Lecture 2: Advanced Instructions, Control, and Branching

EEN 312: Processors: Hardware, Software, and Interfacing

Department of Electrical and Computer Engineering

Spring 2014, Dr. Rozier (UM)

COURSE PLAN FOR TODAY

1.Representing Numbers2.Logical Operations3.Control Instructions

REPRESENTING NUMBERS

Unsigned Binary Integers• Given an n-bit number

00

11

2n2n

1n1n 2x2x2x2xx

Range: 0 to +2n – 1 Example

0000 0000 0000 0000 0000 0000 0000 10112

= 0 + … + 1×23 + 0×22 +1×21 +1×20

= 0 + … + 8 + 0 + 2 + 1 = 1110

Using 32 bits 0 to +4,294,967,295

2s-Complement Signed Integers• Given an n-bit number

00

11

2n2n

1n1n 2x2x2x2xx

Range: –2n – 1 to +2n – 1 – 1 Example

1111 1111 1111 1111 1111 1111 1111 11002

= –1×231 + 1×230 + … + 1×22 +0×21 +0×20

= –2,147,483,648 + 2,147,483,644 = –410

Using 32 bits –2,147,483,648 to +2,147,483,647

2s-Complement Signed Integers• Bit 31 is sign bit

– 1 for negative numbers– 0 for non-negative numbers

• –(–2n – 1) can’t be represented• Non-negative numbers have the same unsigned and

2s-complement representation• Some specific numbers

– 0: 0000 0000 … 0000– –1: 1111 1111 … 1111– Most-negative: 1000 0000 … 0000– Most-positive: 0111 1111 … 1111

2s-Complement Signed Integers• Complement and add 1

– Complement means 1 → 0, 0 → 1

x1x

11111...111xx 2

Example: negate +2 +2 = 0000 0000 … 00102

–2 = 1111 1111 … 11012 + 1 = 1111 1111 … 11102

Hexadecimal• Base 16

– Compact representation of bit strings– 4 bits per hex digit

0 0000 4 0100 8 1000 c 1100

1 0001 5 0101 9 1001 d 1101

2 0010 6 0110 a 1010 e 1110

3 0011 7 0111 b 1011 f 1111

Example: eca8 6420 1110 1100 1010 1000 0110 0100 0010 0000

LOGICAL OPERATIONS

Bitwise Operations

• Sometimes we want to operate on registers in a bitwise fashion.

• Logical Operations• Shifts• Rotates

Logical Operations

• Instructions for bitwise manipulation

Examplebic r0, r1, r2 @ bitwise NAND r1 and r2, store

the result in r0

Operation C Java ARM

Bitwise AND & & and

Bitwise OR | | orr

Bitwise XOR ^ ^ eor

Bitwise NAND ~(A & B) ~(A&B) bic

The ARM Barrel Shifter

• ARM architectures have a unique piece of hardware known as a barrel shifter.– Device moves bits in a word left or right.

• Most processors have stand alone instructions for shifting bits.

• ARM allows shifts as part of regular instructions.

• Allows for quick multiplication and division.

The ARM Barrel Shifter

The ARM Barrel Shifter

• Reality of the hardware– There are no shift

instructions– Barrel shifter can be

controlled WITH an instruction

– Can only be applied to operand 2 on instructions which use the ALU

Types of Shifting

• Logical Shifts– lsl – left– lsr – right

• Arithmetic Shifts– asr – right

• Rotates– ror – right– rrx – right with extend

Example

mov r0, r1, lsl #1

This would perform a logical shift left of 1 bit on r1, and then copy the result into r0.

mov r0, r1, lsl r2

This would do the same as before, but use the value of r2 for the shift amount.

Logical Shifts

• Logical shifting a number left or right has the effect of doubling or halving it.

• lsl– Highest order bit shifts into the carry flag– Lowest order bit is filled with 0.

• lsr– Lowest order bit shifts into the carry flag– Highest order bit is filled with 0.

LSL C b7 b6 b5 b4 b3 b2 b1 b0

Before 0 1 0 0 0 1 1 1 1

After 1 0 0 0 1 1 1 1 0

Arithmetic Shift

• Preserves the sign bit.

• asr– Extends the sign bit to the second most significant– Shifts the least significant into the carry flag.

LSL C b7 b6 b5 b4 b3 b2 b1 b0

Before 0 1 0 0 0 1 1 1 1

After 1 1 1 0 0 0 1 1 1

Rotations

• Rotates bits from low order to high order

• ror– Moves bits from the lowest order to the highest, setting the carry bit in the

process with the last bit rotated out.

• rrx– Always and only rotates by one position. – Carry flag is dropped into the highest order bit. Lowest order bit is moved to

the carry flag

LSL C b7 b6 b5 b4 b3 b2 b1 b0

Before 0 0 0 0 0 1 1 1 1

After 1 1 0 0 0 0 1 1 1

Rotations

• ror

• rrx

Adding a Shift or Rotate

• Shifts and rotates can be used with:– adc, add, and– bic– cmn, cmp– eor– mov, mvn– orr– rsb– sbc, sub– teq, tst

BRANCHING

Branching

• What makes a computer different from a calculator?

Branching

• Branches allow us to transfer control of the program to a new address.– b (<suffix>) <label>– bl (<suffix>) <label>

b startbl start

Branch (b)

• Branch, possibly conditionally, to a new address.

beq subroutine @ If Z=1, branch

• Good practice to use bal instead of b.

Branch with link (bl)

• Branch, possibly conditionally, to a new address.– Before the branch is complete, store the PC in the

LR.– Allows easy return from the branch.

bleq subroutine @ If Z=1, branch, saving the PC

Branch with link (bl)

• How do we get back once we’ve saved the PC?

mov pc, lr

• Moves the contents of the link register to the program counter.

Implementing If Statements

• C code:if (i == j) f = g+h;else f = g - h;

• ARM code cmp r0, r1 @ Set flags via r0-r1 and discard

beq Elseadd r2, r3, r4 @ r2 = r3 + r4bal Exit

Else:sub r2, r3, r4 @ r2 = r3 + r4

Exit:

Implementing Loop Statements

• C code:while (i < j) i += 1;

• ARM code Loop:

cmp r0, r1bge Exitadd r0, r0, #1bal Loop

Exit:

i < j?i < j?

i=i+1i=i+1

i<j

ExitExit

i>=j

Basic Blocks• A basic block is a sequence of instructions with

– No embedded branches (except at end)– No branch targets (except at beginning)

A compiler identifies basic blocks for optimization

An advanced processor can accelerate execution of basic blocks

EXERCISE

THE HUMAN PROCESSOR

WRAP UP

For next time

• Read Chapter 2, Sections 2.6 – 2.8

• Learn about control, branch, loops, etc.