3 Examples
Bill HomerThis document incorporates the change proposed in X3J11.1/93-040 to Draft 1 of the Final Report, WG14/N274 (also known as X3J11.1/93-026 and X3J11/93-020). The change consists of a revision of the section entitled ``Aliasing of unmodified objects'' (formerly numbered 1.6 in the Rationale), and small changes to section 2 (in the subsection entitled ``Semantics'') and section 3 (for the examples in Figure 7 and Figure 8). There are also some purely editorial changes, which include reordering some of the sections. In particular, three sections that discuss design decisions were moved into an Appendix.
Cray Research, Inc.
655F Lone Oak Drive
Eagan, MN 55121
homer@cray.com or uunet!cray!homerApril 25, 1994
For many compiler optimizations, ranging from simply holding a value in a register to the parallel execution of a loop, it is necessary to determine whether two distinct lvalues designate distinct objects. If the objects are not distinct, the lvalues are said to be aliases. It is aliasing through pointers that presents the greatest difficulty, because there is often not enough information available within a single function, or even within a single compilation unit, to determine whether two pointers can point to the same object. Even when enough information is available, this analysis can require substantial time and space. For example, it could require an analysis of a whole program to determine the possible values of a pointer that is a function parameter.
Consider how potential aliasing enters into implementations in C of two
Standard C library functions. There are no restrictions on the use of
memmove, and the implementation shown below follows the model
described in the Standard by copying through a temporary array.
(Other approaches are possible, but this one is straightforward and
strictly conforming.) Since memcpy cannot be used for
copying between overlapping arrays, its implementation can be a direct copy.
void *memmove(void *s1, const void *s2, size_t n) {
char * t1 = s1;
const char * t2 = s2;
char * t3 = malloc(n);
size_t i;
for(i=0; i<n; i++) t3[i] = t2[i];
for(i=0; i<n; i++) t1[i] = t3[i];
free(t3);
return s1;
}
void *memcpy(void *s1, const void *s2, size_t n);
char * t1 = s1;
const char * t2 = s2;
while(n-- > 0) *t1++ = *t2++;
return s1;
}
Note that the restriction on memcpy is expressed only in its
Description in the Standard, and cannot be expressed directly in
its implementation in C. While this does allow the source-level
optimization of eliminating the temporary used in memmove,
it does not provide for compiler optimization of the resulting single
loop. In many architectures, it is faster to copy bytes in blocks,
rather than one at a time. The implementation of memmove
uses malloc to obtain the temporary array, and this guarantees
that the temporary is disjoint from the source and target
arrays. From this a compiler can deduce that block copies may
safely be used for both loops. The implementation of
memcpy, on the other hand, provides the compiler no basis
for ruling out the possibility that, for example, s1 and
s2 point to successive bytes. Therefore unconditional
use of block copies does not appear to be safe, and the code generated for
the single loop in memcpy may not be as fast as the code for
each loop in memmove.
memcpy prohibits
copying between ``overlapping objects.'' A recent interpretation
from X3J11 in response to RFI #42, X3J11 92-001, clarified what is meant by
``objects'' in this context. In the following quotation from that
interpretation, the section numbers prefixed with ## refer to the
American National Standard X3.159-1989. (The number of the
corresponding section in ISO/IEC 9899:1990(E) is three greater.)
void f1(void) {
extern char a[2][N];
memcpy(a[1], a[0], N);
}
N bytes in length (i.e. treated as an
array of N elements of character type).
(A) So, no, the objects are not ``the largest objects into which the arguments can be construed as pointing''.
(B) In Figure 3, the call to memcpy has defined
behavior.
(C) The behavior is defined because the pointers point into different (non-overlapping) objects.
void f2(void) {
extern char b[2*N];
memcpy(b+N, b, N);
}
(A) So, yes, for memcpy, a contiguous sequence of elements
within an array can be regarded as an object in its own right.
(B) The objects are not the smallest contiguous sequence of bytes that
can be construed, they are exactly the regions of data storage starting
at the pointers and of N bytes in length.
(C) Yes, the non-overlapping halves of array b can be
regarded as objects in their own rights.
(D) Behavior is defined.
...
Length is determined by ``various methods.'' For strings in which all
elements are accessed, length is inferred by null byte
termination. For mbstowcs, wcstombs,
strftime, vsprintf, sscanf,
sprintf, and all other similar functions, it was the intent
of the standard that the rules in ##4.11.1 be applicable by extension
(i.e., the objects and lengths are similarly dynamically determined).
