FFT with dsPIC33E returns no frequency - c

I'm working with a dsPIC33EP128GP502 and try to run a FFT to measure the dominant frequency on the input. The compiler shows no errors and the ADC itself seems to work... (for single values)
I expect as result some frequency value between 0 Hz and ~96 kHz in the variable peakFrequency. With a noise signal (or no signal at all) the value should be more or less random. With an external applied single tone signal I expect to measure the input frequency +/- ~100 Hz. Sadly, my frequency output is always 0.
The test signals are generated by external signal generators and the ADC works fine if I want to measure single values!
The FFT has to run on the DSP-core of the dsPIC33E due to some performance needs.
Has anyone any experience with the dsPIC33E and an idea were my mistake is?
ADC: TAD -> 629.3 ns, Conversion Trigger -> Clearing sample bit ends sampling and starts conversion, Output Format -> Fractional result, signed, Auto Sampling -> enabled
#include "mcc_generated_files/mcc.h"
#include <xc.h>
#include <dsp.h>
#define FFT_BLOCK_LENGTH 1024
#define LOG2_BLOCK_LENGTH 10
#define AUDIO_FS 192042
int16_t peakFrequencyBin;
uint16_t ix_MicADCbuff;
uint16_t peakFrequency;
fractional fftMaxValue;
fractcomplex twiddleFactors[FFT_BLOCK_LENGTH/2] __attribute__ ((space(xmemory)));
fractcomplex sigCmpx[FFT_BLOCK_LENGTH] __attribute__ ((space(ymemory), aligned(FFT_BLOCK_LENGTH * 2 *2)));
bool timeGetAdcSample = false;
void My_ADC_IRS(void)
{
timeGetAdcSample = true;
}
void readOutput(void)//Sample output
{
for(ix_MicADCbuff=0;ix_MicADCbuff<FFT_BLOCK_LENGTH;ix_MicADCbuff++)
{
ADC1_ChannelSelect(mix_output);
ADC1_SoftwareTriggerEnable();
while(!timeGetAdcSample); //wait for TMR1 interrupt (5.2072 us)
timeGetAdcSample = false;
ADC1_SoftwareTriggerDisable();
while(!ADC1_IsConversionComplete(mix_output));
sigCmpx[ix_MicADCbuff].real = ADC1_Channel0ConversionResultGet();
sigCmpx[ix_MicADCbuff].imag = 0;
}
}
void signalFreq(void)//Detect the dominant frequency
{
readOutput();
FFTComplexIP(LOG2_BLOCK_LENGTH, &sigCmpx[0], &twiddleFactors[0], COEFFS_IN_DATA);/
BitReverseComplex(LOG2_BLOCK_LENGTH, &sigCmpx[0]);
SquareMagnitudeCplx(FFT_BLOCK_LENGTH, &sigCmpx[0], &sigCmpx[0].real);
VectorMax(FFT_BLOCK_LENGTH/2, &sigCmpx[0].real, &peakFrequencyBin);
peakFrequency = peakFrequencyBin*(AUDIO_FS/FFT_BLOCK_LENGTH);
}
int main(void)
{
SYSTEM_Initialize();
TwidFactorInit(LOG2_BLOCK_LENGTH, &twiddleFactors[0], 0);
TMR1_SetInterruptHandler(My_ADC_IRS);
TMR1_Start();
while (1)
{
signalFreq();
UART1_32_Write((uint32_T)peakFrequency); // output via UART
}
return 1;
}
Perhaps anyone can figure out the error/problem in my code!

Related

Big latency in bluetooth communication

I have tried to write wireless servo control using two arduino nano v3 boards and two bluetooth 4.0 modules. First code is transmitter. It's very simple. It reads PPM signals and transform to separates PWM values for each channel. I use hardware serial port.
#include <PPMReader.h>
#include <InterruptHandler.h>
int ppmInputPin = 3;
int channelAmount = 2;
PPMReader ppm(ppmInputPin, channelAmount);
void setup()
{
Serial.begin(9600);
Serial.write("AT\r\n");
delay(10);
Serial.write("AT\r\n");
Serial.write("AT+INQ\r\n");
delay(5000);
Serial.write("AT+CONN1\r\n");
}
void loop()
{
unsigned long value1 = ppm.latestValidChannelValue(1, 0);
Serial.println(value1);
}
Receiver is simple too. It reads values from bluetooth and parse into integer value and sends to servo by 7th pin. Again I have used hardware serial port.
#include <Servo.h>
int PWM_OUTPUT = 7;
Servo servo;
void setup() {
servo.attach(PWM_OUTPUT);
Serial.begin(9600);
}
void loop() {
int pwmValue = Serial.parseInt();
if (Serial.available()) {
if(pwmValue > 900 && pwmValue < 2001) {
servo.writeMicroseconds(pwmValue);
}
}
}
All it works. But it has delay around 2-3 seconds. Can be problem in "spamming" serial port?
The first thing you need to ask yourself when implementing a device-to-device communication is how fast should I be sending? and if I send at that rate: is the receiver going to be able to keep pace (reading, doing processing or whatever it needs to do and answer back)?
This is obviously not about the baud rate but about what your loops are doing. You are using two different libraries: PPMReader and Servo. Now, pay attention to what each device is doing in their respective loops:
//Sending
void loop() {
unsigned long value1 = ppm.latestValidChannelValue(1, 0);
Serial.println(value1);
}
//Receiving
void loop() {
int pwmValue = Serial.parseInt();
if(pwmValue > 900 && pwmValue < 2001) {
servo.writeMicroseconds(pwmValue);
}
}
I don't really know how long it takes to execute each line of code (take a look here for some comments on that) but you cannot seriously expect both loops to magically synchronize themselves. Considering they are doing very different things (leaving out the serial part) dealing with different hardware, I would expect one of them to take significantly longer than the other. Think about what happens if that's the case.
As I said, I have no idea how long it takes to call ppm.latestValidChannelValue(1, 0) but for the sake of my argument let's say it takes 0.1 milliseconds. To have an estimate of the time it takes to complete one iteration around the loop you need to add the time it takes to print one (or two) bytes to the port with Serial.println(value1) but that's easier, maybe around 20-100 microseconds is a good ballpark figure. With these estimates, you end up reading 5000 times per second. If you are not happy or you don't trust my estimates I would suggest you do your own tests with a counter or a timer. If you do the same exercise for the other side of the link and let's say you get it's twice as fast, it runs 10000 times per second, how do you think it would happen with the communication? Yes, that's right: it will get clogged and run at snail pace.
