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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 Numbers 2. Logical Operations 3. Control Instructions REPRESENTING NUMBERS Unsigned Binary Integers • Given an n-bit number n1 x xn12 xn2 2 x12 x0 2 1 0 Range: 0 to +2n – 1 Example n2 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 n1 x xn12 xn2 2 x12 x0 2 1 0 Range: –2n – 1 to +2n – 1 – 1 Example n2 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 x x 1111...1112 1 x 1 x 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 1 2 3 0000 0001 0010 0011 4 5 6 7 0100 0101 0110 0111 8 9 a b 1000 1001 1010 1011 c d e f 1100 1101 1110 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 Operation C Java ARM Bitwise AND & & and Bitwise OR | | orr Bitwise XOR ^ ^ eor Bitwise NAND ~(A & B) ~(A&B) bic Example bic r0, r1, r2 @ bitwise NAND r1 and r2, store the result in r0 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 C b7 b6 b5 b4 b3 b2 b1 b0 Before 0 1 0 0 0 1 1 1 1 After 0 0 0 1 1 1 1 0 1 • 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. Arithmetic Shift • Preserves the sign bit. LSL C b7 b6 b5 b4 b3 b2 b1 b0 Before 0 1 0 0 0 1 1 1 1 After 1 1 0 0 0 1 1 1 1 • asr – Extends the sign bit to the second most significant – Shifts the least significant into the carry flag. Rotations • Rotates bits from low order to high order LSL C b7 b6 b5 b4 b3 b2 b1 b0 Before 0 0 0 0 0 1 1 1 1 After 1 0 0 0 0 1 1 1 1 • 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 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 start bl 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 Else add r2, r3, r4 @ r2 = r3 + r4 bal Exit Else: sub r2, r3, r4 @ r2 = r3 + r4 Exit: Implementing Loop Statements • C code: while (i < j) i += 1; • ARM code Loop: i<j i>=j cmp r0, r1 bge Exit add r0, r0, #1 bal Loop Exit: i < j? i=i+1 Exit 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.