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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>CS 2150: 12-memory slide set</title>
<meta name="description" content="A set of slides for a course on Program and Data Representation">
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<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section data-markdown id="cover"><script type="text/template">
# CS 2150
### Program and Data Representation
<p class='titlep'> </p>
<div class="titlesmall"><p>
<a href="http://www.cs.virginia.edu/~mrf8t">Mark Floryan</a> (mrf8t@virginia.edu)<br>
<a href="http://www.cs.virginia.edu/~asb">Aaron Bloomfield</a> (aaron@virginia.edu)<br>
<a href="http://github.com/uva-cs/pdr">@github</a> | <a href="index.html">↑</a> | <a href="./12-memory.html?print-pdf"><img class="print" width="20" src="../slides/images/print-icon.png" style="top:0px;vertical-align:middle"></a>
</p></div>
<p class='titlep'> </p>
## Memory
</script></section>
<section>
<h2>CS 2150 Roadmap</h2>
<table class="wide">
<tr><td colspan="3"><p class="center">Data Representation</p></td><td></td><td colspan="3"><p class="center">Program Representation</p></td></tr>
<tr>
<td class="top"><small> <br> <br>string<br> <br> <br> <br>int x[3]<br> <br> <br> <br>char x<br> <br> <br> <br>0x9cd0f0ad<br> <br> <br> <br>01101011</small></td>
<!-- image adapted from http://openclipart.org/detail/3677/arrow-left-right-by-torfnase -->
<td><img class="noborder" src="images/red-double-arrow.png" height="500" alt="vertical red double arrow"></td>
<td class="top"> <br>Objects<br> <br>Arrays<br> <br>Primitive types<br> <br>Addresses<br> <br>bits</td>
<td> </td>
<td class="top"><small> <br> <br>Java code<br> <br> <br>C++ code<br> <br> <br>C code<br> <br> <br>x86 code<br> <br> <br>IBCM<br> <br> <br>hexadecimal</small></td>
<!-- image adapted from http://openclipart.org/detail/3677/arrow-left-right-by-torfnase -->
<td><img class="noborder" src="images/green-double-arrow.png" height="500" alt="vertical green double arrow"></td>
<td class="top"> <br>High-level language<br> <br>Low-level language<br> <br>Assembly language<br> <br>Machine code</td>
</tr>
</table>
</section>
<section data-markdown><script type="text/template">
# Contents
[Memory Hierarchy](#memorysec)
[String Functions](#strings)
</script></section>
<section>
<section id="memorysec" data-markdown class="center"><script type="text/template">
# Memory Hierarchy
</script></section>
<section data-markdown><script type="text/template">
## Static/Dynamic Allocation
- Static: space required is *known* before program starts (at "compile time")
- Dynamic: space required is *not known* before the program starts
- Can be placed on either the stack or the heap
- But most often on the heap
</script></section>
<section data-markdown><script type="text/template">
## Memory in C
- Stack
- Managed by compiler automatically
- Lifetime is determined by program scope
- Cannot outlive procedure return
- Address space grows "down" from the top
- Heap
- Managed by programmer explicitly
- Lifetime is controlled by programmer
- Lives until freed by program
- Address space grows "up" from the bottom
</script></section>
<section data-markdown><script type="text/template">
## Memory Layout
</script></section>
<section>
<h2>Memory Allocators</h2>
<table>
<tr style="background-color:transparent"><td colspan="2" style="border-bottom:0em"></td><th colspan="2">Lifetime</th></tr>
<tr style="background-color:transparent"><td colspan="2"></td><th style="border-right:1px solid">Scoped</th><th>Unlimited</th></tr>
<tr><th style="border-bottom:0em;border-right:1px solid"> <br>Size</th><th>Known</th><td style="border-right:1px solid">local variable declarations</td><td>global, static variable declarations</td></tr>
<tr><th style="border-right:1px solid"></th><th>Unknown</th><td style="border-right:1px solid"><code>alloca()</code></td><td><code>new</code> & <code>malloc()</code></td></tr>
</table>
<p> </p>
<p><code>alloca()</code>: like <code>malloc()</code>, but on the stack, not the heap (rarely used)</p>
</section>
<section>
<h2>x86 callee epilogue</h2>
<table class="transparent">
<tr><td class="top"><pre><code>; subroutine epilogue
; recover saved registers,
; reverse of push order
pop esi
pop edi
; deallocate local var(s)
mov esp, ebp
; restore base pointer
pop ebp
; return
ret </code></pre></td><td style="width:50px"></td>
<td><img src="images/08-x86/x86-activation-record.svg" alt="activation record"></td></tr></table>
<p> </p>
<p>How would this change with <code>alloca()</code>?</p>
</section>
<section data-markdown><script type="text/template">
## malloc
```
void *malloc (size_t size)
```
- Returns an untyped pointer (can point to anything)
- Returns an address that is the location of at least size bytes of previously unused memory, and reserves that space.