Here you should carefully consider if you really need that many readings (you did not elaborate on what you're actually doing so I have no idea, but I lean on thinking you don't). If you don't, just add a delay on the sender's side to slow it down to a reasonable (maybe 10-20 iterations per second) speed.
There are other things to improve on your code: you should check you have received data in the buffer before reading it (not after). And you need to be careful with Serial.parseInt(), which sometimes leads to unexpected results but this answer is already too long and I don't want to extend it even more.
I found problem. It was in serial port spamming. I have added check if current value is not equal with previous value and it have started work and next small issue was in receiver. I read value before it was available.
#include <PPMReader.h>
#include <InterruptHandler.h>
int ppmInputPin = 3;
int channelAmount = 2;
PPMReader ppm(ppmInputPin, channelAmount);
volatile unsigned long previousValue1 = 0;
void setup()
{
Serial.begin(9600);
Serial.write("AT\r\n");
delay(10);
Serial.write("AT\r\n");
Serial.write("AT+INQ\r\n");
delay(5000);
Serial.write("AT+CONN1\r\n");
Serial.println("Transmitter started");
}
void loop()
{
unsigned long value1 = ppm.latestValidChannelValue(1, 0);
if(previousValue1 != value1) {
previousValue1 = value1;
Serial.println(value1);
}
}

Best way to read from a sensor that doesn't have interrupt pin and requires some time before the measurement is ready

I'm trying to interface a pressure sensor (MS5803-14BA) with my board (NUCLEO-STM32L073RZ).
According to the datasheet (page 3), the pressure sensor requires some milliseconds before the measurement is ready to be read. For my project, I would be interested in the highest resolution that requires around 10 ms for the conversion of the raw data.
Unfortunately, this pressure sensor doesn't have any interrupt pin that can be exploited to see when the measurement is ready, and therefore I temporarily solved the problem putting a delay after the request of new data.
I don't like my current solution, since in those 10 ms I could put the mcu working on something else (I have several other sensors attached to my board), but without any interrupt pin, I'm not sure about what is the best way to solve this problem.
Another solution came into my mind: Using a timer that triggers every say 20 ms and performs the following operations:
1.a Read the current value stored in the registers (discarding the first value)
1.b Ask for a new value
In this way, at the next iteration I would just need to read the value requested at the end of the previous iteration.
What I don't like is that my measurement would be always 20 ms old. Until the delay remains 20 ms, it should be still fine, but if I need to reduce the rate, the "age" of the reading with my solution would increase.
Do you have any other idea about how to deal with this?
Thank you.
Note: Please let me know if you would need to see my current implementation.
How to do high-resolution, timestamp-based, non-blocking, single-threaded cooperative multi-tasking
This isn't a "how to read a sensor" problem, this is a "how to do non-blocking cooperative multi-tasking" problem. Assuming you are running bare-metal (no operating system, such as FreeRTOS), you have two good options.
First, the datasheet shows you need to wait up to 9.04 ms, or 9040 us.
Now, here are your cooperative multi-tasking options:
Send a command to tell the device to do an ADC conversion (ie: to take an analog measurement), then configure a hardware timer to interrupt you exactly 9040 us later. In your ISR you then can either set a flag to tell your main loop to send a read command to read the result, OR you can just send the read command right inside the ISR.
Use non-blocking time-stamp-based cooperative multi-tasking in your main loop. This will likely require a basic state machine. Send the conversion command, then move on, doing other things. When your time stamp indicates it's been long enough, send the read command to read the converted result from the sensor.
Number 1 above is my preferred approach for time-critical tasks. This isn't time-critical, however, and a little jitter won't make any difference, so Number 2 above is my preferred approach for general, bare-metal cooperative multi-tasking, so let's do that.
Here's a sample program to demonstrate the principle of time-stamp-based bare-metal cooperative multi-tasking for your specific case where you need to:
request a data sample (start ADC conversion in your external sensor)
wait 9040 us for the conversion to complete
read in the data sample from your external sensor (now that the ADC conversion is complete)
Code:
enum sensorState_t
{
SENSOR_START_CONVERSION,
SENSOR_WAIT,
SENSOR_GET_CONVERSION
}
int main(void)
{
doSetupStuff();
configureHardwareTimer(); // required for getMicros() to work
while (1)
{
//
// COOPERATIVE TASK #1
// Read the under-water pressure sensor as fast as permitted by the datasheet
//
static sensorState_t sensorState = SENSOR_START_CONVERSION; // initialize state machine
static uint32_t task1_tStart; // us; start time
static uint32_t sensorVal; // the sensor value you are trying to obtain
static bool newSensorVal = false; // set to true whenever a new value arrives
switch (sensorState)
{
case SENSOR_START_CONVERSION:
{
startConversion(); // send command to sensor to start ADC conversion
task1_tStart = getMicros(); // get a microsecond time stamp
sensorState = SENSOR_WAIT; // next state
break;
}
case SENSOR_WAIT:
{
const uint32_t DESIRED_WAIT_TIME = 9040; // us
uint32_t tNow = getMicros();
if (tNow - task1_tStart >= DESIRED_WAIT_TIME)
{
sensorState = SENSOR_GET_CONVERSION; // next state
}
break;
}
case SENSOR_GET_CONVERSION:
{
sensorVal = readConvertedResult(); // send command to read value from the sensor
newSensorVal = true;
sensorState = SENSOR_START_CONVERSION; // next state
break;
}
}
//
// COOPERATIVE TASK #2
// use the under-water pressure sensor data right when it comes in (this will be an event-based task
// whose running frequency depends on the rate of new data coming in, for example)
//
if (newSensorVal == true)
{
newSensorVal = false; // reset this flag
// use the sensorVal data here now for whatever you need it for
}
//
// COOPERATIVE TASK #3
//
//
// COOPERATIVE TASK #4
//
// etc etc
} // end of while (1)
} // end of main
For another really simple timestamp-based multi-tasking example see Arduino's "Blink Without Delay" example here.
