• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.05a
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• pp.809-811
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• 2010

In most floating-point operations related with 3D graphic applications for mobile devices, properly approximated data calculations with reduced complexity and low power are preferable to exactly rounded floating-point operations with unnecessary preciseness with cost. Among all the sophisticated floating-point arithmetic operations, multiplication and division are the most complicated and time-consuming, and they can be transformed into addition and subtraction repectively by adopting the logarithmic conversion. In this process, the most important factor for performance is how high we can make an approximation of the logarithm conversion. In this paper, we cover the trends in studying the logarithm conversion circuit designs. We also discuss the important factor in design issues and the applicable fields in detail.

• The KIPS Transactions:PartA
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• v.13A no.3 s.100
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• pp.185-190
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• 2006

JPEG 2000 is used as an alternative to solve the blocking artifact problem with the existing still image compression JPEG algorithm. However, it has shortcomings such as longer floating point computation time and more complexity in the procedure of enhancing the image compression rate and decompression rate. To compensate for these we implemented with hardware the JPEG 2000 algorithm's filter part which requires a lot of floating point computation. This DWT Filter[1] chip is designed on the basis of Daubechies 9/7 filter[6] and is composed of 3-stage pipeline system to optimize the performance and chip size. Our implemented Filter was 7 times faster than software based Filter in the floating point computation.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.886-889
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• 2006

수치연산 보조프로세서로도 알려져 있는 부동 소수점 연산장치(FPU)는 컴퓨터가 사용하는 기본 마이크로프로세서보다 더 빠르게 숫자를 다를 수 있는 특별한 회로 설계 또는 마이크로프로세서를 말한다. FPU는 전적으로 대형 수학적 연산에만 초점을 맞춘 특별한 명령 셋을 가지고 있어서 그렇게 빠르게 계산을 수행할 수 있는 것이다. FPU는 오늘날의 거의 모든 PC에 장착되고 있지만, 실은 그것은 그래픽 이미지 처리나 표현 등과 같은 특별할 일을 수행할 때에 필요하다. 초창기 컴퓨터 회사들은 각기 다른 연산방식을 사용했다. 이에 따라 연산결과가 컴퓨터마다 다른 문제점을 해결하기 위해 IEEE에서는 부동 소수점에 대한 표준안을 제안하였다. 이 표준안은 IEEE Standard 754 이며, 오늘날 인텔 CPU 기반의 PC, 매킨토시 및 대부분의 유닉스 플랫폼에서 컴퓨터 상의 실수를 표현하기 위해 사용하는 가장 일반적인 표현 방식으로 발전하였다. 본 논문에서는 부동 소수점 표준안 중 32-bit 단일 정밀도 부동 소수점 가산기를 VHDL로 구현하여 FPGA칩으로 다운하고 PCI 인터페이스를 통해 Visual C++로 데이터의 입출력을 검증하였다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.3
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• pp.547-554
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• 2008

In this paper, two-stage pipelined floating-point multiplier (FP-MUL) is designed. The FP-MUL processor supports single precision multiplication for 3D graphic APIs, such as OpenGL and Direct3D and has area-efficient and low-latency architecture via saturated arithmetic, area-efficient sticky-bit generator, and flagged prefix adder. The FP-MUL has about 4-ns delay time under $0.13{\mu}m$ CMOS standard cell library and consists of about 7,500 gates. Because its maximum performance is about 250 MFLOPS, it can be applicable to mobile 3D graphics application.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.48 no.10
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• pp.72-81
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• 2011

In this paper, we proposed and designed a novel floating point converter which supports single and double precisions of IEEE754 standard. The proposed convertor supports conversions between floating point number single/double precision and signed fixed point number(32bits/64bits) as well as conversions between signed integer(32bits/64bits) and floating point number single/double precision and conversions between floating point number single and double precisions. We defined a new internal format to convert various input types into one type so that overflow checking could be conducted easily according to range of output types. The internal format is similar to the extended format of floating point double precision defined in IEEE754 2008 standard. This standard specifies that minimum exponent bit-width of the extended format of floating point double precision is 15bits, but 11bits are enough to implement the proposed converting unit. Also, we optimized rounding stage of the convertor unit so that we could make it possible to operate rounding and represent correct negative numbers using an incrementer instead an adder. We designed single cycle data path and 5 cycles data path. After describing the HDL model for two data paths of the convertor, we synthesized them with TSMC 180nm technology library using Synopsys design compiler. Cell area of synthesis result occupies 12,886 gates(2 input NAND gate), and maximum operating frequency is 411MHz.

