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Altera_Forum's avatar
Altera_Forum
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13 years ago

Math calculations in VHDL

Hi all,

I need a little help with my design, there are a few issues that I'm trying to resolve.

My design flow is as following: A signal is sampled by a 16bit A2D, multiplied by 2 another 16bit signals (which results in 2 32bit signals). After a few manipulations I need to implement a formula that uses those 2 signals with division, multiplication and a few other functions that are calculated using LUTs. The LUTs are designed for a signal normalized to the range of 0 - pi/2. Note that after the formula the signals will be converted to 32bit floating-point signals.

The formula requires some fractional calculations so I'm trying to use the fixed point package by David Bishop but I'm facing a few issues:

1. How am I supposed to convert the 32bit signals (integer) to 32 fixed point numbers?

2. I'm trying to divide the 2 32bit signals - what is the best way to do this? I tried the lpm_divide megafunction but I get a quotient and a remain while I need the whole number (i.e. 5.65 and not only 5).

3. How exactly am I supposed to use the fixed-point package? I have the following libraries, is that enough?

Library ieee;

use ieee.std_logic_1164.all;

use ieee.std_logic_unsigned.all;

use ieee.fixed_float_types.all;

use ieee.fixed_pkg.all;

Thanks in advance, help will be very appreciated.

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  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    How can I find the whole result of the division. For example if I calculate 5/3 I need the result to be 1.666 and not 1 with a remain of 2.

    I found here (http://www.vhdl.org/fphdl/fixed_ug.pdf) all the functions that I need, including mod and /, is there a way I can use them (actually I thought that I can do that by including use ieee.fixed_float_types.all; use ieee.fixed_pkg.all;)
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    you can use them, but like I said you cannot pipeline them, which will lead to an extremely low fmax.

    In Fixed point your results are limited by the number of bits you have. So you cannot store irrational numbers and you will only get within 2^-f (where f is the number of fraction bits) of the actual result.

    It sounds like you are more a software guy and not a hardware guy. Do you really need 32 bit integers? do you really need a 64 bit result? these numbers are getting very big and going to chew up a large chunk of your FPGA. have you analysed your algorithm to see if you really need all of the bits? can you cut down on accuracy anywhere?
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    Oh, and a 64bit LUT is going to be impossible inside an FPGA, it would require a 2^64 memory locations, which is rather large! the biggest LUT you could implement in the largest FPGAs is about 22 bits.

  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    Actually I'm a board design guy :)

    I understand the meaning of fixed point 32bit numbers and it's fine for my purpose.

    The LUTs and calculations that I need will work with 1.31 fractional numbers. I need 64bit only for the division result, after the modulus operation I will use 32bit numbers.

    I need to implement it first and then test it, possibly I'll be able to reduce the number of bits but for now I want to use 32bits. So back to my question, what will be the best way to do that?
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    5 over 3 in binary 101 / 011 is 001 remainder 010 when you have 3 bit values

    with 6 bit: 101.000 / 011 the result would be 1.101 = 1.625
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    My LUTs are going to be stored on external memories and they will be much smaller than 64bit, I'll need to use the "round" function in order to use the LUTs.

    I understand your division example (actually that's exactly what I need) but how can I implement it? I don't get a x.y result when using lpm_divide.
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    a 32 bit LUT needs 4GWords of memory, that is a HUGE amount of memory for a lut, and seems rather pointless. Do you really need all that accuracy?

    for the LPM divide, you need to keep track of the separation of the bits yourself. remember a 32.32 / 0.32 number would give a 64.32 result, wider than the limits of LPM divide. You need to zero pad to the right for the numerator and zero pad to the left for the denominator.
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    My LUTs are rather small, the biggest one has less then 4000 values. I can't exactly say how much accurate the calculations should be until I test the whole system but they should be pretty accurate as I'm dealing with a very tricky signal.

    I got the division part, thank you very much. Any tips about the modulus operation?
  • Altera_Forum's avatar
    Altera_Forum
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    13 years ago

    divide, truncate, mutiply, subtract.

    In this case, you should be able to replace the division with a multply by 2/pi.