General time-stamp-based bare-metal cooperative multi-tasking architecture notes:
Depending on how you do it all, in the end, you basically end up with this type of code layout, which simply runs each task at fixed time intervals. Each task should be non-blocking to ensure it does not conflict with the run intervals of the other tasks. Non-blocking on bare metal means simply "do not use clock-wasting delays, busy-loops, or other types of polling, repeating, counting, or busy delays!". (This is opposed to "blocking" on an operating-system-based (OS-based) system, which means "giving the clock back to the scheduler to let it run another thread while this task 'sleeps'." Remember: bare metal means no operating system!). Instead, if something isn't quite ready to run yet, simply save your state via a state machine, exit this task's code (this is the "cooperative" part, as your task must voluntarily give up the processor by returning), and let another task run!
Here's the basic architecture, showing a simple timestamp-based way to get 3 Tasks to run at independent, fixed frequencies withOUT relying on any interrupts, and with minimal jitter, due to the thorough and methodical approach I take to check the timestamps and update the start time at each run time.
1st, the definition for the main() function and main loop:
int main(void)
{
doSetupStuff();
configureHardwareTimer();
while (1)
{
doTask1();
doTask2();
doTask3();
}
}
2nd, the definitions for the doTask() functions:
// Task 1: Let's run this one at 100 Hz (every 10ms)
void doTask1(void)
{
const uint32_t DT_DESIRED_US = 10000; // 10000us = 10ms, or 100Hz run freq
static uint32_t t_start_us = getMicros();
uint32_t t_now_us = getMicros();
uint32_t dt_us = t_now_us - t_start_us;
// See if it's time to run this Task
if (dt_us >= DT_DESIRED_US)
{
// 1. Add DT_DESIRED_US to t_start_us rather than setting t_start_us to t_now_us (which many
// people do) in order to ***avoid introducing artificial jitter into the timing!***
t_start_us += DT_DESIRED_US;
// 2. Handle edge case where it's already time to run again because just completing one of the main
// "scheduler" loops in the main() function takes longer than DT_DESIRED_US; in other words, here
// we are seeing that t_start_us is lagging too far behind (more than one DT_DESIRED_US time width
// from t_now_us), so we are "fast-forwarding" t_start_us up to the point where it is exactly
// 1 DT_DESIRED_US time width back now, thereby causing this task to instantly run again the
// next time it is called (trying as hard as we can to run at the specified frequency) while
// at the same time protecting t_start_us from lagging farther and farther behind, as that would
// eventually cause buggy and incorrect behavior when the (unsigned) timestamps start to roll over
// back to zero.
dt_us = t_now_us - t_start_us; // calculate new time delta with newly-updated t_start_us
if (dt_us >= DT_DESIRED_US)
{
t_start_us = t_now_us - DT_DESIRED_US;
}
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
// Task 2: Let's run this one at 1000 Hz (every 1ms)
void doTask2(void)
{
const uint32_t DT_DESIRED_US = 1000; // 1000us = 1ms, or 1000Hz run freq
static uint32_t t_start_us = getMicros();
uint32_t t_now_us = getMicros();
uint32_t dt_us = t_now_us - t_start_us;
// See if it's time to run this Task
if (dt_us >= DT_DESIRED_US)
{
t_start_us += DT_DESIRED_US;
dt_us = t_now_us - t_start_us; // calculate new time delta with newly-updated t_start_us
if (dt_us >= DT_DESIRED_US)
{
t_start_us = t_now_us - DT_DESIRED_US;
}
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
// Task 3: Let's run this one at 10 Hz (every 100ms)
void doTask3(void)
{
const uint32_t DT_DESIRED_US = 100000; // 100000us = 100ms, or 10Hz run freq
static uint32_t t_start_us = getMicros();
uint32_t t_now_us = getMicros();
uint32_t dt_us = t_now_us - t_start_us;
// See if it's time to run this Task
if (dt_us >= DT_DESIRED_US)
{
t_start_us += DT_DESIRED_US;
dt_us = t_now_us - t_start_us; // calculate new time delta with newly-updated t_start_us
if (dt_us >= DT_DESIRED_US)
{
t_start_us = t_now_us - DT_DESIRED_US;
}
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
The code above works perfectly but as you can see is pretty redundant and a bit irritating to set up new tasks. This job can be a bit more automated and much much easier to do by simply defining a macro, CREATE_TASK_TIMER(), as follows, to do all of the redundant timing stuff and timestamp variable creation for us:
/// #brief A function-like macro to get a certain set of events to run at a desired, fixed
/// interval period or frequency.
/// #details This is a timestamp-based time polling technique frequently used in bare-metal
/// programming as a basic means of achieving cooperative multi-tasking. Note
/// that getting the timing details right is difficult, hence one reason this macro
/// is so useful. The other reason is that this maro significantly reduces the number of
/// lines of code you need to write to introduce a new timestamp-based cooperative
/// task. The technique used herein achieves a perfect desired period (or freq)
/// on average, as it centers the jitter inherent in any polling technique around
/// the desired time delta set-point, rather than always lagging as many other
/// approaches do.
