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15 The Often Misunderstood GEP Instruction
19 <li><a href="#intro">Introduction</a></li>
20 <li><a href="#addresses">Address Computation</a>
22 <li><a href="#extra_index">Why is the extra 0 index required?</a></li>
23 <li><a href="#deref">What is dereferenced by GEP?</a></li>
24 <li><a href="#firstptr">Why can you index through the first pointer but not
25 subsequent ones?</a></li>
26 <li><a href="#lead0">Why don't GEP x,0,0,1 and GEP x,1 alias? </a></li>
27 <li><a href="#trail0">Why do GEP x,1,0,0 and GEP x,1 alias? </a></li>
28 <li><a href="#vectors">Can GEP index into vector elements?</a>
29 <li><a href="#addrspace">What effect do address spaces have on GEPs?</a>
30 <li><a href="#int">How is GEP different from ptrtoint, arithmetic, and inttoptr?</a></li>
31 <li><a href="#be">I'm writing a backend for a target which needs custom lowering for GEP. How do I do this?</a>
32 <li><a href="#vla">How does VLA addressing work with GEPs?</a>
34 <li><a href="#rules">Rules</a>
36 <li><a href="#bounds">What happens if an array index is out of bounds?</a>
37 <li><a href="#negative">Can array indices be negative?</a>
38 <li><a href="#compare">Can I compare two values computed with GEPs?</a>
39 <li><a href="#types">Can I do GEP with a different pointer type than the type of the underlying object?</a>
40 <li><a href="#null">Can I cast an object's address to integer and add it to null?</a>
41 <li><a href="#ptrdiff">Can I compute the distance between two objects, and add that value to one address to compute the other address?</a>
42 <li><a href="#tbaa">Can I do type-based alias analysis on LLVM IR?</a>
43 <li><a href="#overflow">What happens if a GEP computation overflows?</a>
44 <li><a href="#check">How can I tell if my front-end is following the rules?</a>
46 <li><a href="#rationale">Rationale</a>
48 <li><a href="#goals">Why is GEP designed this way?</a></li>
49 <li><a href="#i32">Why do struct member indices always use i32?</a></li>
50 <li><a href="#uglygep">What's an uglygep?</a>
52 <li><a href="#summary">Summary</a></li>
55 <div class="doc_author">
56 <p>Written by: <a href="mailto:rspencer@reidspencer.com">Reid Spencer</a>.</p>
60 <!-- *********************************************************************** -->
61 <h2><a name="intro">Introduction</a></h2>
62 <!-- *********************************************************************** -->
65 <p>This document seeks to dispel the mystery and confusion surrounding LLVM's
66 <a href="LangRef.html#i_getelementptr">GetElementPtr</a> (GEP) instruction.
67 Questions about the wily GEP instruction are
68 probably the most frequently occurring questions once a developer gets down to
69 coding with LLVM. Here we lay out the sources of confusion and show that the
70 GEP instruction is really quite simple.
74 <!-- *********************************************************************** -->
75 <h2><a name="addresses">Address Computation</a></h2>
76 <!-- *********************************************************************** -->
78 <p>When people are first confronted with the GEP instruction, they tend to
79 relate it to known concepts from other programming paradigms, most notably C
80 array indexing and field selection. GEP closely resembles C array indexing
81 and field selection, however it's is a little different and this leads to
82 the following questions.</p>
84 <!-- *********************************************************************** -->
86 <a name="firstptr">What is the first index of the GEP instruction?</a>
89 <p>Quick answer: The index stepping through the first operand.</p>
90 <p>The confusion with the first index usually arises from thinking about
91 the GetElementPtr instruction as if it was a C index operator. They aren't the
92 same. For example, when we write, in "C":</p>
94 <div class="doc_code">
102 <p>it is natural to think that there is only one index, the selection of the
103 field <tt>F</tt>. However, in this example, <tt>Foo</tt> is a pointer. That
104 pointer must be indexed explicitly in LLVM. C, on the other hand, indices
105 through it transparently. To arrive at the same address location as the C
106 code, you would provide the GEP instruction with two index operands. The
107 first operand indexes through the pointer; the second operand indexes the
108 field <tt>F</tt> of the structure, just as if you wrote:</p>
110 <div class="doc_code">
116 <p>Sometimes this question gets rephrased as:</p>
117 <blockquote><p><i>Why is it okay to index through the first pointer, but
118 subsequent pointers won't be dereferenced?</i></p></blockquote>
119 <p>The answer is simply because memory does not have to be accessed to
120 perform the computation. The first operand to the GEP instruction must be a
121 value of a pointer type. The value of the pointer is provided directly to
122 the GEP instruction as an operand without any need for accessing memory. It
123 must, therefore be indexed and requires an index operand. Consider this
126 <div class="doc_code">
128 struct munger_struct {
132 void munge(struct munger_struct *P) {
133 P[0].f1 = P[1].f1 + P[2].f2;
136 munger_struct Array[3];
142 <p>In this "C" example, the front end compiler (llvm-gcc) will generate three
143 GEP instructions for the three indices through "P" in the assignment
144 statement. The function argument <tt>P</tt> will be the first operand of each
145 of these GEP instructions. The second operand indexes through that pointer.
