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@c -*-texinfo-*-
@c This is part of the GNU Guile Reference Manual.
@c Copyright (C) 1996, 1997, 2000, 2001, 2002, 2003, 2004, 2010, 2015, 2018
@c Free Software Foundation, Inc.
@c See the file guile.texi for copying conditions.
@node Data Representation
@section Data Representation
Scheme is a latently-typed language; this means that the system cannot,
in general, determine the type of a given expression at compile time.
Types only become apparent at run time. Variables do not have fixed
types; a variable may hold a pair at one point, an integer at the next,
and a thousand-element vector later. Instead, values, not variables,
have fixed types.
In order to implement standard Scheme functions like @code{pair?} and
@code{string?} and provide garbage collection, the representation of
every value must contain enough information to accurately determine its
type at run time. Often, Scheme systems also use this information to
determine whether a program has attempted to apply an operation to an
inappropriately typed value (such as taking the @code{car} of a string).
Because variables, pairs, and vectors may hold values of any type,
Scheme implementations use a uniform representation for values --- a
single type large enough to hold either a complete value or a pointer
to a complete value, along with the necessary typing information.
The following sections will present a simple typing system, and then
make some refinements to correct its major weaknesses. We then conclude
with a discussion of specific choices that Guile has made regarding
garbage collection and data representation.
@menu
* A Simple Representation::
* Faster Integers::
* Cheaper Pairs::
* Conservative GC::
* The SCM Type in Guile::
@end menu
@node A Simple Representation
@subsection A Simple Representation
The simplest way to represent Scheme values in C would be to represent
each value as a pointer to a structure containing a type indicator,
followed by a union carrying the real value. Assuming that @code{SCM} is
the name of our universal type, we can write:
@example
enum type @{ integer, pair, string, vector, ... @};
typedef struct value *SCM;
struct value @{
enum type type;
union @{
int integer;
struct @{ SCM car, cdr; @} pair;
struct @{ int length; char *elts; @} string;
struct @{ int length; SCM *elts; @} vector;
...
@} value;
@};
@end example
with the ellipses replaced with code for the remaining Scheme types.
This representation is sufficient to implement all of Scheme's
semantics. If @var{x} is an @code{SCM} value:
@itemize @bullet
@item
To test if @var{x} is an integer, we can write @code{@var{x}->type == integer}.
@item
To find its value, we can write @code{@var{x}->value.integer}.
@item
To test if @var{x} is a vector, we can write @code{@var{x}->type == vector}.
@item
If we know @var{x} is a vector, we can write
@code{@var{x}->value.vector.elts[0]} to refer to its first element.
@item
If we know @var{x} is a pair, we can write
@code{@var{x}->value.pair.car} to extract its car.
@end itemize
@node Faster Integers
@subsection Faster Integers
Unfortunately, the above representation has a serious disadvantage. In
order to return an integer, an expression must allocate a @code{struct
value}, initialize it to represent that integer, and return a pointer to
it. Furthermore, fetching an integer's value requires a memory
reference, which is much slower than a register reference on most
processors. Since integers are extremely common, this representation is
too costly, in both time and space. Integers should be very cheap to
create and manipulate.
One possible solution comes from the observation that, on many
architectures, heap-allocated data (i.e., what you get when you call
@code{malloc}) must be aligned on an eight-byte boundary. (Whether or
not the machine actually requires it, we can write our own allocator for
@code{struct value} objects that assures this is true.) In this case,
the lower three bits of the structure's address are known to be zero.
This gives us the room we need to provide an improved representation
for integers. We make the following rules:
@itemize @bullet
@item
If the lower three bits of an @code{SCM} value are zero, then the SCM
value is a pointer to a @code{struct value}, and everything proceeds as
before.
@item
Otherwise, the @code{SCM} value represents an integer, whose value
appears in its upper bits.
@end itemize
Here is C code implementing this convention:
@example
enum type @{ pair, string, vector, ... @};
typedef struct value *SCM;
struct value @{
enum type type;
union @{
struct @{ SCM car, cdr; @} pair;
struct @{ int length; char *elts; @} string;
struct @{ int length; SCM *elts; @} vector;
...