///
/// USAGE EX:
/// ```
/// // Create a task timer to run at 500 Hz (every 2000 us, or 2 ms; 1/0.002 sec = 500 Hz)
/// const uint32_t PERIOD_US = 2000; // 2000 us pd --> 500 Hz freq
/// bool time_to_run;
/// CREATE_TASK_TIMER(PERIOD_US, time_to_run);
/// if (time_to_run)
/// {
/// run_task_2();
/// }
/// ```
///
/// Source: Gabriel Staples
/// https://stackoverflow.com/questions/50028821/best-way-to-read-from-a-sensors-that-doesnt-have-interrupt-pin-and-require-some/50032992#50032992
/// #param[in] dt_desired_us The desired delta time period, in microseconds; note: pd = 1/freq;
/// the type must be `uint32_t`
/// #param[out] time_to_run A `bool` whose scope will enter *into* the brace-based scope block
/// below; used as an *output* flag to the caller: this variable will
/// be set to true if it is time to run your code, according to the
/// timestamps, and will be set to false otherwise
/// #return NA--this is not a true function
#define CREATE_TASK_TIMER(dt_desired_us, time_to_run) \
{ /* Use scoping braces to allow multiple calls of this macro all in one outer scope while */ \
/* allowing each variable created below to be treated as unique to its own scope */ \
time_to_run = false; \
\
/* set the desired run pd / freq */ \
const uint32_t DT_DESIRED_US = dt_desired_us; \
static uint32_t t_start_us = getMicros(); \
uint32_t t_now_us = getMicros(); \
uint32_t dt_us = t_now_us - t_start_us; \
\
/* See if it's time to run this Task */ \
if (dt_us >= DT_DESIRED_US) \
{ \
/* 1. Add DT_DESIRED_US to t_start_us rather than setting t_start_us to t_now_us (which many */ \
/* people do) in order to ***avoid introducing artificial jitter into the timing!*** */ \
t_start_us += DT_DESIRED_US; \
/* 2. Handle edge case where it's already time to run again because just completing one of the main */ \
/* "scheduler" loops in the main() function takes longer than DT_DESIRED_US; in other words, here */ \
/* we are seeing that t_start_us is lagging too far behind (more than one DT_DESIRED_US time width */ \
/* from t_now_us), so we are "fast-forwarding" t_start_us up to the point where it is exactly */ \
/* 1 DT_DESIRED_US time width back now, thereby causing this task to instantly run again the */ \
/* next time it is called (trying as hard as we can to run at the specified frequency) while */ \
/* at the same time protecting t_start_us from lagging farther and farther behind, as that would */ \
/* eventually cause buggy and incorrect behavior when the (unsigned) timestamps start to roll over */ \
/* back to zero. */ \
dt_us = t_now_us - t_start_us; /* calculate new time delta with newly-updated t_start_us */ \
if (dt_us >= DT_DESIRED_US) \
{ \
t_start_us = t_now_us - DT_DESIRED_US; \
} \
\
time_to_run = true; \
} \
}
Now, there are multiple ways to use it, but for the sake of this demo, in order to keep the really clean main() loop code which looks like this:
int main(void)
{
doSetupStuff();
configureHardwareTimer();
while (1)
{
doTask1();
doTask2();
doTask3();
}
}
Let's use the CREATE_TASK_TIMER() macro like this. As you can see, the code is now much cleaner and easier to set up a new task. This is my preferred approach, because it creates the really clean main loop shown just above, with just the various doTask() calls, which are also easy to write and maintain:
// Task 1: Let's run this one at 100 Hz (every 10ms, or 10000us)
void doTask1(void)
{
bool time_to_run;
const uint32_t DT_DESIRED_US = 10000; // 10000us = 10ms, or 100Hz run freq
CREATE_TASK_TIMER(DT_DESIRED_US, time_to_run);
if (time_to_run)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
// Task 2: Let's run this one at 1000 Hz (every 1ms)
void doTask2(void)
{
bool time_to_run;
const uint32_t DT_DESIRED_US = 1000; // 1000us = 1ms, or 1000Hz run freq
CREATE_TASK_TIMER(DT_DESIRED_US, time_to_run);
if (time_to_run)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
// Task 3: Let's run this one at 10 Hz (every 100ms)
void doTask3(void)
{
bool time_to_run;
const uint32_t DT_DESIRED_US = 100000; // 100000us = 100ms, or 10Hz run freq
CREATE_TASK_TIMER(DT_DESIRED_US, time_to_run);
if (time_to_run)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
}
Alternatively, however, you could structure the code more like this, which works equally as well and produces the same effect, just in a slightly different way:
#include <stdbool.h>
#include <stdint.h>
#define TASK1_PD_US (10000) // 10ms pd, or 100 Hz run freq
#define TASK2_PD_US (1000) // 1ms pd, or 1000 Hz run freq
#define TASK3_PD_US (100000) // 100ms pd, or 10 Hz run freq
// Task 1: Let's run this one at 100 Hz (every 10ms, or 10000us)
void doTask1(void)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
// Task 2: Let's run this one at 1000 Hz (every 1ms)
void doTask2(void)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
// Task 3: Let's run this one at 10 Hz (every 100ms)
void doTask3(void)
{
// PERFORM THIS TASK'S OPERATIONS HERE!
}
int main(void)
{
doSetupStuff();
configureHardwareTimer();
while (1)
{
bool time_to_run;
CREATE_TASK_TIMER(TASK1_PD_US, time_to_run);
if (time_to_run)
{
doTask1();
}
CREATE_TASK_TIMER(TASK2_PD_US, time_to_run);
if (time_to_run)
{
doTask2();
}
CREATE_TASK_TIMER(TASK3_PD_US, time_to_run);
if (time_to_run)
{
doTask3();
}
}
}
Part of the art (and fun!) of embedded bare-metal microcontroller programming is the skill and ingenuity involved in deciding exactly how you want to interleave each task and get them to run together, all as though they were running in parallel. Use one of the above formats as a starting point, and adapt to your particular circumstances. Message-passing can be added between tasks or between tasks and interrupts, tasks and a user, etc, as desired, and as required for your particular application.
Here's an example of how to configure a timer for use as a timestamp-generator on an STM32F2 microcontroller.
This shows functions for configureHardwareTimer() and getMicros(), used above:
// Timer handle to be used for Timer 2 below
TIM_HandleTypeDef TimHandle;
// Configure Timer 2 to be used as a free-running 32-bit hardware timer for general-purpose use as a 1-us-resolution
// timestamp source
void configureHardwareTimer()
{
// Timer clock must be enabled before you can configure it
__HAL_RCC_TIM2_CLK_ENABLE();
// Calculate prescaler
// Here are some references to show how this is done:
// 1) "STM32Cube_FW_F2_V1.7.0/Projects/STM32F207ZG-Nucleo/Examples/TIM/TIM_OnePulse/Src/main.c" shows the
// following (slightly modified) equation on line 95: `Prescaler = (TIMxCLK/TIMx_counter_clock) - 1`
// 2) "STM32F20x and STM32F21x Reference Manual" states the following on pg 419: "14.4.11 TIMx prescaler (TIMx_PSC)"
// "The counter clock frequency CK_CNT is equal to fCK_PSC / (PSC[15:0] + 1)"
// This means that TIMx_counter_clock_freq = TIMxCLK/(prescaler + 1). Now, solve for prescaler and you
// get the exact same equation as above: `prescaler = TIMxCLK/TIMx_counter_clock_freq - 1`
// Calculating TIMxCLK:
// - We must divide SystemCoreClock (returned by HAL_RCC_GetHCLKFreq()) by 2 because TIM2 uses clock APB1
// as its clock source, and on my board this is configured to be 1/2 of the SystemCoreClock.
