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Title Algorithms and architectures for decimal transcendental function computation
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University/Publisher University of Saskatchewan
Abstract Nowadays, there are many commercial demands for decimal floating-point (DFP) arithmetic operations such as financial analysis, tax calculation, currency conversion, Internet based applications, and e-commerce. This trend gives rise to further development on DFP arithmetic units which can perform accurate computations with exact decimal operands. Due to the significance of DFP arithmetic, the IEEE 754-2008 standard for floating-point arithmetic includes it in its specifications. The basic decimal arithmetic unit, such as decimal adder, subtracter, multiplier, divider or square-root unit, as a main part of a decimal microprocessor, is attracting more and more researchers' attentions. Recently, the decimal-encoded formats and DFP arithmetic units have been implemented in IBM's system z900, POWER6, and z10 microprocessors. Increasing chip densities and transistor count provide more room for designers to add more essential functions on application domains into upcoming microprocessors. Decimal transcendental functions, such as DFP logarithm, antilogarithm, exponential, reciprocal and trigonometric, etc, as useful arithmetic operations in many areas of science and engineering, has been specified as the recommended arithmetic in the IEEE 754-2008 standard. Thus, virtually all the computing systems that are compliant with the IEEE 754-2008 standard could include a DFP mathematical library providing transcendental function computation. Based on the development of basic decimal arithmetic units, more complex DFP transcendental arithmetic will be the next building blocks in microprocessors. In this dissertation, we researched and developed several new decimal algorithms and architectures for the DFP transcendental function computation. These designs are composed of several different methods: 1) the decimal transcendental function computation based on the table-based first-order polynomial approximation method; 2) DFP logarithmic and antilogarithmic converters based on the decimal digit-recurrence algorithm with selection by rounding; 3) a decimal reciprocal unit using the efficient table look-up based on Newton-Raphson iterations; and 4) a first radix-100 division unit based on the non-restoring algorithm with pre-scaling method. Most decimal algorithms and architectures for the DFP transcendental function computation developed in this dissertation have been the first attempt to analyze and implement the DFP transcendental arithmetic in order to achieve faithful results of DFP operands, specified in IEEE 754-2008. To help researchers evaluate the hardware performance of DFP transcendental arithmetic units, the proposed architectures based on the different methods are modeled, verified and synthesized using FPGAs or with CMOS standard cells libraries in ASIC. Some of implementation results are compared with those of the binary radix-16 logarithmic and exponential converters; recent developed high performance decimal CORDIC based architecture; and Intel's DFP transcendental function computation software library. The comparison…
Subjects/Keywords Decimal Floating-Point; ASIC; FPGA; Transcendental Function Computation
Contributors Ko, Seok-Bum; Eager, Derek; Wahid, Khan A.; Teng, Daniel; Nguyen, Ha; Aamodt, Tor M.; Cunfer, Geoff
Language en
Country of Publication ca
Record ID handle:10388/etd-01272011-010720
Other Identifiers TC-SSU-01272011010720
Repository sask
Date Retrieved
Date Indexed 2020-07-20

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…x5B;33]. The decimal transcendental function computation is also very useful for some specific applications, such as some computations used in financial applications in banks [38] (eg. the compound interest computation), the…

…computing 5 systems that are compliant with the IEEE 754-2008 standard should provide a software or hardware solution for the decimal transcendental function computation. Recently, Intel Cooperation provides the first software solution to compute DFP and…

…DXP transcendental functions using an existing and well-established BFP transcendental function mathematical library [41]. However, with the strict requirement on computational speed and accuracy in the future, the hardware components may be…

…included in the high-end microprocessor to support the decimal transcendental computation. The previous hardware implementations of the decimal transcendental function computation are reported in several patents [42, 43, 44, 45, 46] in which the…

…decimal transcendental function computation is based on a binary arithmetic, rather than decimal. Therefore, they are not compliant with the DFP formats specified in the IEEE 754-2008 standard. In [40], a radix-10 BKM algorithm is presented for…

…demands of high-performance decimal transcendental computations. 6 1.3 Research Overview A set of new algorithms and architectures for the DFP and DXP transcendental function computation based on different approaches are investigated in this…

…approximate the transcendental function by an optimized linear approximation with few non-uniform segments. Compared with previous non-uniform static method, the proposed method can significantly reduce the memory size occupied in hardware. Moreover, the…

…algorithms and architectures for the DFP transcendental function computation. Some of them are the first published designs which can achieve faithful logarithm or antilogarithm results of DFP or DXP operands, specified in the IEEE 754-2008 standard. The…

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