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Thread: Teensyduino 1.20 Release Candidate #1 Available

  1. #1
    Administrator Paul's Avatar
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    Teensyduino 1.20 Release Candidate #1 Available

    Here is a first release candidate for Teensyduino 1.20:


    Old beta download links removed. Please use the latest version:
    https://www.pjrc.com/teensy/td_download.html



    Please give this a try and report any bugs. Try to include a sample program that reproduces the problem!

    These are the changes since Teensyduino 1.19:

    • Add serialEvent (usb serial) & serialEvent# (hardware serial)
    • Add Serial.writeBufferFree() & Serial#.writeBufferFree()
    • Add IntervalTimer priority()
    • Add DMAChannel & DMASetting objects
    • Don't mix CPU speed setting switching from Teensy 2.0 to 3.x
    • Add FASTRUN, for functions in RAM on Teensy 3.x
    • Interrupt vector table moved to RAM for Teensy 3.x
    • Add attachInterruptVector()
    • Optimize Teensy 3.x hardware register definitions
    • Serial port names added to pins_arduino.h
    • Add AVR emulation for util/parity.h
    • Fix ARM toolchain linker & zlib issue (thanks to Andrew Kroll)
    • Add libraries: Adafruit_ILI9341 (optimized)
    • Updated libraries: Adafruit_SSD1306, Adafruit_ST7735, ShiftPWM
    • Libraries ported to Teensy 3.x: AltSoftSerial, CapacitiveSensor, FlexiTimer2, FreqCount, FreqMeasure, FrequencyTimer2, MsTimer2, ShiftPWM, TimerOne, TimerThree, Tlc5940

  2. #2
    Senior Member PaulStoffregen's Avatar
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    test reply

  3. #3
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    Tested with fresh install of Arduino 1.0.5-r2 on Windows 7. No problems installing. Not noticed any breakage reversion so far.

    A quick look at code sizes:
    Code:
    All tests with Arduino 1.0.5-r2
    
    ssd1306_128x64_spi,  Teensy 3.0, hardware spi
    
    1.20-rc1
    Binary sketch size: 24,848 bytes (of a 131,072 byte maximum)
    Estimated memory use: 3,684 bytes (of a 16,384 byte maximum)
    
    1.19
    Binary sketch size: 27,784 bytes (of a 131,072 byte maximum)
    Estimated memory use: 4,836 bytes (of a 16,384 byte maximum)
    
    orgone_accumulator_official, Teensy 3.1
    
    1.20-rc1
    Binary sketch size: 63,204 bytes (of a 262,144 byte maximum)
    Estimated memory use: 6,900 bytes (of a 65,536 byte maximum)
    
    1.19
    Binary sketch size: 63,436 bytes (of a 262,144 byte maximum)
    Estimated memory use: 6,428 bytes (of a 65,536 byte maximum)

  4. #4
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    (restarted browser, works now)

  5. #5
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    Czech keyboard

    I'm not seeing the Czech keyboard in the Arduino menu. According to this thread it is tested as working.

  6. #6
    Senior Member PaulStoffregen's Avatar
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    Opps, yeah, Czech is in the code but was never added to boards.txt. I'll get it into rc2.

  7. #7
    Senior Member onehorse's Avatar
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    Just downloaded the new version and fired up a sketch I wrote today for AVR and it's working beautifully on the Teensy 3.1. I noticed that now there are a greater variety of clock speeds available. Does 'no USB' mean that one cannot use the USB in a program at these low clock speeds or that one cannot enter a new program through the USB at these low clock speed settings? Could you comment on this increase in clock speed setting choices? Thanks.

  8. #8
    Senior Member onehorse's Avatar
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    Problem with Teensyduino 1.20 and i2c_t3?

    I'm getting this error message when I try to compile using the i2c_t3.h library, which was working for me with the previous 1.18 version on teensyduino. I am going back to v 1.19 to try and see if it's the new version or my new laptop.

