Block floating point

Block floating point (BFP) is a method used to provide an arithmetic approaching floating point while using a fixed-point processor. The algorithm will assign an entire block of data an exponent, rather than single units themselves being assigned an exponent, thus making them a block, rather than a simple floating point. Block floating-point algorithm operations are done through a block using a common exponent, and can be advantageous to limit the space use in the hardware to perform the same functions as floating-point algorithms.[1]

The common exponent is found by data with the largest amplitude in the block. To find the value of the exponent, the number of leading bits must be found. For this to be done, the number of left shifts needed for the data must be normalized to the dynamic range of the processor used. Some processors have means to find this out themselves, such as exponent detection and normalization instructions.[2][3]

Block floating-point algorithms were extensively studied by James Hardy Wilkinson.[4][5][6]

A similar arithmetic can be used on top of a floating-point format having a limited range.

See also

References

  1. ↑ "Block floating point". BDTI DSP Dictionary. Berkeley Design Technology, Inc. (BDTI). Archived from the original on 2018-07-11. Retrieved 2015-11-01.
  2. ↑ Chhabra, Arun; Iyer, Ramesh (December 1999). "TMS320C55x A Block Floating Point Implementation on the TMS320C54x DSP" (PDF) (Application report). Digital Signal Processing Solutions. Texas Instruments. SPRA610. Archived (PDF) from the original on 2018-07-11. Retrieved 2018-07-11.
  3. ↑ Elam, David; Iovescu, Cesar (September 2003). "A Block Floating Point Implementation for an N-Point FFT on the TMS320C55x DSP" (PDF) (Application report). TMS320C5000 Software Applications. Texas Instruments. SPRA948. Archived (PDF) from the original on 2018-07-11. Retrieved 2015-11-01.
  4. ↑ Wilkinson, James Hardy (1963). Rounding Errors in Algebraic Processes (1 ed.). Englewood Cliffs, NJ, USA: Prentice-Hall, Inc. MR 0161456.
  5. ↑ Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1 ed.). Birkhäuser. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
  6. ↑ Overton, Michael L. (2001). Numerical Computing with IEEE Floating Point Arithmetic - Including One Theorem, One Rule of Thumb and One Hundred and One Exercises (1 ed.). Society for Industrial and Applied Mathematics (SIAM). ISBN 0-89871-482-6. 9-780898-714821-90000.

Further reading

  • "FFT/IFFT Block Floating Point Scaling" (PDF) (Application note). San Jose, CA, USA: Altera Corporation. October 2005. 404-1.0. Archived (PDF) from the original on 2018-07-11. Retrieved 2018-07-11.
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