Este documento descreve uma implementação híbrida e paralela da Transformada Rápida de Fourier (FFT) no supercomputador Cray XD1, que combina processamento em CPU e FPGA. A abordagem é dividida entre software em C e hardware em VHDL, com diferentes tamanhos de entrada sendo processados em cada componente. Os resultados mostram um ganho de desempenho para certos tamanhos de entrada. Trabalhos futuros incluem melhorias no pipeline e uso de radix-4.
This document reviews best practice in pricing processes to provide a reference against which current practices and proposals can be tested. Our objectives have been: to research the attributes of world-class pricing through publications and academic sources; to investigate how these attributes are applied in practice to products and services; to assess pricing processes in successful businesses.
In recent years a new attitude toward pricing has emerged. Deregulation and international free trade agreements have increased competition. Price promotion has eroded the power of brand loyalty. Pricing has assumed greater importance to most businesses.
As markets increasingly assume a global dimension, customers can more easily compare prices between one region or country and another, using the internet or a fax machine. They can often locate the same product, or an
acceptable substitute, from another source. Customers are more demanding and fickle, and their expectations increasingly difficult to fulfil.
Price inflation in western economies is now at its lowest for decades. Price increases are no longer accepted without protest from customers, if at all.
The Chairman of General Electric has predicted the onset of the ‘Value Decade’. Global price competition will strengthen because of: reduced product differentiation; global over-capacity for production; significantly diminished trade barriers; efficient information and distribution systems; providing customers with easy access to the prices of suppliers; a growing lack of customers’ loyalty to individual suppliers. Choice will be increasingly driven by price.
This is a challenging scenario that reinforces the need for an integrated strategy and concerted managerial action on pricing.
Pricing processes have lagged behind developments in the market place. They are often characterised by internal conflict between accountants wishing to maximise profit per unit and marketing specialists who seek to maximise
throughput. They are also affected by the potential for strained relations with good customers.
Some companies have downsized their operations to a level where diminishing returns cause them to question the benefits of continuing to focus upon reducing costs. As they switch their attention from cost cutting to adding
value, pricing naturally assumes increased weight in the marketing mix.
We have found many companies reluctant to discuss their own processes.
Some may wish to avoid betraying a lack of sophistication.
The paper presents an overview of nucleating agents and their effects on crystallization rate, mechanical properties, and thermal properties in polypropylene. Presented at the SPE Automotive TPO Engineered Polyolefins Global Conference, October 2002, while working at Ciba Specialty Chemicals.
This document reviews best practice in pricing processes to provide a reference against which current practices and proposals can be tested. Our objectives have been: to research the attributes of world-class pricing through publications and academic sources; to investigate how these attributes are applied in practice to products and services; to assess pricing processes in successful businesses.
In recent years a new attitude toward pricing has emerged. Deregulation and international free trade agreements have increased competition. Price promotion has eroded the power of brand loyalty. Pricing has assumed greater importance to most businesses.
As markets increasingly assume a global dimension, customers can more easily compare prices between one region or country and another, using the internet or a fax machine. They can often locate the same product, or an
acceptable substitute, from another source. Customers are more demanding and fickle, and their expectations increasingly difficult to fulfil.
Price inflation in western economies is now at its lowest for decades. Price increases are no longer accepted without protest from customers, if at all.
The Chairman of General Electric has predicted the onset of the ‘Value Decade’. Global price competition will strengthen because of: reduced product differentiation; global over-capacity for production; significantly diminished trade barriers; efficient information and distribution systems; providing customers with easy access to the prices of suppliers; a growing lack of customers’ loyalty to individual suppliers. Choice will be increasingly driven by price.
This is a challenging scenario that reinforces the need for an integrated strategy and concerted managerial action on pricing.
Pricing processes have lagged behind developments in the market place. They are often characterised by internal conflict between accountants wishing to maximise profit per unit and marketing specialists who seek to maximise
throughput. They are also affected by the potential for strained relations with good customers.
