CDA 3101 Fall 2013 Introduction to Computer Organization Alternative Architectures Arithmetic/Logic Operations 18 September 2013.

CDA 3101 Fall 2013

Introduction to Computer Organization

Alternative Architectures

Arithmetic/Logic Operations

18 September 2013

Concept Review

• Variable allocation– Stack frames (caller/callee), static, heap

• Pointers– Memory addresses– Necessary (to pass arguments: arrays, structures)– Efficient (pointer arithmetic)– Problems

• Reference wrong memory location (segmentation fault)

• Memory leakage

Overview

• ISA design alternatives

• Design principles (tradeoffs)

• CPU performance equation

• RISC vs. CISC

• Historical perspective

• PowerPC and 80x86

Computer Architectures• Accumulator

– Hardware expensive => only one register– Accumulator: one of the operands and result– Memory-based operand addressing mode

• Stack– No registers (simple compilers, compact encoding)

• Special purpose registers (e.g. 8086)• General purpose registers

– Register-memory– Register-register (load-store)

• HLL computer architecture

Instruction Set Architectures

Load AddressB

Add AddressC

Store AddressA

A = B + C;

Push AddressC

Push AddressB

Add

Pop AddressA

Load R1, AddressB

Load R2, AddressC

Add R3, R1, R2

Store R3, AddressA

Accumulator Stack Load-store

Add AddressA, AddressB, AddressC

Memory-memory

CPUtime = IC * CPI * Cycle_time

ISA Trends• Hardware and compiler technology trends

– Hardware / software boundary swings back and forth

EDSAC CISC RISC Post RISC (FISC) EPIC

Multi-Core Compiler support Hardware support

RISC Architecture• Reduced Instruction Set Computer• Design philosophy

– Load-store– Fixed-length instructions– Three-address architecture– Plenty of registers– Simple addressing modes– Instruction pipelining

• Many ideas used in modern computers have been taken from CDC 6600 (1963)

PowerPC

• Similar to MIPS: 32 registers, 32-bit instructions, RISC• Differences (tradeoffs: simplicity vs. common case)

– Indexed addressing• Example: lw $t1,$a0+$s3 #$t1=Memory[$a0+$s3]• MIPS: add $t0, $a0, $s3; lw $t1,0($t0)

– Update addressing• Update a register as part of load (for marching through arrays)• Example: lwu $t0,4($s3) #lw $t0,4($s3); addi $s3,$s3,4

– Unique instructions• Load multiple/store multiple: up to 32 words in a single instruction

• Special counter register– bc Loop, $ctr!=0 #decrement counter, if not 0 goto loop

– MIPS: addi, $t0, $t0, -1; bne $t0, $zero, Loop

80x86 Milestones• 1978: 8086, 16 bit architecture (64KB), no GPRs• 1980: 8087 FP coprocessor, 60+ instructions, 80-bit

stack, no GPRs• 1982: 80286, 24-bit address space, protection model• 1985: 80386, 32 bits, new addressing modes, 8 GPRs• 1989-1995: The 80486, Pentium, Pentium Pro add a few

instructions (designed for higher performance)• 1997: MMX +57 instructions (SIMD)• 1999: PIII +70 multimedia instructions• 2000: P4 +144 multimedia instructionsGolden handcuffs of upward compatibility => architecture

is difficult to explain and impossible to love

X86 Architecture• Two-address architecture

– The destination is also one of the sources

add $s1,$s0 # s0=s0+s1 (C: a += b;)– Benefit: smaller instructions smaller code faster

• Register-memory architecture– One operand can be in memory; other operand is register

add 12(%gp),%s0 # s0=s0+Mem[12+gp]– Benefit: fewer instructions smaller code

• Variable-length instructions (1 to 17 bytes)– Small code size (30% smaller)

– Better instruction cache hit rates

– Instructions can include 8- or 32-bit immediates

X86 Features• Operating modes: real (8088), virtual, and protected• Four protection levels• Memory

– Address space: 16,384 segments (4GB)– Little endian

• 8 32-bit Registers (16-bit 8086 names with e prefix):– eax, ecx, edx, ebx, esp, ebp, esi, edi

• Data types– Signed/unsigned integers (8, 16, and 32 bits)– Binary coded decimal integers– Floating point (32 and 64 bits)

• Floating point uses a separate stack

X86 Registers

Main arithmetic register

Pointers (memory addresses)Loops

Multiplication and division

Pointer to source string

Pointer to destination stringBase of the current stack frame ($fp)

Stack pointer

Support for 8088 attempt to address 220 bytes using 16-bit addresses

Program counter

Processor State Word

X86 Instruction Formats

• Highly complex and irregular• Six variable-length fields• Five fields are optional