146 The third operand will be the field offset into the
147 <tt>struct munger_struct</tt> type, for either the <tt>f1</tt> or
148 <tt>f2</tt> field. So, in LLVM assembly the <tt>munge</tt> function looks
151 <div class="doc_code">
153 void %munge(%struct.munger_struct* %P) {
155 %tmp = getelementptr %struct.munger_struct* %P, i32 1, i32 0
156 %tmp = load i32* %tmp
157 %tmp6 = getelementptr %struct.munger_struct* %P, i32 2, i32 1
158 %tmp7 = load i32* %tmp6
159 %tmp8 = add i32 %tmp7, %tmp
160 %tmp9 = getelementptr %struct.munger_struct* %P, i32 0, i32 0
161 store i32 %tmp8, i32* %tmp9
167 <p>In each case the first operand is the pointer through which the GEP
168 instruction starts. The same is true whether the first operand is an
169 argument, allocated memory, or a global variable. </p>
170 <p>To make this clear, let's consider a more obtuse example:</p>
172 <div class="doc_code">
174 %MyVar = uninitialized global i32
176 %idx1 = getelementptr i32* %MyVar, i64 0
177 %idx2 = getelementptr i32* %MyVar, i64 1
178 %idx3 = getelementptr i32* %MyVar, i64 2
182 <p>These GEP instructions are simply making address computations from the
183 base address of <tt>MyVar</tt>. They compute, as follows (using C syntax):
186 <div class="doc_code">
188 idx1 = (char*) &MyVar + 0
189 idx2 = (char*) &MyVar + 4
190 idx3 = (char*) &MyVar + 8
194 <p>Since the type <tt>i32</tt> is known to be four bytes long, the indices
195 0, 1 and 2 translate into memory offsets of 0, 4, and 8, respectively. No
196 memory is accessed to make these computations because the address of
197 <tt>%MyVar</tt> is passed directly to the GEP instructions.</p>
198 <p>The obtuse part of this example is in the cases of <tt>%idx2</tt> and
199 <tt>%idx3</tt>. They result in the computation of addresses that point to
200 memory past the end of the <tt>%MyVar</tt> global, which is only one
201 <tt>i32</tt> long, not three <tt>i32</tt>s long. While this is legal in LLVM,
202 it is inadvisable because any load or store with the pointer that results
203 from these GEP instructions would produce undefined results.</p>
206 <!-- *********************************************************************** -->
208 <a name="extra_index">Why is the extra 0 index required?</a>
210 <!-- *********************************************************************** -->
212 <p>Quick answer: there are no superfluous indices.</p>
213 <p>This question arises most often when the GEP instruction is applied to a
214 global variable which is always a pointer type. For example, consider
217 <div class="doc_code">
219 %MyStruct = uninitialized global { float*, i32 }
221 %idx = getelementptr { float*, i32 }* %MyStruct, i64 0, i32 1
225 <p>The GEP above yields an <tt>i32*</tt> by indexing the <tt>i32</tt> typed
226 field of the structure <tt>%MyStruct</tt>. When people first look at it, they
227 wonder why the <tt>i64 0</tt> index is needed. However, a closer inspection
228 of how globals and GEPs work reveals the need. Becoming aware of the following
229 facts will dispel the confusion:</p>
231 <li>The type of <tt>%MyStruct</tt> is <i>not</i> <tt>{ float*, i32 }</tt>
232 but rather <tt>{ float*, i32 }*</tt>. That is, <tt>%MyStruct</tt> is a
233 pointer to a structure containing a pointer to a <tt>float</tt> and an
235 <li>Point #1 is evidenced by noticing the type of the first operand of
236 the GEP instruction (<tt>%MyStruct</tt>) which is
237 <tt>{ float*, i32 }*</tt>.</li>
238 <li>The first index, <tt>i64 0</tt> is required to step over the global
239 variable <tt>%MyStruct</tt>. Since the first argument to the GEP
240 instruction must always be a value of pointer type, the first index
241 steps through that pointer. A value of 0 means 0 elements offset from that
243 <li>The second index, <tt>i32 1</tt> selects the second field of the
244 structure (the <tt>i32</tt>). </li>
248 <!-- *********************************************************************** -->
250 <a name="deref">What is dereferenced by GEP?</a>
253 <p>Quick answer: nothing.</p>
254 <p>The GetElementPtr instruction dereferences nothing. That is, it doesn't
255 access memory in any way. That's what the Load and Store instructions are for.