- Returns `NULL` if there isn't enough space.
- Parameter is the size in bytes
</script></section>
<section data-markdown><script type="text/template">
## malloc Example
```
char *s = (char *) malloc (sizeof(*s) * n)
```
- `(char *s)`
- Type cast: malloc only returns `void *`
- Cast tells compiler that program will use it as a `char *`
- `sizeof(*s)`
- sizeof operator: Takes a type or expression, evaluates to the number of bytes to store it
</script></section>
<section data-markdown><script type="text/template">
## How is the heap managed?
- Compiled into the program's code is a heap directory management routine
- (it's in the libc library, really)
- This adds extra time to a new or `malloc()`
- It allocates memory in two ways:
- Fixed-size-blocks allocation
- A free list of available blocks is kept, and the appropriate number are allocated
- Buddy blocks
- Blocks are divided into powers of 2, so the memory takes up the next highest power of 2 bytes
</script></section>
<section data-markdown><script type="text/template">
## What happens on dynamic memory allocation
- A subroutine is invoked (for either `new` or `malloc()`)
- The OS is consulted, if necessary, to allocate a *page* of memory
- This requires switching context back to the OS
- The heap directory is examined
- And new space is determined somehow
- The subroutine returns
How expensive would this be?
</script></section>
<section data-markdown><script type="text/template">
## Why Do We Care About Memory?
- Memory hierarchy, locality
- Computer architecture
- What does this have to do with this course?
- Course: Program and data representation
- Does the memory hierarchy affect how we think about efficiency?
- What about data in memory?
</script></section>
<section>
<h2>Memory Hierarchy, part 1</h2>
<table class="transparent"><tr><td class="top">
<img src="images/07-ibcm/memory-hierarchy.png" alt="memory hierarchy">
</td><td>
<ul>
<li>CPU registers<ul>
<li>1 access per CPU cycle</li>
<li>3*10<sup>9</sup> accesses per sec</li>
<li>1 Kb total storage</li></ul></li>
<li>Cache<ul>
<li>SDRAM: 10 ns</li>
<li>10<sup>8</sup> accesses per sec</li>
<li>Multiple levels possible</li>
<li>Higher levels are bigger and slower</li>
<li>1 Mb total storage</li></ul></li>
</ul>
</td>
</tr></table>
</section>
<section>
<h2>Memory Hierarchy, part 2</h2>
<table class="transparent"><tr><td class="top">
<img src="images/07-ibcm/memory-hierarchy.png" alt="memory hierarchy">
</td><td class="top">
<ul>
<li>Main memory<ul>
<li>DRAM: 60 ns</li>
<li>2*10<sup>7</sup> accesses per sec</li>
<li>Limited by bus speeds</li>
<li>1 Gb total storage</li></ul></li>
<li>Disk<ul>
<li>HDD speeds: 5 ms</li>
<li>200 accesses per sec</li>
<li>1 Tb total storage</li></ul></li>
</ul>
</td></tr></table>
</section>
<section data-markdown><script type="text/template">
## Definitions
- Processor Cycle
- (for our purposes) the time it takes to execute a "simple" instruction
- E.g., add eax, ebx
- Memory access time (Latency)
- Time it takes to access memory
- Memory cycle time
- Time to write to memory
</script></section>
<section data-markdown><script type="text/template">
## Some (older) numbers
- Typical numbers for 1 GHz processor
- Cycle time 1 ns (10<sup>-9</sup>)
- L1 cache: accessed in 2-3 ns
- L2 cache: 20-50 ns
- Main memory: 60-100 ns
- Disk: 5-12 ms (5 x 10<sup>6</sup> ns to 12 x 10<sup>6</sup> ns)
1 ns = 10<sup>-9</sup> s; 1 ms = 10<sup>-3</sup> s
</script></section>
<section data-markdown><script type="text/template">
## More Example Numbers: Memory Capacities
- Page size: 1 Kb
- L1 cache: 64 Kb
- L2 cache: 0.5 Mb
- L3 cache: 6 Mb
- Main memory: 4 Gb
- Disk: 1 Tb
</script></section>
<section data-markdown><script type="text/template">
## Caches
- Content at each level is a *subset* of the level below
- Cache Hit: address requested is in cache
- Cache Miss: address requested is NOT in cache
- Cache page size (chunk size, line size): the number of contiguous bytes that are moved into the cache at one time
