Dr. Chuck Cartledge. 15 July 2015

Transcription

1 Miscellanea 6.5 Fun with Fibonacci Break 1.5 Exam Conclusion References CSC-205 Computer Organization Lecture #008 Chapter 6, section 5, Chapter 1, section 5 Dr. Chuck Cartledge 15 July /30

2 Table of contents I Miscellanea Fun with Fibonacci 4 Break 6 Exam 7 Conclusion 8 References 2/30

3 Corrections and additions since last lecture. Return chapter 5 homework Return remaining tests 3/30

4 Dynamic memory allocation What is it and why should I care?? Different types of memory allocation: Static you know in advance how much you need and you want to keep stuff around Allocated by the compiler/translator Dynamic you don t know how much you ll need and your needs may change as the program executes Allocated by the application Released by the application Released dynamically allocated memory can cause memory to become fragmented and unusable. Released dynamically allocated memory can be cleaned up via garbage collection techniques. Allocation and consolidation of dynamic memory usually handled by the Operating System. 4/30

5 Dynamic memory allocation Translating global pointers A new C++ token, the asterisk * means the variable points to a memory location. It strips away one layer of information hiding. Create three pointers and give those pointers names. new dynamically sets aside a number of bytes that the pointer points to Need to tell the compiler to use the value of the pointer vice the location of the pointer (that s what all those asterisks are about) Assembler code uses indirect addressing to get to the actual value of things (0x0012 and 0x0018 for example) Pages /30

6 Dynamic memory allocation Translating local pointers Very similar in structure to translating global pointers. The variables live on the stack. Pointers point to locations in the stack. Pages /30

7 Dynamic memory allocation Translating structures (ideas) What is a structure?? It is a group of data elements brought together under the same name. Data elements can be of different types and sizes Data elements can be in any order The structure name refers to the entire group Structure data element name refers to the element within the structure In many ways, like predefined types on steroids. 7/30

8 Dynamic memory allocation Translating structures (example) Load the offset into the INDEX register (0x0008) The INPUT a character into the base memory location plus the offset in the INDEX register (0x000B) Same sort of process to output the data (load offset into INDEX, output relative to base address) Pages /30

9 Dynamic memory allocation Translating linked list structures (ideas) What is a linked list?? And why do I care?? A linked list is an ordered set of data elements, each containing a link to its successor What is a ordered list?? A collection of elements where you can say one follows (or proceeds) another. What is a link?? A pointer (our friend from before) to the another (usually the next one) element. The link from the last element to the next one is usually NULL. Somehow you have to have a pointer to the first item in the list. 9/30

10 Dynamic memory allocation Translating linked list structures (example) We define a structure that we will used to link things. We create a couple or pointers for the current and next structure We create a structure (0x0021), update the structure s pointers (0x0018), enter a value, store it into a structure (0x002A based on the base of the structure and an offset), and repeat Pages (program 10/30

11 Hystorical perspective (no that isn t a typo) Leonardo Bonacci (c c. 1250) Considered to be the most talented Western mathematician of the Middle Ages. Most notable work Liber Abaci (1202) introduced: Arabic numbers Place values Promoted his ideas by applying them to bookkeeping Image from [2]. Posed a problem having to do with rabbits. 11/30

12 Hystorical perspective (no that isn t a typo) Fibonacci s rabbits (the background) The growth of an idealized rabbit population, assuming that: 1 A newly born pair of rabbits, one male, one female, are put in a field; 2 Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; 3 Rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month. 12/30

13 Hystorical perspective (no that isn t a typo) Fibonacci s rabbits (the puzzle) How many pairs will there be in one year? 1 At the end of the first month, they mate, but there is still only 1 pair. 2 At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. 3 At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. 4 At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n - 2) plus the number of pairs alive last month (n - 1). 13/30

14 Hystorical perspective (no that isn t a typo) Fibonacci s rabbits (math) The Fibonacci series: F n =F n 1 +F n 2 It starts: Traditional: F 1 =F 2 =1 Modern: F 0 =0,F 1 =1 Negative Fibonacci number exist as well F n 2 =F n F n 1 F n =( 1) n+1 F n 14/30