256 GEP is only involved in the computation of addresses. For example, consider
259 <div class="doc_code">
261 %MyVar = uninitialized global { [40 x i32 ]* }
263 %idx = getelementptr { [40 x i32]* }* %MyVar, i64 0, i32 0, i64 0, i64 17
267 <p>In this example, we have a global variable, <tt>%MyVar</tt> that is a
268 pointer to a structure containing a pointer to an array of 40 ints. The
269 GEP instruction seems to be accessing the 18th integer of the structure's
270 array of ints. However, this is actually an illegal GEP instruction. It
271 won't compile. The reason is that the pointer in the structure <i>must</i>
272 be dereferenced in order to index into the array of 40 ints. Since the
273 GEP instruction never accesses memory, it is illegal.</p>
274 <p>In order to access the 18th integer in the array, you would need to do the
277 <div class="doc_code">
279 %idx = getelementptr { [40 x i32]* }* %, i64 0, i32 0
280 %arr = load [40 x i32]** %idx
281 %idx = getelementptr [40 x i32]* %arr, i64 0, i64 17
285 <p>In this case, we have to load the pointer in the structure with a load
286 instruction before we can index into the array. If the example was changed
289 <div class="doc_code">
291 %MyVar = uninitialized global { [40 x i32 ] }
293 %idx = getelementptr { [40 x i32] }*, i64 0, i32 0, i64 17
297 <p>then everything works fine. In this case, the structure does not contain a
298 pointer and the GEP instruction can index through the global variable,
299 into the first field of the structure and access the 18th <tt>i32</tt> in the
303 <!-- *********************************************************************** -->
305 <a name="lead0">Why don't GEP x,0,0,1 and GEP x,1 alias?</a>
308 <p>Quick Answer: They compute different address locations.</p>
309 <p>If you look at the first indices in these GEP
310 instructions you find that they are different (0 and 1), therefore the address
311 computation diverges with that index. Consider this example:</p>
313 <div class="doc_code">
315 %MyVar = global { [10 x i32 ] }
316 %idx1 = getelementptr { [10 x i32 ] }* %MyVar, i64 0, i32 0, i64 1
317 %idx2 = getelementptr { [10 x i32 ] }* %MyVar, i64 1
321 <p>In this example, <tt>idx1</tt> computes the address of the second integer
322 in the array that is in the structure in <tt>%MyVar</tt>, that is
323 <tt>MyVar+4</tt>. The type of <tt>idx1</tt> is <tt>i32*</tt>. However,
324 <tt>idx2</tt> computes the address of <i>the next</i> structure after
325 <tt>%MyVar</tt>. The type of <tt>idx2</tt> is <tt>{ [10 x i32] }*</tt> and its
326 value is equivalent to <tt>MyVar + 40</tt> because it indexes past the ten
327 4-byte integers in <tt>MyVar</tt>. Obviously, in such a situation, the
328 pointers don't alias.</p>
332 <!-- *********************************************************************** -->
334 <a name="trail0">Why do GEP x,1,0,0 and GEP x,1 alias?</a>
337 <p>Quick Answer: They compute the same address location.</p>
338 <p>These two GEP instructions will compute the same address because indexing
339 through the 0th element does not change the address. However, it does change
340 the type. Consider this example:</p>
342 <div class="doc_code">
344 %MyVar = global { [10 x i32 ] }
345 %idx1 = getelementptr { [10 x i32 ] }* %MyVar, i64 1, i32 0, i64 0
346 %idx2 = getelementptr { [10 x i32 ] }* %MyVar, i64 1
350 <p>In this example, the value of <tt>%idx1</tt> is <tt>%MyVar+40</tt> and
351 its type is <tt>i32*</tt>. The value of <tt>%idx2</tt> is also
352 <tt>MyVar+40</tt> but its type is <tt>{ [10 x i32] }*</tt>.</p>
355 <!-- *********************************************************************** -->
358 <a name="vectors">Can GEP index into vector elements?</a>
361 <p>This hasn't always been forcefully disallowed, though it's not recommended.
