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Issue No.04 - April (2008 vol.57)

pp: 490-504

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.12

ABSTRACT

A unified computation method of vector and transcendental function is proposed for handheld 3D graphics systems. It unifies vector operations like vector multiply, multiply-and-add, divide, divide-by-square-root and dot product and transcendental functions like trigonometric, inverse trigonometric, hyperbolic, inverse hyperbolic, power (x<sup>y</sup> with two variables) and logarithm to arbitrary base in a single four-way arithmetic platform. A number system called fixed-point hybrid number system (FXP-HNS), which combines the fixed-point number system (FXP) and logarithmic number system (LNS), is proposed for the power- and area-efficient unification. Low power and small area logarithmic and antilogarithmic conversion schemes are also proposed for the data conversion between FXP and LNS in the FXP-HNS and achieve 0.41 percent and 0.08 percent maximum conversion error, respectively. The unified arithmetic unit based on the proposed schemes is presented with fully pipelined architecture and achieves single cycle throughput with maximum four-cycle latency for all the supported operations.

INDEX TERMS

Computer Arithmetic, unified arithmetic unit, vector operations, transcendental functions, logarithmic number system, 3D computer graphics, handheld systems

CITATION

Byeong-Gyu Nam, Hyejung Kim, Hoi-Jun Yoo, "Power and Area-Efficient Unified Computation of Vector and Elementary Functions for Handheld 3D Graphics Systems",

*IEEE Transactions on Computers*, vol.57, no. 4, pp. 490-504, April 2008, doi:10.1109/TC.2008.12REFERENCES

- [1] Khro nos Group,
OpenGL-ES 2.0, http:/www.khronos.org, 2007.- [3] OpenGL ARB,
OpenGL Programming Guide, third ed. Addison-Wesley, 1999.- [4] Analog Devices,
ADSP-21000 Family Application Handbook, 1994.- [7] J.N. Mitchell Jr., “Computer Multiplication and Division Using Binary Logarithms,”
IRE Trans. Electronic Computers, vol. 11, pp.512-517, Aug. 1962.- [8] R. Zhang, J.H. Han, A.T. Erdogan, and T. Arslan, “Low Power CORDIC IP Core Implementation,”
Proc. Int'l Conf. Acoustic, Speech, and Signal Processing, pp. 956-959, May 2006.- [9] J.S. Walther, “A Unified Algorithm for Elementary Functions,”
Proc. Spring Joint Computer Conf., pp. 379-385, 1971.- [13] D. Harris, “A Powering Unit for an OpenGL Lighting Engine,”
Proc. 35th Asilomar Conf. Signals, Systems, and Computers, pp. 1641-1645, 2001.- [14]
IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985, 1985.- [16] G.K. Kolli, “3D Graphics Optimization for ARM Architecture,”
Proc. Game Developer Conf., 2002.- [17] J.-H. Sohn, R. Woo, and H.-J. Yoo, “A Programmable Vertex Shader with Fixed-Point SIMD Datapath for Low Power Wireless Applications,”
Proc. ACM Siggraph/Eurographics Workshop Graphics Hardware, pp. 107-114, Aug. 2004.- [19] M. Combet, H. Zonneveld, and L. Verbeek, “Computation of the Base Two Logarithm of Binary Numbers,”
IEEE Trans. Electronic Computers, vol. 14, pp. 863-867, Dec. 1965.- [24] Microsoft Corp.,
Microsoft DirectX Technology Overview, http://www.microsoft.com/windowsdirectx, 2007. |