    Code:
      This report would have more information with
      "Show verbose output during compilation"
      enabled in File > Preferences.
    Arduino: 1.0.5-r2 (Windows 7), Board: "Teensy 3.1"
    MPU9250BasicAHRS_t3.cpp.o: In function `writeByte(unsigned char, unsigned char, unsigned char)':
    C:\Program Files\Arduino/quaternionFilters.ino:192: undefined reference to `i2c_t3::beginTransmission(unsigned char)'
    C:\Program Files\Arduino/quaternionFilters.ino:192: undefined reference to `i2c_t3::write(unsigned char)'
    C:\Program Files\Arduino/quaternionFilters.ino:192: undefined reference to `i2c_t3::write(unsigned char)'
    MPU9250BasicAHRS_t3.cpp.o: In function `writeByte(unsigned char, unsigned char, unsigned char)':
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:965: undefined reference to `Wire'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:965: undefined reference to `i2c_t3::endTransmission()'
    MPU9250BasicAHRS_t3.cpp.o: In function `readByte(unsigned char, unsigned char)':
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:971: undefined reference to `i2c_t3::beginTransmission(unsigned char)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:972: undefined reference to `i2c_t3::write(unsigned char)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:973: undefined reference to `i2c_t3::endTransmission(i2c_stop)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:976: undefined reference to `i2c_t3::requestFrom(unsigned char, unsigned int)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:977: undefined reference to `i2c_t3::read()'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:979: undefined reference to `Wire'
    MPU9250BasicAHRS_t3.cpp.o: In function `readBytes(unsigned char, unsigned char, unsigned char, unsigned char*)':
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:983: undefined reference to `i2c_t3::beginTransmission(unsigned char)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:984: undefined reference to `i2c_t3::write(unsigned char)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:985: undefined reference to `i2c_t3::endTransmission(i2c_stop)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:989: undefined reference to `i2c_t3::requestFrom(unsigned char, unsigned int)'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:991: undefined reference to `i2c_t3::read()'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:990: undefined reference to `i2c_t3::available()'
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:992: undefined reference to `Wire'
    MPU9250BasicAHRS_t3.cpp.o: In function `setup':
    C:\Program Files\Arduino/MPU9250BasicAHRS_t3.ino:276: undefined reference to `i2c_t3::begin(i2c_mode, unsigned char, i2c_pins, i2c_pullup, i2c_rate)'
    MPU9250BasicAHRS_t3.cpp.o: In function `Print::println(int, int)':
    C:\Program Files\Arduino\hardware\teensy\cores\teensy3/Print.h:89: undefined reference to `Wire'
    collect2.exe: error: ld returned 1 exit status
    This is the program I am running:

    Code:
    /* MPU9250 Basic Example Code
     by: Kris Winer
     date: April 1, 2014
     license: Beerware - Use this code however you'd like. If you 
     find it useful you can buy me a beer some time.
     
     Demonstrate basic MPU-9250 functionality including parameterizing the register addresses, initializing the sensor, 
     getting properly scaled accelerometer, gyroscope, and magnetometer data out. Added display functions to 
     allow display to on breadboard monitor. Addition of 9 DoF sensor fusion using open source Madgwick and 
     Mahony filter algorithms. Sketch runs on the 3.3 V 8 MHz Pro Mini and the Teensy 3.1.
     
     SDA and SCL should have external pull-up resistors (to 3.3V).
     10k resistors are on the EMSENSR-9250 breakout board.
     
     Hardware setup:
     MPU9250 Breakout --------- Arduino
     VDD ---------------------- 3.3V
     VDDI --------------------- 3.3V
     SDA ----------------------- A4
     SCL ----------------------- A5
     GND ---------------------- GND
     
     Note: The MPU9250 is an I2C sensor and uses the Arduino Wire library. 
     Because the sensor is not 5V tolerant, we are using a 3.3 V 8 MHz Pro Mini or a 3.3 V Teensy 3.1.
     We have disabled the internal pull-ups used by the Wire library in the Wire.h/twi.c utility file.
     We are also using the 400 kHz fast I2C mode by setting the TWI_FREQ  to 400000L /twi.h utility file.
     */
    //#include "Wire.h"   
    #include <i2c_t3.h>
    #include <SPI.h>
    #include <Adafruit_GFX.h>
    #include <Adafruit_PCD8544.h>
    
    // Using NOKIA 5110 monochrome 84 x 48 pixel display
    // pin 9 - Serial clock out (SCLK)
    // pin 8 - Serial data out (DIN)
    // pin 7 - Data/Command select (D/C)
    // pin 5 - LCD chip select (CS)
    // pin 6 - LCD reset (RST)
    Adafruit_PCD8544 display = Adafruit_PCD8544(9, 8, 7, 5, 6);
    