362 It leads to awkward special cases in the optimizers, and fundamental
363 inconsistency in the IR. In the future, it will probably be outright
368 <!-- *********************************************************************** -->
371 <a name="addrspace">What effect do address spaces have on GEPs?</a>
374 <p>None, except that the address space qualifier on the first operand pointer
375 type always matches the address space qualifier on the result type.</p>
379 <!-- *********************************************************************** -->
383 How is GEP different from ptrtoint, arithmetic, and inttoptr?
387 <p>It's very similar; there are only subtle differences.</p>
389 <p>With ptrtoint, you have to pick an integer type. One approach is to pick i64;
390 this is safe on everything LLVM supports (LLVM internally assumes pointers
391 are never wider than 64 bits in many places), and the optimizer will actually
392 narrow the i64 arithmetic down to the actual pointer size on targets which
393 don't support 64-bit arithmetic in most cases. However, there are some cases
394 where it doesn't do this. With GEP you can avoid this problem.
396 <p>Also, GEP carries additional pointer aliasing rules. It's invalid to take a
397 GEP from one object, address into a different separately allocated
398 object, and dereference it. IR producers (front-ends) must follow this rule,
399 and consumers (optimizers, specifically alias analysis) benefit from being
400 able to rely on it. See the <a href="#rules">Rules</a> section for more
403 <p>And, GEP is more concise in common cases.</p>
405 <p>However, for the underlying integer computation implied, there
406 is no difference.</p>
410 <!-- *********************************************************************** -->
414 I'm writing a backend for a target which needs custom lowering for GEP.
419 <p>You don't. The integer computation implied by a GEP is target-independent.
420 Typically what you'll need to do is make your backend pattern-match
421 expressions trees involving ADD, MUL, etc., which are what GEP is lowered
422 into. This has the advantage of letting your code work correctly in more
425 <p>GEP does use target-dependent parameters for the size and layout of data
426 types, which targets can customize.</p>
428 <p>If you require support for addressing units which are not 8 bits, you'll
429 need to fix a lot of code in the backend, with GEP lowering being only a
430 small piece of the overall picture.</p>
434 <!-- *********************************************************************** -->
437 <a name="vla">How does VLA addressing work with GEPs?</a>
440 <p>GEPs don't natively support VLAs. LLVM's type system is entirely static,
441 and GEP address computations are guided by an LLVM type.</p>
443 <p>VLA indices can be implemented as linearized indices. For example, an
444 expression like X[a][b][c], must be effectively lowered into a form
445 like X[a*m+b*n+c], so that it appears to the GEP as a single-dimensional
448 <p>This means if you want to write an analysis which understands array
449 indices and you want to support VLAs, your code will have to be
450 prepared to reverse-engineer the linearization. One way to solve this
451 problem is to use the ScalarEvolution library, which always presents
452 VLA and non-VLA indexing in the same manner.</p>
457 <!-- *********************************************************************** -->
458 <h2><a name="rules">Rules</a></h2>
459 <!-- *********************************************************************** -->
461 <!-- *********************************************************************** -->
464 <a name="bounds">What happens if an array index is out of bounds?</a>
467 <p>There are two senses in which an array index can be out of bounds.</p>
469 <p>First, there's the array type which comes from the (static) type of
470 the first operand to the GEP. Indices greater than the number of elements
471 in the corresponding static array type are valid. There is no problem with
472 out of bounds indices in this sense. Indexing into an array only depends
473 on the size of the array element, not the number of elements.</p>
475 <p>A common example of how this is used is arrays where the size is not known.
