### 电子工程代写|并行计算代写Parallel Computing代考|CSC267

statistics-lab™ 为您的留学生涯保驾护航 在代写并行计算Parallel Computing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写并行计算Parallel Computing方面经验极为丰富，各种代写并行计算Parallel Computing相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电子工程代写|并行计算代写Parallel Computing代考|Moore’s Law

For decades, computational scientists have been in a comfortable situation: They wrote code and made this code fast on a particular architecture. Everybody knew that architectures evolve kind of continuously, i.e. with every new generation of machines “old”ish codes ran faster, too. They might not benefit from the latest hardware features, but there was a performance improvement. Some people claim this were Moore’s law, which is not correct. Let’s revisit this “law”‘ :

Gordon Moore, one of the co-founders of Intel, observed that the cost to put transistors onto a chip decreases if we squeeze more transistors on the circuit. From a certain point on, however, the manufacturing cost rises again, since the integration of all the transistors becomes expensive. Consequently, there’s a sweet spot: a magic number of transistors per chip where the chip is most profitable. Moore observed that the “complexity for minimum component costs has increased at a rate of roughly a factor of two per year”. So the number of transistors on a chip around the sweet spot grows exponentially according to this law. The manufacturing sweet spot moves and therefore vendor designs move with the spot.

Intel’s executive David House later corrected the statement-to 18 months-so it is even more aggressive, while Carver Mead from CalTech coined the term “Moore’s Law”. Today, the law continues to hold though the rate of the increase has slowed down (Fig. 2.1).For simulation codes as we have sketched them before, it is not directly clear why the transistor count makes a difference. We are interested in speed. However, there is a correlation: First, vendors use the opportunity to have more transistors to allow the computer to do more powerful things. A computer architecture provides some services (certain types of calculations). With more transistors, we can offer more of these calculation types, i.e. broaden the service set. Furthermore, vendors use the opportunity to squeeze more cores onto the chip. Finally, the more of transistors historically did go hand in hand with a shrinkage of the transistors.

## 电子工程代写|并行计算代写Parallel Computing代考|Dennard Scaling

Definition $2.1$ (Dennard scaling) The power cost $P$ to drive a transistor follows roughly
$$P=\alpha \cdot C F V^{2}$$
This law is called Dennard scaling.
$C$ is the capacitance, i.e. encodes the size of the individual transistors. I use $C$ here for historic reasons. In the remainder of this manuscript, $C$ is some generic constant without a particular meaning. $F$ is the frequency and $V$ the voltage. $\alpha$ is some fixed constant so we can safely skip it in our follow-up discussions. Note that the original Dennard scaling ignores that we also have some leakage. Leakage did not play a major role when the law was formulated in $1974 .$

Dennard’s scaling law is all about power. For both chip designers and computing centres buying and running chips, controlling the power envelope of a chip is a sine qua non, as

• buying power is expensive, and as
• a chip “converts” power into heat. To get the heat out of the system again requires even more power to drive fans, pumps and cooling liquids. But if we don’t get it out of the system on time, the chip will eventually melt down.

While we want to bring the power needs down, we still want a computer to be as capable as possible. That means, it should be able to do as many calculations per seconds as possible. The Dennard scaling tells us that we have only three degrees of freedom:

1. Reduce the voltage. This is clearly the gold solution as the $V$ term enters the equation squared. Reducing the voltage however is not trivial: If we reduce it too much, the transistors don’t switch reliably anymore. As long as we need a reliable chip, i.e. a chip that always gives us the right answer, we work already close to the minimum voltage limit with modern architectures.
2. Reduce the transistor size. Chip vendors always try to decrease transistor sizes with the launch of most new chip factories or assembly lines. Unfortunately, this option now is, more or less, maxed out. You can’t go below a few atoms. A further shrinkage of transistors means that the reliability of the machine starts to suffer-we ultimately might have to add additional transistors to handle the errors which once more need energy. Most importantly, smaller chips are more expensive to build (if they have to meet high quality constraints) which makes further shrinking less attractive.
3. Reduce the frequency. If we reduce the frequency, we usually also get away with a slightly lower voltage, so this amplifies the savings effect further. However, we want to have a faster transistor, not a slower one!

## 电子工程代写|并行计算代写Parallel Computing代考|Dennard Scaling

C是电容，即编码单个晶体管的大小。我用C出于历史原因。在这份手稿的其余部分，C是一些没有特定含义的通用常数。F是频率和在电压。一个是一些固定常数，因此我们可以在后续讨论中安全地跳过它。请注意，原始的 Dennard 缩放忽略了我们也有一些泄漏。在制定法律时，泄漏并没有起主要作用1974.

• 购买力是昂贵的，并且作为
• 芯片将功率“转换”为热量。要再次将热量从系统中排出，需要更多的功率来驱动风扇、泵和冷却液。但如果我们不按时将其从系统中取出，芯片最终会熔化。

1. 降低电压。这显然是黄金解决方案在项进入方程的平方。然而，降低电压并非易事：如果我们降低太多，晶体管将不再可靠地切换。只要我们需要一个可靠的芯片，即总是给我们正确答案的芯片，我们的工作就已经接近现代架构的最低电压限制。
2. 减小晶体管尺寸。随着大多数新芯片工厂或装配线的推出，芯片供应商总是试图减小晶体管尺寸。不幸的是，这个选项现在或多或少地被最大化了。你不能低于几个原子。晶体管的进一步缩小意味着机器的可靠性开始受到影响——我们最终可能不得不添加额外的晶体管来处理再次需要能量的错误。最重要的是，较小的芯片制造成本更高（如果它们必须满足高质量的限制），这使得进一步缩小的吸引力降低。
3. 减少频率。如果我们降低频率，我们通常也会使用稍低的电压，因此这会进一步放大节能效果。但是，我们想要更快的晶体管，而不是更慢的晶体管！

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。