• Journal of Advanced Navigation Technology
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• v.4 no.1
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• pp.45-49
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• 2000

A GPS measurement solution, in general, is obtained as a least squares solution since the measurement includes errors such as clock errors, ionospheric and tropospheric delays, multipath effect etc. Because of the nonlinearity of the measurement equation, we utilize the nonlinear Newton algorithm to obtain a least squares solution, or mostly, use its linearized algorithm which is more convenient and effective. In this study we developed a fixed point algorithm and proved its availability to replace the nonlinear Newton algorithm and the linearized algorithm. A nonlinear Newton algorithm and a linearized algorithm have the advantage of fast convergence, while their initial values have to be near the unknown solution. On the contrary, the fixed point algorithm provides more reliable but slower convergence even if the initial values are quite far from the solution. Therefore, two types of algorithms may be combined to achieve better performance.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.37 no.12
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• pp.79-90
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• 2000

In this paper, a high-performance floating point unit, which is suitable for high-performance superscalar microprocessors and supports IEEE 754 standard, is designed. Floating-point arithmetic unit (AU) supports all denormalized number processing through hardware, while eliminating the additional delay time due to the denormalized number processing by proposing the proposed gradual underflow prediction (GUP) scheme. Contrary to the existing fixed-radix implementations, floating-point divide/square root unit adopts a new architecture which determines variable length quotient bits per cycle. The new architecture is superior to the SRT implementations in terms of performance and design complexity. Moreover, sophisticated exception prediction scheme enables precise exception to be implemented with ease on various superscalar microprocessors, and removes the stall cycles in division. Designed floating-point AU and divide/square root unit are integrated with and instruction decoder, register file, memory model and multiplier to form a floating-point unit, and its function and performance is verified.

• Proceedings of the IEEK Conference
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• 2000.06d
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• pp.174-177
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• 2000

본 논문에서는 높은 압축률과 고음질을 제공하는 MPEG-1 Layer Ⅲ 오디오 디코더를 고정소수점 DSP인 TMS320C6201을 이용하여 실시간으로 동작하도록 구현하였다. ISO/IEC에서 제공하는 부동소수점 C 프로그램을 음질의 손실 없이 고정소수점 연산으로 변환하었고 실시간 동작을 위하여 최적화 작업을 수행하였다. 연산의 정확성을 높이기 위해서 Descaling 모듈에 중점을 두어 부동소수점 연산을 고정소수점 연산으로 변환하였고 IMDCT 모듈과 Synthesis Polyphase Filter Bank 모듈에 대해 고속 알고리즘을 적용하여 연산량과 프로그램 크기를 크게 줄일 수 있었다. 구현된 디코더는 TMS320C6201 DSP가 수행할 수 있는 최대 연산량의 26%만으로 실시간 동작이 가능하였고 부동소수점 연산 결과와 고정소수점 연산 결과를 비교하여 60 dB 이상의 높은 SNR을 가짐을 확인하였다. 또한 사운드 입출력과 호스트 통신을 통하여 EVM 보드에서 실시간으로 동작함을 확인하였다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10c
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• pp.213-215
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• 2000

디지털 신호처리 알고리즘의 구현은 속도나 메모리의 사용측면에서 고정 소수점 구현이 필요하다. 특히, 정수형 연산 프로세서에서는 소프트웨어에 의한 부동 소수점보다는 고정 소수점 구현이 훨씬 성능이 뛰어나다. 디지털 신호처리 알고리즘의 복잡함과 일반 프로세서의 처리능력의 부족으로 이제까지는 신호처리 알고리즘의 실시간 구현을 위하여 대개 전용 프로세서나 디지털 신호처리를 위한 전용 명령어가 하드웨어적으로 구현되어 있는 프로세서를 사용하여 왔다. 하지만 현재 범용 프로세서의 주파수 속도가 빨라짐에 따라 복잡한 디지털 신호처리 알고리즘을 실시간에 처리할 수 있게 되었다. 하지만 정수형 연산 프로세서에서의 부동 소수점 연산은 프로세서에서 실시간 처리에 많은 어려움을 주게 된다. 본 연구에서는 데이터 타입이 고정된 범용 정수형 연산 프로세서(ARM RISC 32bit CPU)를 가지고 부동 소수점 연산 알고리즘을 고정 소수점 연산형으로 바꾸어서 속도측면과 메모리 측면의 성능을 비교해 보았다.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.11 s.353
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• pp.95-117
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• 2006

In this paper, we describe the optimization of the link-level performance and the complexity of floating-point and fixed-point methods in IEEE 802.16e OFDMA/TDD mobile modem. In floating-point design, we propose the channel estimation methods for downlink traffic channel and select the optimized method using computer simulation. So we also propose efficent algorithms for time and frequency synchronization, Digital Front End and CINR estimation scheme to optimize the system performance. Furthermore, we describe fixed-point method of uplink traffic and control channels. The superiority of the proposed algorithm is validated using the performances of Detection, False Alarm, Missing Probability and Mean Acquisition Time, PER Curve, etc. For fixed-point design, we propose an efficient methodology for optimized fixed-point design from floating-point At last, we design fixed-point of traffic channel, time and frequency synchronization, DFE block in uplink and downlink. The tradeoff between performance and complexity are optimized through computer simulations.