Actions
Forum Thread Details
  • Replies 34 replies
  • Subscribers 244 subscribers
  • Views 4678 views
  • Users 0 members are here
Related

If I Had a Hammer

jack.chaney56

I used this as a clever draw to get more readers.  The actual intent is to start a discussion and get input from people for software.  Most of the discussions I have seen on the site are about inventing hardware solutions to popular problems.  I guess I am getting overloaded with how many ways there are to turn on an LED.  A significant amount of computer work is actually in the realm of information technology,  Too often what is lacking are skilled individuals that bring an array of tools to the task. The expression "If the only tool you have is a hammer, all your problems look like nails" is a problem I deal with in my professional life. I am constantly faced with vendors who provide the one pony circus (a million ways to make a state machine).

 

Embedded programming is a discipline that requires the developer to be expert at OS scheduling, database management, hardware interfacing, design architecture, and structured objects, as well as proper coding style, and best solution language. It is a constant process of sharpening the tool set to get the best solution. I have taken to putting some tools into retirement as well. Archiving example code and hint/help files is done periodically so I don't have to keep my COBOL skills current, but, by archiving properly, it is possible with a bit of effort, to blow the dust off a few brain cells, and get back in step with my Fortran lines starting in column 7. (...how old is this guy?)

 

Getting back to where I started with this, I wanted to put a call out to all you embedded PROGRAMMERS for tips and techniques and tricks learned that can become the foundation for tool boxes.

 

Tips like:

  • Thinking like a computer
  • Faster graphics and ray tracing
  • Integer only formulas
  • Weight loss (or wait loss) compression
  • T...I...M...I...N...G...

 

Again, some of these are done with hardware these days, but not all solutions have bottomless bank accounts. Sometimes a one chip 8-bit piece of hardware needs to run an 8 cylinder diesel fueling operation.

Parents

  • Needed to say something about tables versus formulas. For real time systems, tables always win.

    • Given a non-linear curve where Y=f(x) and x is a measured value, the value at any point can be calculated using the function f(x)
    • For simple linear equations accuracy is high and calculation can be performed simply with a single multiply and add
    • For complex equations, accuracy becomes an issue, and the calculation can become difficult and time consuming.

    image

    • For short ranges, a linear interpolation can be used for a close approximation, but this becomes highly inaccurate outside a specified range

    image

    • Using fundamental calculus, if the range of delta X is distributed evenly, the linear interpolation between any two points more closely approximates any curve
    • If greater accuracy is required the number of sections can be increased

      image

    • By producing a table of these values, the equation becomes simple for any value Xn where Xn is between Xa and Xb
    • The equation becomes:


       ƒ (X)=Ya+(((Yb−Ya)·(Xb−Xn))(Xb−Xa) )

  • in reply to jack.chaney56

    Hi Jack,

     

    I completely agree about tables.

    They are very fast, good enough and you can do approximation between values if you need them

     

    Back when I was programming 8085 processors, I built a single table that enabled me to do sine and cosine very quickly from the same table.

    The time savings was immense, providing answers in a dozen microseconds verses using a math coprocessor that took milliseconds.

     

    When I build an integrated avionics simulator, I used tables for most functions and the run time result was very nice as opposed to trying to replicate all of the functions dynamically.

     

    Tables rule!

     

    If you look inside any real time game, you will find tables everywhere.

     

    DAB

Reply
  • in reply to jack.chaney56

    Hi Jack,

     

    I completely agree about tables.

    They are very fast, good enough and you can do approximation between values if you need them

     

    Back when I was programming 8085 processors, I built a single table that enabled me to do sine and cosine very quickly from the same table.

    The time savings was immense, providing answers in a dozen microseconds verses using a math coprocessor that took milliseconds.

     

    When I build an integrated avionics simulator, I used tables for most functions and the run time result was very nice as opposed to trying to replicate all of the functions dynamically.

     

    Tables rule!

     

    If you look inside any real time game, you will find tables everywhere.

     

    DAB

Children
  • in reply to DAB

    , I probably built the exact same table.  I was going to provide it as another installment for tips and tricks.

     

    If you build a 1/4 wave table using the binary radians that I described earlier, where 2pi = 215, bits 14 and 15 get used for determining the quadrant, and bits 0 through 13 get used for the table lookup.

    The other trick to use is cos(n) = sin(n+8192) so everything comes out of the same table lookup.

    if bit 15 == 1, return the negative value

    if bit 14 == 1, use 8192 - n so the table reads backward.