15 Hystorical perspective (no that isn t a typo) Fibonacci numbers (solutions) More than one way to skin a cat (number 49 with duct tape is exciting): For loops Recursive function Function (direct look up) State machine A process queue is left for conjecture. Sample programs are attached to this pdf. Image from [1]. 15/30

16 Break time. Take about 10 minutes. 16/30

17 Real and floating point numbers So far we have only looked at integers, the counting numbers. What about real or floating point numbers?? How do we represent the value 5.375?? For integers: n= positions i=1 val i base (i 1) For floating point: n= positions i=1 val i base (i 1 m) m is the number of bits to the right of the decimal point If m=3 then = Like so many other things, we change the definition of the bits. 17/30

18 Real and floating point numbers So how does this work?? We ll pick it apart. n= cellsize i=1 val i base (i 1 m) base =2,m=3 How do we represent the decimal point in binary?? 18/30

19 Real and floating point numbers Another mechanical way to convert to binary. Repeatedly divide the integer portion by 2 and record the remainder Repeatedly multiply the fractional portion by 2 and record the overflow = Stop converting when the integer and fractional part are 0. 19/30

20 Real and floating point numbers What happens with messy numbers?? As an exercise, convert 1.2 (10) to binary Some fractions can not be represented by a fixed length binary number... 20/30

21 Real and floating point numbers Our friend, scientific notation. A short hand way of writing numbers. Makes things like multiplication and division of large numbers trivial. A couple of examples = Three parts: 1 Sign (- in this case) 2 Coefficient (3.284 in this case), sometimes called the significand 3 Exponent (2 in this case) 4 Base (10 in this case) value = SignCoefficient Base Exponent Writing numbers in scientific notation is called normalized form. 21/30

22 Real and floating point numbers Remember the question about where do we store the decimal point?? When dealing with numbers in the normalized form, everyone knows where the decimal is, so no one has to store it. And because everyone knows that the most significant bit has to be 1, no has to store it. Hidden and excess bits are conventions that allow more bits to be used where they are needed. 22/30

23 Real and floating point numbers Special Values The limitation on the cell size (i.e., the number of bits we can use) places a limit on the range of values we can represent. We ve seen how ADDing can overflow a cell. Normalization limits the smallest coefficient that we can have greater than 0. Operations using values in range can result in values that can not be represented. Sign bit, 7 bit coeff, 5 bit expon. All of these errors can to caught by the CPU and software. 23/30

24 Real and floating point numbers There are too many possibilities. We need standardization. The IEEE 754 Floating Point Standard to the rescue. Each CPU manufacturer had their own floating point representation. Each felt their s was the best. Application software on one machine may not run correctly on another machine. 24/30

25 Real and floating point numbers IEEE 754 Special Values and Notes Predefined special values by the specification: Positive and negative infinity: sign 0/1, expon. all 1s, coeff all 0s Not a Number (NaN): sign 0/1, expon. all 1s, coeff anything except all 0s Precision: or Rounding: nearest, even, 0, +/- infinity 25/30

26 Miscellanea 6.5 Fun with Fibonacci Break 1.5 Exam Conclusion References Steps to succeed on the exam. General guidelines and directions Pay attention to the examples Understand the homework Work questions that have answers Ask questions 26/30

27 Miscellanea 6.5 Fun with Fibonacci Break 1.5 Exam Conclusion References Steps to succeed on the exam. Things of real interest in chapter 5 Assembly language: Understanding figures 1 and 2 What do the pseudo-operators do How does the von Neumann cycle work What does it mean to translate from HOL6 to ISA3 or ASL5 27/30

28 Steps to succeed on the exam. Things of real interest in chapter 6 Compiling to the Assembly level Understanding the stack and the heap Understanding the addressing modes (and there are several of them) What purpose does the stack and the heap serve relative to variables and functions How are C++ statements translated into Pep/8 How are values passed between callers and callees How are indexes into arrays handled What types of memory allocation are there and how are they 28/30

29 What have we covered? Chapter 6, section 5 Different ways to have fun with Fibonacci Repeat of Chapter 1, section 5 Preps for the exam covering chapters 5 and 6 Next week: Exam covering chapters 5 and 6 Fun with von Neumann 29/30

30 References I [1] Hanson Schmidt-Cornelius, Recursion for runaways, [2] Wikipedia Staff, Fibonacci, /30