If an aliasing restriction like the one for memcpy could
be expressed in a function definition, then it would be available
to a compiler to facilitate effective pointer alias
analysis. The preceding discussion suggests the form
that the restriction should take.
It should be possible to specify in the declaration of a pointer that it
provides ``exclusive initial access'' to the object to which it points, as
though the pointer were initialized with a call to
malloc. Because it is the unqualified versions
of function parameter types that are compared for type compatibility,
it is convenient to specify the restriction with a type qualifier,
spelled restrict, on the pointer type. The
following prototype for memcpy thus both expresses the
desired restriction and is compatible with the current prototype.
void *memcpy(void * restrict s1, const void * restrict s2, size_t n);
Given this general concept of restricted pointers, there remain a number of design choices. Three of these are discussed in detail in the an appendix. Most such choices may be characterized as a choice between simplicity and expressive power. To some, it seems better to simplify the analysis of restricted pointers by confining their use to the simplest paradigms. For example, restricted pointers would be quite useful even if they could be declared only as function parameters and if the restricted pointers themselves could not be modified. This would support what is clearly the most important paradigm, an alias-free function call interface in C, analogous to that in Fortran. To others, it seems better to support the expression of aliasing restrictions in as many paradigms as feasible. This would be helpful in converting existing programs to use restricted pointers, and would allow more freedom of style in new programs.
The definition given in section 2 favors the second view. It allows restricted pointers to be modifiable, to be members of structures and elements of arrays, and to be ``strongly scoped,'' in the sense that a restricted pointer declared in a nested block makes a non-aliasing assertion only within that block.
What follows are proposed additions to the document International Standard Programming Languages --- C (ISO/IEC 9899:1990(E)). The relevant sections are noted in brackets in each header, with the corresponding section in American National Standard X3.159-1989 noted in parentheses.
Types other than pointer types derived from object or incomplete types shall not be restrict-qualified.
Add the following text after line 22.
Let D be a declaration of an ordinary identifier that provides a
means of designating an object P as a restrict-qualified
pointer.
If D appears inside a block and does not have storage-class
extern, let B denote the block.
If D appears in the list of parameter declarations of a
function definition, let B denote the associated
block. Otherwise, let B denote the block of
main (or the block of whatever function is called at
program startup, in a freestanding environment).
In what follows, a pointer expression E is said to be
based on object P if (at some sequence point in the
execution of B prior to the evaluation of E)
modifying P to point to a copy of the array object into
which it formerly pointed would change the value of E.
(In other words, E depends on the value of P
itself rather than on the value of an object referenced indirectly
through P. For example, if identifier p
has type (int ** restrict), then the pointer expressions
p and p+1 are based on the restricted pointer
object designated by p, but the pointer expressions
*p and p[1] are not.)
During each execution of B, let O be the
array object that is determined dynamically by all references through
pointer expressions based on P. All references
to values of O shall be through pointer expressions based
on P. Furthermore, if P is assigned
the value of a pointer expression E that is based on
another restricted pointer object P2, associated with block
B2, then either the execution of B2 shall begin
before the execution of B, or the execution of
B2 shall end prior to the assignment.
If this requirement is not met, then the behavior is undefined.
Here an execution of B means that portion of the
execution of the program during which storage is guaranteed to be reserved
for an instance of an object that is associated with B and has
automatic storage duration. A reference to a value means either
an access to or a modification of the value.
During an execution of B, attention is confined to those
references that are actually evaluated (this excludes references that
appear in unevaluated expressions, and also excludes references that
are ``available,'' in the sense of employing visible identifiers,
but do not actually appear in the text of B).
A translator is free to ignore any or all aliasing implications of uses of
restrict.
a, b,
and c.
Notice how the single block of allocated storage is ``subdivided''
into two unique arrays in init.
float * restrict a, * restrict b;
float c[100];
int init(int n) {
float * t = malloc(2*n*sizeof(float));
a = t; /* a refers to 1st half. */
b = t + n; /* b refers to 2nd half. */
}
Restricted pointers are also very useful as pointer parameters
of a function. In the function f3 in
Figure 7, it is possible for a compiler to infer that
there is no aliasing of modified objects, and so to optimize the loop
aggressively.