Some companies have downsized their operations to a level where diminishing returns cause them to question the benefits of continuing to focus upon reducing costs. As they switch their attention from cost cutting to adding
value, pricing naturally assumes increased weight in the marketing mix.
We have found many companies reluctant to discuss their own processes.
Some may wish to avoid betraying a lack of sophistication.
The paper presents an overview of nucleating agents and their effects on crystallization rate, mechanical properties, and thermal properties in polypropylene. Presented at the SPE Automotive TPO Engineered Polyolefins Global Conference, October 2002, while working at Ciba Specialty Chemicals.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
WSCAD2009
1. Roteiro
Transformada de Fourier
Cray XD1
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Uma FFT H´brida e Paralela para o
ı
Supercomputador Cray XD1
Vitor Gomes1,2 Andrea Charao1
˜ Haroldo de Campos Velho2
1
´ ¸˜
LSC - Laboratorio de Sistemas de Computacao
UFSM - Universidade Federal de Santa Maria
2
´ ¸˜ ´
LAC - Laboratorio Associado de Computacao e Matematica Aplicada
INPE - Instituto Nacional de Pesquisas Espaciais
1 / 17
2. Roteiro
Transformada de Fourier
Cray XD1
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Roteiro
1 Transformada de Fourier
2 Cray XD1
3 FFT H´brida e Paralela
ı
4 ˜
Conclusoes e Trabalhos Futuros
2 / 17
3. Roteiro
Transformada de Fourier
Transformada de Fourier
Cray XD1
´
Transformada Rapida de Fourier - FFT
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Transformada de Fourier
Transformada Linear
Nucleo Computacional
´
Processamento de Sinais
¸˜ ¸˜
Solucao de equacoes parciais
Processamento de Imagens
...
Mudanca de dom´nio:
¸ ı
Ex.: tempo ↔ frequencia
ˆ
3 / 17
4. Roteiro
Transformada de Fourier
Transformada de Fourier
Cray XD1
´
Transformada Rapida de Fourier - FFT
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Transformada de Fourier
´
Transformada Rapida de Fourier - FFT
Fast Fourier Transform - FFT
Cooley e Tukey (1965)
Complexidade O (N 2 ) → O (NlogN )
´
Nucleo basico: Borboleta
´
6 somas em ponto flutuante
¸˜
4 multiplicacoes em ponto flutuante
¸˜
Figura: Fluxo de execucao
4 / 17
5. Roteiro
Transformada de Fourier
Transformada de Fourier
Cray XD1
´
Transformada Rapida de Fourier - FFT
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Transformada de Fourier
´
Transformada Rapida de Fourier - FFT
Fast Fourier Transform - FFT
Cooley e Tukey (1965)
Complexidade O (N 2 ) → O (NlogN )
´
Nucleo basico: Borboleta
´
6 somas em ponto flutuante
¸˜
4 multiplicacoes em ponto flutuante
¸˜
Figura: Fluxo de execucao
5 / 17
6. Roteiro
Transformada de Fourier
Transformada de Fourier
Cray XD1
´
Transformada Rapida de Fourier - FFT
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Transformada de Fourier
Abordagem Paralela
Uso intensivo de processamento
Algoritmo binary-exchange
ˆ
Dependencia de dados entre passos
¸˜
Custo de comunicac ao
¸˜
Figura: Fluxo de execucao
6 / 17
7. Roteiro
Transformada de Fourier
Transformada de Fourier
Cray XD1
´
Transformada Rapida de Fourier - FFT
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Transformada de Fourier
Abordagem Paralela
Uso intensivo de processamento
Algoritmo binary-exchange
ˆ
Dependencia de dados entre passos
¸˜
Custo de comunicac ao
¸˜
Figura: Fluxo de execucao
7 / 17
8. Roteiro
Transformada de Fourier
Cray XD1
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Cray XD1