// - Note: To know which clock source each peripheral and timer uses, you can look at
// "Table 25. Peripheral current consumption" in the datasheet, p86-88.
const uint32_t DESIRED_TIMER_FREQ = 1e6; // 1 MHz clock freq --> 1 us pd per tick, which is what I want
uint32_t Tim2Clk = HAL_RCC_GetHCLKFreq() / 2;
uint32_t prescaler = Tim2Clk / DESIRED_TIMER_FREQ - 1; // Don't forget the minus 1!
// Configure timer
// TIM2 is a 32-bit timer; See datasheet "Table 4. Timer feature comparison", p30-31
TimHandle.Instance = TIM2;
TimHandle.Init.Period = 0xFFFFFFFF; // Set pd to max possible for a 32-bit timer
TimHandle.Init.Prescaler = prescaler;
TimHandle.Init.ClockDivision = TIM_CLOCKDIVISION_DIV1;
TimHandle.Init.CounterMode = TIM_COUNTERMODE_UP;
TimHandle.Init.RepetitionCounter = 0; // NA (has no significance) for this timer
// Initialize the timer
if (HAL_TIM_Base_Init(&TimHandle) != HAL_OK)
{
// handle error condition
}
// Start the timer
if (HAL_TIM_Base_Start(&TimHandle) != HAL_OK)
{
// handle error condition
}
}
// Get the 1 us count value on Timer 2.
// This timer will be used for general purpose hardware timing that does NOT rely on interrupts.
// Therefore, the counter will continue to increment even with interrupts disabled.
// The count value increments every 1 microsecond.
// Since it is a 32-bit counter it overflows every 2^32 counts, which means the highest value it can
// store is 2^32 - 1 = 4294967295. Overflows occur every 2^32 counts / 1 count/us / 1e6us/sec
// = ~4294.97 sec = ~71.6 min.
uint32_t getMicros()
{
return __HAL_TIM_GET_COUNTER(&TimHandle);
}
References:
https://www.arduino.cc/en/tutorial/BlinkWithoutDelay
Doxygen: What's the right way to reference a parameter in Doxygen?
Enum-based error codes for error handling: Error handling in C code
Other architectural styles in C, such as "object-based" C via opaque pointers: Opaque C structs: various ways to declare them
See also:
A full, runnable Arduino example with an even better version of my CREATE_TASK_TIMER() macro from above:
My answer for C and C++, including microcontrollers and Arduino (or any other system): Full coulomb counter example demonstrating the above concept with timestamp-based, single-threaded, cooperative multi-tasking
First of all thank you for your suggestions. I tried to analyze every single possible solution you proposed.
The solution proposed by Peter seemed very interesting but I have to say that, after having gone through the datasheet several times, I don't believe that is feasible. My consideration is based on the following facts.
Using a scope I see that the acknowledge is received right after sending the command for doing conversion. See following image concerning the temperature conversion:
It seems quite clear to me the acknowledge bit right after the command. After that the SDA line (yellow) goes high, therefore I don't see how it is possible that I can exploit that for detecting when the conversion is ready.
Concerning the solution when using SPI, yes, the SDO remains low during the conversion, but I cannot use it: I need to stick with I2C. Furthermore, I have other sensors attached to that SPI bus and I agree with what Gabriel Staples says.
After my consideration I went for the solution proposed by Gabriel Staples (considering that, in order to read pressure value, I also need to read and convert temperature).
My current solution is based on a state machine with 6 states. In my solution, I distinguish between the wait time for the pressure conversion and the wait time for the temperature conversion with the idea the I could try to see how much the pressure reading degrades if I use a less precise temperature reading.
Here is my current solution. The following function is called inside the main while:
void MS5803_update()
{
static uint32_t tStart; // us; start time
switch (sensor_state)
{
case MS5803_REQUEST_TEMPERATURE:
{
MS5803_send_command(MS5803_CMD_ADC_CONV + TEMPERATURE + baro.resolution);
tStart = HAL_GetTick();
sensor_state = MS5803_WAIT_RAW_TEMPERATURE;
break;
}
case MS5803_WAIT_RAW_TEMPERATURE:
{
uint32_t tNow = HAL_GetTick();
if (tNow - tStart >= conversion_time)
{
sensor_state = MS5803_CONVERTING_TEMPERATURE;
}
break;
}
case MS5803_CONVERTING_TEMPERATURE:
{
MS5803_send_command(MS5803_CMD_ADC_READ);
uint8_t raw_value[3]; // Read 24 bit
MS5803_read_value(raw_value,3);
temperature_raw = ((uint32_t)raw_value[0] << 16) + ((uint32_t)raw_value[1] << 8) + raw_value[2];
sensor_state = MS5803_REQUEST_PRESSURE;
break;
}
case MS5803_REQUEST_PRESSURE:
{
MS5803_send_command(MS5803_CMD_ADC_CONV + PRESSURE + baro.resolution);
tStart = HAL_GetTick();
sensor_state = MS5803_WAIT_RAW_PRESSURE;
break;
}
case MS5803_WAIT_RAW_PRESSURE:
{
uint32_t tNow = HAL_GetTick();
if (tNow - tStart >= conversion_time)
{
sensor_state = MS5803_CONVERTING_PRESSURE;
}
break;
}
case MS5803_CONVERTING_PRESSURE:
{
MS5803_send_command(MS5803_CMD_ADC_READ);
uint8_t raw_value[3]; // Read 24 bit
MS5803_read_value(raw_value,3);
pressure_raw = ((uint32_t)raw_value[0] << 16) + ((uint32_t)raw_value[1] << 8) + raw_value[2];
// Now I have both temperature and pressure raw and I can convert them
MS5803_updateMeasurements();
// Reset the state machine to perform a new measurement
sensor_state = MS5803_REQUEST_TEMPERATURE;
break;
}
}
}
I don't pretend that my solution is better. I just post it in order to have an opinion from you guys. Note: I'm still working on it. Therefore I cannot guarantee is bug-free!
For PeterJ_01: I could agree that this is not strictly a teaching portal, but I believe that everybody around here asks questions to learn something new or to improve theirselves. Therefore, if you believe that the solution using the ack is better, it would be great if you could show us a draft of your idea. For me it would be something new to learn.
Any further comment is appreciated.

