Floating point Mathematics

Discussion in 'VHDL' started by Joseph, Sep 15, 2007.

  1. Joseph

    Joseph Guest

    I am working on a project to implement an FFT using an FPGA. For the
    FFT i would need to use floating point numbers. I have read about the
    IEEE 754 standard but I think that it is too cumbersome for this
    application. I would prefer to implement a fix point representation.

    Can anyone suggest a fixed point representation that that is efficient
    and relatively accurate at the same time?

    Joseph
    Joseph, Sep 15, 2007
    #1
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  2. Joseph

    David Bishop Guest

    Joseph wrote:
    > I am working on a project to implement an FFT using an FPGA. For the
    > FFT i would need to use floating point numbers. I have read about the
    > IEEE 754 standard but I think that it is too cumbersome for this
    > application. I would prefer to implement a fix point representation.
    >
    > Can anyone suggest a fixed point representation that that is efficient
    > and relatively accurate at the same time?


    In VHDL-2007 there will be synthesizable fixed and floating point
    packages. You will find copies VHDL-93 compatible copies of these
    packages at this web page:

    http://www.eda.org/fphdl/vhdl.html

    Right now this page is pretty minimal, but I plan to expand the number
    of vendors, and add some examples and some support code.

    Documentation for these packages:
    http://www.vhdl.org/vhdl-200x/vhdl-200x-ft/packages/Fixed_ug.pdf
    http://www.vhdl.org/vhdl-200x/vhdl-200x-ft/packages/Float_ug.pdf
    David Bishop, Sep 15, 2007
    #2
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  3. Joseph

    Tricky Guest

    On Sep 15, 7:58 am, Joseph <> wrote:
    > I am working on a project to implement an FFT using an FPGA. For the
    > FFT i would need to use floating point numbers. I have read about the
    > IEEE 754 standard but I think that it is too cumbersome for this
    > application. I would prefer to implement a fix point representation.
    >
    > Can anyone suggest a fixed point representation that that is efficient
    > and relatively accurate at the same time?
    >
    > Joseph


    Altera provide floating point entities in their megafunction library.
    Xilinx have similar libraries.

    Converting to a fixed point representation can often be advantageous
    as it offers greater precision at the expense of range. dedicated
    multipliers are normally in 9x9,18x18 or 36x36 configurations, so to
    be efficient it is often best to stick to a multiple of this (or
    less). Also bear in mind that 1 18x18 multipler uses 4 9x9 multiplers,
    and 36x36 4 18 bit multipliers, so 18 bits is often the most
    efficient. FPGAs are designed for efficient fixed point number
    mathematics, but the accuracy is up to you to decide.

    No on can suggest a fixed point representaion that will be efficient
    and accurate for your application unless you detail the application.
    If you need floating point numbers to cover the range of possible
    values, then fixed point numbers will probably not be practical:
    Tricky, Sep 17, 2007
    #3
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