@} value;
@};
#define POINTER_P(x) (((int) (x) & 7) == 0)
#define INTEGER_P(x) (! POINTER_P (x))
#define GET_INTEGER(x) ((int) (x) >> 3)
#define MAKE_INTEGER(x) ((SCM) (((x) << 3) | 1))
@end example
Notice that @code{integer} no longer appears as an element of @code{enum
type}, and the union has lost its @code{integer} member. Instead, we
use the @code{POINTER_P} and @code{INTEGER_P} macros to make a coarse
classification of values into integers and non-integers, and do further
type testing as before.
Here's how we would answer the questions posed above (again, assume
@var{x} is an @code{SCM} value):
@itemize @bullet
@item
To test if @var{x} is an integer, we can write @code{INTEGER_P (@var{x})}.
@item
To find its value, we can write @code{GET_INTEGER (@var{x})}.
@item
To test if @var{x} is a vector, we can write:
@example
@code{POINTER_P (@var{x}) && @var{x}->type == vector}
@end example
Given the new representation, we must make sure @var{x} is truly a
pointer before we dereference it to determine its complete type.
@item
If we know @var{x} is a vector, we can write
@code{@var{x}->value.vector.elts[0]} to refer to its first element, as
before.
@item
If we know @var{x} is a pair, we can write
@code{@var{x}->value.pair.car} to extract its car, just as before.
@end itemize
This representation allows us to operate more efficiently on integers
than the first. For example, if @var{x} and @var{y} are known to be
integers, we can compute their sum as follows:
@example
MAKE_INTEGER (GET_INTEGER (@var{x}) + GET_INTEGER (@var{y}))
@end example
Now, integer math requires no allocation or memory references. Most real
Scheme systems actually implement addition and other operations using an
even more efficient algorithm, but this essay isn't about
bit-twiddling. (Hint: how do you decide when to overflow to a bignum?
How would you do it in assembly?)
@node Cheaper Pairs
@subsection Cheaper Pairs
However, there is yet another issue to confront. Most Scheme heaps
contain more pairs than any other type of object; Jonathan Rees said at
one point that pairs occupy 45% of the heap in his Scheme
implementation, Scheme 48. However, our representation above spends
three @code{SCM}-sized words per pair --- one for the type, and two for
the @sc{car} and @sc{cdr}. Is there any way to represent pairs using
only two words?
Let us refine the convention we established earlier. Let us assert
that:
@itemize @bullet
@item
If the bottom three bits of an @code{SCM} value are @code{#b000}, then
it is a pointer, as before.
@item
If the bottom three bits are @code{#b001}, then the upper bits are an
integer. This is a bit more restrictive than before.
@item
If the bottom two bits are @code{#b010}, then the value, with the bottom
three bits masked out, is the address of a pair.
@end itemize
Here is the new C code:
@example
enum type @{ string, vector, ... @};
typedef struct value *SCM;
struct value @{
enum type type;
union @{
struct @{ int length; char *elts; @} string;
struct @{ int length; SCM *elts; @} vector;
...
@} value;
@};
struct pair @{
SCM car, cdr;
@};
#define POINTER_P(x) (((int) (x) & 7) == 0)
#define INTEGER_P(x) (((int) (x) & 7) == 1)
#define GET_INTEGER(x) ((int) (x) >> 3)
#define MAKE_INTEGER(x) ((SCM) (((x) << 3) | 1))
#define PAIR_P(x) (((int) (x) & 7) == 2)
#define GET_PAIR(x) ((struct pair *) ((int) (x) & ~7))
@end example
Notice that @code{enum type} and @code{struct value} now only contain
provisions for vectors and strings; both integers and pairs have become
special cases. The code above also assumes that an @code{int} is large
enough to hold a pointer, which isn't generally true.
Our list of examples is now as follows:
@itemize @bullet
@item
To test if @var{x} is an integer, we can write @code{INTEGER_P
(@var{x})}; this is as before.
@item
To find its value, we can write @code{GET_INTEGER (@var{x})}, as
before.
@item
To test if @var{x} is a vector, we can write:
@example
@code{POINTER_P (@var{x}) && @var{x}->type == vector}
@end example
We must still make sure that @var{x} is a pointer to a @code{struct
value} before dereferencing it to find its type.
@item
If we know @var{x} is a vector, we can write
@code{@var{x}->value.vector.elts[0]} to refer to its first element, as
before.
@item
We can write @code{PAIR_P (@var{x})} to determine if @var{x} is a
pair, and then write @code{GET_PAIR (@var{x})->car} to refer to its
car.
