Compiling a Lisp: Primitive unary functions

September 5, 2020

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Welcome back to the “Compiling a Lisp” series. Last time, we finished adding the rest of the constants as tagged pointer immediates. Since it’s not very useful to have only values (no way to operate on them), we’re going to add some primitive unary functions.

“Primitive” means here that they are built into the compiler, so we won’t actually compile the call to an assembly procedure call. This is also called a compiler intrinsic. “Unary” means the functions will take only one argument. “Function” is a bit of a misnomer because these functions won’t be real values that you can pass around as variables. You’ll only be able to use them as literal names in calls.

Though we’re still not adding a reader/parser, we can imagine the syntax for this looks like the following:

(integer? (integer->char (add1 96)))

Today we also tackle nested function calls and subexpressions.

Adding function calls will require adding a new compiler datastructure, an addition to the AST, but not to the compiled code. The compiled code will still only know about the immediate types.

Ghuloum proposes we add the following functions:

The functions add1, sub1, and the char/integer conversion functions will be our first real experience dealing with object encoding in the compiled code. What fun!

The implementations for null?, zero?, not, integer?, and bool? are so similar that I am only going to reproduce one or two in this post. The rest will be visible at assets/code/lisp/compiling-unary.c.

In order to implement these functions, we’ll also need some more instructions than mov and ret. Today we’ll add:

Because the implementations of shl, shr, or, and and are so straightforward — just like mov, really — I’ll also omit them from the post. The implementations of add, sub, cmp, and setcc are more interesting.

The fundamental data structure of Lisp

Pairs, also called cons cells, two-tuples, and probably other things too, are the fundamental data structure of Lisp. At least the original Lisp. Nowadays we have fancy structures like vectors, too.

Pairs are a container for precisely two other objects. I’ll call them car and cdr for historical1 and consistency reasons, but you can call them whatever you like. Regardless of name, they could be represented as a C struct like this:

typedef struct Pair {
  ASTNode *car;
  ASTNode *cdr;
} Pair;

This is useful for holding pairs of objects (think coordinates, complex numbers, …) but it is also incredibly useful for making linked lists. Linked lists in Lisp are comprised of a car holding an object and the cdr holding another list. Eventually the last cdr holds nil, signifying the end of the list. Take a look at this handy diagram.

Fig. 1 - Cons cell list, courtesy of Wikipedia.

This represents the list (list 42 69 613), which can also be denoted (cons 42 (cons 69 (cons 613 nil))).

We’ll use these lists to represent the syntax trees for Lisp, so we’ll need to implement pairs to compile list programs.

Implementing pairs

In previous posts we implemented the immediate types the same way in the compiler and in the compiled code. I originally wrote this post doing the same thing: manually laying out object offsets myself, reading and writing from objects manually. The motivation was to get you familiar with the memory layout in the compiled code, but ultimately it ended up being too much content too fast. We’ll get to memory layouts when we start allocating pairs in the compiled code.

In the compiler we’re going to use C structs instead of manual memory layout. This makes the code a little bit easier to read. We’ll still tag the pointers, though.

const unsigned int kPairTag = 0x1;        // 0b001
const uword kHeapTagMask = ((uword)0x7);  // 0b000...0111
const uword kHeapPtrMask = ~kHeapTagMask; // 0b1111...1000

This adds the pair tag and some masks. As we noted in the previous posts, the heap object tags are all in the lowest three bits of the pointer. We can mask those out using this handy utility function.

uword Object_address(void *obj) { return (uword)obj & kHeapPtrMask; }

We’ll need to use this whenever we want to actually access a struct member. Speaking of struct members, here’s the definition of Pair:

typedef struct Pair {
  ASTNode *car;
  ASTNode *cdr;
} Pair;

And here are some functions for allocating and manipulating the Pair struct, to keep the implementation details hidden:

ASTNode *AST_heap_alloc(unsigned char tag, uword size) {
  // Initialize to 0
  uword address = (uword)calloc(size, 1);
  return (ASTNode *)(address | tag);
}

void AST_pair_set_car(ASTNode *node, ASTNode *car);
void AST_pair_set_cdr(ASTNode *node, ASTNode *cdr);

ASTNode *AST_new_pair(ASTNode *car, ASTNode *cdr) {
  ASTNode *node = AST_heap_alloc(kPairTag, sizeof(Pair));
  AST_pair_set_car(node, car);
  AST_pair_set_cdr(node, cdr);
  return node;
}

bool AST_is_pair(ASTNode *node) {
  return ((uword)node & kHeapTagMask) == kPairTag;
}

