Introduction to Computer Systems 15-213/18-243, spring 2009

Introduction to Computer Systems 15-213/18-243, spring 2009

Carnegie Mellon 14-513 Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 18-613 1 Carnegie Mellon Dynamic Memory Allocation: Advanced Concepts 15-213/18-213/14-513/15-513/18-613: Introduction to Computer Systems 16th Lecture, October 17, 2019 Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 2 Carnegie Mellon Review: Dynamic Memory Allocation Application Kernel virtual memory

Dynamic Memory Allocator User stack (created at runtime) Heap Programmers use dynamic memory allocators (such as malloc) to acquire virtual memory (VM) at run time. brk Run-time heap (created by malloc) is only known at runtime Read/write segment (.data, .bss) Dynamic memory allocators manage an area of process VM known as the heap. Read-only segment (.init, .text, .rodata)

0x400000 Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition %rsp (stack pointer) Memory-mapped region for shared libraries for data structures whose size Memory invisible to user code 0 Unused Loaded from the executable file 3 Carnegie Mellon

Review: Keeping Track of Free Blocks Method 1: Implicit list using lengthlinks all blocks Unused 32 32 16 Method 2: Explicit list among the free blocks using pointers 32 48 Need to tag each block as allocated/free 48 32

16 Need space for pointers Method 3: Segregated free list Different free lists for different size classes Method 4: Blocks sorted by size Can use a balanced tree (e.g. Red-Black tree) with pointers within each free block, and the length used as a key Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 4 Carnegie Mellon Review: Implicit Lists Summary Implementation: very simple Allocate cost: linear time worst case

Free cost: constant time worst case even with coalescing Memory Overhead: Depends on placement policy Strategies include first fit, next fit, and best fit Not used in practice for malloc/free because of lineartime allocation used in many special purpose applications However, the concepts of splitting and boundary tag coalescing are general to all allocators Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 5 Carnegie Mellon Today

Explicit free lists Segregated free lists Garbage collection Memory-related perils and pitfalls Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 6 Carnegie Mellon Keeping Track of Free Blocks Method 1: Implicit list using lengthlinks all blocks Unused 32 32 16

Method 2: Explicit list among the free blocks using pointers 32 48 48 32 16 Method 3: Segregated free list Different free lists for different size classes Method 4: Blocks sorted by size Can use a balanced tree (e.g. Red-Black tree) with pointers within each free block, and the length used as a key Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 7 Carnegie Mellon

Explicit Free Lists Allocated (as before) Size a Free Size a Next Prev Payload and padding Optional Size a Size a Maintain list(s) of free blocks, not all blocks Luckily we track only free blocks, so we can use payload area

The next free block could be anywhere So we need to store forward/back pointers, not just sizes Still need boundary tags for coalescing To find adjacent blocks according to memory order Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 8 Carnegie Mellon Explicit Free Lists Logically: A B C Physically: blocks can be in any order Forward (next) links A 32

B 32 32 32 48 48 32 C Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 32 32 32 Back (prev) links 9 Carnegie Mellon Allocating From Explicit Free Lists conceptual graphic Before After (with splitting)

= malloc() Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 10 Carnegie Mellon Freeing With Explicit Free Lists Insertion policy: Where in the free list do you put a newly freed block? Unordered LIFO (last-in-first-out) policy Insert freed block at the beginning of the free list FIFO (first-in-first-out) policy Insert freed block at the end of the free list Pro: simple and constant time Con: studies suggest fragmentation is worse than address ordered Address-ordered policy Insert freed blocks so that free list blocks are always in address order: addr(prev) < addr(curr) < addr(next) Con: requires search

Pro: studies suggest fragmentation is lower than LIFO/FIFO Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 11 Carnegie Mellon Freeing With a LIFO Policy (Case 1) Allocated Before Allocated conceptual graphic free( ) Root Insert the freed block at the root of the list After Root Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition

12 Carnegie Mellon Freeing With a LIFO Policy (Case 2) Allocated Before Free conceptual graphic free( ) Root Splice out adjacent successor block, coalesce both memory blocks, and insert the new block at the root of the list After Root Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 13

Carnegie Mellon Freeing With a LIFO Policy (Case 3) Free Before Allocated conceptual graphic free( ) Root Splice out adjacent predecessor block, coalesce both memory blocks, and insert the new block at the root of the list After Root Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 14 Carnegie Mellon

Freeing With a LIFO Policy (Case 4) Free Before Free conceptual graphic free( ) Root Splice out adjacent predecessor and successor blocks, coalesce all 3 blocks, and insert the new block at the root of the list After Root Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 15 Carnegie Mellon Some Advice: An Implementation Trick LIFO Insertion

