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### Advanced C Programming

### Typedef’s

### Fixed-Point Math

### Overflow Protection

### Switch Debouncing

### State Machines

### Filtering

### Oversampling

### Optimizations

Real Time Programming Like the Pros

About Us

Chris Hibner

- BSME University of Michigan, Ann Arbor (1996) – Dynamics and Control
- MSME University of Michigan, Ann Arbor (2002) – Control Systems and Computational Mechanics
- TRW Automotive; Algorithm Development and Applications Group, 1996 – present.
- chiefdelphi.com user name: “Chris Hibner”
Michael Shaul

- BSEE Rose-Hulman Institute of Technology (2002) – Computer Engineering
- MSEE University of Michigan, Dearborn (2005) – Control Systems
- TRW Automotive; Product Development Group, Software Validation Group, and Core Components Group
- chiefdelphi.com user name: “Mike Shaul”

Contents

- typedef’s
- Fixed-Point Math
- Overflow Protection
- Switch Debouncing
- State Machines
- Filtering
- Oversampling

Good Coding Practices

- Signed (good) vs Unsigned (bad) Math
- for physical calculations

- Use Braces{ Always}
- Simple Readable Code
- Concept of “Self Documenting Code”
- Code as if your grandmother is reading it

- Never use Recursion
- (watch your stack)

- Treat Warnings as Errors

*Disclaimer: Not all code in this presentation follows these

practices due to space limitations

Using Naturally Named Data Types

Why Typedef?

- You use variable with logical names, why not use data types with logical names?
- Is an “int” 8-bits or 16-bits? What’s a “long”? Better question: why memorize it?
- Most integer data types are platform dependent!!!
- typedef’s make your code more portable.

How to use typedef’s

- Create a logical data type scheme. For example, a signed 8-bit number could be “s8”.
- Create a “typedef.h” file for each microcontroller platform you use.
- #include “typedef.h” in each of your files.
- Use your new data type names.

typedef.h Example

typedef unsigned char u8;

typedef signed char s8;

typedef unsigned short u16;

typedef signed short s16;

typedef unsigned long u32;

typedef signed long s32;

In your code:

unsigned char variable;

Is replaced with:

u8 variable;

Fractional Numbers Using Integer Data Types

Creating Fractions

- Fractions are created by using extra bits below your whole numbers.
- The programmer is responsible for knowing where the “decimal place” is.
- Move the decimal place by using the shift operator (<< or >>).
- Shifting is multiplying by powers of 2. Ex.: x<<5 = x*2^5; x>>5 = x*2^-5

Fixed Point Fraction Example

A/D Sample (10-bit)

Shift left by 6 (i.e. A2D << 6;):

Fractional part

Whole part

Fractional Example, continued

- We know 5/2 = 2.5
- If we used pure integers, 5/2 = 2 (i.e. the number is rounded toward negative infinity)
- Using a fixed-point fractional portion can recover the lost decimal portion.

Fractional Example, continued

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

= 5

A/D Sample (10-bit)

Shift left by 6 (i.e. A2D << 6;):

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

= “5.0”

Fractional part

Whole part

Fractional Example, continued

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

Fractional part

Whole part

Divide by 2 (i.e. A2D / 2;):

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

Fractional part

Whole part

The whole part: 0000000010(binary) = 2(decimal)

The fractional part: 100000(binary) = 32 (huh???)

Fractional Example, continued

Divide by 2 (i.e. A2D / 2;):

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

Fractional part

Whole part

The fractional part: 100000(binary) = 32 (huh???)

How many different values can the fractional part be?

Answer: we have 6 bits => 2^6 values = 64 values

(i.e.) 111111 + 1(binary) = 64(decimal)

Therefore:

Fractional part is actually 32/64 = 0.5

Fractional Example, conclusion

Divide by 2 (i.e. A2D / 2;):

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

Fractional part

Whole part

- By using a fixed-point fractional part, we can have 5/2 = 2.5
- The more bits you use in your fractional part, the more accuracy you will have.
- Accuracy is 2^-(fraction bits).
- For example, if we have 6 bits in our fractional part (like the above example), our accuracy is 2^-6 = 0.015625. In other words, every bit is equal to 0.015625

Fractional Example, example

If we look diving and adding multiple values using this method we can see the benefit of fixed point math. This example assumes we are adding two “5/2” operations as shown.

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

Adding 2.5 + 2.5

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

+

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

Once our math operations are complete, we right shift our data to regain our original resolution and data position.

= 5

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

Without using the fixed point math the result of the addition would have been 4 due to the truncation of the integer division.

Making Sure Your Code Is Predictable

What is Overflow? Why is it Bad?