Pair *AST_as_pair(ASTNode *node) {
  assert(AST_is_pair(node));
  return (Pair *)Object_address(node);
}

ASTNode *AST_pair_car(ASTNode *node) { return AST_as_pair(node)->car; }

void AST_pair_set_car(ASTNode *node, ASTNode *car) {
  AST_as_pair(node)->car = car;
}

ASTNode *AST_pair_cdr(ASTNode *node) { return AST_as_pair(node)->cdr; }

void AST_pair_set_cdr(ASTNode *node, ASTNode *cdr) {
  AST_as_pair(node)->cdr = cdr;
}

There a couple important things to note.

First, AST_heap_alloc very intentionally zeroes out the memory it allocates. If the members were left uninitialized, it might be possible to read off a struct member that had an invalid pointer in car or cdr. If we zero-initialize it, the member pointers represent the object 0 by default. Nothing will crash.

Second, we keep moving our ASTNode pointers through AST_as_pair. This function has two purposes: catch invalid uses (via the assert that the object is indeed a Pair) and also mask out the lower bits. Otherwise we’d have to do the masking in every operation individually.

Third, I abstracted out the AST_heap_alloc so we don’t expose the calloc function everywhere. This allows us to later swap out the allocator for something more intelligent, like a bump allocator, an arena allocator, etc.

And since memory allocated must eventually be freed, there’s a freeing function too:

void AST_heap_free(ASTNode *node) {
  if (!AST_is_heap_object(node)) {
    return;
  }
  if (AST_is_pair(node)) {
    AST_heap_free(AST_pair_car(node));
    AST_heap_free(AST_pair_cdr(node));
  }
  free((void *)Object_address(node));
}

This assumes that each ASTNode* owns the references to all of its members. So don’t borrow references to share between objects. If you need to store a reference to an object, make sure you own it. Otherwise you’ll get a double free. In practice this shouldn’t bite us too much because each program is one big tree.

Implementing symbols

We also need symbols! I mean, we could try mapping all the functions we need to integers, but that wouldn’t be very fun. Who wants to try and debug a program crashing on function#67? Not me. So let’s add a datatype that can represent names of things.

As above, we’ll need to tag the pointers.

const unsigned int kSymbolTag = 0x5;      // 0b101

And then our struct definition.

typedef struct Symbol {
  word length;
  char cstr[];
} Symbol;

I’ve chosen this variable-length object representation because it’s similar to how we’re going to allocate symbols in assembly and the mechanism in C isn’t so gnarly. This struct indicates that the memory layout of a Symbol is a length field immediately followed by that number of bytes in memory. Note that having this variable array in a struct is a C99 feature.

If you don’t have C99 or don’t like this implementation, that’s fine. Just store a char* and allocate another object for that string.

You could also opt to not store the length at all and instead NUL-terminate it. This has the advantage of not dealing with variable-length arrays (it’s just a tagged char*) but has the disadvantage of an O(n) length lookup.

Now we can add our Symbol allocator:

Symbol *AST_as_symbol(ASTNode *node);

ASTNode *AST_new_symbol(const char *str) {
  word data_length = strlen(str) + 1; // for NUL
  ASTNode *node = AST_heap_alloc(kSymbolTag, sizeof(Symbol) + data_length);
  Symbol *s = AST_as_symbol(node);
  s->length = data_length;
  memcpy(s->cstr, str, data_length);
  return node;
}

See how we have to manually specify the size we want. It’s a little fussy, but it works.

Storing the NUL byte or not is up to you. It saves one byte per string if you don’t, but it makes printing out strings in the debugger a bit of a pain since you can’t just treat them like normal C strings.

Some Lisp implementations use a symbol table to ensure that symbols allocated with equivalent C-string values return the same pointer. This allows the implementations to test for symbol equality by testing pointer equality. I think we can sacrifice a bit of memory and runtime speed for implementation simplicity, so I’m not going to do that.

