Block floating point (BFP) is a method used to provide an arithmetic approaching
floating point while using a
fixed-point processor. BFP assigns a group of ''
significand
The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on ...
s'' (the non-exponent part of the floating-point number) to a single exponent, rather than single significand being assigned its own exponent. BFP can be advantageous to limit space use in hardware to perform the same functions as floating-point algorithms, by reusing the exponent; some operations over multiple values between blocks can also be done with a reduced amount of computation.
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 zeros must be found (
count leading zeros). 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.
Block floating-point algorithms were extensively studied by
James Hardy Wilkinson.
BFP can be recreated in software for smaller performance gains.
See also
*
Binary scaling
*
Fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...
(FFT)
*
Digital signal processor
A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio si ...
(DSP)
References
Further reading
* {{cite web , title=FFT/IFFT Block Floating Point Scaling , date=October 2005 , publisher=
Altera Corporation , type=Application note , id=404-1.0 , location=San Jose, CA, USA , url=https://www.altera.com/content/dam/altera-www/global/en_US/pdfs/literature/an/an404.pdf , access-date=2018-07-11 , url-status=live , archive-url=https://web.archive.org/web/20180711174144/https://www.altera.com/content/dam/altera-www/global/en_US/pdfs/literature/an/an404.pdf , archive-date=2018-07-11
Floating point
Computer arithmetic