- Overflow is when you try to store a number that is too large for its data type.
- For example, what happens to the following code?
s8 test = 100;

test = test + 50;

answer: -105

(that’s not good!!!)

Integer Data Types: Valid Ranges

- u8 : 0 - 255
- s8 : -128 - 127
- u16 : 0 - 65535
- s16 : -32768 - 32767
- u32 : 0 - 4.294967295e9
- s32 : -2.147483648e9 - 2.147483647e9
Note: ranges given are decimal.

Overflow Protection Methods

- Create a new temporary variable using a data type with a larger range to do the calculation.
- Compare the sign of the variable before and after the calculation. Did the sign change when it shouldn’t have? (for signed variables)
- Compare the variable after the calculation to the value before. Did the value decrease when it should have increased?

Overflow Protection, Example 1

s16 add16(s16 adder1, s16 adder2); // prototype

S16 add16(s16 adder1, s16 adder2)

{

s32 temp = (s32)adder1 + (s32)adder2;

if (temp > 32767) // overflow will occur

return 32767;

else if (temp < -32768) // underflow

return -32768;

else

return (s16)temp;

}

*This example uses a s32 (larger) data value for overflow checking

Overflow Protection, Example 2

// prototype

s16 addTo16bit(s16 start, s16 adder);

S16 addTo16bit(s16 start, s16 adder)

{

s16 temp = start;

start += adder;

if ((start > 0) && (adder > 0) && (temp <= 0))

return 32767; // Overflow occurred

else if ((start < 0) && (adder < 0) && (temp >= 0))

return -32768; // Underflow occurred

else

return start;

}

*This example uses 16 bit values only to check for overflow on signed

values this provides improved efficiency on 16 bit platforms.

Overflow Protection, Example 3

// prototype

u16 addToUnsigned16bit(u16 start, s16 adder);

S16 addToUnsigned16bit(u16 start, s16 adder)

{

u16 temp = start;

start += adder;

if ((adder > 0) && (start < temp))

return 65536; // Overflow occurred

else if ((adder < 0) && (start > temp))

return 0; // underflow occurred

else

return start;

}

*This example checks for overflow on unsigned values

Having Confidence in Switch Inputs

Why Debounce? When to Use It?

- Debouncing a switch input reduces erroneous inputs.
- Use debouncing when pressing a switch starts a sequence or changes the state of something.

When to Debounce Examples

- Debounce when a single push of the switch changes a state. Examples:
- pneumatic gripper

- motorized gripper where a single push causes the motor to go until a limit switch is reached

- Do not debounce if constant driver input is needed.

What is Debouncing?

- Basically, debouncing means to require a certain number of samples before you confirm the switch input.
- Various debounce schemes can be used:
- require N consecutive samples (i.e. reset the counter if one sample fails)

- count up / count down (i.e., if one sample fails, decrement the counter by 1 rather than resetting to zero.

Debounce Example

// debounce opening gripper

if (!pneumaticGripperOpenState)

{

if (gripperOpenSwitch == ON)

gripperOpenDebCount++;

else

gripperOpenDebCount = 0;

if (gripperOpenDebCount >= DEBOUNCE_LIMIT)

{

gripperOpenDebCount = 0;

pneumaticGripperOpenState = TRUE;

}

}

Systematic Approach to Complicated Logic

What is a state machine?

- A state machine is a method for organizing complicated logic.
- A state machine is broken up into discrete “states”. Logic is defined to switch from one state to another.
- Only one state can be active at any time.
- It takes one sample (i.e. one time through the code) to switch from one state to another.

When should I use a state machine?

- When performing an automated routine which has many steps.
- When the logic is very large and/or difficult to grasp. (Like C programming: break up a large program into smaller functions)
- When the problem has physical states (like a light – it has two states: ON and OFF).

What does it look like?

- Light bulb example:

Automated Process Code

/* single shot state machine states */

#define START_SINGLE_SHOT 0

#define BALL_NOT_AT_SENSOR 1

#define BALL_AT_SENSOR 2

#define END_SINGLE_SHOT 3

static u8 singleShotState = END_SINGLE_SHOT;

// single shot state machine

switch (singleShotState)

{

case START_SINGLE_SHOT:

singleShotTimer = 0;

if (upperBallDebounced)

{

singleShotState = BALL_AT_SENSOR;

}

else

{

singleShotState = BALL_NOT_AT_SENSOR;

}

break;

Automated Process Code, cont.

case BALL_NOT_AT_SENSOR:

chutePWM = CHUTE_FORWARD;

if (upperBallDebounced)