476 It's common to use array types with zero length to represent these. The
477 fact that the static type says there are zero elements is irrelevant; it's
478 perfectly valid to compute arbitrary element indices, as the computation
479 only depends on the size of the array element, not the number of
480 elements. Note that zero-sized arrays are not a special case here.</p>
482 <p>This sense is unconnected with <tt>inbounds</tt> keyword. The
483 <tt>inbounds</tt> keyword is designed to describe low-level pointer
484 arithmetic overflow conditions, rather than high-level array
487 <p>Analysis passes which wish to understand array indexing should not
488 assume that the static array type bounds are respected.</p>
490 <p>The second sense of being out of bounds is computing an address that's
491 beyond the actual underlying allocated object.</p>
493 <p>With the <tt>inbounds</tt> keyword, the result value of the GEP is
494 undefined if the address is outside the actual underlying allocated
495 object and not the address one-past-the-end.</p>
497 <p>Without the <tt>inbounds</tt> keyword, there are no restrictions
498 on computing out-of-bounds addresses. Obviously, performing a load or
499 a store requires an address of allocated and sufficiently aligned
500 memory. But the GEP itself is only concerned with computing addresses.</p>
504 <!-- *********************************************************************** -->
506 <a name="negative">Can array indices be negative?</a>
509 <p>Yes. This is basically a special case of array indices being out
514 <!-- *********************************************************************** -->
516 <a name="compare">Can I compare two values computed with GEPs?</a>
519 <p>Yes. If both addresses are within the same allocated object, or
520 one-past-the-end, you'll get the comparison result you expect. If either
521 is outside of it, integer arithmetic wrapping may occur, so the
522 comparison may not be meaningful.</p>
526 <!-- *********************************************************************** -->
529 Can I do GEP with a different pointer type than the type of
530 the underlying object?
534 <p>Yes. There are no restrictions on bitcasting a pointer value to an arbitrary
535 pointer type. The types in a GEP serve only to define the parameters for the
536 underlying integer computation. They need not correspond with the actual
537 type of the underlying object.</p>
539 <p>Furthermore, loads and stores don't have to use the same types as the type
540 of the underlying object. Types in this context serve only to specify
541 memory size and alignment. Beyond that there are merely a hint to the
542 optimizer indicating how the value will likely be used.</p>
546 <!-- *********************************************************************** -->
549 Can I cast an object's address to integer and add it to null?
553 <p>You can compute an address that way, but if you use GEP to do the add,
554 you can't use that pointer to actually access the object, unless the
555 object is managed outside of LLVM.</p>
557 <p>The underlying integer computation is sufficiently defined; null has a
558 defined value -- zero -- and you can add whatever value you want to it.</p>
560 <p>However, it's invalid to access (load from or store to) an LLVM-aware
561 object with such a pointer. This includes GlobalVariables, Allocas, and
562 objects pointed to by noalias pointers.</p>
564 <p>If you really need this functionality, you can do the arithmetic with
565 explicit integer instructions, and use inttoptr to convert the result to
566 an address. Most of GEP's special aliasing rules do not apply to pointers
567 computed from ptrtoint, arithmetic, and inttoptr sequences.</p>
571 <!-- *********************************************************************** -->
574 Can I compute the distance between two objects, and add
575 that value to one address to compute the other address?
579 <p>As with arithmetic on null, You can use GEP to compute an address that
580 way, but you can't use that pointer to actually access the object if you
581 do, unless the object is managed outside of LLVM.</p>
583 <p>Also as above, ptrtoint and inttoptr provide an alternative way to do this
584 which do not have this restriction.</p>
588 <!-- *********************************************************************** -->
590 <a name="tbaa">Can I do type-based alias analysis on LLVM IR?</a>
593 <p>You can't do type-based alias analysis using LLVM's built-in type system,
594 because LLVM has no restrictions on mixing types in addressing, loads or
597 <p>LLVM's type-based alias analysis pass uses metadata to describe a different
598 type system (such as the C type system), and performs type-based aliasing
599 on top of that. Further details are in the
600 <a href="LangRef.html#tbaa">language reference</a>.</p>
604 <!-- *********************************************************************** -->
607 <a name="overflow">What happens if a GEP computation overflows?</a>
610 <p>If the GEP lacks the <tt>inbounds</tt> keyword, the value is the result
611 from evaluating the implied two's complement integer computation. However,
612 since there's no guarantee of where an object will be allocated in the
613 address space, such values have limited meaning.</p>
615 <p>If the GEP has the <tt>inbounds</tt> keyword, the result value is
616 undefined (a "<a href="LangRef.html#trapvalues">trap value</a>") if the GEP
617 overflows (i.e. wraps around the end of the address space).</p>
619 <p>As such, there are some ramifications of this for inbounds GEPs: scales
620 implied by array/vector/pointer indices are always known to be "nsw" since
621 they are signed values that are scaled by the element size. These values
622 are also allowed to be negative (e.g. "gep i32 *%P, i32 -1") but the
623 pointer itself is logically treated as an unsigned value. This means that
624 GEPs have an asymmetric relation between the pointer base (which is treated
625 as unsigned) and the offset applied to it (which is treated as signed). The
626 result of the additions within the offset calculation cannot have signed
627 overflow, but when applied to the base pointer, there can be signed
634 <!-- *********************************************************************** -->