Let’s add the rest of the utility functions:

bool AST_is_symbol(ASTNode *node) {
  return ((uword)node & kHeapTagMask) == kSymbolTag;
}

Symbol *AST_as_symbol(ASTNode *node) {
  assert(AST_is_symbol(node));
  return (Symbol *)Object_address(node);
}

const char *AST_symbol_cstr(ASTNode *node) {
  return (const char *)AST_as_symbol(node)->cstr;
}

bool AST_symbol_matches(ASTNode *node, const char *cstr) {
  return strcmp(AST_symbol_cstr(node), cstr) == 0;
}

Now we can represent names.

Representing function calls

We’re going to represent function calls as lists. That means that the following program:

(add1 5)

can be represented by the following C program:

Pair *args = AST_new_pair(AST_new_integer(5), AST_nil());
Pair *program = AST_new_pair(AST_new_symbol("add1"), args);

This is a little wordy. We can make some utilities to trim the length down.

ASTNode *list1(ASTNode *item0) {
  return AST_new_pair(item0, AST_nil());
}

ASTNode *list2(ASTNode *item0, ASTNode *item1) {
  return AST_new_pair(item0, list1(item1));
}

ASTNode *new_unary_call(const char *name, ASTNode *arg) {
  return list2(AST_new_symbol(name), arg);
}

And now we can represent the program as:

list2(AST_new_symbol("add1"), AST_new_integer(5));
// or, shorter,
new_unary_call("add1", AST_new_integer(5));

This is great news because we’ll be adding many tests today.

Compiling primitive unary function calls

Whew. We’ve built up all these data structures and tagged pointers and whatnot but haven’t actually done anything with them yet. Let’s get to the compilers part of the compilers series, please!

First, we have to revisit Compile_expr and add another case. If we see a pair in an expression, then that indicates a call.

int Compile_expr(Buffer *buf, ASTNode *node) {
  // Tests for the immediates ...
  if (AST_is_pair(node)) {
    return Compile_call(buf, AST_pair_car(node), AST_pair_cdr(node));
  }
  assert(0 && "unexpected node type");
}

I took the liberty of separating out the callable and the args so that the Compile_call function has less to deal with.

We’re only supporting primitive unary function calls today, which means that we have a very limited pattern of what is accepted by the compiler. (add1 5) is ok. (add1 (add1 5)) is ok. (blargle 5) is not, because the blargle isn’t on the list above. ((foo) 1) is not, because the thing being called is not a symbol.

int Compile_call(Buffer *buf, ASTNode *callable, ASTNode *args) {
  assert(AST_pair_cdr(args) == AST_nil() &&
         "only unary function calls supported");
  if (AST_is_symbol(callable)) {
    // Switch on the different primitives here...
  }
  assert(0 && "unexpected call type");
}

Compile_call should look at what symbol it is, and depending on which symbol it is, emit different code. The overall pattern will look like this, though:

Let’s start with add1 since it’s the most straightforward.

    if (AST_symbol_matches(callable, "add1")) {
      _(Compile_expr(buf, operand1(args)));
      Emit_add_reg_imm32(buf, kRax, Object_encode_integer(1));
      return 0;
    }

If we see add1, compile the argument (as above). Then, add 1 to rax. Note that we’re not just adding the literal 1, though. We’re adding the object representation of 1, ie 1 << 2. Think about why! When you have an idea, click the footnote.2

If you’re wondering what the underscore (_) function is, it’s a macro that I made to test the return value of the compile expression and return if there was an error. We don’t have any non-aborting error cases just yet, but I got tired of writing if (result != 0) return result; over and over again.

Note that there is no runtime error checking. Our compiler will allow (add1 nil) to slip through and mangle the pointer. This isn’t ideal, but we don’t have the facilities for error reporting just yet.

sub1 is similar to add1, except it uses the sub instruction. You could also just use add with the immediate representation of -1.

integer->char is different. We have to change the tag of the object. In order to do that, we shift the integer left and then drop the character tag onto it. This is made simple by integers having a 0b00 tag (nothing to mask out).