Point FIFO Insertion Point A B C Free Pointer D Next fit Use circular, doubly-linked list Support multiple approaches with single data structure First-fit vs. next-fit Either keep free pointer fixed or move as search list LIFO vs. FIFO

Insert as next block (LIFO), or previous block (FIFO) Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 16 Carnegie Mellon Explicit List Summary Comparison to implicit list: Allocate is linear time in number of free blocks instead of all blocks Much faster when most of the memory is full Slightly more complicated allocate and free because need to splice blocks in and out of the list Some extra space for the links (2 extra words needed for each block) Does this increase internal fragmentation? Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 17 Carnegie Mellon Today

Explicit free lists Segregated free lists Garbage collection Memory-related perils and pitfalls Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 18 Carnegie Mellon Segregated List (Seglist) Allocators Each size class of blocks has its own free list 16 32-48 64inf Often have separate classes for each small size For larger sizes: One class for each size []

Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 19 Carnegie Mellon Seglist Allocator Given an array of free lists, each one for some size class To allocate a block of size n: Search appropriate free list for block of size m > n (i.e., first fit) If an appropriate block is found: Split block and place fragment on appropriate list If no block is found, try next larger class Repeat until block is found If no block is found: Request additional heap memory from OS (using sbrk()) Allocate block of n bytes from this new memory Place remainder as a single free block in appropriate size class. Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition

20 Carnegie Mellon Seglist Allocator (cont.) To free a block: Coalesce and place on appropriate list Advantages of seglist allocators vs. non-seglist allocators (both with first-fit) Higher throughput log time for power-of-two size classes vs. linear time Better memory utilization First-fit search of segregated free list approximates a best-fit search of entire heap. Extreme case: Giving each block its own size class is equivalent to best-fit. Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 21

Carnegie Mellon More Info on Allocators D. Knuth, The Art of Computer Programming, vol 1, 3rd edition, Addison Wesley, 1997 The classic reference on dynamic storage allocation Wilson et al, Dynamic Storage Allocation: A Survey and Critical Review, Proc. 1995 Intl Workshop on Memory Management, Kinross, Scotland, Sept, 1995. Comprehensive survey Available from CS:APP student site (csapp.cs.cmu.edu) Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 22 Carnegie Mellon Quiz Time! Check out: https://canvas.cmu.edu/courses/10968 Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition

23 Carnegie Mellon Today Explicit free lists Segregated free lists Garbage collection Memory-related perils and pitfalls Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 24 Carnegie Mellon Implicit Memory Management: Garbage Collection Garbage collection: automatic reclamation of heap-allocated storageapplication never has to explicitly free memory void foo() {

int *p = malloc(128); return; /* p block is now garbage */ } Common in many dynamic languages: Python, Ruby, Java, Perl, ML, Lisp, Mathematica Variants (conservative garbage collectors) exist for C and C++ However, cannot necessarily collect all garbage Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 25 Carnegie Mellon Garbage Collection How does the memory manager know when memory can be freed? In general we cannot know what is going to be used in the future since it depends on conditionals But we can tell that certain blocks cannot be used if there are no pointers to them

Must make certain assumptions about pointers Memory manager can distinguish pointers from non-pointers All pointers point to the start of a block Cannot hide pointers (e.g., by coercing them to an int, and then back again) Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 26 Carnegie Mellon Classical GC Algorithms Mark-and-sweep collection (McCarthy, 1960) Does not move blocks (unless you also compact) Reference counting (Collins, 1960) Does not move blocks (not discussed) Copying collection (Minsky, 1963)

Moves blocks (not discussed) Generational Collectors (Lieberman and Hewitt, 1983) Collection based on lifetimes Most allocations become garbage very soon So focus reclamation work on zones of memory recently allocated For more information: Jones and Lin, Garbage Collection: Algorithms for Automatic Dynamic Memory, John Wiley & Sons, 1996. Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 27 Carnegie Mellon Memory as a Graph We view memory as a directed graph Each block is a node in the graph

Each pointer is an edge in the graph Locations not in the heap that contain pointers into the heap are called root nodes (e.g. registers, locations on the stack, global variables) Root nodes Heap nodes reachable Not-reachable (garbage) A node (block) is reachable if there is a path from any root to that node. Non-reachable nodes are garbage (cannot be needed by the application) Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 28 Carnegie Mellon Mark and Sweep Collecting Can build on top of malloc/free package Allocate using malloc until you run out of space When out of space: Use extra mark bit in the head of each block