    // See also MPU-9250 Register Map and Descriptions, Revision 4.0, RM-MPU-9250A-00, Rev. 1.4, 9/9/2013 for registers not listed in 
    // above document; the MPU9250 and MPU9150 are virtually identical but the latter has a different register map
    //
    //Magnetometer Registers
    #define AK8963_ADDRESS   0x0C
    #define WHO_AM_I_AK8963  0x00 // should return 0x48
    #define INFO             0x01
    #define AK8963_ST1       0x02  // data ready status bit 0
    #define AK8963_XOUT_L	 0x03  // data
    #define AK8963_XOUT_H	 0x04
    #define AK8963_YOUT_L	 0x05
    #define AK8963_YOUT_H	 0x06
    #define AK8963_ZOUT_L	 0x07
    #define AK8963_ZOUT_H	 0x08
    #define AK8963_ST2       0x09  // Data overflow bit 3 and data read error status bit 2
    #define AK8963_CNTL      0x0A  // Power down (0000), single-measurement (0001), self-test (1000) and Fuse ROM (1111) modes on bits 3:0
    #define AK8963_ASTC      0x0C  // Self test control
    #define AK8963_I2CDIS    0x0F  // I2C disable
    #define AK8963_ASAX      0x10  // Fuse ROM x-axis sensitivity adjustment value
    #define AK8963_ASAY      0x11  // Fuse ROM y-axis sensitivity adjustment value
    #define AK8963_ASAZ      0x12  // Fuse ROM z-axis sensitivity adjustment value
    
    #define SELF_TEST_X_GYRO 0x00                  
    #define SELF_TEST_Y_GYRO 0x01                                                                          
    #define SELF_TEST_Z_GYRO 0x02
    
    /*#define X_FINE_GAIN      0x03 // [7:0] fine gain
    #define Y_FINE_GAIN      0x04
    #define Z_FINE_GAIN      0x05
    #define XA_OFFSET_H      0x06 // User-defined trim values for accelerometer
    #define XA_OFFSET_L_TC   0x07
    #define YA_OFFSET_H      0x08
    #define YA_OFFSET_L_TC   0x09
    #define ZA_OFFSET_H      0x0A
    #define ZA_OFFSET_L_TC   0x0B */
    
    #define SELF_TEST_X_ACCEL 0x0D
    #define SELF_TEST_Y_ACCEL 0x0E    
    #define SELF_TEST_Z_ACCEL 0x0F
    
    #define SELF_TEST_A      0x10
    
    #define XG_OFFSET_H      0x13  // User-defined trim values for gyroscope
    #define XG_OFFSET_L      0x14
    #define YG_OFFSET_H      0x15
    #define YG_OFFSET_L      0x16
    #define ZG_OFFSET_H      0x17
    #define ZG_OFFSET_L      0x18
    #define SMPLRT_DIV       0x19
    #define CONFIG           0x1A
    #define GYRO_CONFIG      0x1B
    #define ACCEL_CONFIG     0x1C
    #define ACCEL_CONFIG2    0x1D
    #define LP_ACCEL_ODR     0x1E   
    #define WOM_THR          0x1F   
    
    #define MOT_DUR          0x20  // Duration counter threshold for motion interrupt generation, 1 kHz rate, LSB = 1 ms
    #define ZMOT_THR         0x21  // Zero-motion detection threshold bits [7:0]
    #define ZRMOT_DUR        0x22  // Duration counter threshold for zero motion interrupt generation, 16 Hz rate, LSB = 64 ms
    
