See here if you are interested:
;; https://matt.might.net/articles/a-normalization/
;;
;; The algorithm is tricky but intersting.
(define (value? v)
(match v
[(? lit? l) #t]
[(? symbol? x) #t]
[_ #f]))
(define (ifarith-tiny->anf e)
(define (normalize-term M) (normalize M (lambda (x) x)))
(define (normalize M k)
(pretty-print M)
(match M
[(? lit? l) (let ([t (gensym "x")]) `(let ([,t ,l]) ,(k t)))]
[(? value?) (k M)]
[`(if ,e0 ,e1 ,e2)
(normalize-name e0 (lambda (t) (k `(if ,t ,(normalize-term e1) ,(normalize-term e2)))))]
[`(let ([,x ,e]) ,e-b)
(normalize e (lambda (N1) `(let ([,x ,N1]) ,(normalize e-b k))))]
[`(,f ,e0 ,e1)
(normalize-name e0
(lambda (t0) (normalize-name e1
(lambda (t1) (let ([t (gensym "x")])
`(let ([,t (,f ,t0 ,t1)]) ,(k t)))))))]
[`(,f ,e0)
(normalize-name e0 (lambda (t0) (k `(,f ,t0))))]
[`(print ,e0)
(normalize-name e0 (lambda (t) (k `(print ,t))))]))
(define (normalize-name M k)
(normalize M
(lambda (N) (if (symbol? N)
(k N)
(let ([t (gensym "x")]) `(let ([,t ,N]) ,(k t)))))))
(normalize-term e))
;; Stage 4: IR-Virtual
;;
;; Instructions in ir-virtual? are very simple. Notice that it is a
;; very restrictive language, which requires *everything* be put in a
;; virtual register. This is a pain to write manually, but it's
;; simpler to compile fewer forms, so we take this shortcut; in
;; practice, many architectures (x86, etc.) do enable instructions
;; whose operands are a mix of registers, constants, and memory
;; addresses. A more advanced compiler would employ an instruction
;; selection phase to particularize these to a given ISA; we use a
;; naive strategy: stack allocate everything, shuffle into and out of
;; registers. It will work but it will not be as fast as if we used
;; registers more optimally.
(define label? symbol?) ;; labels will be symbols
(define (virtual-instr? instr)
(define register? symbol?)
(match instr
;; move a literal into a register
[`(mov-lit ,(? register? dst) ,(? lit? src)) #t]
[`(mov-reg ,(? register? dst) ,(? register? src)) #t]
;; instructions
[`(add ,(? register? dst) ,(? register? src)) #t]
[`(mul ,(? register? dst) ,(? register? src)) #t]
[`(idiv ,(? register? dst) ,(? register? src)) #t]
[`(sub ,(? register? dst) ,(? register? src)) #t]
[`(shr ,(? register? dst) ,(? register? src)) #t]
[`(shl ,(? register? dst) ,(? register? src)) #t]
[`(cmp ,(? register? dst) ,(? register? src)) #t]
;; unconditional jump
[`(jmp ,(? label? symbol?)) #t]
;; jump if not zero
[`(jnz ,(? label? symbol?)) #t]
;; print the (64-bit integer) in the register src
[`(print ,(? register? src)) #t]
[_ #f]))
;; a possibly-labeled (or not) instruction. When lists of instructions
;; are put in sequence, you may jump between them using the various
;; jump instructions, jmp and jnz
(define (labeled-virtual-instr? instr)
(match instr
[`((label ,l) ,(? virtual-instr? i)) #t]
[(? virtual-instr? i) #t]
[_ #f]))
;; ir-virtual is just a list of these possibly-labeled virtual
;; instructions.
(define (ir-virtual? instrs)
(and (list? instrs)
(andmap labeled-virtual-instr? instrs)))
;; Translation: ANF |--> Ir-Virtual
;;
;; In this stage we will take an expression that is, essentially, a
;; decision tree (with `let`-binding and primitive application) and
;; turn it into a linearized list of instructions.
(define (anf->ir-virtual e)
(define (name->op op)
(hash-ref (hash '* 'imul '+ 'add '- 'sub) op))
;; helper function which does the bulk of the work, labels
;; everything in the return value.
(define (linearize e)
(define my-lab (gensym "lab"))
(match e
;; these forms terminate; we mark them with a special mark,
;; exit. When we ultimately emit x86 code, we will need to
;; ensure that these points all branch to an "exit" node.
[`(print ,x)
`(((label ,my-lab) (print ,x)) (return 0))]
#;[(? symbol? x) `((mov-rax ,x) (exit))]
#;[(? integer? i) `((mov-rax ,i) (exit))]
[(? value? v) `((return ,v))]
;; the rest of the forms either (a) contain explicit branches,
;; or (b) fallthrough to the rest.