CodeWarrior Get variable value from a event.c

to enter context I'm doing this:
Drive a stepper motor through the variation of pulse frequency input to a Driver (A4988) (It is not necessary to know the functioning of this for this question). Now and got varying the frequency of the pulses (They change the engine speed). You need to know that for the motor shaft 1 full turn have to get 200 pulses (The engine is 1.8 ° degrees per step).
I got the engine and make him a full turn in 1 second.
Period = 0.005s
To program this I am using the component: TimerUnit_LDD.
With a frequency of 163840 Hz count
In the case of the whole turn 1 to get that frequently use this function.
---- main.c
TU1_Enable (TU1_DeviceData);
 TU1_SetPeriodTicks (TU1_DeviceData, 410);
  
The parameter 410 is compared to the period I want, as is sending pulses programmed by changing the value of a pin taken into account both the high and the low pulse, like this:
----- Events.c
TU1_OnCounterRestart void (* UserDataPtr LDD_TUserData)
{
 Step1_NegVal ();
 }
The period for serious formulates 819.2, having in mind the above serious approximates 409.6 and 410 (seen in a oscilloscope frequency is 200 Hz (ok).
Already entered in context the problem is this:
---- main.c
TU1_Enable (TU1_DeviceData); // Enable the counter
TU1_SetPeriodTicks (TU1_DeviceData, 410); // Setting the desired period
for (;;) {
           TU1_Enable (TU1_DeviceData);
           WAIT1_Waitms (1000); // Rotation time
 TU1_Enable (TU1_DeviceData); // Disable the counter
}
With this code is what I try to check that the frequency calculation was correct and that in one second would 1 turn. But what happens is that it gives the rotation but is offset a little more. I guess this goes through the runtime required for each line of code.
What I want to know is, how could obtain the numerical value of a variable in an event? how could I do something like this.
---- main.c
TU1_Enable (TU1_DeviceData); // Initialize the counter
TU1_SetPeriodTicks (TU1_DeviceData, 410); // Setting the desired period
for (;;) {
for (;;) {
      if (GetValue (x) == 200) break; // GetValue (x) This function is what I want to achieve
}
WAIT1_Waitms (1000);
}
----- Events.c
TU1_OnCounterRestart void (* UserDataPtr LDD_TUserData)
{
 Step1_NegVal ();
x = x + 1;
 }
GetValue (x) this function would obtain the value of x which is in Events.c and define a number of pulses to control espefico.
Take a variable and is affected by the counter, and that this gets to 200 (for 1 turn in 1 second).
This would have the certainty that menera be sent alone and lonely, neither more nor less, only 200 pulses.
I require this as specific as I am desarrolando the program for a CNC machine and is too importanto precision is the highest.
I hope you understand and I speak Spanish and this was translated by Chrome
Programmed in C language,
Freescale KL25Z,
CodeWarrior,
OPEN_SDA,
I managed to implement something but I think it may be easier to get
-----(main.c)
extern int count;//called external variable
int main(void){
PE_low_level_init();
TU1_Enable(TU1_DeviceData);
TU1_SetPeriodTicks(TU1_DeviceData,410);//T=0.005 sec
for(;;){
Term1_Cls();// Clear Console
WAIT1_Waitms(1000);
Term1_MoveTo(0,0);// Set 0,0 in Console
for(;;){
TU1_Enable(TU1_DeviceData);
Term1_SendNum(count);
Term1_CRLF();
if (count>400){//amount of high and low pulse counting
count=0;
TU1_Disable(TU1_DeviceData);
break;
}
}
WAIT1_Waitms(1000);
Dir1_NegVal();
}
----(Events.c)
int count;
void TU1_OnCounterRestart(LDD_TUserData *UserDataPtr)
{
Step1_NegVal();
count=count+1; //counter
}

calculation in C for C2000 device

I'm having some trouble with my C code. I have an ADC which will be used to determine whether to shut down (trip zone) the PWM which I'm using. But my calculation seem to not work as intended, because the ADC shuts down the PWM at the wrong voltage levels. I initiate my variables as:
float32 current = 5;
Uint16 shutdown = 0;
and then I calculate as:
// Save the ADC input to variable
adc_info->adc_result0 = AdcRegs.ADCRESULT0>>4; //bit shift 4 steps because adcresult0 is effectively a 12-bit register not 16-bit, ADCRESULT0 defined as Uint16
current = -3.462*((adc_info->adc_result0/1365) - 2.8);
// Evaluate if too high or too low
if(current > 9 || current < 1)
{
shutdown = 1;
}
else
{
shutdown = 0;
}
after which I use this if statement:
if(shutdown == 1)
{
EALLOW; // EALLOW protected register
EPwm1Regs.TZFRC.bit.OST = 1; // Force a one-shot trip-zone interrupt
EDIS; // end write to EALLOW protected register
}
So I want to trip the PWM if current is above 9 or below 1 which should coincide with an adc result of <273 (0x111) and >3428 (0xD64) respectively. The ADC values correspond to the voltages 0.2V and 2.51V respectively. The ADC measure with a 12-bit accuracy between the voltages 0 and 3V.
However, this is not the case. Instead, the trip zone goes off at approximately 1V and 2.97V. So what am I doing wrong?
adc_info->adc_result0/1365
Did you do integer division here while assuming float?
Try this fix:
adc_info->adc_result0/1365.0
Also, the #pmg's suggestion is good. Why spending cycles on calculating the voltage, when you can compare the ADC value immediately against the known bounds?
if (adc_info->adc_result0 < 273 || adc_info->adc_result0 > 3428)
{
shutdown = 1;
}
else
{
shutdown = 0;
}
If you don't want to hardcode the calculated bounds (which is totally understandable), then define them as calculated from values which you'd want to hardcode literally:
#define VOLTAGE_MIN 0.2
#define VOLTAGE_MAX 2.51
#define AREF 3.0
#define ADC_PER_VOLT (4096 / AREF)
#define ADC_MIN (VOLTAGE_MIN * ADC_PER_VOLT) /* 273 */
#define ADC_MAX (VOLTAGE_MAX * ADC_PER_VOLT) /* 3427 */
/* ... */
shutdown = (adcresult < ADC_MIN || adcresult > ADC_MAX) ? 1 : 0;
/* ... */
When you've made sure to grasp the integer division rules in C, consider a little addition to your code style: to always write constant coefficients and divisors with a decimal (to make sure they get a floating point type), e.g. 10.0 instead of 10 — unless you specifically mean integer division with truncation. Sometimes it may also be a good idea to specify float literal precision with appropriate suffix.

