Add initial bignum implementation

compiler.py

@@ -304,7 +304,11 @@ def _is_const(self, exp: Object) -> bool:
             return True
         return False
 
+    def _make_tag(self, tag: str, size_bytes: str) -> str:
+        return f"((({size_bytes}) << kBitsPerByte) | {tag})"
+
     def _const_obj(self, type: str, tag: str, contents: str) -> str:
+        # TODO(max): Emulate make_tag here to encode size
         result = self.gensym(f"const_{type}")
         self.const_heap.append(f"CONST_HEAP struct {type} {result} = {{.HEAD.tag={tag}, {contents} }};")
         return f"ptrto({result})"
@@ -328,8 +332,20 @@ def _emit_const(self, exp: Object) -> str:
         if isinstance(exp, Hole):
             return "hole()"
         if isinstance(exp, Int):
-            # TODO(max): Bignum
-            return f"_mksmallint({exp.value})"
+            if -0x4000000000000000 <= exp.value <= 0x3FFFFFFFFFFFFFFF:
+                return f"_mksmallint({exp.value}ULL)"
+            # Divide number into 64-bit digits
+            if exp.value < 0:
+                # TODO(max): Handle negative largeint
+                raise NotImplementedError(f"negative largeint64({exp.value})")
+            value = exp.value
+            digits = []
+            while value:
+                digits.append(value & 0xFFFFFFFFFFFFFFFF)
+                value >>= 64
+            tag = self._make_tag("TAG_LARGEINT", f"sizeof(struct large_int)+{len(digits)}ULL*kLargeIntDigitSize")
+            parts = ", ".join(f"{digit}ULL" for digit in digits)
+            return self._const_obj("large_int", tag, f".digits={{ {parts} }}")
         if isinstance(exp, List):
             items = [self._emit_const(item) for item in exp.items]
             result = "empty_list()"
@@ -469,6 +485,7 @@ def compile_to_string(program: Object, debug: bool) -> str:
         ("uword", "kPrimaryTagMask", "(1ULL << kPrimaryTagBits) - 1"),
         ("uword", "kImmediateTagMask", "(1ULL << kImmediateTagBits) - 1"),
         ("uword", "kWordSize", "sizeof(word)"),
+        ("uword", "kLargeIntDigitSize", "sizeof(large_int_digit)"),
         ("uword", "kMaxSmallStringLength", "kWordSize - 1"),
         ("uword", "kBitsPerByte", 8),
         # Up to the five least significant bits are used to tag the object's layout.
@@ -496,7 +513,6 @@ def compile_to_string(program: Object, debug: bool) -> str:
     dirname = os.path.dirname(__file__)
     with open(os.path.join(dirname, "runtime.c"), "r") as runtime:
         print(runtime.read(), file=f)
-    print("#define OBJECT_HANDLE(name, exp) GC_HANDLE(struct object*, name, exp)", file=f)
     if compiler.record_keys:
         print("const char* record_keys[] = {", file=f)
         for key in compiler.record_keys:

compiler_tests.py

@@ -42,6 +42,28 @@ def _run(self, code: str) -> str:
     def test_int(self) -> None:
         self.assertEqual(self._run("1"), "1\n")
 
+    def test_int_small_int_max(self) -> None:
+        self.assertEqual(self._run("4611686018427387903"), "4611686018427387903\n")
+
+    def test_int_small_int_min(self) -> None:
+        self.assertEqual(self._run("-4611686018427387904"), "-4611686018427387904\n")
+
+    def test_int_small_int_too_small(self) -> None:
+        with self.assertRaisesRegex(NotImplementedError, "negative largeint"):
+            self._run("-4611686018427387905")
+
+    def test_int_add_to_large_int(self) -> None:
+        self.assertEqual(self._run("4611686018427387903 + 1"), "largeint64(0x4000000000000000)\n")
+        self.assertEqual(self._run("4611686018427387904"), "largeint64(0x4000000000000000)\n")
+
+    def test_int_add_to_large_int_two_digits(self) -> None:
+        program = "4611686018427387903 + 4611686018427387903 + 4611686018427387903 + 4611686018427387903 + 4611686018427387903 + 4611686018427387903 + 4611686018427387903"
+        self.assertEqual(hex(eval(program)), "0x1bffffffffffffff9")
+        self.assertEqual(self._run(program), "largeint64(0x1, 0xbffffffffffffff9)\n")
+
+    def test_literal_positive_large_int(self) -> None:
+        self.assertEqual(self._run("340282366920938463463374607431768211456"), "largeint64(0x1, 0x0, 0x0)\n")
+
     def test_small_string(self) -> None:
         self.assertEqual(self._run('"hello"'), '"hello"\n')
 

