title: Computing the fast Fourier transform on SIMD microprocessors

authors: Blake, Anthony Martin

subjects: Fourier transform

abstract: This thesis describes how to compute the fast Fourier transform (FFT) of a power-of-two length signal on single-instruction, multiple-data (SIMD) microprocessors faster than or very close to the speed of state of the art libraries such as FFTW (“Fastest Fourier Transform in the West”), SPIRAL and Intel Integrated Performance Primitives (IPP).

The conjugate-pair algorithm has advantages in terms of memory bandwidth, and three implementations of this algorithm, which incorporate latency and spatial locality optimizations, are automatically vectorized at the algorithm level of abstraction. Performance results on 2- way, 4-way and 8-way SIMD machines show that the performance scales much better than FFTW or SPIRAL.

The implementations presented in this thesis are compiled into a high-performance FFT library called SFFT (“Streaming Fast Fourier Trans- form”), and benchmarked against FFTW, SPIRAL, Intel IPP and Apple Accelerate on sixteen x86 machines and two ARM NEON machines, and shown to be, in many cases, faster than these state of the art libraries, but without having to perform extensive machine specific calibration, thus demonstrating that there are good heuristics for predicting the performance of the FFT on SIMD microprocessors (i.e., the need for empirical optimization may be overstated).

text: Computing the fast Fourier transform on SIMD microprocessors This thesis describes how to compute the fast Fourier transform (FFT) of a power-of-two length signal on single-instruction, multiple-data (SIMD) microprocessors faster than or very close to the speed of state of the art libraries such as FFTW (“Fastest Fourier Transform in the West”), SPIRAL and Intel Integrated Performance Primitives (IPP).

The conjugate-pair algorithm has advantages in terms of memory bandwidth, and three implementations of this algorithm, which incorporate latency and spatial locality optimizations, are automatically vectorized at the algorithm level of abstraction. Performance results on 2- way, 4-way and 8-way SIMD machines show that the performance scales much better than FFTW or SPIRAL.

The implementations presented in this thesis are compiled into a high-performance FFT library called SFFT (“Streaming Fast Fourier Trans- form”), and benchmarked against FFTW, SPIRAL, Intel IPP and Apple Accelerate on sixteen x86 machines and two ARM NEON machines, and shown to be, in many cases, faster than these state of the art libraries, but without having to perform extensive machine specific calibration, thus demonstrating that there are good heuristics for predicting the performance of the FFT on SIMD microprocessors (i.e., the need for empirical optimization may be overstated).

year: 2012

title: Nurturing the designerly thinking and design capabilities of five-year-olds: technology in the new entrant classroom

authors: Milne, Louise

subjects: technology

abstract: Technology is one of eight learning areas of the New Zealand national curriculum. It aims to develop a broad technological literacy through students participating in programmes in which the practice of technological development is experienced, as is knowledge informing practice, and students gain an understanding of technology as a domain in its own right. In New Zealand children begin school at 5 years of age and this paper describes a classroom research project during which these students design and then construct a photo frame. The inducement for this development arose from students needing to safely transport home and then display a class photograph. This provided the opportunity for developing technological knowledge and skills within a real and relevant context—two key drivers when working with young students (Ministry of Education 2007) [MoE]. The results of this project suggest that teaching technology to five-year-old students is achievable and a valuable addition to other learning opportunities provided in the new entrant classroom. Strategies are suggested that will enable students to successfully achieve their goals whilst gaining a simple understanding of the technological process. By making good use of these it is possible to create a worthwhile and imaginatively challenging activity that reflects the essence of the technology education curriculum.

text: Nurturing the designerly thinking and design capabilities of five-year-olds: technology in the new entrant classroom Technology is one of eight learning areas of the New Zealand national curriculum. It aims to develop a broad technological literacy through students participating in programmes in which the practice of technological development is experienced, as is knowledge informing practice, and students gain an understanding of technology as a domain in its own right. In New Zealand children begin school at 5 years of age and this paper describes a classroom research project during which these students design and then construct a photo frame. The inducement for this development arose from students needing to safely transport home and then display a class photograph. This provided the opportunity for developing technological knowledge and skills within a real and relevant context—two key drivers when working with young students (Ministry of Education 2007) [MoE]. The results of this project suggest that teaching technology to five-year-old students is achievable and a valuable addition to other learning opportunities provided in the new entrant classroom. Strategies are suggested that will enable students to successfully achieve their goals whilst gaining a simple understanding of the technological process. By making good use of these it is possible to create a worthwhile and imaginatively challenging activity that reflects the essence of the technology education curriculum.

year: 2013

title: Empirical analysis of Pacific, Māori and ethnic pay gaps in New Zealand

authors: Cochrane, William

abstract: A descriptive profile of the four ethnic groups, by gender, is provided to illustrate the heterogeneities across populations in terms of a number of variables grouped into the following categories: individual characteristics, educational attainment, region, household and job-related characteristics. The main empirical analysis involves estimation of the statistical contribution of observed factors (within each of the aforementioned categories) towards explaining the ethnic pay gaps. As this research is primarily aimed as an input towards the Pacific Pay Gap Inquiry being conducted by the Human Rights Commission, we focus our summary of the key findings on the Pacific – European pay gap.
This includes variables on permanent contract status, an indicator if in part-time work, occupation, and industry. These results are therefore likely an indication of the strong role of occupational segregation in the labour market. An additional factor that had a relatively strong contribution to the pay gap, particularly for the Pacific – European female gap, was educational attainment. Overall, even after accounting for differences in job-related characteristics and educational attainment, amongst a number of other observed factors, it was still found that only 27 percent of the pay gap for Pacific males (relative to Europeans) could be explained; and the corresponding proportion for females was 39 percent. The remaining portion of the Pacific Pay Gap is likely to reflect a range of causes that cannot be quantified or disentangled in this analysis – such as not including other factors of importance as they weren’t observed in the data (for example, literacy proficiency or field of study for qualification attained); ethnic differences in preferences for non-wage components of the job; unconscious bias; and discrimination.

text: Empirical analysis of Pacific, Māori and ethnic pay gaps in New Zealand A descriptive profile of the four ethnic groups, by gender, is provided to illustrate the heterogeneities across populations in terms of a number of variables grouped into the following categories: individual characteristics, educational attainment, region, household and job-related characteristics. The main empirical analysis involves estimation of the statistical contribution of observed factors (within each of the aforementioned categories) towards explaining the ethnic pay gaps. As this research is primarily aimed as an input towards the Pacific Pay Gap Inquiry being conducted by the Human Rights Commission, we focus our summary of the key findings on the Pacific – European pay gap.
This includes variables on permanent contract status, an indicator if in part-time work, occupation, and industry. These results are therefore likely an indication of the strong role of occupational segregation in the labour market. An additional factor that had a relatively strong contribution to the pay gap, particularly for the Pacific – European female gap, was educational attainment. Overall, even after accounting for differences in job-related characteristics and educational attainment, amongst a number of other observed factors, it was still found that only 27 percent of the pay gap for Pacific males (relative to Europeans) could be explained; and the corresponding proportion for females was 39 percent. The remaining portion of the Pacific Pay Gap is likely to reflect a range of causes that cannot be quantified or disentangled in this analysis – such as not including other factors of importance as they weren’t observed in the data (for example, literacy proficiency or field of study for qualification attained); ethnic differences in preferences for non-wage components of the job; unconscious bias; and discrimination.

year: 2022-07