638 How can I tell if my front-end is following the rules?
642 <p>There is currently no checker for the getelementptr rules. Currently,
643 the only way to do this is to manually check each place in your front-end
644 where GetElementPtr operators are created.</p>
646 <p>It's not possible to write a checker which could find all rule
647 violations statically. It would be possible to write a checker which
648 works by instrumenting the code with dynamic checks though. Alternatively,
649 it would be possible to write a static checker which catches a subset of
650 possible problems. However, no such checker exists today.</p>
656 <!-- *********************************************************************** -->
657 <h2><a name="rationale">Rationale</a></h2>
658 <!-- *********************************************************************** -->
660 <!-- *********************************************************************** -->
663 <a name="goals">Why is GEP designed this way?</a>
666 <p>The design of GEP has the following goals, in rough unofficial
667 order of priority:</p>
669 <li>Support C, C-like languages, and languages which can be
670 conceptually lowered into C (this covers a lot).</li>
671 <li>Support optimizations such as those that are common in
672 C compilers. In particular, GEP is a cornerstone of LLVM's
673 <a href="LangRef.html#pointeraliasing">pointer aliasing model</a>.</li>
674 <li>Provide a consistent method for computing addresses so that
675 address computations don't need to be a part of load and
676 store instructions in the IR.</li>
677 <li>Support non-C-like languages, to the extent that it doesn't
678 interfere with other goals.</li>
679 <li>Minimize target-specific information in the IR.</li>
683 <!-- *********************************************************************** -->
685 <a name="i32">Why do struct member indices always use i32?</a>
688 <p>The specific type i32 is probably just a historical artifact, however it's
689 wide enough for all practical purposes, so there's been no need to change it.
690 It doesn't necessarily imply i32 address arithmetic; it's just an identifier
691 which identifies a field in a struct. Requiring that all struct indices be
692 the same reduces the range of possibilities for cases where two GEPs are
693 effectively the same but have distinct operand types.</p>
697 <!-- *********************************************************************** -->
700 <a name="uglygep">What's an uglygep?</a>
703 <p>Some LLVM optimizers operate on GEPs by internally lowering them into
704 more primitive integer expressions, which allows them to be combined
705 with other integer expressions and/or split into multiple separate
706 integer expressions. If they've made non-trivial changes, translating
707 back into LLVM IR can involve reverse-engineering the structure of
708 the addressing in order to fit it into the static type of the original
709 first operand. It isn't always possibly to fully reconstruct this
710 structure; sometimes the underlying addressing doesn't correspond with
711 the static type at all. In such cases the optimizer instead will emit
712 a GEP with the base pointer casted to a simple address-unit pointer,
713 using the name "uglygep". This isn't pretty, but it's just as
714 valid, and it's sufficient to preserve the pointer aliasing guarantees
715 that GEP provides.</p>
721 <!-- *********************************************************************** -->
722 <h2><a name="summary">Summary</a></h2>
723 <!-- *********************************************************************** -->
726 <p>In summary, here's some things to always remember about the GetElementPtr
729 <li>The GEP instruction never accesses memory, it only provides pointer
731 <li>The first operand to the GEP instruction is always a pointer and it must
733 <li>There are no superfluous indices for the GEP instruction.</li>
734 <li>Trailing zero indices are superfluous for pointer aliasing, but not for
735 the types of the pointers.</li>
736 <li>Leading zero indices are not superfluous for pointer aliasing nor the
737 types of the pointers.</li>
741 <!-- *********************************************************************** -->
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