runtime.c

@@ -17,6 +17,10 @@ const int kPointerSize = sizeof(void*);
 typedef intptr_t word;
 typedef uintptr_t uword;
 typedef unsigned char byte;
+typedef uint64_t large_int_digit;
+const word kMinWord = INTPTR_MIN;
+const word kMaxWord = INTPTR_MAX;
+const uword kMaxUword = UINTPTR_MAX;
 
 // Garbage collector core by Andy Wingo <[email protected]>.
 
@@ -360,7 +364,8 @@ static ALWAYS_INLINE ALLOCATOR struct object* allocate(struct gc_heap* heap,
   TAG(TAG_CLOSURE)                                                             \
   TAG(TAG_RECORD)                                                              \
   TAG(TAG_STRING)                                                              \
-  TAG(TAG_VARIANT)
+  TAG(TAG_VARIANT)                                                             \
+  TAG(TAG_LARGEINT)
 
 enum {
 // All odd becase of the kNotForwardedBit
@@ -411,9 +416,15 @@ struct variant {
   struct object* value;
 } HEAP_ALIGNED;
 
+struct large_int {
+  struct gc_obj HEAD;
+  large_int_digit digits[];
+};  // Not HEAP_ALIGNED; digits is variable size
+
 size_t heap_object_size(struct gc_obj* obj) {
   size_t result = obj->tag >> kBitsPerByte;
-  assert(is_size_aligned(result));
+  // Size need not be aligned if the object is in the constant heap.
+  assert(in_const_heap(obj) || is_size_aligned(result));
   return result;
 }
 
@@ -435,6 +446,7 @@ size_t trace_heap_object(struct gc_obj* obj, struct gc_heap* heap,
       }
       break;
     case TAG_STRING:
+    case TAG_LARGEINT:
       break;
     case TAG_VARIANT:
       visit(&((struct variant*)obj)->value, heap);
@@ -458,12 +470,83 @@ struct object* mksmallint(word value) {
   return _mksmallint(value);
 }
 
+static ALWAYS_INLINE bool is_large_int(struct object* obj) {
+  return is_heap_object(obj) && obj_has_tag(as_heap_object(obj), TAG_LARGEINT);
+}
+
+static ALWAYS_INLINE struct large_int* as_large_int(struct object* obj) {
+  assert(is_large_int(obj));
+  return (struct large_int*)as_heap_object(obj);
+}
+
+uword large_int_num_digits(struct object* obj) {
+  assert(is_large_int(obj));
+  size_t size = heap_object_size(as_heap_object(obj)) - sizeof(struct gc_obj);
+  return size / kLargeIntDigitSize;
+}
+
+uword num_digits(struct object* obj) {
+  if (is_small_int(obj)) {
+    return 1;
+  }
+  assert(is_large_int(obj));
+  return large_int_num_digits(obj);
+}
+
+large_int_digit large_int_digit_at(struct object* obj, uword index) {
+  assert(is_large_int(obj));
+  assert(index < large_int_num_digits(obj));
+  return as_large_int(obj)->digits[index];
+}
+
+void large_int_digit_at_put(struct object* obj, uword index,
+                            large_int_digit digit) {
+  assert(is_large_int(obj));
+  assert(index < large_int_num_digits(obj));
+  as_large_int(obj)->digits[index] = digit;
+}
+
+word small_int_value(struct object* obj) {
+  assert(is_small_int(obj));
+  return ((word)obj) >> kSmallIntTagBits;  // sign extend
+}
+
+uword digit_at(struct object* obj, uword index) {
+  if (is_small_int(obj)) {
+    assert(index == 0);
+    return small_int_value(obj);
+  }
+  assert(is_large_int(obj));
+  return large_int_digit_at(obj, index);
+}
+
+struct object* _mklarge_int_uninit_private(struct gc_heap* heap,
+                                           uword num_digits) {
+  uword digits_size = num_digits * kLargeIntDigitSize;
+  uword size = align_size(sizeof(struct large_int) + digits_size);
+  return allocate(heap, TAG_LARGEINT, size);
+}
+
+struct object* _mklarge_int(struct gc_heap* heap, uword num_digits,
+                            large_int_digit* digits) {
+  struct object* result = _mklarge_int_uninit_private(heap, num_digits);
+  uword digits_size = num_digits * kLargeIntDigitSize;
+  memcpy(as_large_int(result)->digits, digits, digits_size);
+  return result;
+}
+
 struct object* mknum(struct gc_heap* heap, word value) {
-  (void)heap;
-  return mksmallint(value);
+  if (smallint_is_valid(value)) {
+    return _mksmallint(value);
+  }
+  assert(sizeof(word) == sizeof(large_int_digit));
+  large_int_digit digits[] = {value};
+  return _mklarge_int(heap, 1, digits);
 }
 