Upon entry to f3, the restricted pointer a
must provide exclusive access to its associated array.
In particular, within f3 neither b nor
c may point into the array associated with
a, because neither is assigned a pointer value based
on a.
For b, this is evident from the const-qualifier in its
declaration, but for c, an inspection of the body of f3
is required.
float x[100];
float *c;
void f3(int n, float * restrict a, float * const b) {
int i;
for ( i=0; i<n; i++ )
a[i] = b[i] + c[i];
}
void g3(void) {
float d[100], e[100];
c = x; f3(100, d, e); /* Behavior defined. */
f3( 50, d, d+50); /* Behavior defined. */
f3( 99, d+1, d); /* Behavior undefined. */
c = d; f3( 99, d+1, e); /* Behavior undefined. */
f3( 99, e, d+1); /* Behavior defined. */
}
g3 result in aliasing that is
inconsistent with the restrict qualifier, and their
behavior is undefined. Note that it is permitted for
c to point into the array associated with b.
Note also that, for these purposes, the ``array'' associated
with a particular pointer means only that portion of an array object
which is actually referenced through that pointer.
A block scope restricted pointer makes an aliasing assertion that is limited to its block. This seems more natural than allowing the assertion to have function scope. It allows local assertions that apply only to key loops, for example. It also allows equivalent assertions to be made when inlining a function by converting it into a macro. In Figure 8, the original restricted pointer parameter is represented by a block scope restricted pointer.
float x[100];
float *c;
#define f3(N, A, B) \
{ int n = (N); \
float * restrict a = (A); \
float * const b = (B); \
int i; \
for ( i=0; i<n; i++ ) \
a[i] = b[i] + c[i]; \
}
A restricted pointer member of a structure makes an aliasing
assertion, and the scope of that assertion is the scope of the
ordinary identifier used to access the structure.
Thus although the structure type is declared at file scope
in Figure 9, the assertions made by the declarations of the parameters
of f4 have block (of the function) scope.
struct t { /* Restricted pointers assert that */
int n; /* members point to disjoint storage. */
float * restrict p;
float * restrict q;
};
void f4(struct t r, struct t s) {
/* r.p, r.q, s.p, s.q should all point to */
/* disjoint storage during each execution of f4. */
/* ... */
}
A restrict qualifier in a type definition makes an aliasing
assertion when the typedef name is used in the declaration of
an ordinary identifier that provides access to an object.
As with members of structures, it is the scope of the latter
identifier, not the scope of the typedef name, that determines the
scope of the aliasing assertion.
#include <stdlib.h>
#include <string.h>
struct t { int * q; int i; } a[2] = { /* ... */ };
void f5(struct t * restrict p, int c)
{
struct t * q;
int n;
if(c) {
struct t * r;
r = malloc(2*sizeof(*p));
memcpy(r, p, 2*sizeof(*p));
p = r;
}
q = p;
n = (int)p;
/* - - - - - - - - - - - - - - - - - - - - - - -
Pointer expressions Pointer expressions
based on p not based on p
p p->q
p+1 p[1].q
&p[1] &p
&p[1].i
q q->p
++q
(char *)p (char *)(p->i)
(struct t *)n ((struct t *)n)->q
- - - - - - - - - - - - - - - - - - - - - - - - */
}
main() {
f5(a, 0);
f5(a, 1);
}
p
is potentially adjusted to point into a copy of its original array
of two structures. By definition, a subsequent pointer
expression is said to be based on pif and only if
its value is changed by this adjustment. In the comment,
the values of the pointer expressions in the first column are changed
by this adjustment, and so those expressions are based on
p. The values of the pointer expressions in
the second column are not changed by the adjustment, and so those
expressions are not based on p. This can be
verified by adding appropriate print statements for the expressions,
and comparing the values produced bz the two calls of f5
in main.
It is important to note that the definition of ``based on'' applies
to expressions that rely on implementation-defined behavior.
This is illustrated in the example, which assumes that the casts
(int) followed by (struct t *)
give the original value.
int * restrict p1, * restrict p2;
void f6(int * restrict q1, * restrict q2)
{
p1 = p2; /* Behavior undefined. */
p1 = q1; /* Behavior undefined. */
q1 = q2; /* Behavior undefined. */
{
int * restrict r1, * restrict r2;
...
r1 = r2; /* Behavior undefined. */
q1 = r1; /* Behavior undefined. */
p1 = r1; /* Behavior undefined. */
...