Here’s a small diagram showing the transitions when converting 97 to 'a':

High                                                           Low
0000000000000000000000000000000000000000000000000000000[1100001]00  Integer
0000000000000000000000000000000000000000000000000[1100001]00000000  Shifted
0000000000000000000000000000000000000000000000000[1100001]00001111  Character

where the number in enclosed in [brackets] is 97. And here’s the code to emit assembly that does just that:

    if (AST_symbol_matches(callable, "integer->char")) {
      _(Compile_expr(buf, operand1(args)));
      Emit_shl_reg_imm8(buf, kRax, kCharShift - kIntegerShift);
      Emit_or_reg_imm8(buf, kRax, kCharTag);
      return 0;
    }

Note that we’re not shifting left by the full amount. We’re only shifting by the difference, since integers are already two bits shifted.

char->integer is similar, except it’s just a shr. Once the value is shifted right, the char tag gets dropped off the end, so there’s no need to mask it out.

nil? is our first primitive with ~ exciting assembly instructions ~. We get to use cmp and setcc. The basic idea is:

al is the name for the lower 8 bits of rax. There’s also ah (for the next 8 bits, but not the highest bits), cl/ch, etc.

    if (AST_symbol_matches(callable, "nil?")) {
      _(Compile_expr(buf, operand1(args)));
      Emit_cmp_reg_imm32(buf, kRax, Object_nil());
      Emit_mov_reg_imm32(buf, kRax, 0);
      Emit_setcc_imm8(buf, kEqual, kAl);
      Emit_shl_reg_imm8(buf, kRax, kBoolShift);
      Emit_or_reg_imm8(buf, kRax, kBoolTag);
      return 0;
    }

The cmp leaves a bit set (ZF) in the flags register, which setcc then checks. setcc, by the way, is the name for the group of instructions that set a register if some condition happened. It took me a long time to realize that since people normally write sete or setnz or something. And cc means “condition code”.

If you want to simplify your life — we’re going to do a lot of comparisons today – we can extract that into a function that compares rax with some immediate value, and then refactor Compile_call to call that.

void Compile_compare_imm32(Buffer *buf, int32_t value) {
  Emit_cmp_reg_imm32(buf, kRax, value);
  Emit_mov_reg_imm32(buf, kRax, 0);
  Emit_setcc_imm8(buf, kEqual, kAl);
  Emit_shl_reg_imm8(buf, kRax, kBoolShift);
  Emit_or_reg_imm8(buf, kRax, kBoolTag);
}

Let’s also poke at the implementations of cmp and setcc, since they involve some fun instruction encoding.

cmp, as it turns out, has a short-path when the register it’s comparing against is rax. This means we get to save one (1) whole byte if we want to!

void Emit_cmp_reg_imm32(Buffer *buf, Register left, int32_t right) {
  Buffer_write8(buf, kRexPrefix);
  if (left == kRax) {
    // Optimization: cmp rax, {imm32} can either be encoded as 3d {imm32} or 81
    // f8 {imm32}.
    Buffer_write8(buf, 0x3d);
  } else {
    Buffer_write8(buf, 0x81);
    Buffer_write8(buf, 0xf8 + left);
  }
  Buffer_write32(buf, right);
}

If you don’t want to, just use the 81 f8+ pattern.

For setcc, we have to define this new notion of “partial registers” so that we can encode the instruction properly. We can’t re-use Register because there are two partial registers for rax. So we add a PartialRegister.

typedef enum {
  kAl = 0,
  kCl,
  kDl,
  kBl,
  kAh,
  kCh,
  kDh,
  kBh,
} PartialRegister;

And then we can use those in the setcc implementation:

void Emit_setcc_imm8(Buffer *buf, Condition cond, PartialRegister dst) {
  Buffer_write8(buf, 0x0f);
  Buffer_write8(buf, 0x90 + cond);
  Buffer_write8(buf, 0xc0 + dst);
}

Again, I didn’t come up with this encoding. This is Intel’s design.

The zero? primitive is much the same as nil?, and we can re-use that Compile_compare_imm32 function.

    if (AST_symbol_matches(callable, "zero?")) {
      _(Compile_expr(buf, operand1(args)));
      Compile_compare_imm32(buf, Object_encode_integer(0));
      return 0;
    }

not is more of the same — compare against false.

Now we get to integer?. This is similar, but different enough that I’ll reproduce the implementation below. Instead of comparing the whole number in rax, we only want to look at the lowest 2 bits. This can be accomplished by masking out the other bits, and then doing the comparison. For that, we emit an and first and compare against the tag.

    if (AST_symbol_matches(callable, "integer?")) {
      _(Compile_expr(buf, operand1(args)));
      Emit_and_reg_imm8(buf, kRax, kIntegerTagMask);
      Compile_compare_imm32(buf, kIntegerTag);
      return 0;
    }

It’s possible to shorten the implementation a little bit because and sets the zero flag. This means we can skip the cmp. But it’s only one instruction and I’m lazy so I’m reusing the existing infrastructure.

