Modification of Power Series Expansion

Modification of Power Series Expansion The available methods to compute the logarithm of a number using digital circuits can be divided in two main groups. On the one hand, we have the look-up table based algorithms and, on the other, iterative methods. The first approach is faster and straightforward, but only useful for low precision. For implementing it, requires large amount of memory for increasing the accuracy. This is due to the size of the look-up table. We only evaluated iterative algorithms that need small look-up tables. The second group is slower, but suitable for high precision. Taylors series expansion is among the most popular methods to manually compute logarithms, but it has a slow convergence and requires slow operations like the division. Hence, they are slow when no embedded multipliers are available. Many studies explore hybrid implementations that take advantages from both groups. Our project required an algorithm that could be implemented on FPGAs from any vendor. It should be platform independent. Our algorithm requires less memory and no multiplier at all to implement exponential and logarithm function. To the best of our knowledge there are only two previous works focused on the exponential  function [8] [9], and only one for the logarithm function [10] (from the same authors of [9]). The first one [8], employs an algorithm that does not exploit the FPGA characteristics, and  consequently presents poor performance. The other two implementations [9, 10] are part of  a common work and are designed suiting with FPGA flexibility (using internal tailored fixed  arithmetic and exploiting the parallelism features of the FPGA) achieving much better results. They are parameterizable implementations that, additionally to single f.p. format, also allow  smaller exponent and mantissa bit-widths and are both based on input range reduction and  table-driven methods to calculate the function in the reduced range. Our ex and ln x units,  based on these units, include the following innovative features: Single precision f.p. arithmetic extension. [9, 10] were designed considering only normalized numbers, not denormalized. Additional logic has been introduced to handle  denormalized numbers at the output of ex and the input of ln x.  ² Redesign of units to deal only with single precision. The feature of bit-width config-urability of the base designs has been removed. Thus, the resources needed have been  reduced because specific units, just for single precision, have been developed.  ² Simplification of constant multiplications. As suggested in [9], conventional multipliers  have been removed where the multiplications involved constant coe ±cients, improving  performance and reducing size.  ² Unsigned arithmetic. In [9, 10] internal fixed arithmetic with sign is used. However,  some operations (like the ones involving range reduction and calculation of the exponent  for the result in ex) are consecutive and related, and the sign of the result can be inferred  from the input sign. For such operations signed arithmetic has been replaced by unsigned  arithmetic with the corresponding logic reduction.  ² Improved pipelining. The speed is enhanced by systematically introducing pipeline  stages to the datapath of the exponential and logarithm units and their subunits   The paper [11] explains about the implementation of power and log function based on a simple modification of power series expansion of Taylor series. In power function implementation, the paper aims at reducing the exponent number to a smaller value. It requires a large amount of block ram and hardware multipliers as well. It becomes platform dependent and the clock frequency may vary from vendor to vendor. The degradation in throughput rate is due to the use of 18 X 18 embedded multipliers in it. The powering unit also requires more number of stages which may be reduced further. In the proposed method, we are going to reduce delay and improve the throughput rate by avoiding the embedded multipliers and block RAMs. In this paper, we are not completely avoid look up tables, but any value of logarithm or exponential can be calculated, by adjusting the look up table values to the desired number [8] C. C. Doss and R. L. Riley, FPGA-Based implementation of a robust IEEE-754 ex-ponential unit, in IEEE Field-Programmable Custom Computing Machines, 2004, pp.  229{238. [9] J. Detrey and F. de Dinechin, A parameterized  °oating-point exponential function for  FPGAs, in IEEE International Conference Field-Programmable Technology, 2005, pp.27{34. [10] ||, A parameterized  °oating-point logarithm operator for FPGAs, in Signals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference,  2005, pp. 1186{1190. [11] Pedro Echeverra, Marisa Lopez-Vallejo,†An FPGA Implementation of the Powering Function with Single Precision Floating-Point Arithmetic† â€Å"An FPGA Implementation of the Powering Function with Single Precision Floating-Point Arithmetic† PROPOSED METHOD The proposed method avoids multiplication and division operations, and is thus suitable for implementation in software on processors that lack such instructions (or where the instructions are slow) or in hardware on a programmable logic device or dedicated chip. This method is suitable when shifters are available in abundant. It is an extension to the implementation of sine and cosine explained in CORDIC. The proposed algorithm evaluates the power functions for both positive and negative values. There are some constants by which it is easy to multiply. For example, multiplying by 2n, where n is a positive or a negative integer, can be achieved by simply shifting a number by n places. The shift will be to the left (division) if n is positive, to the right (multiplication) if n is negative. It is nearly as easy to multiply by numbers of the form  ±2n ±1. These simply involve an add (or) subtract a shift. Implementation of EXP:     Ã‚   For implementing y = exp(x). The algorithm is going to generate a sequence of values for x and y, and we are going to make sure that for each pair K Exp(k) 5.5452 256 2.7726 16 1.3863 4 0.6931 2 0.4055 3/2 0.2231 5/4 0.1178 9/8 0.0606 17/16 0.0308 33/32 0.0155 65/64 0.0078 129/128 y=exp(4) · y†²=exp(4) ·exp(-(xk)) =exp(4) ·exp(-x) ·exp(k) =y ·exp(k). In other words, if we subtractkfromx, we have to multiplyyby exp(k). All we have to do now is make sure that exp(k) is a nice number, so we can multiply by it easily, and the rest is straightforward. Note thatkitself does not have to be nice, as we are only subtracting that, not multiplying by it. Here are some nice values of exp(k) and the corresponding (not necessarily nice) values ofk. The flow of algorithm is as follows for positive powers of x: Here in each iteration, we subtract the input from the nearest value of exp(k) as listed in the table. If the difference is negative, we multiply the output by the corresponding exp(k). The process continues withmore entities in our table of k, finally we get the result. In the same way the flow chart is mentioned for nagative powers of x. K Exp(k) 5.5452 256 2.7726 16 1.3863 4 0.6931 2 0.2877 3/4 0.1335 7/8 0.0645 15/16 0.0317 31/32 0.0157 63/64 0.0078 127/128 0.0039 255/256 The flow of algorithm is as follows for negative powers of x: Here in each iteration, we subtract the input from the nearest value of exp(k) as listed in the table. If the difference is positive, we divide the output by the corresponding exp(k). The process continues withmore entities in our table of k, finally we get the result. Implementation of LOG : For implementing Y=log (x), the procedure is similar to the implementation of exponential function