-bool is_num(struct object* obj) { return is_small_int(obj); }
+bool is_num(struct object* obj) {
+  return is_small_int(obj) || is_large_int(obj);
+}
 
 bool is_num_equal_word(struct object* obj, word value) {
   assert(smallint_is_valid(value));
@@ -472,7 +555,12 @@ bool is_num_equal_word(struct object* obj, word value) {
 
 word num_value(struct object* obj) {
   assert(is_num(obj));
-  return ((word)obj) >> 1;  // sign extend
+  if (is_small_int(obj)) {
+    return small_int_value(obj);
+  }
+  assert(is_large_int(obj));
+  assert(large_int_num_digits(obj) == 1);
+  return large_int_digit_at(obj, 0);
 }
 
 bool is_list(struct object* obj) {
@@ -688,6 +776,7 @@ void pop_handles(void* local_handles) {
 #define GC_HANDLE(type, name, val)                                             \
   type name = val;                                                             \
   GC_PROTECT(name)
+#define OBJECT_HANDLE(name, exp) GC_HANDLE(struct object*, name, exp)
 
 void trace_roots(struct gc_heap* heap, VisitFn visit) {
   for (struct object*** h = handle_stack; h != handles; h++) {
@@ -698,17 +787,115 @@ void trace_roots(struct gc_heap* heap, VisitFn visit) {
 struct gc_heap heap_object;
 struct gc_heap* heap = &heap_object;
 