Assign delays for 1 ms or 2 ms in C?

I'm using code to configure a simple robot. I'm using WinAVR, and the code used there is similar to C, but without stdio.h libraries and such, so code for simple stuff should be entered manually (for example, converting decimal numbers to hexadecimal numbers is a multiple-step procedure involving ASCII character manipulation).
Example of code used is (just to show you what I'm talking about :) )
.
.
.
DDRA = 0x00;
A = adc(0); // Right-hand sensor
u = A>>4;
l = A&0x0F;
TransmitByte(h[u]);
TransmitByte(h[l]);
TransmitByte(' ');
.
.
.
For some circumstances, I must use WinAVR and cannot external libraries (such as stdio.h). ANYWAY, I want to apply a signal with pulse width of 1 ms or 2 ms via a servo motor. I know what port to set and such; all I need to do is apply a delay to keep that port set before clearing it.
Now I know how to set delays, we should create empty for loops such as:
int value= **??**
for(i = 0; i<value; i++)
;
What value am I supposed to put in "value" for a 1 ms loop ?
Chances are you'll have to calculate a reasonable value, then look at the signal that's generated (e.g., with an oscilloscope) and adjust your value until you hit the right time range. Given that you apparently have a 2:1 margin, you might hit it reasonably close the first time, but I wouldn't be much on it.
For your first approximation, generate an empty loop and count the instruction cycles for one loop, and multiply that by the time for one clock cycle. That should give at least a reasonable approximation of time taken by a single execution of the loop, so dividing the time you need by that should get you into the ballpark for the right number of iterations.
Edit: I should also note, however, that (at least most) AVRs have on-board timers, so you might be able to use them instead. This can 1) let you do other processing and/or 2) reduce power consumption for the duration.
If you do use delay loops, you might want to use AVR-libc's delay loop utilities to handle the details.
If my program is simple enough there is not a need of explicit timer programming, but it should be portable. One of my choices for a defined delay would be AVR Libc's delay function:
#include <delay.h>
_delay_ms (2) // Sleeps 2 ms
Is this going to go to a real robot? All you have is a CPU, no other integrated circuits that can give a measure of time?
If both answers are 'yes', well... if you know the exact timing for the operations, you can use the loop to create precise delays. Output your code to assembly code, and see the exact sequence of instructions used. Then, check the manual of the processor, it'll have that information.
If you need a more precise time value you should employ an interrupt service routine based on an internal timer. Remember a For loop is a blocking instruction, so while it is iterating the rest of your program is blocked. You could set up a timer based ISR with a global variable that counts up by 1 every time the ISR runs. You could then use that variable in an "if statement" to set the width time. Also that core probably supports PWM for use with the RC type servos. So that may be a better route.
This is a really neat little tasker that I use sometimes. It's for an AVR.
************************Header File***********************************
// Scheduler data structure for storing task data
typedef struct
{
// Pointer to task
void (* pTask)(void);
// Initial delay in ticks
unsigned int Delay;
// Periodic interval in ticks
unsigned int Period;
// Runme flag (indicating when the task is due to run)
unsigned char RunMe;
} sTask;
// Function prototypes
//-------------------------------------------------------------------
void SCH_Init_T1(void);
void SCH_Start(void);
// Core scheduler functions
void SCH_Dispatch_Tasks(void);
unsigned char SCH_Add_Task(void (*)(void), const unsigned int, const unsigned int);
unsigned char SCH_Delete_Task(const unsigned char);
// Maximum number of tasks
// MUST BE ADJUSTED FOR EACH NEW PROJECT
#define SCH_MAX_TASKS (1)
************************Header File***********************************
************************C File***********************************
#include "SCH_AVR.h"
#include <avr/io.h>
#include <avr/interrupt.h>
// The array of tasks
sTask SCH_tasks_G[SCH_MAX_TASKS];
/*------------------------------------------------------------------*-
SCH_Dispatch_Tasks()
This is the 'dispatcher' function. When a task (function)
is due to run, SCH_Dispatch_Tasks() will run it.
This function must be called (repeatedly) from the main loop.
-*------------------------------------------------------------------*/
void SCH_Dispatch_Tasks(void)
{
unsigned char Index;
// Dispatches (runs) the next task (if one is ready)
for(Index = 0; Index < SCH_MAX_TASKS; Index++)
{
if((SCH_tasks_G[Index].RunMe > 0) && (SCH_tasks_G[Index].pTask != 0))
{
(*SCH_tasks_G[Index].pTask)(); // Run the task
SCH_tasks_G[Index].RunMe -= 1; // Reset / reduce RunMe flag
// Periodic tasks will automatically run again
// - if this is a 'one shot' task, remove it from the array
if(SCH_tasks_G[Index].Period == 0)
{
SCH_Delete_Task(Index);
}
}
}
}
/*------------------------------------------------------------------*-
SCH_Add_Task()
Causes a task (function) to be executed at regular intervals
or after a user-defined delay
pFunction - The name of the function which is to be scheduled.
NOTE: All scheduled functions must be 'void, void' -
that is, they must take no parameters, and have
a void return type.
DELAY - The interval (TICKS) before the task is first executed
PERIOD - If 'PERIOD' is 0, the function is only called once,
at the time determined by 'DELAY'. If PERIOD is non-zero,
then the function is called repeatedly at an interval
determined by the value of PERIOD (see below for examples
which should help clarify this).
RETURN VALUE:
Returns the position in the task array at which the task has been
added. If the return value is SCH_MAX_TASKS then the task could
not be added to the array (there was insufficient space). If the
return value is < SCH_MAX_TASKS, then the task was added
successfully.
Note: this return value may be required, if a task is
to be subsequently deleted - see SCH_Delete_Task().
EXAMPLES:
Task_ID = SCH_Add_Task(Do_X,1000,0);
Causes the function Do_X() to be executed once after 1000 sch ticks.
Task_ID = SCH_Add_Task(Do_X,0,1000);
Causes the function Do_X() to be executed regularly, every 1000 sch ticks.
Task_ID = SCH_Add_Task(Do_X,300,1000);
Causes the function Do_X() to be executed regularly, every 1000 ticks.
