Ruby Internals: Why RUBY_FIXNUM_FLAG should be 0x00

Type tags in MRI Ruby VALUE

Internally, values in MRI Ruby are 32-bit (at least for 32-bit processors). Some of the least-significant bits are used to store type information. See the VALUE definition in include/ruby/ruby.h. Using type tag bits avoids allocating additional memory for commonly-used immutable values, like integers.

Ruby uses a single-bit tag of 0x01 as the Fixnum type tag. The remaining bits, are used to store the Fixnum’s signed value. This is an immediate value; it doesn’t require storage for the Fixnum value to be allocated, unlike the heap space that would be required for a String. Other types will use different tag bits.

Since Ruby uses 31 bits to store the Fixnum’s value, all the other types use 0 for least-significant bit; Ruby uses dynamic length tags:

 3         2         1
10987654321098765432109876543210 bit index 
--------------------------------
sxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx1 Fixnum
00000000000000000000000000000000 false
00000000000000000000000000000010 true
00000000000000000000000000000100 nil
00000000000000000000000000000110 undef
xxxxxxxxxxxxxxxxxxxxxxxx00001110 Symbol
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx0x0 All other types

A non-zero Fixnum type tag requires that the tag must be masked or shifted away on Fixnum operands before numeric operations. In a running program, Fixnum is probably the most common numeric type and quite possibly the most common type of all; it makes sense to make the most common operations on Fixnum: +, -, *, / as fast and as simple as possible. It’s also likely that addition is the most common operation applied to Fixnum.

Imagine the following bit of Ruby code:

x = 1
y = 3
puts x + y

Internally, INT2FIX(X) is used to create a Ruby value from a C int X:

#define INT2FIX(X) (((X) << 1) | RUBY_FIXNUM_FLAG)
#define FIX2INT(X) ((X) >> 1)

Thus:

INT2FIX(1) => 3
INT2FIX(3) => 7

FIX2INT(X) shifts one bit down which removes the tag and returns the original integer.

To compute x + y, Ruby internally, in numeric.c: fix_plus(), does the following:

x + y                             =>
INT2FIX(FIX2INT(x) + FIX2INT(y))  =>
((3 >> 1) + (7 >> 1)) << 1 | 1    =>
9

FIX2INT(9)                        => 
(9 >> 1)                          =>
4

If a type-tag of 0x00 was used for Fixnums, there is no tag to remove and addition or subtraction on Fixnums requires no tag manipulations. Assume:

#define INT2FIX(X) ((X) << 1)
#define FIX2INT(X) ((X) >> 1)

The Ruby expression x + y would simply be x + y in C code, assuming no underflow or overflow into Bignum.

Multiplication with zero Fixnum tags is very simple: only one of the operands needs to be shifted down:

#define FIXMUL(X, Y)((X) >> 1) * (Y))

Fixnum division: the result of the division is shifted up:

#define FIXDIV(X, Y) (((X) / (Y)) << 1)

Two-bit type tags on 32-bit architectures

Oaklisp and LL (http://kurtstephens.com/pub/ll/) use 2-bit tags for all values. LL uses the following tag scheme:

 3         2         1
10987654321098765432109876543210 bit index 
--------------------------------
sxxxxxxxxxxxxxxxxxxxxxxxxxxxxx00 <fixnum>
pppppppppppppppppppppppppppppp01 <locative>
seeeeeeeemmmmmmmmmmmmmmmmmmmmm10 <flonum>
pppppppppppppppppppppppppppppp11 All other types

Floating-point (<flonum>) values are C floats which sacrifice the 2 least-significant mantissa bits for the type tag. Locatives are safe pointers to other values. Oaklisp stores floating-point values as allocated objects and uses a tag for other common immediate values: characters, etc.

The rationale for choosing a fixed-size lower 2-bit type tag, opposed to a dynamic-length type tag, as in Ruby, or high-bit tags, like some older Lisp implementations, is as follows:

C compilers and dynamic memory allocators will align allocations to word boundaries for performance reasons, so there cannot not be a pointer to an object that would require some of the lower bits of a pointer, except for sub-word access, e.g.: char *. 32-bit words are 4 bytes long; the lower 2 bits of any object pointer will always be zero, and are free to be used for type tagging.

If references to allocated objects are encoded using a 0x03 type tag, tag removal could be:

  #define RBASIC(X) ((struct RBasic*)((X) - 3))

Assuming that most of the time the interpreter is referencing structure members of the object, and does not need the actual address of the object:

  struct RBasic {
      VALUE flags; /* struct offset: + 0 */
      VALUE klass; /* struct offset: + 4 */
  };

  RBASIC(X)->klass =>
  ((struct RBasic*)((X) - 3))->klass

C compilers convert the pointer->member expression into an offset from an address. For 32-bit VALUEs:

  RBASIC(X)->flags => *(VALUE*)((X) - 3 + 0)
  RBASIC(X)->klass => *(VALUE*)((X) - 3 + 4)

Using subtraction as the tag removal operation, instead of (X & ~3),
allows the C compiler to constant fold the tag removal and the structure offset:

  RBASIC(X)->flags => *(VALUE*)((X) - 3)
  RBASIC(X)->klass => *(VALUE*)((X) + 1)

Therefore, there is no additional tag removal cost to reference structure members with non-zero offsets. One could reorder the members depending on which is “hotter”.

Research shows that tag manipulation is a heavy cost, esp. for numerics; any tagging scheme should be as simple and consistent as possible.

For example, determining the class of a VALUE could be inlined:

  #define CLASS_OF(v) ((v) & 3) ? RBASIC(v)->klass : rb_cFixnum)

Two-bit tags naturally align with word boundaries on 32-bit processors. Thus, zero tags for integers on 32-bit processors allows pointer arithmetic on VALUE*, as in the Array#[] method, to require no tag manipulation or multiplication to offset into the allocated Array’s elements.

Thanks to Gary Wright for inspiring me to write about this.

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