Mark: Start at roots and set mark bit on each reachable block Sweep: Scan all blocks and free blocks that are not marked root Note: arrows here denote memory refs, not free list ptrs. Before mark After mark After sweep Mark bit set free Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition free 29 Carnegie Mellon Assumptions For a Simple Implementation

Application new(n): returns pointer to new block with all locations cleared read(b,i): read location i of block b into register write(b,i,v): write v into location i of block b Each block will have a header word addressed as b[-1], for a block b Used for different purposes in different collectors Instructions used by the Garbage Collector is_ptr(p): determines whether p is a pointer length(b): returns the length of block b, not including the header get_roots(): returns all the roots Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 30 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return;

setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit recursively call mark on all words in the block 31 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return;

setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit recursively call mark on all words in the block 32 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return;

setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit recursively call mark on all words in the block 33 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return;

setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit recursively call mark on all words in the block 34 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return;

setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block 35 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++)

mark(p[i]); return; } // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call 36 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++)

mark(p[i]); return; } // // // // // if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) { // for entire heap if markBitSet(p) clearMarkBit(); else if (allocateBitSet(p)) free(p); p += length(p+1); } Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 37

Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) {

// for entire heap if markBitSet(p) // did we reach this block? clearMarkBit(); else if (allocateBitSet(p)) free(p); p += length(p+1); } Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 38 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // //

// if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) { // for entire heap if markBitSet(p) // did we reach this block? clearMarkBit(); // yes -> so just clear mark bit else if (allocateBitSet(p)) free(p); p += length(p+1); } Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 39 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) {

if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) { if markBitSet(p) clearMarkBit(); else if (allocateBitSet(p)) free(p); p += length(p+1); }

// for entire heap // did we reach this block? // yes -> so just clear mark bit // never reached: is it allocated? Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 40 Carnegie Mellon Mark and Sweep Pseudocode Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // //

if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) { if markBitSet(p) clearMarkBit(); else if (allocateBitSet(p)) free(p); p += length(p+1); } // for entire heap // did we reach this block? // yes -> so just clear mark bit // never reached: is it allocated? // yes -> its garbage, free it Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 41 Carnegie Mellon Mark and Sweep Pseudocode

Mark using depth-first traversal of the memory graph ptr mark(ptr p) { if (!is_ptr(p)) return; if (markBitSet(p)) return; setMarkBit(p); for (i=0; i < length(p); i++) mark(p[i]); return; } // // // // // if not pointer -> do nothing if already marked -> do nothing set the mark bit for each word in ps block make recursive call Sweep using lengths to find next block ptr sweep(ptr p, ptr end) { while (p < end) { if markBitSet(p) clearMarkBit(); else if (allocateBitSet(p)) free(p);

p += length(p+1); } // // // // // // Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition for entire heap did we reach this block? yes -> so just clear mark bit never reached: is it allocated? yes -> its garbage, free it goto next block 42 Carnegie Mellon Today

Explicit free lists Segregated free lists Garbage collection Memory-related perils and pitfalls Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 43 Carnegie Mellon Memory-Related Perils and Pitfalls Dereferencing bad pointers Reading uninitialized memory Overwriting memory Referencing nonexistent variables Freeing blocks multiple times Referencing freed blocks Failing to free blocks Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition

44 Carnegie Mellon Dereferencing Bad Pointers The classic scanf bug int val; ... scanf("%d", val); Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 45 Carnegie Mellon Reading Uninitialized Memory Assuming that heap data is initialized to zero /* return y = Ax */ int *matvec(int **A, int *x) { int *y = malloc(N*sizeof(int)); int i, j; for (i=0; i

y[i] += A[i][j]*x[j]; return y; } Can avoid by using calloc Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 46 Carnegie Mellon Overwriting Memory Allocating the (possibly) wrong sized object int **p; p = malloc(N*sizeof(int)); for (i=0; i

47 Carnegie Mellon Overwriting Memory Off-by-one errors char **p; p = malloc(N*sizeof(int *)); for (i=0; i<=N; i++) { p[i] = malloc(M*sizeof(int)); } char *p; p = malloc(strlen(s)); strcpy(p,s); Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 48 Carnegie Mellon Overwriting Memory Not checking the max string size char s[8];

int i; gets(s); /* reads 123456789 from stdin */ Basis for classic buffer overflow attacks Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 49 Carnegie Mellon Overwriting Memory Misunderstanding pointer arithmetic int *search(int *p, int val) { while (p && *p != val) p += sizeof(int); return p; } Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 50