@end itemize
This change in representation reduces our heap size by 15%. It also
makes it cheaper to decide if a value is a pair, because no memory
references are necessary; it suffices to check the bottom two bits of
the @code{SCM} value. This may be significant when traversing lists, a
common activity in a Scheme system.
Again, most real Scheme systems use a slightly different implementation;
for example, if GET_PAIR subtracts off the low bits of @code{x}, instead
of masking them off, the optimizer will often be able to combine that
subtraction with the addition of the offset of the structure member we
are referencing, making a modified pointer as fast to use as an
unmodified pointer.
@node Conservative GC
@subsection Conservative Garbage Collection
Aside from the latent typing, the major source of constraints on a
Scheme implementation's data representation is the garbage collector.
The collector must be able to traverse every live object in the heap, to
determine which objects are not live, and thus collectable.
There are many ways to implement this. Guile's garbage collection is
built on a library, the Boehm-Demers-Weiser conservative garbage
collector (BDW-GC). The BDW-GC ``just works'', for the most part. But
since it is interesting to know how these things work, we include here a
high-level description of what the BDW-GC does.
Garbage collection has two logical phases: a @dfn{mark} phase, in which
the set of live objects is enumerated, and a @dfn{sweep} phase, in which
objects not traversed in the mark phase are collected. Correct
functioning of the collector depends on being able to traverse the
entire set of live objects.
In the mark phase, the collector scans the system's global variables and
the local variables on the stack to determine which objects are
immediately accessible by the C code. It then scans those objects to
find the objects they point to, and so on. The collector logically sets
a @dfn{mark bit} on each object it finds, so each object is traversed
only once.
When the collector can find no unmarked objects pointed to by marked
objects, it assumes that any objects that are still unmarked will never
be used by the program (since there is no path of dereferences from any
global or local variable that reaches them) and deallocates them.
In the above paragraphs, we did not specify how the garbage collector
finds the global and local variables; as usual, there are many different
approaches. Frequently, the programmer must maintain a list of pointers
to all global variables that refer to the heap, and another list
(adjusted upon entry to and exit from each function) of local variables,
for the collector's benefit.
The list of global variables is usually not too difficult to maintain,
since global variables are relatively rare. However, an explicitly
maintained list of local variables (in the author's personal experience)
is a nightmare to maintain. Thus, the BDW-GC uses a technique called
@dfn{conservative garbage collection}, to make the local variable list
unnecessary.
The trick to conservative collection is to treat the C stack as an
ordinary range of memory, and assume that @emph{every} word on the C
stack is a pointer into the heap. Thus, the collector marks all objects
whose addresses appear anywhere in the C stack, without knowing for sure
how that word is meant to be interpreted.
In addition to the stack, the BDW-GC will also scan static data
sections. This means that global variables are also scanned when looking
for live Scheme objects.
Obviously, such a system will occasionally retain objects that are
actually garbage, and should be freed. In practice, this is not a
problem, as the set of conservatively-scanned locations is fixed; the
Scheme stack is maintained apart from the C stack, and is scanned
precisely (as opposed to conservatively). The GC-managed heap is also
partitioned into parts that can contain pointers (such as vectors) and
parts that can't (such as bytevectors), limiting the potential for
confusing a raw integer with a pointer to a live object.
Interested readers should see the BDW-GC web page at
@uref{http://www.hboehm.info/gc/}, for more information on conservative
GC in general and the BDW-GC implementation in particular.
@node The SCM Type in Guile
@subsection The SCM Type in Guile
Guile classifies Scheme objects into two kinds: those that fit entirely
within an @code{SCM}, and those that require heap storage.
The former class are called @dfn{immediates}. The class of immediates
includes small integers, characters, boolean values, the empty list, the
mysterious end-of-file object, and some others.
The remaining types are called, not surprisingly, @dfn{non-immediates}.
They include pairs, procedures, strings, vectors, and all other data
types in Guile. For non-immediates, the @code{SCM} word contains a
pointer to data on the heap, with further information about the object
in question is stored in that data.
This section describes how the @code{SCM} type is actually represented
and used at the C level. Interested readers should see
@code{libguile/scm.h} for an exposition of how Guile stores type
information.