Examples of X86 Instruction Formats

Integer Instructions• Control

– JNZ, JZ– JMP– CALL– RET– LOOP

• Data Transfer– MOV– PUSH, POP– LES

• Arithmetic– ADD, SUB– CMP– SHL, SHR, RCR– CBW– TEST– INC, DEC– OR, NOR

• String– MOVS– LODS

Examples of X86 Instructions• leal (load effective address)

– Calculate address like a load, but load address into register

– Load 32-bit address: leal -4000000(%ebp),%esi # esi = ebp – 4000000

• Memory Stack is part of instruction set– call label (esp-=4; M[esp]=eip+5; eip = label)– push places value onto stack, increments esp– pop gets value from stack, decrements esp

• incl, decl (increment, decrement)incl %edx # edx = edx + 1

Addressing Modes Encoding

• Highly irregular, non-orthogonal addressing modes• Instruction in 16-bit or 32-bit mode?• Not all modes apply to all instructions• Not all registers can be used in all modes

Addressing Modes

• Base reg + offset (like MIPS)– movl -8000044(%ebp), %eax

• Base reg + index reg (2 regs form addr.)– movl (%eax,%ebx),%edi # edi = Mem[ebx + eax]

• Scaled reg + index (shift one reg by 1,2)– movl(%eax,%edx,4),%ebx # ebx = Mem[edx*4 + eax]

• Scaled reg + index + offset– movl 12(%eax,%edx,4),%ebx # ebx = Mem[edx*4 + eax + 12]

Branch Support• Rather than compare registers, x86 uses special 1-

bit registers called “condition codes” that are set as a side-effect of ALU operations– S - Sign Bit

– Z - Zero (result is all 0)

– C - Carry Out

– P - Parity: set to 1 if even number of ones in rightmost 8 bits of operation

• Conditional Branch instructions then use condition flags for all comparisons: <, <=, >, >=, ==, !=

While Loop

while (save[i]==k) i = i + j;

(i,j,k => %edx, %esi, %ebx)

leal -400(%ebp),%eax

.Loop: cmpl %ebx,(%eax,%edx,4)

jne .Exit

addl %esi,%edx

j .Loop

.Exit:

(i,j,k => $s3, $s4, $s5)

Loop: sll $t1, $s3, 2add $t1, $t1, $s6lw $t0, 0($t1)bne $t0, $s5, Exitadd $s3, $s3, $s4j Loop

Exit:

X86 MIPS

PIII, P4, and AMD• PC World magazine, Nov. 20, 2000

– WorldBench 2000 benchmark (business applications)– P4 score @ 1.5 GHz: 164 (higher is better)– PIII score @ 1.0 GHz: 167– AMD Althon @ 1.2 GHz: 180– (Media applications do better on P4 vs. PIII)

• Why? => CPU performance equation– Time = Instruction count x CPI x 1/Clock rate– Instruction count is the same for x86– Clock rates: P4 > Althon > PIII– How can P4 be slower?– Average CPI of P4 must be worse than Althon, PIII

Summary• Instruction complexity is only one variable

– lower instruction count vs. higher CPI / lower clock rate

• Design Principles:– simplicity favors regularity– smaller is faster– good design demands compromise– make the common case fast

• Instruction set architecture– a very important abstraction!

New Topic – Arithmetic/Logic Ops• Arithmetic and logic unit (ALU)

– Core of the a computer– Performs arithmetic and logical operations on data

• Computer arithmetic issues– Number representation

• Integers and floating point• Finite precision (overflow / underflow)

– Algorithms used for the basic operations

• Properties of number representation– One zero– As many positive numbers as negative numbers– Efficient hardware implementation of algorithms

• 2’s complement: negate positive number and add one

Review

N decimal (+N) Positive

(-N)Sign/magnitude

(-N)1’s complement

(-N)2’s complement

0 00000000 10000000 11111111 000000001 00000001 10000001 11111110 111111112 00000010 10000010 11111101 111111103 00000011 10000011 11111100 111111014 00000100 10000100 11111011 111111005 00000101 10000101 11111010 111110116 00000110 10000110 11111001 111110107 00000111 10000111 11111000 111110018 00001000 10001000 11110111 111110009 00001001 10001001 11110110 1111011110 00001010 10001010 11110101 1111011020 00010100 10010100 11101011 1110110050 00110010 10110010 11001101 11001110100 01100100 11100100 10011011 10011100127 01111111 11111111 10000000 10000001128 NA NA NA 10000000

Overview

I- instruction

32-bit memory address

Addition

• 5ten + 6ten

0000 0000 0000 0000 0000 0000 0000 0101 (5ten)

0000 0000 0000 0000 0000 0000 0000 0110 (6ten)

0000 0000 0000 0000 0000 0000 0000 1011 (11ten)

+

=

Carries. . . (0) (1) (0) (0) (0)