Philosophy Life Examination

My Life Examination First of all, my previous essay was a part of my life examination. I am glad you caught me on plagiarizing because now I really know that you read all of our essays. Unfortunately a few of my classmates and I did have doubts about it. Also, I feel like I can argue a lot for plagiarizing, but that is not what this assignment is about. Even though I agree with Sergey Trufanov’s ideas about life in general, I do not feel like I can explore them further and simply reciting them would also be considered as plagiarism.But I do have my own conclusions about life examination, disappointments, and death. I cannot say that I am a philosopher, just like I cannot say that I can speak English. In order to claim that, a person needs to be comfortable using his tools to be considered a professional, which unfortunately, I am not, but I do believe that my ideas deserve to exist and to be explored in philosophical ways. Life examination. To examine life you need to test it, challenge it. Everyone knows that you won’t know till you try, but for some reason not everyone does it.In my opinion it is better to do something and regret it than not do anything and regret not even trying. It refers even to the smallest things, like a new flavor of ice-cream. How would you know that you do not like it unless you taste it? Trying things is the only way to figure them out. I have so much of personal experience about trying new things, and it proved itself every single time. Like when I came to United States five years ago; I did not speak a word of English, I did not know how to drive, I was scared beyond belief, but trying new things got me to where I am.It is okay to be scared, but it is not okay not to challenge your fears and examine life in every way possible with everything that raises questions. Here I agree with Socrates â€Å"The unexamined life is not worth living. † Disappointments. Disappointments are worthless. They are based on our exp ectations of results. If you do not want to be disappointed, stop waiting for things and people to meet your expectations. We all are our own people. We do not live to please everyone around us. Why expect everyone around me to please me, if I am not doing it for everyone else?Why expect a sunny day and get disappointed if it rains? I am not the center of the universe, so why should it be sunny for me? We are causing things to upset us and at the same time we are blaming everyone and everything else. Of course people are selfish, it is just a human nature, but if we are selfish, why do we let things ruin our lives simply by expecting good things to happen? Everyone is trying to do whatever makes them happy and feels good. Why get disappointed if it upsets us. People are so controversial. Death.I agree with Arthur Schopenhauer on the subject of death. Crying for dead is like crying for someone who was never born. Why we are so scared of death? We all know that we are going to die, so I believe that being ready for it is more important than being scared of it. But how can we be ready? Well, examining life to its fullest would do the trick. Doing new things, answering questions, exploring the unknown, all of that makes death just one of the projects. Possibly one the last ones, but we do not know, till we try.We are scared of death because we do not know what is waiting for us after we leave this world and this life. But exploring everything here and now makes it easier and simpler to move on and accept the fact that we are done. Thinking that after we die the world will not be the same is just another example of human selfishness. How many people have died before us? How many will die after? And the universe is still here, it is still growing, it is still alive. One death is just one drop in the ocean; it will not change the world.And Schopenhauer’s quote â€Å"Matter, which now lies before you as dust and ashes now, dissolved in water, will settle as cr ystal, will shine in a metal, scatter electric sparks in a galvanic voltage show the power, that by expanding the strongest connection, turn the earth mass into metal; and not only that: by itself it will embody in plant and animal, from its mysterious womb will produce the very life, the loss of which you are so afraid of in your narrow-mindedness† shows that we never die completely, therefore being afraid of death thinking that without us the world will not be the same is very much silly.As you can see, in this essay I did not use any philosophical terms, but this is My Life Examination, in my life I do not use terms, I use simple language because like Einstein said â€Å"If you can't explain it simply, you don't understand it well enough. †