In fact, there are two basic C data types to represent objects in
Guile: @code{SCM} and @code{scm_t_bits}.
@menu
* Relationship Between SCM and scm_t_bits::
* Immediate Objects::
* Non-Immediate Objects::
* Allocating Heap Objects::
* Heap Object Type Information::
* Accessing Heap Object Fields::
@end menu
@node Relationship Between SCM and scm_t_bits
@subsubsection Relationship Between @code{SCM} and @code{scm_t_bits}
A variable of type @code{SCM} is guaranteed to hold a valid Scheme
object. A variable of type @code{scm_t_bits}, on the other hand, may
hold a representation of a @code{SCM} value as a C integral type, but
may also hold any C value, even if it does not correspond to a valid
Scheme object.
For a variable @var{x} of type @code{SCM}, the Scheme object's type
information is stored in a form that is not directly usable. To be able
to work on the type encoding of the scheme value, the @code{SCM}
variable has to be transformed into the corresponding representation as
a @code{scm_t_bits} variable @var{y} by using the @code{SCM_UNPACK}
macro. Once this has been done, the type of the scheme object @var{x}
can be derived from the content of the bits of the @code{scm_t_bits}
value @var{y}, in the way illustrated by the example earlier in this
chapter (@pxref{Cheaper Pairs}). Conversely, a valid bit encoding of a
Scheme value as a @code{scm_t_bits} variable can be transformed into the
corresponding @code{SCM} value using the @code{SCM_PACK} macro.
@node Immediate Objects
@subsubsection Immediate Objects
A Scheme object may either be an immediate, i.e.@: carrying all
necessary information by itself, or it may contain a reference to a
@dfn{heap object} which is, as the name implies, data on the heap.
Although in general it should be irrelevant for user code whether an
object is an immediate or not, within Guile's own code the distinction
is sometimes of importance. Thus, the following low level macro is
provided:
@deftypefn Macro int SCM_IMP (SCM @var{x})
A Scheme object is an immediate if it fulfills the @code{SCM_IMP}
predicate, otherwise it holds an encoded reference to a heap object. The
result of the predicate is delivered as a C style boolean value. User
code and code that extends Guile should normally not be required to use
this macro.
@end deftypefn
@noindent
Summary:
@itemize @bullet
@item
Given a Scheme object @var{x} of unknown type, check first
with @code{SCM_IMP (@var{x})} if it is an immediate object.
@item
If so, all of the type and value information can be determined from the
@code{scm_t_bits} value that is delivered by @code{SCM_UNPACK
(@var{x})}.
@end itemize
There are a number of special values in Scheme, most of them documented
elsewhere in this manual. It's not quite the right place to put them,
but for now, here's a list of the C names given to some of these values:
@deftypefn Macro SCM SCM_EOL
The Scheme empty list object, or ``End Of List'' object, usually written
in Scheme as @code{'()}.
@end deftypefn
@deftypefn Macro SCM SCM_EOF_VAL
The Scheme end-of-file value. It has no standard written
representation, for obvious reasons.
@end deftypefn
@deftypefn Macro SCM SCM_UNSPECIFIED
The value returned by some (but not all) expressions that the Scheme
standard says return an ``unspecified'' value.
This is sort of a weirdly literal way to take things, but the standard
read-eval-print loop prints nothing when the expression returns this
value, so it's not a bad idea to return this when you can't think of
anything else helpful.
@end deftypefn
@deftypefn Macro SCM SCM_UNDEFINED
The ``undefined'' value. Its most important property is that is not
equal to any valid Scheme value. This is put to various internal uses
by C code interacting with Guile.
For example, when you write a C function that is callable from Scheme
and which takes optional arguments, the interpreter passes
@code{SCM_UNDEFINED} for any arguments you did not receive.
We also use this to mark unbound variables.
@end deftypefn
@deftypefn Macro int SCM_UNBNDP (SCM @var{x})
Return true if @var{x} is @code{SCM_UNDEFINED}. Note that this is not a
check to see if @var{x} is @code{SCM_UNBOUND}. History will not be kind
to us.
@end deftypefn
@node Non-Immediate Objects
@subsubsection Non-Immediate Objects
A Scheme object of type @code{SCM} that does not fulfill the
@code{SCM_IMP} predicate holds an encoded reference to a heap object.