</script></section>
<section data-markdown><script type="text/template">
## So What?
- Program speed is affected by where the data is
- Data in main memory much slower to access than data in cache
- Goal: attempt to reduce the number of access to slower levels
- How?
</script></section>
<section data-markdown><script type="text/template">
## Locality
- Temporal Locality
- Locality in time
- If an item is referenced, it will tend to be referenced again soon
- Spatial Locality
- Locality in space
- If an item is referenced, items whose addresses are close by will tend to be referenced soon
</script></section>
<section data-markdown><script type="text/template">
## A Locality Example
```
int sum = 0;
for ( int i = 0; i < n; i++ ) {
sum += a[i];
}
```
</script></section>
<section data-markdown><script type="text/template">
## Example code
Source code: [cache.cpp](code/12-memory/cache.cpp.html) ([src](code/12-memory/cache.cpp))
```
cout << "page size: " << getpagesize() << endl;
int array[1024][1024];
for ( int i = 0; i < 1024; i++ )
for ( int j = 0; j < 1024; j++ )
array[i][j] = 0;
for ( int c = 0; c < 1024; c++ )
for ( int i = 0; i < 1024; i++ )
for ( int j = 0; j < 1024; j++ )
array[i][j]++;
int sum = 0;
for ( int i = 0; i < 1024; i++ )
for ( int j = 0; j < 1024; j++ )
sum += array[i][j];
cout << sum << endl;
```
What if we swap each of the three `i` and `j` loops?
</script></section>
<section data-markdown><script type="text/template">
## Execution of cache.cpp
- On an older Linux machine (3 Ghz Intel)
- Page size is 4Kb (4096 bytes)
- With `i` as the outer and `j` as the inner: 2.7 seconds
- With `j` as the outer and `i` as the inner: 124.9 seconds
- A factor of almost 50!
- On a more modern Linux machine (3.4 Ghz AMD)
- Page size is also 4Kb (4096 bytes)
- With `i` as the outer and `j` as the inner: 0.696 seconds
- With `j` as the outer and `i` as the inner: 31.4 seconds
- Also a factor of almost 50!
</script></section>
<section data-markdown><script type="text/template">
## Trends (Example)
Over a 20 year period:
- CPU speed: 600x speed
- SRAM (cache memory):
- 200x capacity
- 100x latency
- DRAM (main memory):
- 8,000x capacity
- 6x latency
- Disk:
- 50,000x capacity
- 10x latency
See any implications?
</script></section>
<section data-markdown><script type="text/template">
## Who is Working on This Problem?
- Architects
- Compiler writers
- Programmers
- Operating system
</script></section>
<section data-markdown><script type="text/template">
## Locality and Data Structures
- Which has better spatial locality?
- Between arrays or linked lists?
- How does this change the big-theta analysis of the data structures?
</script></section>
<section data-markdown><script type="text/template">
## Some actual numbers
</script></section>
</section>
<section>
<section id="strings" data-markdown class="center"><script type="text/template">
# String Functions
</script></section>
<section data-markdown><script type="text/template">
## C-strings
- A C-style string is just a pointer to a `char`
- Consider:
```
char *str = "hello world";
```
- This produces:
- Each byte is the ASCII encoding of the character
- The last byte is binary zero
</script></section>
<section data-markdown><script type="text/template">
## C-strings
How we view it:
How the computer views it:
</script></section>
<section data-markdown><script type="text/template">
## C-string functions
- `int strlen(char *s)`: returns number of chars in `s`
- `char *strcpy(char *s1, const char *s2)`: copies `s2` to `s1`
- `char *strcat(char *s1, const char * s2)`: appends `s2` to `s1`
</script></section>
<section data-markdown><script type="text/template">
## String Concatenation
Source code: [strings.c](code/12-memory/strings.c.html) ([src](code/12-memory/strings.c))
```
int main (int argc, char **argv) {
int i = 0;
// allocate a space in memory for result
char *result = (char *) malloc (sizeof (*result));
*result = '\0';
while (i < argc) { // while there are still args
char *s = (char *) malloc (sizeof (*s) *
(strlen(result) + strlen(argv[i]) + 1));
strcpy (s, result);
strcat (s, argv[i]);
result = s;
i++;
}
printf ("Concatenation: %s\n", result);
return 0;
}
```
Do you see any memory leak problems?