Carnegie Mellon Overwriting Memory Referencing a pointer instead of the object it points to int *BinheapDelete(int **binheap, int *size) { int *packet; packet = binheap[0]; binheap[0] = binheap[*size - 1]; *size--; Heapify(binheap, *size, 0); return(packet); } What gets decremented? (See next slide) Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 51 Carnegie Mellon C operators Postfix

Operators Associativity () [] -> . ++ -left to right ! ~ ++ -- + - * & (type) sizeof right to left * / % left to right Unary Unary + left to right Prefix Binary << >> left to right < <= > >= left to right == != left to right & left to right ^ left to right Binary | left to right &&

left to right || left to right ?: right to left = += -= *= /= %= &= ^= != <<= >>= right to left , left to right ->, (), and [] have high precedence, with * and & just below Unary +, -, and * have higher precedence than binary forms Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition Source: K&R page 53, updated52 Carnegie Mellon Overwriting Memory Referencing a pointer instead of the object it points to int *BinheapDelete(int **binheap, int *size) { int *packet; packet = binheap[0]; binheap[0] = binheap[*size - 1]; *size--;

Heapify(binheap, *size, 0); return(packet); } Same effect as size--; Rewrite as (*size)--; Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 53 Carnegie Mellon Referencing Nonexistent Variables Forgetting that local variables disappear when a function returns int *foo () { int val; return &val; }

Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 54 Carnegie Mellon Freeing Blocks Multiple Times Nasty! x = malloc(N*sizeof(int)); free(x); y = malloc(M*sizeof(int)); free(x); Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 55 Carnegie Mellon Referencing Freed Blocks Evil! x = malloc(N*sizeof(int));

free(x); ... y = malloc(M*sizeof(int)); for (i=0; i

Failing to Free Blocks (Memory Leaks) Freeing only part of a data structure struct list { int val; struct list *next; }; foo() { struct list *head = malloc(sizeof(struct list)); head->val = 0; head->next = NULL; ... free(head); return; } Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 58 Carnegie Mellon Dealing With Memory Bugs Debugger: gdb Good for finding bad pointer dereferences

Hard to detect the other memory bugs Data structure consistency checker Runs silently, prints message only on error Use as a probe to zero in on error Binary translator: valgrind Powerful debugging and analysis technique Rewrites text section of executable object file Checks each individual reference at runtime Bad pointers, overwrites, refs outside of allocated block glibc malloc contains checking code setenv MALLOC_CHECK_ 3 Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 59 Carnegie Mellon

Supplemental slides Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 60 Carnegie Mellon Conservative Mark & Sweep in C A conservative garbage collector for C programs is_ptr() determines if a word is a pointer by checking if it points to an allocated block of memory But, in C pointers can point to the middle of a block ptr Assumes ptr in middle can be used to reach anywhere in the block, but no other block Header To mark header, need to find the beginning of the block Can use a balanced binary tree to keep track of all allocated blocks (key is start-of-block) Balanced-tree pointers can be stored in header (use two additional

words) Head Data Size Left Right Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition Left: smaller addresses Right: larger addresses 61 Carnegie Mellon C Pointer Declarations: Test Yourself! int *p p is a pointer to int int *p[13] p is an array[13] of pointer to int int *(p[13])

p is an array[13] of pointer to int int **p p is a pointer to a pointer to an int int (*p)[13] p is a pointer to an array[13] of int int *f() f is a function returning a pointer to int int (*f)() f is a pointer to a function returning int int (*(*x[3])())[5] x is an array[3] of pointers to functions returning pointers to array[5] of ints Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition Source: K&R Sec 5.12 62

Carnegie Mellon C Pointer Declarations: Test Yourself! int *p p is a pointer to int int *p[13] p is an array[13] of pointer to int int *(p[13]) p is an array[13] of pointer to int int **p p is a pointer to a pointer to an int int (*p)[13] p is a pointer to an array[13] of int int *f() f is a function returning a pointer to int int (*f)()

f is a pointer to a function returning int int (*(*x[3])())[5] x is an array[3] of pointers to functions returning pointers to array[5] of ints int (*(*f())[13])() f is a function returning ptr to an array[13] of pointers to functions returning int Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition Source: K&R Sec 5.12 63 Carnegie Mellon Parsing: int (*(*f())[13])() int (*(*f())[13])() f int (*(*f())[13])() f is a function

int (*(*f())[13])() f is a function that returns a ptr int (*(*f())[13])() f is a function that returns a ptr to an array of 13 int (*(*f())[13])() f is a function that returns a ptr to an array of 13 ptrs int (*(*f())[13])() f is a function that returns a ptr to an array of 13 ptrs to functions returning an int Bryant and OHallaron, Computer Systems: A Programmers Perspective, Third Edition 64

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