-struct object* num_add(struct object* a, struct object* b) {
-  // NB: doesn't use pointers after allocating
-  return mknum(heap, num_value(a) + num_value(b));
+#ifndef __has_builtin
+// Some versions of TCC don't have __has_builtin.
+#define __has_builtin(x) 0
+#endif
+
+#if !__has_builtin(__builtin_uaddl_overflow)
+// No version of TCC has __builtin_uaddl_overflow.
+bool __builtin_uaddl_overflow(uword left, uword right, uword* result) {
+  *result = left + right;
+  return *result < left;
+}
+#endif
+
+static uword add_with_carry(uword x, uword y, uword carry_in,
+                            uword* carry_out) {
+  assert(carry_in <= 1 && "carry must be 0 or 1");
+  uword sum;
+  uword carry0 = __builtin_uaddl_overflow(x, y, &sum);
+  uword carry1 = __builtin_uaddl_overflow(sum, carry_in, &sum);
+  *carry_out = carry0 | carry1;
+  return sum;
+}
+
+struct object* normalize_large_int(struct gc_heap* heap, struct object* obj) {
+  (void)heap;
+  word num_digits = large_int_num_digits(obj);
+  word shrink_to_digits = num_digits;
+  for (word digit = large_int_digit_at(obj, shrink_to_digits - 1), next_digit;
+       shrink_to_digits > 1; shrink_to_digits--, digit = next_digit) {
+    next_digit = large_int_digit_at(obj, shrink_to_digits - 2);
+    // break if we have neither a redundant sign-extension nor a redundnant
+    // zero-extension.
+    if ((digit != -1 || next_digit >= 0) && (digit != 0 || next_digit < 0)) {
+      break;
+    }
+  }
+  if (shrink_to_digits == 1 && smallint_is_valid(large_int_digit_at(obj, 0))) {
+    return mksmallint(large_int_digit_at(obj, 0));
+  }
+  if (shrink_to_digits == num_digits) {
+    return obj;
+  }
+  HANDLES();
+  GC_PROTECT(obj);
+  OBJECT_HANDLE(result, _mklarge_int_uninit_private(heap, shrink_to_digits));
+  for (word i = 0; i < shrink_to_digits; i++) {
+    large_int_digit_at_put(result, i, large_int_digit_at(obj, i));
+  }
+  return result;
+}
+
+bool small_int_is_negative(struct object* obj) {
+  return small_int_value(obj) < 0;
+}
+
+bool large_int_is_negative(struct object* obj) {
+  return (word)large_int_digit_at(obj, large_int_num_digits(obj) - 1) < 0;
+}
+
+bool is_negative(struct object* obj) {
+  if (is_small_int(obj)) {
+    return small_int_is_negative(obj);
+  }
+  return large_int_is_negative(obj);
+}
+
+struct object* num_add(struct object* left, struct object* right) {
+  if (is_small_int(left) && is_small_int(right)) {
+    // Take a shortcut because we know the result fits in a word.
+    word result = num_value(left) + num_value(right);
+    return mknum(heap, result);
+  }
+  HANDLES();
+  uword left_digits = num_digits(left);
+  uword right_digits = num_digits(right);
+  GC_PROTECT(left);
+  GC_PROTECT(right);
+  OBJECT_HANDLE(longer, left_digits > right_digits ? left : right);
+  OBJECT_HANDLE(shorter, left_digits > right_digits ? right : left);
+  uword shorter_digits = num_digits(shorter);
+  uword longer_digits = num_digits(longer);
+  uword result_digits = longer_digits + 1;
+  OBJECT_HANDLE(result, _mklarge_int_uninit_private(heap, result_digits));
+  uword carry = 0;
+  for (uword i = 0; i < shorter_digits; i++) {
+    uword sum = add_with_carry(digit_at(longer, i), digit_at(shorter, i), carry,
+                               &carry);
+    large_int_digit_at_put(result, i, sum);
+  }
+  uword shorter_sign_extension = is_negative(shorter) ? kMaxUword : 0;
+  for (uword i = shorter_digits; i < longer_digits; i++) {
+    uword sum = add_with_carry(digit_at(longer, i), shorter_sign_extension,
+                               carry, &carry);
+    large_int_digit_at_put(result, i, sum);
+  }
+  uword longer_sign_extension = is_negative(longer) ? kMaxUword : 0;
+  uword high_digit = longer_sign_extension + shorter_sign_extension + carry;
+  large_int_digit_at_put(result, result_digits - 1, high_digit);
+  return normalize_large_int(heap, result);
 }
 
 struct object* num_sub(struct object* a, struct object* b) {
+  // TODO(max): Implement large_int subtraction
   // NB: doesn't use pointers after allocating
   return mknum(heap, num_value(a) - num_value(b));
 }
 
 struct object* num_mul(struct object* a, struct object* b) {
+  // TODO(max): Implement large_int multiplication
   // NB: doesn't use pointers after allocating
   return mknum(heap, num_value(a) * num_value(b));
 }
@@ -793,8 +980,19 @@ extern const char* record_keys[];
 extern const char* variant_names[];
 
 struct object* print(struct object* obj) {
-  if (is_num(obj)) {
+  if (is_small_int(obj)) {
     printf("%ld", num_value(obj));
+  } else if (is_large_int(obj)) {
+    printf("largeint%d(", kLargeIntDigitSize * kPointerSize);
+    uword num_digits = large_int_num_digits(obj);
+    for (uword i = 0; i < num_digits; i++) {
+      if (i > 0) {
+        fprintf(stdout, ", ");
+      }
+      fprintf(stdout, "0x%lx", large_int_digit_at(obj, num_digits - i - 1));
+    }
+    printf(")");
+    return obj;
   } else if (is_list(obj)) {
     putchar('[');
     while (!is_empty_list(obj)) {