Implement Synthesizable Square Root Algorithm On Fpga Engineering Essay

Implement Synthesizable Square Root Algorithm On Fpga Engineering Essay The main objective of this paper is to implement synthesizable square root algorithm on FPGA. As square root function is not synthesizable on Silicon, this paper proposes optimized non restoring square root algorithm for unsigned 8 bit number on ED2C20F484C7 device in Cyclone II family. This algorithm is implemented in gate level abstraction of Verilog HDL. The basic building block of the design is CSM (Controlled Subtract Multiplex) block. It makes use of only subtract operation and append 01 which is an improvement over restoring algorithm. Keyword: FPGA,CSM,Verilog HDL,fixed point Introduction The square root function is a basic operation in computer graphic and scientific calculation application. Due to its algorithm complexity, the square root operation is hard to be designed in digital system. As known, digital system has been used in daily life or industrial purpose that may have been in need of square root operation to fully execute its functions. Scientists have developed various algorithms for square root calculation. But the implementation of algorithms is difficult because of their complexities and thus results into long delays for its completion. There are two main families of algorithms that can be used to extract square roots. The first family is that of digit recurrence, which provides one digit (often one bit) of the result at each iteration[6]. Each iteration consists of additions and digit-by-number multiplications (which have comparable cost) Such algorithms have been widely used in microprocessors that didnt include hardware multipliers. Most of the FPGA implementations in vendor tools or in the literature use this approach. Second family of algorithms uses multiplications. It includes quadratic convergence recurrences derived from the Newton-Raphson iteration [5]. The digit recurrence approaches allow one to build minimal hardware, while multiplicative approaches allow one to make the best use of available resources when these include multipliers. Also there are estimation method and digit-by-digit method. Digit-by-digit method is classified into two distinct classes: restoring and non- restoring algorithm [1]. In restoring algorithm, remainder is restored in the regular flow. So its implementation needs more hardware. Compared to the restoring algorithm, the non restoring algorithm does not restore the remainder, which can be implemented with fewest hardware resource and the result is hardware simple implementation. It is most suitable for FPGA implementation. Restoring and non restoring square root calculation Restoring Algorithm Step 1: If it is a 2n bit number then divide it in a group of 2 bits Step2: Subtract 1 from the first 2 digits (starting from MSB) Step3: Whenever the result of the subtraction is positive then the developed root is 1 otherwise 0 Step4: Whenever the result is negative, write it as it is. We have to restore the wrong guess by appending 01 and guessed square root. Step5: Now take the next two digits Step6: Append 01 (to be subtracted from next two digits of dividend) and guessed square root to subtract from the remainder. Step7: If the result of subtraction is negative then restore previous remainder by adding wrong guess by appending 01 and guessed square root. Step8: Every time guessed square root has to be updated while appending 01. Step9: Continue the steps until the group of two digits end 1 0 0 1.1 0 1 0 01 01 11 01.00 00 00 00 01 00 01 take next two digits from dividend 1 01 Append 01 Negative value 11 00 + 1 01 0 0 01 11 -10 01 11 10 Negative value + 10 01 01 11 01 10 00 01 11 00 00 10 01 01 01 01 1 00 10011 01 1011111 + 1001101 010110 00 010011001 000010111 00 100110101 1100100111 Figure 1: The example of restoring algorithm to solve square root B. Proposed Modified Non Restoring Algorithm A little modification in non restoring algorithm makes calculation faster. It uses only subtract operation and appends 01. It uses n stage pipelining to find square root of 2n bit number. The following algorithm describes the modified non restoring square root algorithm. Step1: Start Step2: Initialize the radicand (p) which is 2n bit number. Divide the radicand in two bits beginning at binary point in both directions. Step3: Beginning on the left (most significant), select the first group of one or two digit (If n is odd then first group is one digit ,else two bits) Step4: Select the first group of bits and subtract 01 from it. If borrow is zero, result is positive and quotient is 1 else it is 0. Step5: Append 01(to be subtracted next two digits of dividend) and guessed square root to subtract from remainder of previous stage Step6: If result of subtraction is negative, write previous remainder as it is and quotient is considered as 0, else write the difference as remainder and quotient as 1. Step7: Repeat step 5 and step 6 until end group of two digits. Step8: End 1 0 0 1.1 0 1 0 01 01 11 01.00 00 00 00 00 01 00 01 take next two digits from dividend 1 01 Append 01 11 10 01 01 11 01 100 01 11 00 00 1001 01 001011 00 1001101 00101100 00 10011001 0000010111 00 100110101 001011100 Figure 2: The example of modified non restoring algorithm to solve square root Basic Building Block for Non restoring algorithm Inputs of the building block are x,y,b and u while d and b0(borrow) are outputs. If b0=0, then d b0=( ~ x .y)+(b.~x)+(by); d= (~x.y.~b.~u)+(~x.~y.b.~u)+(x~y.~b)+(x.u)+(x.y.b); csmblock.jpg Figure 3: RTL schematic of CSM block The generalization of simple implementation of non restoring digit by digit algorithm for unsigned 6 bit square root by array structure is shown in Fig.4. Each row of the circuit executes one iteration of non restoring digit by digit square algorithm, where it only uses subtract operation and appends 01. Figure 4: Pipelined structure of 6 bit unsigned square root number The design can be optimized by minimizing the logic expressions and can be implemented by modifying CSM block. The specialized entities A,B,C,D,E,F,G and H are derived from CSM block and are defined as follows: For csmA, ybu = 100 b0 = ~x d = ~x For csmB, yu = 00 b0 = ~x.b d = ~x.b + ~b.x For csmC, u = 0 b0 = ~x.y + ~x.b + y.b d = ~x.y.~b + ~x.~y.b + x.~y.~b + x.y.b For csmD, yb = 10 b0 = ~x d = ~x.~u + x.u For csmE, y = 0 b0 = ~x.b d = ~x.b.~u + ~b.x + x.u For csmF, xy = 00 b0 = b d = b.~u For csmG, xyb = 010 b0 = ~x d = ~u For csmH, xyu = 000 b0 = b Figure 5: Optimized Pipelined structure of 8 bit unsigned square root number Results and analysis The Non Restoring algorithm can be implemented with least hardware resources and the result will be the faster than restoring square rooting techniques. The source code is implemented in such a way that it can be extended according to users requirement to calculate complicated square root in FPGA. Figure 6: Simulation result of 8 bit square root using non restoring algorithm The DE1 kit has 4 seven segment displays only so the maximum number which can be displayed is 9999d and also it doesnt have a decimal point. Hence output obtained is less precise if one of the displays is considered as a decimal point. Table 1 shows the list of Logic Elements usage for 8 bit implementation. This indicates the size of the implemented circuit hardware resource. Table 1: Comparison of LEs usage in 8 bit implementation No Implementation of non restoring algorithm for 8 bit LEs 1 8 bit (with seven segment) 85 2 8 bit (without seven segment) 71 3 optimized 8 bit (with seven segment) 64 4 optimized 8 bit (without seven segment) 50 Table 2: PowerPlay Power Analyzer Status No PowerPlay Power Analyzer Status 8 bit with optimization (mW) 8 bit without optimization (mW) Low Medium Low 1 Total Thermal Power Dissipation 71.65 447.96 72.84 2 Core Dynamic Thermal Power Dissipation 0 190.47 0 3 Core Static Thermal Power Dissipation 47.36 48.06 47.36 4 I/O Thermal Power Dissipation 24.29 209.44 25.48 Conclusion: This implementation and analysis shows that proposed method is most efficient of hardware resource. This is reasonable, because it only uses subtract operation and append 01. The result shows that the proposed algorithm is easy to implement and also uses less resources. The result is extended for square root implementation of 8 bit floating point number and also it can be expanded to larger numbers to solve complicated square root problem in FPGA implementation.