This reference can be decoded to a C pointer to a heap object using the
@code{SCM_UNPACK_POINTER} macro. The encoding of a pointer to a heap
object into a @code{SCM} value is done using the @code{SCM_PACK_POINTER}
macro.
@cindex cells, deprecated concept
Before Guile 2.0, Guile had a custom garbage collector that allocated
heap objects in units of 2-word @dfn{cells}. With the move to the
BDW-GC collector in Guile 2.0, Guile can allocate heap objects of any
size, and the concept of a cell is now obsolete. Still, we mention
it here as the name still appears in various low-level interfaces.
@deftypefn Macro {scm_t_bits *} SCM_UNPACK_POINTER (SCM @var{x})
@deftypefnx Macro {scm_t_cell *} SCM2PTR (SCM @var{x})
Extract and return the heap object pointer from a non-immediate
@code{SCM} object @var{x}. The name @code{SCM2PTR} is deprecated but
still common.
@end deftypefn
@deftypefn Macro SCM_PACK_POINTER (scm_t_bits * @var{x})
@deftypefnx Macro SCM PTR2SCM (scm_t_cell * @var{x})
Return a @code{SCM} value that encodes a reference to the heap object
pointer @var{x}. The name @code{PTR2SCM} is deprecated but still
common.
@end deftypefn
Note that it is also possible to transform a non-immediate @code{SCM}
value by using @code{SCM_UNPACK} into a @code{scm_t_bits} variable.
However, the result of @code{SCM_UNPACK} may not be used as a pointer to
a heap object: only @code{SCM_UNPACK_POINTER} is guaranteed to transform
a @code{SCM} object into a valid pointer to a heap object. Also, it is
not allowed to apply @code{SCM_PACK_POINTER} to anything that is not a
valid pointer to a heap object.
@noindent
Summary:
@itemize @bullet
@item
Only use @code{SCM_UNPACK_POINTER} on @code{SCM} values for which
@code{SCM_IMP} is false!
@item
Don't use @code{(scm_t_cell *) SCM_UNPACK (@var{x})}! Use
@code{SCM_UNPACK_POINTER (@var{x})} instead!
@item
Don't use @code{SCM_PACK_POINTER} for anything but a heap object pointer!
@end itemize
@node Allocating Heap Objects
@subsubsection Allocating Heap Objects
Heap objects are heap-allocated data pointed to by non-immediate
@code{SCM} value. The first word of the heap object should contain a
type code. The object may be any number of words in length, and is
generally scanned by the garbage collector for additional unless the
object was allocated using a ``pointerless'' allocation function.
You should generally not need these functions, unless you are
implementing a new data type, and thoroughly understand the code in
@code{<libguile/scm.h>}.
If you just want to allocate pairs, use @code{scm_cons}.
@deftypefn Function SCM scm_words (scm_t_bits word_0, uint32_t n_words)
Allocate a new heap object containing @var{n_words}, and initialize the
first slot to @var{word_0}, and return a non-immediate @code{SCM} value
encoding a pointer to the object. Typically @var{word_0} will contain
the type tag.
@end deftypefn
There are also deprecated but common variants of @code{scm_words} that
use the term ``cell'' to indicate 2-word objects.
@deftypefn Function SCM scm_cell (scm_t_bits word_0, scm_t_bits word_1)
Allocate a new 2-word heap object, initialize the two slots with
@var{word_0} and @var{word_1}, and return it. Just like calling
@code{scm_words (@var{word_0}, 2)}, then initializing the second slot to
@var{word_1}.
Note that @var{word_0} and @var{word_1} are of type @code{scm_t_bits}.
If you want to pass a @code{SCM} object, you need to use
@code{SCM_UNPACK}.
@end deftypefn
@deftypefn Function SCM scm_double_cell (scm_t_bits word_0, scm_t_bits word_1, scm_t_bits word_2, scm_t_bits word_3)
Like @code{scm_cell}, but allocates a 4-word heap object.
@end deftypefn
@node Heap Object Type Information
@subsubsection Heap Object Type Information
Heap objects contain a type tag and are followed by a number of
word-sized slots. The interpretation of the object contents depends on
the type of the object.
@deftypefn Macro scm_t_bits SCM_CELL_TYPE (SCM @var{x})
Extract the first word of the heap object pointed to by @var{x}. This
value holds the information about the cell type.