Last, boolean? is almost the same as integer?.

Boom! Compilers! Let’s check our work.

Testing

I’ll only include a couple tests here, since the new tests are a total of 283 lines added and are a little bit repetitive.

First, the simplest test for add1.

TEST compile_unary_add1(Buffer *buf) {
  ASTNode *node = new_unary_call("add1", AST_new_integer(123));
  int compile_result = Compile_function(buf, node);
  ASSERT_EQ(compile_result, 0);
  // mov rax, imm(123); add rax, imm(1); ret
  byte expected[] = {0x48, 0xc7, 0xc0, 0xec, 0x01, 0x00, 0x00,
                     0x48, 0x05, 0x04, 0x00, 0x00, 0x00, 0xc3};
  EXPECT_EQUALS_BYTES(buf, expected);
  Buffer_make_executable(buf);
  uword result = Testing_execute_expr(buf);
  ASSERT_EQ(result, Object_encode_integer(124));
  AST_heap_free(node);
  PASS();
}

Second, a test of nested expressions:

TEST compile_unary_add1_nested(Buffer *buf) {
  ASTNode *node = new_unary_call(
      "add1", new_unary_call("add1", AST_new_integer(123)));
  int compile_result = Compile_function(buf, node);
  ASSERT_EQ(compile_result, 0);
  // mov rax, imm(123); add rax, imm(1); add rax, imm(1); ret
  byte expected[] = {0x48, 0xc7, 0xc0, 0xec, 0x01, 0x00, 0x00,
                     0x48, 0x05, 0x04, 0x00, 0x00, 0x00, 0x48,
                     0x05, 0x04, 0x00, 0x00, 0x00, 0xc3};
  EXPECT_EQUALS_BYTES(buf, expected);
  Buffer_make_executable(buf);
  uword result = Testing_execute_expr(buf);
  ASSERT_EQ(result, Object_encode_integer(125));
  AST_heap_free(node);
  PASS();
}

Third, the test for boolean?.

TEST compile_unary_booleanp_with_non_boolean_returns_false(Buffer *buf) {
  ASTNode *node = new_unary_call("boolean?", AST_new_integer(5));
  int compile_result = Compile_function(buf, node);
  ASSERT_EQ(compile_result, 0);
  // 0:  48 c7 c0 14 00 00 00    mov    rax,0x14
  // 7:  48 83 e0 3f             and    rax,0x3f
  // b:  48 3d 1f 00 00 00       cmp    rax,0x0000001f
  // 11: 48 c7 c0 00 00 00 00    mov    rax,0x0
  // 18: 0f 94 c0                sete   al
  // 1b: 48 c1 e0 07             shl    rax,0x7
  // 1f: 48 83 c8 1f             or     rax,0x1f
  byte expected[] = {0x48, 0xc7, 0xc0, 0x14, 0x00, 0x00, 0x00, 0x48, 0x83,
                     0xe0, 0x3f, 0x48, 0x3d, 0x1f, 0x00, 0x00, 0x00, 0x48,
                     0xc7, 0xc0, 0x00, 0x00, 0x00, 0x00, 0x0f, 0x94, 0xc0,
                     0x48, 0xc1, 0xe0, 0x07, 0x48, 0x83, 0xc8, 0x1f};
  EXPECT_EQUALS_BYTES(buf, expected);
  Buffer_make_executable(buf);
  uword result = Testing_execute_expr(buf);
  ASSERT_EQ(result, Object_false());
  AST_heap_free(node);
  PASS();
}

I’m getting the fancy disassembly from defuse.ca. I include it because it makes the tests easier for me to read and reason about later. You just have to make sure the text and the binary representations in the test don’t go out of sync because that can be very confusing…

Anyway, that’s a wrap for today. Send your comments on the elist! Next time, binary primitives.



  1. There’s a long-running dispute about what to call these two objects. The original Lisp machine (the IBM 704) had a particular hardware layout that led to the creation of the names car and cdr. Nobody uses this hardware anymore, so the names are historical. Some people call them first/fst and second/snd. Others call them head/hd and tail/tl. Some people have other ideas

  2. If you said “to preserve the tag” or “adding 1 would make it a pair” or some variant on that, you’re correct! Otherwise, I recommend going back to the diagram from the last couple of posts and then writing down binary representations of a couple of numbers by hand on a piece of paper.