´
Sistema H´brido Reconfiguravel
ı
Rede de alto desempenho
˜
Inclusao de FPGAs
6x Blades
Blade
2 AMD Opteron 64bits 2.4GHz
1 FPGA Xilinx Virtex II Pro Figura: Cray XD1
8 / 17
10. Roteiro
Objetivo
Transformada de Fourier
¸˜
Implementacao
Cray XD1
Particionamento
FFT H´brida e Paralela
ı
Desempenho
˜
Conclusoes e Trabalhos Futuros
FFT H´brida e Paralela
ı
Objetivo
Objetivo
Aproveitar o poder computacional de CPU e FPGA
¸˜
Estabelecer um perfil de execucao da FFT nesta arquitetura
10 / 17
11. Roteiro
Objetivo
Transformada de Fourier
¸˜
Implementacao
Cray XD1
Particionamento
FFT H´brida e Paralela
ı
Desempenho
˜
Conclusoes e Trabalhos Futuros
FFT H´brida e Paralela
ı
Metodologia
1 ¸˜
Implementacao em Software
2 ¸˜
Implementacao em VHDL
3 ¸˜ ¸˜
Avaliar tempo de execucao de cada implementac ao
4 Particionamento de carga entre CPU e FPGA
5 ¸˜ ¸˜
Execucao e avaliacao da FFT H´brida e Paralela
ı
11 / 17
12. Roteiro
Objetivo
Transformada de Fourier
¸˜
Implementacao
Cray XD1
Particionamento
FFT H´brida e Paralela
ı
Desempenho
˜
Conclusoes e Trabalhos Futuros
FFT H´brida e Paralela
ı
Software
f o r passo from 1 to N by 2
f o r j from 0 to passo by 1
c a l c u l a f a t o r de g i r o
f o r i from j to N by passo ∗2
c a l c u l a b o r b o l e t a ( data [ i ] , data [ i + passo ] )
end f o r
end f o r
end f o r
Implementado em Linguagem C
˜
Compilado com GCC versao 3.3.3
12 / 17
13. Roteiro
Objetivo
Transformada de Fourier
¸˜
Implementacao
Cray XD1
Particionamento
FFT H´brida e Paralela
ı
Desempenho
˜
Conclusoes e Trabalhos Futuros
FFT H´brida e Paralela
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Hardware
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Descricao em VHDL ∼ 3h geracao bitstream
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´
+2000 linhas de codigo Ocupa 97% do FPGA
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14. Roteiro
Objetivo
Transformada de Fourier
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Implementacao
Cray XD1
Particionamento
FFT H´brida e Paralela
ı
Desempenho
˜
Conclusoes e Trabalhos Futuros
FFT H´brida e Paralela
ı
Particionamento
Tabela: Particionamento entre CPU e FPGA
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Tempo Medio (ms)
Amostras FPGA CPU ¸˜
Proporcao
1.024 0, 94 0, 19 3:1
4.096 3, 45 0, 79 3:1 FPGA 160MHz
16.384 14, 68 4, 33 3:1 CPU 2.4GHz
65.536 63, 76 20, 59 3:1
131.072 132, 73 47, 59 3:1
262.144 276, 76 191, 25 1:1
524.288 − 461, 59 1:1
1.048.576 − 979, 56 3:1
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16. Roteiro
Transformada de Fourier
Cray XD1
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
˜
Conclusoes e Trabalhos Futuros
´
E poss´vel utilizar o poder de processamento de CPU combinado
ı
¸˜
com FPGA para computacao de FFT
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Foi obtido aumento de desempenho para execucoes com
262.144, 524.288 e 1.048.576 pontos
Em trabalhos futuros utilizar borboletas com radix-4
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Criar um pipeline na computacao interna da Borboleta
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17. Roteiro
Transformada de Fourier
Cray XD1
FFT H´brida e Paralela
ı
˜
Conclusoes e Trabalhos Futuros
Uma FFT H´brida e Paralela para o
ı
Supercomputador Cray XD1
˜
Vitor Gomes Andrea Charao Haroldo de Campos Velho
{vconrado, andrea}@inf.ufsm, haroldo@lac.inpe.br
http://slideshare.net/vconrado/wscad2009
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