}
}
Conversely, an older restricted pointer may be assigned a value based on a newer restricted pointer only after execution of the block associated with the newer restricted pointer has ended. This allows, for example, a function to return the value of a restricted pointer that is local to the function, and the return value then to be assigned to another restricted pointer.
The behavior of a program is undefined if it contains an assignment between two restricted pointers that does not fall into one of these two categories. Some examples are given in Figure 11.
void f7(int n, float * restrict r, float * restrict s) {
float * p = r, * q = s;
while(n--- > 0)
*p++ = *q++;
}
r
and s were used directly.
More complicated ways of combining restricted and unrestricted pointers are unlikely to be effective because they are too difficult for a compiler to analyze. As always, a programmer concerned about performance must adapt his style to the capabilities of available compilers. A conservative approach would be to avoid using both restricted and unrestricted pointers in the same function.
restrict qualifier behaves in the same way as
const and volatile. In particular,
note that it is not a constraint violation for a function return type
or the type-name in a cast to be qualified, but the qualifier
has no effect because function call and cast expressions are not
lvalues. Thus the presence of the restrict qualifier
in the declaration of f8 in Figure 13 makes no assertion
about aliasing in functions that call f8. Similarly,
the two casts make no assertion about aliasing of the references through
the pointers p and r.
float * restrict f8(void) /* No assertion about aliasing. */
{
extern int i, *p, *q, *r;
r = (int * restrict)q; /* No assertion about aliasing. */
for(i=0; i<100; i++)
*(int * restrict)p++ = r[i]; /* No assertion */
/* about aliasing. */
return p;
}
int restrict x; /* Constraint violation. */
int restrict *p; /* Constraint violation. */
float (* restrict f9)(void); /* Constraint violation. */
This convention is consistent with the specification noted above, that ``except for bit-fields, objects are composed of contiguous sequences of one or more bytes.'' It is also consistent with the notions of objects and argument association in Fortran 77. Thus, in environments that support mixed-language programming, restricted pointer parameters can be used in C prototypes for functions defined in Fortran, and also in definitions of C functions that are called from Fortran.
Note that an implementation is free to support restricted pointers to non-contiguous sets of bytes as an extension. Such support is not mandated, however, because the need for it does not seem compelling, and it could inhibit optimizations for architectures that cannot load and store single bytes or that have software-managed caches. Note that such an extension might be useful in implementation-defined calling conventions between C and Fortran 90, because Fortran 90 permits arguments that are non-contiguous sets of array elements.
a provides exclusive access to the array
into which it points is sufficient to allow the the loop in f10
to be vectorized or executed in parallel.
Knowing that b and c are not used to access
overlapping portions of a single array allows no additional optimizations,
and so, in principle, there is no need to restrict-qualify b
and c.
void f10(int n, float * restrict a, float *b, float *c) {
int i;
for ( i=0; i<n; i++ )
a[i] = b[i] + c[i];
}
f10 and still make calls of the form f10(x, y, y).
This would be analogous to the aliasing semantics of Fortran dummy
arguments.
The simplest way of doing this (proposed in Draft 1 of this report) is to allow aliasing through two restrict-qualified pointers provided the referenced objects are not modified. Unfortunately, if those objects are themselves pointers (i.e., there are two levels of indirection), this aliasing can inhibit optimization, even if the secondary pointers are also restrict-qualified and used to modify the objects to which they, in turn, refer. See X3J11.1/93-040 for examples.
In the final analysis, it did not seem possible to permit aliasing of unmodified objects, have effective assertions for multiple levels of indirection, and still keep the semantics relatively simple.
It was decided to drop the special treatment of unmodified objects,
largely because the practical effect is quite small.
First, as noted, the extra qualifiers are not needed in principle,
though they may be useful for specific compilers. Second, in these
cases, it is also useful, and might be sufficient, to const-qualify
b and c, because this gives a compiler
enough aliasing information in the parameter declarations alone to
optimize f10 (see the discussion of Figure 7). .