[`(let ([,x ,(? lit? l)]) ,e-b)
`(((label ,my-lab) (mov-lit ,x ,l)) . ,(linearize e-b))]
;; by this point, we'll have forced literals into variables
[`(let ([,x (,f ,x0 ,xs ...)]) ,e-b)
`(((label ,my-lab) (mov-reg ,x ,x0))
(,(name->op f) ,x ,@xs)
. ,(linearize e-b))]
[`(let ([,x ,y]) ,e-b)
`(((label ,my-lab) (mov-reg ,x ,y))
. ,(linearize e-b))]
[`(if ,xg ,et ,ef)
(define compilation-of-et (linearize et))
(define compilation-of-ef (linearize ef))
(define (label sequence)
(match sequence
[`(((label ,l) . ,_) . ,_) l]
[_ (error "expected a label to start the instruction sequence")]))
(define x (gensym "zero"))
(append `(((label ,my-lab) (mov-lit ,x 0))
(cmp ,xg ,x)
(jz ,(label compilation-of-et))
(jmp ,(label compilation-of-ef)))
;; notice that the compilation of et/ef must end in a
;; (exit) mark so that we don't "fall through" from the
;; end of et to the beginning of ef.
compilation-of-et
compilation-of-ef)]))
(linearize e))
;; Ir-Virtual |--> x86 (Stage 5)
;;
;; Now we present a dirt-simple compiler from ir-virtual? to x86. The
;; central challenge is how to deal with the unbounded number of
;; registers in ir-virtual. We accomplish this by "spilling:" we
;; stack-allocate all virtual registers. This approach will work,
;; provided we don't run out of stack space, and that we shuffle
;; results into and out of intermediary registers.
;;
;; We should also note here that our approach is really only thinking
;; of a single function: variables are all global. In practice, these
;; will all just be local variables sitting on the stack in the
;; program's main function. It would be more complicated to handle a
;; language with functions, for many reasons, including a more
;; thoughtful handling of environments (closures, etc...).
;;
;; Here, we keep it dirt simple to make it (hopefully) simpler.
;; We skip a formal definition of x86. It is the output of the
;; following function: ir-virtual->x86.
(define (what-is-printf)
(if (i-am-a-mac)
"_printf"
"printf"))
(define (what-is-main)
(if (i-am-a-mac)
"_main"
"main"))
;; Here is a translation into x86
(define (ir-virtual->x86 instrs)
;; calculate the registers used, we need this to determine how much
;; stack space to allocate.
(define (registers-used i)
(match i
[`((label ,l) ,i) (registers-used i)]
[`(,op ,ops ...) (set->list (filter symbol? ops))]))
(define registers (foldl (lambda (instr acc) (set-union (list->set (registers-used instr)) acc)) (set) instrs))
(define num-registers (set-count registers))
(define reg->stackpos (foldl (lambda (reg-name offset acc) (hash-set acc reg-name (- (* offset 8))))
(hash)
(set->list registers)
(range 1 (add1 num-registers))))
;; calculate the labels used: we add tons of unreachable labels; we
;; calculate reachable labels via a foldl.
(define (labels-used i)
(match i
[`((label ,l) ,i) (labels-used i)]
[`(jmp ,l) (set l)]
[`(jz ,l) (set l)]
[`(call ,l) (set l)]
[`(,op ,ops ...) (set)]))
(define reachable-labels (foldl (lambda (instr acc) (set-union (labels-used instr) acc)) (set) instrs))
;; translate into a sequence of x86 instructions
(define (translate instr)
(match instr
[`((label ,l) ,instr)
(define instrs (translate instr))
(if (set-member? reachable-labels l)
`(((label ,l) ,(first instrs)) . ,(rest instrs))
instrs)]
[`(mov-lit ,dst ,src)
`((mov "esi" ,(format "~a" src))
(mov ,(format "[rbp~a]" (hash-ref reg->stackpos dst)) "esi"))]
[`(mov-reg ,dst ,src)
`((mov "esi" ,(format "[rbp~a]" (hash-ref reg->stackpos src)))
(mov ,(format "[rbp~a]" (hash-ref reg->stackpos dst)) "esi"))]
[`(print ,src)
`((mov "esi" ,(format "[rbp~a]" (hash-ref reg->stackpos src)))
(lea "rdi" "[rel int_format]")
(mov "eax" "0")
(call ,(what-is-printf)))]
[`(call ,f) `((call ,f))]
[`(jmp ,f) `((jmp ,f))]
[`(jz ,f) `((jz ,f))]
;; mul needs to go in rax
#;
[`(imul ,dst ,src)
`((mov "rdi" ,(format "[rbp~a]" (hash-ref reg->stackpos src)))
(mov "rax" ,(format "[rbp~a]" (hash-ref reg->stackpos dst)))
(imul "rdi")
(mov "rax" ,(format "[rbp~a]" (hash-ref reg->stackpos dst))))]
[`(,op ,dst ,src)
`((mov "edi" ,(format "[rbp~a]" (hash-ref reg->stackpos src)))
(mov "eax" ,(format "[rbp~a]" (hash-ref reg->stackpos dst)))
(,op "eax" "edi")
(mov ,(format "[rbp~a]" (hash-ref reg->stackpos dst)) "eax"))]
;; emit code to jump to the exit
[`(return ,v)
`((mov "rax" ,(if (number? v) (number->string v) (format "[rbp~a]" (hash-ref reg->stackpos v))))
(jmp "finish_up"))]))
(define translated-instrs
(foldl (λ (instr instrs) (append instrs (translate instr))) '() instrs))
`((function (,(string->symbol (what-is-main)))
(push "rbp")
(mov "rbp" "rsp")
;; allocate num-registers * 16. This is more than we
;; need but the stack needs to be 16-byte aligned :-)
(sub "rsp" ,(format "~a" (* 16 num-registers)))
,@translated-instrs
((label "finish_up") (add "rsp" ,(format "~a" (* 16 num-registers))))
(leave)
(ret))))
;; x86 |--> NASM Assembly (Stage 5)
;;
;; We compile to NASM assembly, which can be compiled, e.g., on Linux:
;; nasm -fmacho64 example.asm.