Interview of a Famous Actor

INTERVIEW AB: Good morning Ladies and Gentlemen. Today we have the honor to welcome a very special guest: your favourite TV-show actor, Hugh Laurie. So, Hugh, let me first ask you why you were attracted by House’s character. Because it is such an outstanding character†¦ AH: Well, it’s a long story†¦ At first, I was unwilling to play House, and I wanted to interpret Wilson, House’s best friend in the hospital. Indeed, I thought that House’s personnality didn’t fit with mine. But when I was asked to play House, I realized that, in fact, I had several points in common with him.For instance, both of us are sadist and sarcastic. AB: What a coincidence! But I can tell you that you did a good choice because nowadays House is one of the most popular TV shows in the world. Hum, I have another question for you: was it difficult to combine shootings and family life? AH: Actually, it was very difficult from 2006 to 2008 because while my family lived i n West America, the shooting took place in East America. This caused problems when I had to â€Å"settle† in California for 6 months.But now my family lives in LA so it is much better for all of us. AB: You seem to have a complicated organization. Now I’d like to finish this interview with more personnal questions asked by your fans on Twitter. So, first, what is your favorite TV show? AH: Well, I’d say that my favourite TV show is prison break. It is an Action-packed serial with fascinating actors. I recommend it to every TV show lover. AB: Okay! Then your fans asked you whether or not you have learnt about medecine while playing house?For example, if I tell you that I’ve got very big pain around my heart, what would you say? AH: Well, I am not exactly sure but in accordance with what I know, I would say that you should go to the Operating Room right now if you don’t want to die from myocardial infarction. AB: Waouh! Do you think you know as much as a doctor about medecine? AH: Absolutely not. I only know a few names of illnesses and of medecines, but no more than that. AB: Right. Thank you Hugh for coming here. I’ll take your advice and I’ll watch Prison Break.

Customer Service Essay - 1247 Words

1. Organisations that intend to be successful need to design products, services and product/ service bundles to meet customer needs. How can they do this and how can they ensure that the organisation’s plans achieve quality, time and cost specifications agreed with customers? What data and records might be drawn upon to make plans intended to meet customer needs? Organisations that use market research to gather feedback from consumers regarding product design and product/ service bundles tend to be more successful that those who do not use market research as a business tool. Data received from the market research records that have been collected from any market research including surveys, questionnaires, focus groups or simply speaking†¦show more content†¦It is necessary to consult with customers and other stakeholders to identify progress towards the results, the likelihood of receiving the results towards quality targets and the impact of work against the targets. Consulting with customers and stakeholders helps to keep the work on track, and can let you know if things are going according to plan. For example The Old Spaghetti Factory has Customer Feedback forms on their dining tables. Customers are able to fill in a feedback form to comment on customer service quality, food quality, speed of service and the dining experience overall. By collecting the feedback forms the managers are able to see if the team is performing up the standard the organisation is aiming for. 4. Within the organisation there will be groups of people or teams which work toward goal achievement. How can managers and supervisors ensure that team members have the skills needed to communicate effectively with customers and to provide excellent customer service? 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