    #define FIFO_EN          0x23
    #define I2C_MST_CTRL     0x24   
    #define I2C_SLV0_ADDR    0x25
    #define I2C_SLV0_REG     0x26
    #define I2C_SLV0_CTRL    0x27
    #define I2C_SLV1_ADDR    0x28
    #define I2C_SLV1_REG     0x29
    #define I2C_SLV1_CTRL    0x2A
    #define I2C_SLV2_ADDR    0x2B
    #define I2C_SLV2_REG     0x2C
    #define I2C_SLV2_CTRL    0x2D
    #define I2C_SLV3_ADDR    0x2E
    #define I2C_SLV3_REG     0x2F
    #define I2C_SLV3_CTRL    0x30
    #define I2C_SLV4_ADDR    0x31
    #define I2C_SLV4_REG     0x32
    #define I2C_SLV4_DO      0x33
    #define I2C_SLV4_CTRL    0x34
    #define I2C_SLV4_DI      0x35
    #define I2C_MST_STATUS   0x36
    #define INT_PIN_CFG      0x37
    #define INT_ENABLE       0x38
    #define DMP_INT_STATUS   0x39  // Check DMP interrupt
    #define INT_STATUS       0x3A
    #define ACCEL_XOUT_H     0x3B
    #define ACCEL_XOUT_L     0x3C
    #define ACCEL_YOUT_H     0x3D
    #define ACCEL_YOUT_L     0x3E
    #define ACCEL_ZOUT_H     0x3F
    #define ACCEL_ZOUT_L     0x40
    #define TEMP_OUT_H       0x41
    #define TEMP_OUT_L       0x42
    #define GYRO_XOUT_H      0x43
    #define GYRO_XOUT_L      0x44
    #define GYRO_YOUT_H      0x45
    #define GYRO_YOUT_L      0x46
    #define GYRO_ZOUT_H      0x47
    #define GYRO_ZOUT_L      0x48
    #define EXT_SENS_DATA_00 0x49
    #define EXT_SENS_DATA_01 0x4A
    #define EXT_SENS_DATA_02 0x4B
    #define EXT_SENS_DATA_03 0x4C
    #define EXT_SENS_DATA_04 0x4D
    #define EXT_SENS_DATA_05 0x4E
    #define EXT_SENS_DATA_06 0x4F
    #define EXT_SENS_DATA_07 0x50
    #define EXT_SENS_DATA_08 0x51
    #define EXT_SENS_DATA_09 0x52
    #define EXT_SENS_DATA_10 0x53
    #define EXT_SENS_DATA_11 0x54
    #define EXT_SENS_DATA_12 0x55
    #define EXT_SENS_DATA_13 0x56
    #define EXT_SENS_DATA_14 0x57
    #define EXT_SENS_DATA_15 0x58
    #define EXT_SENS_DATA_16 0x59
    #define EXT_SENS_DATA_17 0x5A
    #define EXT_SENS_DATA_18 0x5B
    #define EXT_SENS_DATA_19 0x5C
    #define EXT_SENS_DATA_20 0x5D
    #define EXT_SENS_DATA_21 0x5E
    #define EXT_SENS_DATA_22 0x5F
    #define EXT_SENS_DATA_23 0x60
    #define MOT_DETECT_STATUS 0x61
    #define I2C_SLV0_DO      0x63
    #define I2C_SLV1_DO      0x64
    #define I2C_SLV2_DO      0x65
    #define I2C_SLV3_DO      0x66
    #define I2C_MST_DELAY_CTRL 0x67
    #define SIGNAL_PATH_RESET  0x68
    #define MOT_DETECT_CTRL  0x69
    #define USER_CTRL        0x6A  // Bit 7 enable DMP, bit 3 reset DMP
    #define PWR_MGMT_1       0x6B // Device defaults to the SLEEP mode
    #define PWR_MGMT_2       0x6C
    #define DMP_BANK         0x6D  // Activates a specific bank in the DMP
    #define DMP_RW_PNT       0x6E  // Set read/write pointer to a specific start address in specified DMP bank
    #define DMP_REG          0x6F  // Register in DMP from which to read or to which to write
    #define DMP_REG_1        0x70
    #define DMP_REG_2        0x71 
    #define FIFO_COUNTH      0x72
    #define FIFO_COUNTL      0x73
    #define FIFO_R_W         0x74
    #define WHO_AM_I_MPU9250 0x75 // Should return 0x71
    #define XA_OFFSET_H      0x77
    #define XA_OFFSET_L      0x78
    #define YA_OFFSET_H      0x7A
    #define YA_OFFSET_L      0x7B
    #define ZA_OFFSET_H      0x7D
    #define ZA_OFFSET_L      0x7E
    