Finally, even if a specific compiler requires all three restrict qualifiers
to give the desired optimization, it is most unlikely that their
use would give unexpected results for a call such as f10(x,y,y),
even though its behavior is technically undefined. Such
use may therefore be justified in particular cases, as are other instances
of undefined or implementation-defined behavior, such as assigning
to one member of a union and then referring to another.
restrict and const qualifiers to make
assertions that could, in principle, enable effective optimizations.
First note that restricted pointers cannot, in general, be used
for link pointers in portions of the program that modify the lists.
Thus in Figure 17, the assignments to next and head
would give undefined behavior if they were restrict qualified.
struct t { struct t * next; float x; } * head, * item;
void modify_links()
/* Add a list item at the beginning. */
item -> next = head; head = item;
/* Add a list item as the second item. */
item -> next = head -> next; head -> next = item;
/* Delete second list item. */
head -> next = head -> next -> next;
/* Delete first list item. */
head = head -> next;
}
restrict and const qualifiers.
Note that, as in Figure 18, this requires a second structure type,
and a cast from the original to a new type. The comments
describe an optimization that allows parallel execution of the second
loop. Alternatively, the second loop could be fused with the
first, so that both operations are performed during a single walk.
The latter optimization is likely to be beneficial on any architecture.
struct t { struct t * next; float x; };
struct rt { struct rt * const restrict next; float x; };
void modify_values(struct t * head) {
/* Assert that links will not change. */
struct rt * const restrict rhead = (struct rt *)head;
/* Need modifiable unrestricted pointer to walk list. */
struct rt * this = rhead;
/* Can build a cache of link addresses. */
for(this=rhead; this; this = this->next) {
this -> x += 1;
}
/* Can use cached addresses to execute in parallel. */
for(this=rhead; this; this = this->next) {
this -> x *= 2;
}
}
rhead
as a parameter, then there should be a guarantee that the cached links are
not changed during the execution of the called function. The
problem is that there is nothing to prevent the function from modifying
a link via
*(struct rt * restrict *)&(rhead->next) = ...(assuming for the sake of argument that the structures on the list were dynamically allocated as an array of structures). To make the aliasing assertions effective would require forbidding this sort of modification. This might be done be extending the full semantics of the
const qualifier to include objects designated as
const-qualified by a restricted pointer, as well as objects that are
const-qualified by their definitions. (This extension is not part
of the current proposal.)
f11 are
compatible.
void f8(int n, float a[][100], float b[][100]); void f8(int n, float (*a)[100], float (*b)[100]);
a and b are pointers used to access
their respective two-dimensional arrays, but the first form more clearly
conveys the rank of the arrays. It is therefore unfortunate that
only the second form allows the pointers to be qualified, e.g.,
by restrict.
This suggests an extension of the syntax to allow one or more type qualifiers to appear within the ``array of'' type derivation for a function parameter declared to have array type. The declaration is then adjusted to the analogously qualified pointer type.
void f11(int n, float a[restrict][100], float b[restrict][100])
{
int i, j;
for(i=0; i<n; i++)
for(j=0; j<100; j++)
a[i][j] = b[i][j];
}
void g11(int m, int k, float p[][100]) {
f9(m, p, p+k); /* Defined if and only if m <= k. */
}
f12
in g12 is defined, but the second call is potentially
undefined (depending upon which elements of the arrays f12
actually references).
void f12(int m, int n, float a[restrict m][n],
float b[restrict m][n]);
void g12(int n, float *p[n]) {
f20(10, n, p, p+10); /* Defined behavior. */
f20(20, n, p, p+10); /* Potential undefined behavior. */
}
For consistency, the extension would apply to all type qualifiers. The following changes to the Standard would be required for this extension.
Allow an optional type-qualifier-list in the third form of direct-declarator:
direct-declarator
[ type-qualifier-list (opt)
constant-expression (opt) ]
Add a constraint:
Type qualifiers shall appear preceding or in place of a size expression only in a declaration of a function parameter of array type, and then only in the outermost array type derivation.
Modify lines 23-24 to read:
... A declaration of a parameter as ``array of type'' shall be adjusted to ``qualified pointer to type'' (where the type qualifiers are those specified within the square brackets of the array type derivation), ...
Tom MacDonald provided the following overview of the differences
between restrict and the previously proposed
noalias.
The X3J11 committee attempted to solve the aliasing problem in C by
introducing a new type qualifier noalias.
That effort failed because of technical problems with the proposed
semantics of noalias.
This restricted pointer proposal is different in many ways.