Book Review on The Lucky One Essay

In the blink of an eye, something happens by chance – when you least expect it sets you on a course that you never planned, into a future you never imagined. What if someone had saved your life before you even met? How far will you travel to find love? Will you engage in a journey of love and luck that will change your life forever? Will you take the quests to happiness when you know to yourself that you will be taking risks and that the journey you will take is a trial-and-error thing? For him, that was all possible. He was a wonderful man. And when a man is that special, you know it sooner than you think possible. You recognize it instinctively; there will never be another one like him. He was Logan Thibault, a one of a kind man who sets out a journey to find a girl, who was believed to be his lucky charm. Meeting her embarks the roller coaster ride of love, luck, fortune, romance and big secrets. Literary Work and Comment The literary work of Nicholas Sparks is a brilliant one. He had narrated a story of love and romance, of luck and journey. But like any other stories, this depicts lives of people. This is less dreamy and is more realistic even at times pragmatic – in spite of the belief in a lucky charm. The story revolves around the life of a U.S. Marine during his third tour of duty in Iraq and the photograph he had found. That was a photo of a smiling young woman half buried in the dirt. His first instinct is to toss it aside. Instead, he brings it back to the base for someone to claim, but when no one does, he finds himself always carrying the photo in his pocket. Soon Thibault experiences a sudden streak of luck—winning poker games and even surviving deadly combat that kills two of his closest buddies. Only his best friend, Victor, seems to have an explanation for his good fortune: the photograph—his lucky charm. Back home in Colorado, Thibault can’t seem to get the photo—and the woman in it—out of his mind. Believing that she somehow holds the key to his destiny, he sets out on a journey across the country to find her, never expecting the strong but vulnerable woman he encounters in Hampton, North Carolina—Elizabeth, a divorced mother with a young son—to be the girl he’s been waiting his whole life to meet. Caught off guard by the attraction he feels, Thibault keeps the story of the photo, and his luck, a secret. As he and Elizabeth embark upon a passionate and all-consuming love affair, the secret he is keeping will soon threaten to tear them apart—destroying not only their love, but also their lives. Theme and Purpose This story is melodramatic and is more realistic. The author has always written stories where happiness and tragedy meet, full of little coincidences that may change people’s lives forever. The stories he wrote often are sentimental, since they are always about quests for love and romance and all about sadness as well. The author had presented us how a marine lived his life during the times when he was on a duty in Iraq. A lot of scenes in the novel were inspired with the timely events that had happened in Iraq back in 2008. During that time, that war in Iraq dominated the front pages of newspapers and is headlines on almost all television networks all over the world. But then, what the author is pointing out here is that stories about military men and personnel are often personal and focuses on their families or the struggles they faced upon returning home. Thus, the author wanted the readers to have a picture on their minds on what a marine officer is encountering mainly the preparations before the war, during the battle and after their duties. The author wanted us to be more aware on how a marine fought battles. He wanted his readers to experience, even by just reading his work, how to deal things when you are in a real battle in a vast battlefield. Bottom line of it all, the author wanted us to picture out strengths and determination from the main characters of the story. He wanted us to know and feel that pursuance on a certain thing you are into could give you a prosperous life. He is giving us an example, for us to reflect on ourselves, how to deal with problems. Problems are our enemies and every day we are dealing with it. We are living in a great battle field and for you to win and conquer it all, we must have strengths in ourselves and be determined enough to pursue everything we ought to do. We must believe that we can beat every problem that will come in our way. This are just spices in gaining a fruitful life ahead. Techniques Used The author had offered us a good story line. This story is surely be loved by avid romance novel readers most especially because of the beautiful plot he had created. The twists and turns of events are unpredictable that will surely make you crave for more of his works. The very first thing I had noticed was the flashback technique the author had used which is very common for all stories; using this may not let readers enjoy because they already know this kind of technique. So he had come up with a technique that you will notice from this certain novel and that is by using the voice of the characters. The author is writing in the limited third-person omniscient, thus allowing the reader to feel almost â€Å"first-person† closeness with the character, while still allowing all the characters to participate. Each chapter is told through the perspective of a single character. For example, in chapters labeled â€Å"Thibault,† only Thibault’s thoughts are included. Anything another character does is seen through his perspective, one that Thibault must only assume. If he’s talking to Beth, he can intuit what she’s thinking, but the readers are never allowed to know for sure. Until, of course, the next chapter arrives (perhaps labeled â€Å"Beth†) where she might reflect on what she’d actually been thinking. It’s a powerful form of writing and the author had used it effectively. He had overcome the challenge to make each character’s voice distinct enough to be immediately recognizable. In other words, the readers were able to â€Å"know† who’s talking, even if the chapter hadn’t been labeled at all. There was a learning curve associated with this. It made the development of the relationship between Thibault and Beth a bit more difficult (since it was only through one person’s eyes at any given time), but on the other hand, it made the characters themselves a bit easier to craft. And some voices were more difficult than others. Then, of course, there’s the challenge of keeping the story â€Å"linear.† That’s a bit tougher to do when writing with this form of literary voice. This kind of technique used by the author is somewhat confusing at first but as you go on reading the story, you will gradually understand and grasp the technique implied. It is so great that someone had done this kind of technique in writing because not all writers, regardless of what genre they are into, are good in narrating stories with this kind of technique. Opinion This is a great story indeed. Nicholas Sparks had written such a beautiful romance novel. His work is elevated by a very persuasive manner of storytelling. Readers are not expected to read his books because they are true but because they ought to be true. The story is very well plotted. The sequencing of events as well as the techniques used is very much commending. Sparks writes in such a way that it keeps you informed, seduced, captivated, and never bored. The chapters move along swiftly and it is written so well that you are not struggling to make it through each chapter. Each chapter would focus on a particular character and the chapter would be titled with their name: Thibault, Beth or Clayton. I loved that we got to delve into every characters lives. Everyone was explored with the same amount of back story. You never felt a lack of information. The storyline stays true and builds to an exciting climax. Sparks knows how to build a story and keep a reader anxiously turning pages. This is my first time to read a Nicholas Sparks novel and I surely bet this wouldn’t be the last because I had enjoyed reading it. The way he presented his work to his readers is so much appealing that you will surely crave for more.

Find Out Who is Worried About Professional College Paper Writers and Why You Need to be Paying Attention

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Caribbean American Women - 1256 Words

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