    // Using the MSENSR-9250 breakout board, ADO is set to 0 
    // Seven-bit device address is 110100 for ADO = 0 and 110101 for ADO = 1
    #define ADO 0
    #if ADO
    #define MPU9250_ADDRESS 0x69  // Device address when ADO = 1
    #else
    #define MPU9250_ADDRESS 0x68  // Device address when ADO = 0
    #define AK8963_ADDRESS 0x0C   //  Address of magnetometer
    #endif  
    
    #define AHRS true         // set to false for basic data read
    #define SerialDebug true   // set to true to get Serial output for debugging
    
    // Set initial input parameters
    enum Ascale {
      AFS_2G = 0,
      AFS_4G,
      AFS_8G,
      AFS_16G
    };
    
    enum Gscale {
      GFS_250DPS = 0,
      GFS_500DPS,
      GFS_1000DPS,
      GFS_2000DPS
    };
    
    enum Mscale {
      MFS_14BITS = 0, // 0.6 mG per LSB
      MFS_16BITS      // 0.15 mG per LSB
    };
    
    // Specify sensor full scale
    uint8_t Gscale = GFS_250DPS;
    uint8_t Ascale = AFS_2G;
    uint8_t Mscale = MFS_16BITS; // Choose either 14-bit or 16-bit magnetometer resolution
    uint8_t Mmode = 0x02;        // 2 for 8 Hz, 6 for 100 Hz continuous magnetometer data read
    float aRes, gRes, mRes;      // scale resolutions per LSB for the sensors
      
    // Pin definitions
    int intPin = 12;  // These can be changed, 2 and 3 are the Arduinos ext int pins
    
    int16_t accelCount[3];  // Stores the 16-bit signed accelerometer sensor output
    int16_t gyroCount[3];   // Stores the 16-bit signed gyro sensor output
    int16_t magCount[3];    // Stores the 16-bit signed magnetometer sensor output
    float magCalibration[3] = {0, 0, 0}, magbias[3] = {0, 0, 0};  // Factory mag calibration and mag bias
    float gyroBias[3] = {0, 0, 0}, accelBias[3] = {0, 0, 0};      // Bias corrections for gyro and accelerometer
    int16_t tempCount;      // temperature raw count output
    float   temperature;    // Stores the real internal chip temperature in degrees Celsius
    float   SelfTest[6];    // holds results of gyro and accelerometer self test
    
    // global constants for 9 DoF fusion and AHRS (Attitude and Heading Reference System)
    float GyroMeasError = PI * (40.0f / 180.0f);   // gyroscope measurement error in rads/s (start at 40 deg/s)
    float GyroMeasDrift = PI * (0.0f  / 180.0f);   // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
    // There is a tradeoff in the beta parameter between accuracy and response speed.
    // In the original Madgwick study, beta of 0.041 (corresponding to GyroMeasError of 2.7 degrees/s) was found to give optimal accuracy.
    // However, with this value, the LSM9SD0 response time is about 10 seconds to a stable initial quaternion.
    // Subsequent changes also require a longish lag time to a stable output, not fast enough for a quadcopter or robot car!
    // By increasing beta (GyroMeasError) by about a factor of fifteen, the response time constant is reduced to ~2 sec
    // I haven't noticed any reduction in solution accuracy. This is essentially the I coefficient in a PID control sense; 
    // the bigger the feedback coefficient, the faster the solution converges, usually at the expense of accuracy. 
    // In any case, this is the free parameter in the Madgwick filtering and fusion scheme.
    float beta = sqrt(3.0f / 4.0f) * GyroMeasError;   // compute beta
    float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;   // compute zeta, the other free parameter in the Madgwick scheme usually set to a small or zero value
    #define Kp 2.0f * 5.0f // these are the free parameters in the Mahony filter and fusion scheme, Kp for proportional feedback, Ki for integral
    #define Ki 0.0f
    
    uint32_t delt_t = 0; // used to control display output rate
    uint32_t count = 0, sumCount = 0; // used to control display output rate
    float pitch, yaw, roll;
    float deltat = 0.0f, sum = 0.0f;        // integration interval for both filter schemes
    uint32_t lastUpdate = 0, firstUpdate = 0; // used to calculate integration interval
    uint32_t Now = 0;        // used to calculate integration interval
    
    float ax, ay, az, gx, gy, gz, mx, my, mz; // variables to hold latest sensor data values 
    float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};    // vector to hold quaternion
    float eInt[3] = {0.0f, 0.0f, 0.0f};       // vector to hold integral error for Mahony method
    
    
    void setup()
    {
    //  Wire.begin();
    //  TWBR = 12;  // 400 kbit/sec I2C speed
      // Setup for Master mode, pins 18/19, external pullups, 400kHz
      Wire.begin(I2C_MASTER, 0x00, I2C_PINS_18_19, I2C_PULLUP_EXT, I2C_RATE_400);
      Serial.begin(38400);
      