(define (print-x86 x86)
(define (op->string op)
(cond [(symbol? op) (symbol->string op)]
[(string? op) op]
[else (error op)]))
(define (render-instr instr)
(match instr
[`((label ,l) ,i) (string-append (format "~a:" l) (render-instr i))]
[`(,opcode ,ops ...) (format "\t~a ~a\n"
(symbol->string opcode)
(string-join (map op->string ops) ", "))]
[`(call ,name) (format "\tcall ~a\n" name)]
['syscall "\tsyscall"]
['leave "\tleave"]
['ret "\tret"]))
(define (print-function f)
(match f
[`(function (,name) ,instrs ...)
(string-append
(format "~a:" name)
(apply string-append (map render-instr instrs)))]))
;; include a preamble
(displayln "section .data\n\tint_format db \"%ld\",10,0\n\n")
(displayln (format "\tglobal _main\n\textern ~a\nsection .text\n\n" (what-is-printf)))
(displayln (print-function `(function (_start)
(call ,(what-is-main))
(mov "rax" "60")
(xor "rdi" "rdi")
syscall)))
(displayln "\n")
(displayln (print-function (first x86)))) ;; only print the first (main) for now
;;
;; Command-line parsing and actually running the compiler
;;
;; compile from ir-virtual
(define (compile-ir-virtual [ir-virtual (get-input-tree)])
(when (verbose-mode)
(begin
(displayln "ir-virtual:")
(pretty-print ir-virtual)))
(define x86 (ir-virtual->x86 ir-virtual))
(when (verbose-mode)
(begin
(displayln "x86:")
(print-x86 x86)))
;; write the output .asm file
(with-output-to-file file-to-write (lambda ()(print-x86 x86)) #:exists 'replace)
(when (verbose-mode)
(displayln (format "The file has now been written to ~a. You must now assemble and link it." file-to-write))
(if (i-am-a-mac)
(begin
(displayln (format "(Assemble on Mac, requires nasm:)\n\tnasm -fmacho64 ~a" file-to-write))
(displayln (format "(Link on Mac, hopefully)\n\tld ~a -o ~a -macosx_version_min 11.0 -L /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/lib -lSystem" object-file exe-file)))
(begin
(displayln (format "(Assemble on Linux, requires nasm)\n\tnasm ~a" file-to-write))
(displayln (format "(Link on Mac, hopefully)\n\tld ~a -o ~a" object-file exe-file))))))
;; compile from ifarith
(define (compile-ifa)
(define source-tree (get-input-tree))
(when (verbose-mode)
(begin
(displayln "Input source tree in IfArith:")
(pretty-print source-tree)))
;; compile ifarith |--> ifarith-tiny
(define ifarith-tiny (ifarith->ifarith-tiny source-tree))
(when (verbose-mode)
(begin
(displayln "ifarith-tiny:")
(pretty-print ifarith-tiny)))
;; compile ifarith-tiny |--> ir-virtual
(define anf (ifarith-tiny->anf ifarith-tiny))
(when (verbose-mode)
(begin
(displayln "anf:")
(pretty-print anf)))
(define ir-virtual (anf->ir-virtual anf))
(compile-ir-virtual ir-virtual))
;; Entrypoint -- we allow loading .ifa or .irv files to facilitate
;; easy testing.
;; parse the command line
(define filename
(command-line
#:once-each
[("-v" "--verbose") "Run with Verbose output."
(verbose-mode #t)]
[("-m" "--mac") "Generate code that is compatible with MachO."
(i-am-a-mac #t)]
#:args (filename) ; expect one command-line argument: <filename>
; return the argument as a filename to compile
filename))
(define file-to-write (string-append (first (string-split filename ".")) ".asm"))
(define object-file (string-append (first (string-split filename ".")) ".o"))
(define exe-file (string-append (first (string-split filename "."))))
;; parsing is as easy as using Racket's `read`
(define (get-input-tree)
(with-input-from-file filename
(lambda () (read))))
(match (last (string-split filename "."))
["ifa" (compile-ifa)]
["irv" (compile-ir-virtual)]
[_ (print "Error: files must end in .ifa (ifarith) or .irv (ir-virtual)")])
;;
;; Running this compiler:
;;
;; To compile a file, invoke as follows:
;;
;; (MacOS)
;; racket compiler.rkt -v -m test-programs/if2.ifa
;; < output written to test-programs/if2.asm >