Introduction to Computer Systems: Abstraction, Reality, and Performance Optimization, Lecture notes of Computer Networks

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Introduction to Computer Systems

15-213/18-243, spring 2009

1 st^ Lecture, Jan. 12th

Instructors:

Gregory Kesden and Markus Püschel

The course that gives CMU its “Zip”!

Overview

 Course theme

 Five realities

 How the course fits into the CS/ECE curriculum

 Logistics

Great Reality #1:

Int’s are not Integers, Float’s are not Reals

 Example 1: Is x^2 ≥ 0?

 Float’s: Yes!

 Int’s:

 Example 2: Is (x + y) + z = x + (y + z)?

 Unsigned & Signed Int’s: Yes!

 Float’s:

 (1e20 + -1e20) + 3.14 --> 3.

 1e20 + (-1e20 + 3.14) --> ??

Code Security Example

 Similar to code found in FreeBSD’s implementation of

getpeername

 There are legions of smart people trying to find

vulnerabilities in programs

/* Kernel memory region holding user-accessible data */ #define KSIZE 1024 char kbuf[KSIZE];

/* Copy at most maxlen bytes from kernel region to user buffer */ int copy_from_kernel(void user_dest, int maxlen) { / Byte count len is minimum of buffer size and maxlen */ int len = KSIZE < maxlen? KSIZE : maxlen; memcpy(user_dest, kbuf, len); return len; }

Malicious Usage

/* Kernel memory region holding user-accessible data */ #define KSIZE 1024 char kbuf[KSIZE];

/* Copy at most maxlen bytes from kernel region to user buffer */ int copy_from_kernel(void user_dest, int maxlen) { / Byte count len is minimum of buffer size and maxlen */ int len = KSIZE < maxlen? KSIZE : maxlen; memcpy(user_dest, kbuf, len); return len; }

#define MSIZE 528

void getstuff() { char mybuf[MSIZE]; copy_from_kernel(mybuf, -MSIZE);

... }

Computer Arithmetic

 Does not generate random values

 Arithmetic operations have important mathematical properties

 Cannot assume all “usual” mathematical properties

 Due to finiteness of representations

 Integer operations satisfy “ring” properties

 Commutativity, associativity, distributivity

 Floating point operations satisfy “ordering” properties

 Monotonicity, values of signs

 Observation

 Need to understand which abstractions apply in which contexts

 Important issues for compiler writers and serious application

programmers

Assembly Code Example

 Time Stamp Counter

 Special 64-bit register in Intel-compatible machines

 Incremented every clock cycle

 Read with rdtsc instruction

 Application

 Measure time (in clock cycles) required by procedure

double t;

start_counter();

P();

t = get_counter();

printf( " P required %f clock cycles\n " , t);

Code to Read Counter

 Write small amount of assembly code using GCC’s asm facility

 Inserts assembly code into machine code generated by

compiler

static unsigned cyc_hi = 0;

static unsigned cyc_lo = 0;

/* Set *hi and *lo to the high and low order bits

of the cycle counter.

void access_counter(unsigned *hi, unsigned *lo)

asm( "rdtsc; movl %%edx,%0; movl %%eax,%1 "

: "=r" (hi), "=r" (lo)

: "%edx", "%eax");

Memory Referencing Bug Example

double fun(int i)

volatile double d[1] = {3.14};

volatile long int a[2];

a[i] = 1073741824; /* Possibly out of bounds */

return d[0];

fun(0) – > 3.

fun(1) – > 3.

fun(2) – > 3.

fun(3) – > 2.

fun(4) – > 3.14, then segmentation fault

Memory Referencing Bug Example

double fun(int i) { volatile double d[1] = {3.14}; volatile long int a[2]; a[i] = 1073741824; /* Possibly out of bounds */ return d[0]; }

fun(0) – > 3. fun(1) – > 3. fun(2) – > 3. fun(3) – > 2. fun(4) – > 3.14, then segmentation fault

Saved State

d7 … d

d3 … d

a[1]

a[0] 0

Location accessed by

fun(i)

Explanation:

Memory System Performance Example

 Hierarchical memory organization

 Performance depends on access patterns

 Including how step through multi-dimensional array

void copyji(int src[2048][2048], int dst[2048][2048]) { int i,j; for (j = 0; j < 2048; j++) for (i = 0; i < 2048; i++) dst[i][j] = src[i][j]; }

void copyij(int src[2048][2048], int dst[2048][2048]) { int i,j; for (i = 0; i < 2048; i++) for (j = 0; j < 2048; j++) dst[i][j] = src[i][j]; }

21 times slower

(Pentium 4)

The Memory Mountain

s1 s s5 s s s s s15 8m^ 2m^ 512k

128k

32k

8k

2k

0

200

400

600

800

1000

1200

Read throughput (MB/s)

Stride (words) Working set size (bytes)

Pentium III Xeon 550 MHz 16 KB on-chip L1 d-cache 16 KB on-chip L1 i-cache 512 KB off-chip unified L2 cache

L

L

Mem

Example Matrix Multiplication

 Standard desktop computer, vendor compiler, using optimization flags

 Both implementations have exactly the same operations count (2n^3 )

 What is going on?

0

5

10

15

20

25

30

35

40

45

50

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9, matrix size

Matrix-Matrix Multiplication (MMM) on 2 x Core 2 Duo 3 GHz (double precision) Gflop/s

160x

Triple loop

Best code (K. Goto)

MMM Plot: Analysis

0

5

10

15

20

25

30

35

40

45

50

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9, matrix size

Matrix-Matrix Multiplication (MMM) on 2 x Core 2 Duo 3 GHz Gflop/s

Memory hierarchy and other optimizations: 20x

Vector instructions: 4x

Multiple threads: 4x

 Reason for 20x: Blocking or tiling, loop unrolling, array scalarization,

instruction scheduling, search to find best choice

 Effect: less register spills, less L1/L2 cache misses, less TLB misses