. . . 0 0 1 0 1

. . . 0 0 1 1 0

. . . 0 (0)1 (1)0 (0)1 (0)1

+

Subtraction

• 12ten - 5ten

0000 0000 0000 0000 0000 0000 0000 1100 (12ten)

0000 0000 0000 0000 0000 0000 0000 0101 ( 5ten)

0000 0000 0000 0000 0000 0000 0000 0111 ( 7ten)=

-

• 12ten - 5ten = 12ten + (- 5ten)

0000 0000 0000 0000 0000 0000 0000 1100 (12ten)

1111 1111 1111 1111 1111 1111 1111 1011 ( -5ten)

0000 0000 0000 0000 0000 0000 0000 0111 ( 7ten)=

+

Overflow• Computer arithmetic is not closed w.r.t. + - * /• Overflow

– The result can not be expressed with 32 bits

• Overflow can not occur– Addition: if the operands have different signs

– Subtraction: if the operands have the same sign

• Overflow detection– Result needs 33 bits

– Addition: a carry out occurs into the sign bit

– Subtraction: a borrow occurs from the sign bit

Examples

• 4 bits (instead of 32 in MIPS) => can represent integers in [-8 : 7]

7 + 6

0 1 1 1 ( 7ten)

0 1 1 0 ( 6ten)

1 1 0 1 (13ten)

-7 + -6

1 0 0 1 ( -7ten)

1 0 1 0 ( -6ten)

0 0 1 1 (-13ten)

+

+

-7 – 6

1 0 0 1 ( -7ten)

0 1 1 0 ( 6ten)

0 0 1 1 (-13ten)

-7 – 6 = -7 + -6

1 0 0 1 ( -7ten)

1 0 1 0 ( -6ten)

0 0 1 1 (-13ten)

-

+

Overflow Conditions

Operation Operand A Operand B Result

A + B >= 0 >= 0 < 0

A + B < 0 < 0 >= 0

A – B >= 0 < 0 < 0

A – B < 0 >= 0 >= 0

MIPS Support• MIPS raises an Exception when overflow occurs

– Exceptions (or interrupts) act like procedure calls– Register EPC stores address of offending instruction– mfc0 $t1, $epc # moves contents of EPC to $t1– No conditional branch to test overflow

• Two’s complement arithmetic (add, addi, and sub)– Exception on overflow

• Unsigned arithmetic (addu and addiu)– No exception on overflow– Used for address arithmetic

• Compilers– C ignores overflows (always uses addu, addiu, subu)– Fortran uses the appropriate instructions

Conditional branch on overflow

addu $t0, $t1, $t2 # add but do not trapxor $t3, $t1, $t2 # check if sign differslt $t3, $t3, $0 # $t3 =1 if signs differbne $t3, $0, NO_OVFL # signs of t1, t2 differentxor $t3, $t0, $t1 # sign of sum (t0) different?slt $t3, $t3, $0 # $t3 = 1 if sum has different signbne $t3, $0, OVFL # go to overflow

addu $t0, $t1, $t2 # $t0 contains the sumnor $t3, $t1, $0 # negate $t1 ($t3 = NOT $t1)sltu $t3, $t3, $t2 # 232 –1 – t1 < t2?bne $t3, $0, OVFL # t1 + t2 > 232 –1 => overflow

Unsigned addition (range = [0 : 232 – 1] => $t1 + $t2 <= 232 – 1)

Signed addition

Registers $k0 and $k1

Registers

Offending procedure

Exception handling

procedure

EPC

Offending: . . . add $t0, $t1, $t2 . . .

Text

Stack

Data

• Exception handling procedure will use registers

• Procedure calling conventions do not work

• Reserve $k0 $k1 for the operating system

Logical Operations

• Operations on fields of bits within a 32-bit word– Characters (8 bits)– Bit fields (in C)

• Logical operations to pack/unpack bits into words– sll shift left– srl shift right– and, andi bitwise AND– or, ori bitwise OR

• Bitwise operators treat operand as vector of bits

C Bit Fields

#$s0: data; $s1: receiver

sll $s0, $s1, 22srl $s0, $s0, 24andi $s1, $s1, 0xfffeori $s1, $s1, 0x0002

$s0

struct { unsigned int ready: 1; unsigned int enable: 1; unsigned int receivedByte: 8;} receiver;int data = receiver.receiverByte;receiver.ready = 0;receiver.enable = 1;

31 9 2 1 010

$s1 receivedByte re

$s0

$s1 receivedByte 0e

$s1 receivedByte 01

Conclusions

• ISA supports architectural development

• Hardware/Software, RISC/CISC emphasis

• Technology driven

• ALU = core of computer

• ALU problem = overflow

• Exception handling

• Think: Weekend! =>