Task will be first executed at T = 300 ticks, then 1300, 2300, etc.
-*------------------------------------------------------------------*/
unsigned char SCH_Add_Task(void (*pFunction)(), const unsigned int DELAY, const unsigned int PERIOD)
{
unsigned char Index = 0;
// First find a gap in the array (if there is one)
while((SCH_tasks_G[Index].pTask != 0) && (Index < SCH_MAX_TASKS))
{
Index++;
}
// Have we reached the end of the list?
if(Index == SCH_MAX_TASKS)
{
// Task list is full, return an error code
return SCH_MAX_TASKS;
}
// If we're here, there is a space in the task array
SCH_tasks_G[Index].pTask = pFunction;
SCH_tasks_G[Index].Delay =DELAY;
SCH_tasks_G[Index].Period = PERIOD;
SCH_tasks_G[Index].RunMe = 0;
// return position of task (to allow later deletion)
return Index;
}
/*------------------------------------------------------------------*-
SCH_Delete_Task()
Removes a task from the scheduler. Note that this does
*not* delete the associated function from memory:
it simply means that it is no longer called by the scheduler.
TASK_INDEX - The task index. Provided by SCH_Add_Task().
RETURN VALUE: RETURN_ERROR or RETURN_NORMAL
-*------------------------------------------------------------------*/
unsigned char SCH_Delete_Task(const unsigned char TASK_INDEX)
{
// Return_code can be used for error reporting, NOT USED HERE THOUGH!
unsigned char Return_code = 0;
SCH_tasks_G[TASK_INDEX].pTask = 0;
SCH_tasks_G[TASK_INDEX].Delay = 0;
SCH_tasks_G[TASK_INDEX].Period = 0;
SCH_tasks_G[TASK_INDEX].RunMe = 0;
return Return_code;
}
/*------------------------------------------------------------------*-
SCH_Init_T1()
Scheduler initialisation function. Prepares scheduler
data structures and sets up timer interrupts at required rate.
You must call this function before using the scheduler.
-*------------------------------------------------------------------*/
void SCH_Init_T1(void)
{
unsigned char i;
for(i = 0; i < SCH_MAX_TASKS; i++)
{
SCH_Delete_Task(i);
}
// Set up Timer 1
// Values for 1ms and 10ms ticks are provided for various crystals
OCR1A = 15000; // 10ms tick, Crystal 12 MHz
//OCR1A = 20000; // 10ms tick, Crystal 16 MHz
//OCR1A = 12500; // 10ms tick, Crystal 10 MHz
//OCR1A = 10000; // 10ms tick, Crystal 8 MHz
//OCR1A = 2000; // 1ms tick, Crystal 16 MHz
//OCR1A = 1500; // 1ms tick, Crystal 12 MHz
//OCR1A = 1250; // 1ms tick, Crystal 10 MHz
//OCR1A = 1000; // 1ms tick, Crystal 8 MHz
TCCR1B = (1 << CS11) | (1 << WGM12); // Timer clock = system clock/8
TIMSK |= 1 << OCIE1A; //Timer 1 Output Compare A Match Interrupt Enable
}
/*------------------------------------------------------------------*-
SCH_Start()
Starts the scheduler, by enabling interrupts.
NOTE: Usually called after all regular tasks are added,
to keep the tasks synchronised.
NOTE: ONLY THE SCHEDULER INTERRUPT SHOULD BE ENABLED!!!
-*------------------------------------------------------------------*/
void SCH_Start(void)
{
sei();
}
/*------------------------------------------------------------------*-
SCH_Update
This is the scheduler ISR. It is called at a rate
determined by the timer settings in SCH_Init_T1().
-*------------------------------------------------------------------*/
ISR(TIMER1_COMPA_vect)
{
unsigned char Index;
for(Index = 0; Index < SCH_MAX_TASKS; Index++)
{
// Check if there is a task at this location
if(SCH_tasks_G[Index].pTask)
{
if(SCH_tasks_G[Index].Delay == 0)
{
// The task is due to run, Inc. the 'RunMe' flag
SCH_tasks_G[Index].RunMe += 1;
if(SCH_tasks_G[Index].Period)
{
// Schedule periodic tasks to run again
SCH_tasks_G[Index].Delay = SCH_tasks_G[Index].Period;
SCH_tasks_G[Index].Delay -= 1;
}
}
else
{
// Not yet ready to run: just decrement the delay
SCH_tasks_G[Index].Delay -= 1;
}
}
}
}
// ------------------------------------------------------------------
************************C File***********************************
Most ATmega AVR chips, which are commonly used to make simple robots, have a feature known as pulse-width modulation (PWM) that can be used to control servos. This blog post might serve as a quick introduction to controlling servos using PWM. If you were to look at the Arduino platform's servo control library, you would find that it also uses PWM.
This might be a better choice than relying on running a loop a constant number of times as changes to compiler optimization flags and the chip's clock speed could potentially break such a simple delay function.
You should almost certainly have an interrupt configured to run code at a predictable interval. If you look in the example programs supplied with your CPU, you'll probably find an example of such.
Typically, one will use a word/longword of memory to hold a timer, which will be incremented each interrupt. If your timer interrupt runs 10,000 times/second and increments "interrupt_counter" by one each time, a 'wait 1 ms' routine could look like:
extern volatile unsigned long interrupt_counter;
unsigned long temp_value = interrupt_counter;
do {} while(10 > (interrupt_counter - temp_value));
/* Would reverse operands above and use less-than if this weren't HTML. */
Note that as written the code will wait between 900 µs and 1000 µs. If one changed the comparison to greater-or-equal, it would wait between 1000 and 1100. If one needs to do something five times at 1 ms intervals, waiting some arbitrary time up to 1 ms for the first time, one could write the code as:
extern volatile unsigned long interrupt_counter;
unsigned long temp_value = interrupt_counter;
for (int i=0; 5>i; i++)
{
do {} while(!((temp_value - interrupt_counter) & 0x80000000)); /* Wait for underflow */
temp_value += 10;
do_action_thing();
}
This should run the do_something()'s at precise intervals even if they take several hundred microseconds to complete. If they sometimes take over 1 ms, the system will try to run each one at the "proper" time (so if one call takes 1.3 ms and the next one finishes instantly, the following one will happen 700 µs later).

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