</script></section>
<section data-markdown><script type="text/template">
## Concatenating Strings
- Allocate space for result and next argument:
```
char *s = (char *)
malloc (sizeof (*s) *
(strlen(result) + strlen(argv[i]) + 1));
```
- Why +1?
- Copy result to s:
```
strcpy (s, result);
```
- Concatenate next argument:
```
strcat (s, argv[i]);
```
</script></section>
<section data-markdown><script type="text/template">
## Reclaiming Storage
- Storage allocated by malloc is reserved forever
- Give it back by passing it to free
```
void free(void *ptr);
```
</script></section>
<section data-markdown><script type="text/template">
## Memory Leaks
- Program fails to release memory when no longer needed
- Consequences/symptoms
- Reduces amount of available memory, run out of memory available for allocation
- Virtual memory. Effect: once RAM has run out, increasing use of hard disk
- Usually, the performance of the application and/or system will have become so slow that they will be considered to have failed
</script></section>
<section data-markdown><script type="text/template">
## Plugging Memory Leaks
```
while (i < argc) { // while there are still arguments
char *s = (char *) malloc (sizeof (*s) *
(strlen(result) + strlen(argv[i]) + 1));
strcpy (s, result);
// add "free(result);" here...
strcat (s, argv[i]);
// ... or here
result = s;
i++;
}
```
</script></section>
<section data-markdown><script type="text/template">
## Memory Leak
- There is no reference to allocated storage
- It can never be reached
- It can never be reclaimed
- Losing references
- Variable goes out of scope
- Variable reassigned
</script></section>
<section data-markdown><script type="text/template">
## When not to free...
```
while (i < argc) { // while there are still arguments
char *s = (char *) malloc (sizeof (*s) *
(strlen(result) + strlen(argv[i]) + 1));
strcpy (s, result);
// add "free(result)" here ...
strcat (s, argv[i]);
// or here
result = s;
i++;
}
```
- Upon close fo the `while` block, the scope of `s` is closed; should we
`free(s)` first?
- No! `result` now references same storage
- After the `result = s` line, there is no way to reach storage `result` previously pointed to
</script></section>
<section data-markdown><script type="text/template">
## realloc
```
void *realloc(void *ptr, size_t size);
```
- The `realloc()` function changes the size of the memory object pointed to by `ptr` to the size specified by `size`
- But it's risky...
- It changes the address of the pointer
- So other pointers pointing there are now pointing to invalid memory
</script></section>
<section data-markdown><script type="text/template">
## Running time of realloc
- Time to reserve new space: Θ(1)
- Time to copy old data into new space:
- Θ(*n*) where *n* is the size of the old data
</script></section>
<section data-markdown><script type="text/template">
## Efficiency and Order Classes
- Recall Big-Oh, Big-Theta, ...
- When are the differences meaningful?
- Inputs get large
- Difference in order class
- High-level comparison tool
- Not as useful when:
- 2 solutions are in the same order class
- Fine-tuning of an algorithm is important
</script></section>
<section data-markdown><script type="text/template">
## Efficiency and Order Classes
- Order classes based on counting statements
- Is this useful for fine-grained algorithm analysis?
- One assumption
- All operations take the same amount of time
- Is this really true?
</script></section>
<section data-markdown><script type="text/template">
## Factorial: Recursive
```
int factorial_recursive(int x) {
if (x <= 1)
return 1;
else
return x * factorial_recursive(x-1);
}
```
- Note that we have to find the recursive value, and make a modification to it (multiply it by x) before we return it
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## Factorial: Tail Recursion
```
int factorial_tail_recursive(int x, int y) {
if (x <= 1)
return y;
else
return factorial_tail_recursive(x-1, x*y);
}
```
- Note that the answer to a given invocation is exactly the answer to the recursive call
- How could we modify the calling convention for this?
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## Activation Records
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<section data-markdown><script type="text/template">
## Factorial: Loop Implementation
```
int factorial_loop(int x) {
int y = 1;
while (x > 1) {
y *= x;
x--;
}
return y;
}
```
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