@end deftypefn
@deftypefn Macro void SCM_SET_CELL_TYPE (SCM @var{x}, scm_t_bits @var{t})
For a non-immediate Scheme object @var{x}, write the value @var{t} into
the first word of the heap object referenced by @var{x}. The value
@var{t} must hold a valid cell type.
@end deftypefn
@node Accessing Heap Object Fields
@subsubsection Accessing Heap Object Fields
For a non-immediate Scheme object @var{x}, the object type can be
determined by using the @code{SCM_CELL_TYPE} macro described in the
previous section. For each different type of heap object it is known
which fields hold tagged Scheme objects and which fields hold untagged
raw data. To access the different fields appropriately, the following
macros are provided.
@deftypefn Macro scm_t_bits SCM_CELL_WORD (SCM @var{x}, unsigned int @var{n})
@deftypefnx Macro scm_t_bits SCM_CELL_WORD_0 (@var{x})
@deftypefnx Macro scm_t_bits SCM_CELL_WORD_1 (@var{x})
@deftypefnx Macro scm_t_bits SCM_CELL_WORD_2 (@var{x})
@deftypefnx Macro scm_t_bits SCM_CELL_WORD_3 (@var{x})
Deliver the field @var{n} of the heap object referenced by the
non-immediate Scheme object @var{x} as raw untagged data. Only use this
macro for fields containing untagged data; don't use it for fields
containing tagged @code{SCM} objects.
@end deftypefn
@deftypefn Macro SCM SCM_CELL_OBJECT (SCM @var{x}, unsigned int @var{n})
@deftypefnx Macro SCM SCM_CELL_OBJECT_0 (SCM @var{x})
@deftypefnx Macro SCM SCM_CELL_OBJECT_1 (SCM @var{x})
@deftypefnx Macro SCM SCM_CELL_OBJECT_2 (SCM @var{x})
@deftypefnx Macro SCM SCM_CELL_OBJECT_3 (SCM @var{x})
Deliver the field @var{n} of the heap object referenced by the
non-immediate Scheme object @var{x} as a Scheme object. Only use this
macro for fields containing tagged @code{SCM} objects; don't use it for
fields containing untagged data.
@end deftypefn
@deftypefn Macro void SCM_SET_CELL_WORD (SCM @var{x}, unsigned int @var{n}, scm_t_bits @var{w})
@deftypefnx Macro void SCM_SET_CELL_WORD_0 (@var{x}, @var{w})
@deftypefnx Macro void SCM_SET_CELL_WORD_1 (@var{x}, @var{w})
@deftypefnx Macro void SCM_SET_CELL_WORD_2 (@var{x}, @var{w})
@deftypefnx Macro void SCM_SET_CELL_WORD_3 (@var{x}, @var{w})
Write the raw value @var{w} into field number @var{n} of the heap object
referenced by the non-immediate Scheme value @var{x}. Values that are
written into heap objects as raw values should only be read later using
the @code{SCM_CELL_WORD} macros.
@end deftypefn
@deftypefn Macro void SCM_SET_CELL_OBJECT (SCM @var{x}, unsigned int @var{n}, SCM @var{o})
@deftypefnx Macro void SCM_SET_CELL_OBJECT_0 (SCM @var{x}, SCM @var{o})
@deftypefnx Macro void SCM_SET_CELL_OBJECT_1 (SCM @var{x}, SCM @var{o})
@deftypefnx Macro void SCM_SET_CELL_OBJECT_2 (SCM @var{x}, SCM @var{o})
@deftypefnx Macro void SCM_SET_CELL_OBJECT_3 (SCM @var{x}, SCM @var{o})
Write the Scheme object @var{o} into field number @var{n} of the heap
object referenced by the non-immediate Scheme value @var{x}. Values
that are written into heap objects as objects should only be read using
the @code{SCM_CELL_OBJECT} macros.
@end deftypefn
@noindent
Summary:
@itemize @bullet
@item
For a non-immediate Scheme object @var{x} of unknown type, get the type
information by using @code{SCM_CELL_TYPE (@var{x})}.
@item
As soon as the type information is available, only use the appropriate
access methods to read and write data to the different heap object
fields.
@item
Note that field 0 stores the cell type information. Generally speaking,
other data associated with a heap object is stored starting from field
1.
@end itemize
@c Local Variables:
@c TeX-master: "guile.texi"
@c End:
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