{

singleShotState = BALL_AT_SENSOR;

}

break;

case BALL_AT_SENSOR:

chutePWM = CHUTE_FORWARD;

if (singleShotTimer > SINGLE_SHOT_TIMER_LIMIT)

{

singleShotState = END_SINGLE_SHOT;

chutePWM = PWM_OFF;

}

singleShotTimer++;

break;

case END_SINGLE_SHOT:

// this state does nothing

break;

}

// end single shot state machine

Smoothing Your Signals

Filter Types

- Filters are classified by what they allow to pass through (NOT what they filter out).
- For example, a “low pass filter” (abv. LPF) allows low frequencies to pass through – it therefore removes high frequencies.
- The most common filters are: high pass filters, low pass filters, and band pass filters.
- We will only cover low pass filters.

Low Pass Filters

- Low Pass Filters (LPFs) are used to smooth out the signal.
- Common applications:
- Removing sensor noise
- Removing unwanted signal frequencies
- Signal averaging

Low Pass Filters, continued

- There are two basic types of filters:
- Infinite Impulse Response (IIR)
- Finite Impulse Response (FIR)

- FIR filters are “moving averages”
- IIR filters act just like electrical resistor-capacitor filters. IIR filters allow the output of the filter to move a fixed fraction of the way toward the input.

Moving Average (FIR) Filter Example

#define WINDOW_SIZE 16

s16 inputArray[WINDOW_SIZE];

u8 windowPtr;

s32 filter;

s16 temp;

s16 oldestValue = inputArray[windowPtr];

filter += input - oldestValue;

inputArray[windowPtr] = input;

if (++windowPtr >= WINDOW_SIZE)

{

windowPtr = 0;

}

Moving Average Filter Considerations

- For more filtering effect, use more data points in the average.
- Since you are adding a lot of numbers, there is a high chance of overflow – take precautions

IIR Filter Example (Floating Point)

#define FILTER_CONST 0.8

static float filtOut;

static float filtOut_z;

float input;

// filter code

filtOut_z = filtOut;

filtOut = input + FILTER_CONST * (filtOut_z – input);

// optimized filter code (filtOut_z not needed)

filtOut = input + FILTER_CONST * (filtOut – input);

IIR Filter Example (Fixed Point)

// filter constant will be 0.75. Get this by

// (1 – 2^-2). Remember X * 2^-2 = X >> 2

#define FILT_SHIFT 2

static s16 filtOut;

s16 input;

// filter code

filtOut += (input - filtOut) >> FILT_SHIFT;

IIR Filter Example (Fixed Point)

Whoa! How did we get from

filtOut = input + FILTER_CONST * (filtOut – input);

To

filtOut += (input - filtOut) >> FILT_SHIFT;

Math:

filtOut = input + (1 - 2^-2) * (filtOut – input)

= input + filtOut – input – 2^-2*filtOut + 2^-2*input

= filtOut + 2^-2 * (input – filtOut)

filtOut += (input – filtOut) >> 2

IIR Filter Considerations (Fixed Point)

- For more filtering effect, make the shift factor bigger.
- Take precautions for overflow.
- You can get more resolution by using more shift factors. For example, have your filter constant be
(1 – 2^-SHIFT1 – 2^-2SHIFT2)

(you’ll have to work out the math!)

Gain resolution and make your data more reliable.

Oversampling Basics

- Simple oversampling: sample more data (i.e. faster sample rate) than you need and average the samples.
- Even if you don’t sample faster, averaging (or filtering the data) can be beneficial.

Oversampling Effects

- Helps to “smooth” the data.
- Helps to “hide” a bad or unreliable sample.
- Increases A/D resolution if noise is present.

Oversampling Effects

0.3!!!

Make your code run faster.

Optimizations

- Use fixed point math, not floating point.
- If possible, do not use data types larger than the microcontroller’s native data type.
- When possible, use bit-shifts instead of multiplying or dividing.
- WARNING: some micro/compiler combinations do not properly handle signed shifts (the FRC controller is a good example).

- For high speed interrupts: use as little code as possible; try and move any processing to the slower code outside of the interrupt.
- Use overflow to your advantage.

Example (Using Overflow)

Very efficient 8-sample FIR filter:

static u8 filtIndex = 0;

filtOut += (a2dInput - filtArray[(filtIndex & 0x07)]);

filtArray[(filtIndex & 0x07)] = a2dInput;

filtIndex++;

Compare the above filter to the FIR filter example given in the “Filtering” portion of the presentation. Note that it eliminates the need for “if” statements. The overflow automatically handles “wrapping” the array index.

This concept will work as long as the size of the filter is a power of 2.

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