      // Set up the interrupt pin, its set as active high, push-pull
      pinMode(intPin, INPUT);
      digitalWrite(intPin, LOW);
      
      display.begin(); // Ini8ialize the display
      display.setContrast(58); // Set the contrast
      
    // Start device display with ID of sensor
      display.clearDisplay();
      display.setTextSize(2);
      display.setCursor(0,0); display.print("MPU9250");
      display.setTextSize(1);
      display.setCursor(0, 20); display.print("9-DOF 16-bit");
      display.setCursor(0, 30); display.print("motion sensor");
      display.setCursor(20,40); display.print("60 ug LSB");
      display.display();
      delay(1000);
    
    // Set up for data display
      display.setTextSize(1); // Set text size to normal, 2 is twice normal etc.
      display.setTextColor(BLACK); // Set pixel color; 1 on the monochrome screen
      display.clearDisplay();   // clears the screen and buffer
    
      // Read the WHO_AM_I register, this is a good test of communication
      byte c = readByte(MPU9250_ADDRESS, WHO_AM_I_MPU9250);  // Read WHO_AM_I register for MPU-9250
      Serial.print("MPU9250 "); Serial.print("I AM "); Serial.print(c, HEX); Serial.print(" I should be "); Serial.println(0x71, HEX);
      display.setCursor(20,0); display.print("MPU9250");
      display.setCursor(0,10); display.print("I AM");
      display.setCursor(0,20); display.print(c, HEX);  
      display.setCursor(0,30); display.print("I Should Be");
      display.setCursor(0,40); display.print(0x71, HEX); 
      display.display();
      delay(1000); 
    
      if (c == 0x71) // WHO_AM_I should always be 0x68
      {  
        Serial.println("MPU9250 is online...");
        
    /*    MPU6050SelfTest(SelfTest); // Start by performing self test and reporting values
        Serial.print("x-axis self test: acceleration trim within : "); Serial.print(SelfTest[0],1); Serial.println("% of factory value");
        Serial.print("y-axis self test: acceleration trim within : "); Serial.print(SelfTest[1],1); Serial.println("% of factory value");
        Serial.print("z-axis self test: acceleration trim within : "); Serial.print(SelfTest[2],1); Serial.println("% of factory value");
        Serial.print("x-axis self test: gyration trim within : "); Serial.print(SelfTest[3],1); Serial.println("% of factory value");
        Serial.print("y-axis self test: gyration trim within : "); Serial.print(SelfTest[4],1); Serial.println("% of factory value");
        Serial.print("z-axis self test: gyration trim within : "); Serial.print(SelfTest[5],1); Serial.println("% of factory value");
     
    */
      calibrateMPU9250(gyroBias, accelBias); // Calibrate gyro and accelerometers, load biases in bias registers
      display.clearDisplay();
         
      display.setCursor(0, 0); display.print("MPU9250 bias");
      display.setCursor(0, 8); display.print(" x   y   z  ");
    
      display.setCursor(0,  16); display.print((int)(1000*accelBias[0])); 
      display.setCursor(24, 16); display.print((int)(1000*accelBias[1])); 
      display.setCursor(48, 16); display.print((int)(1000*accelBias[2])); 
      display.setCursor(72, 16); display.print("mg");
        
      display.setCursor(0,  24); display.print(gyroBias[0], 1); 
      display.setCursor(24, 24); display.print(gyroBias[1], 1); 
      display.setCursor(48, 24); display.print(gyroBias[2], 1); 
      display.setCursor(66, 24); display.print("o/s");   
     
      display.display();
      delay(1000); 
      
      initMPU9250(); 
      Serial.println("MPU9250 initialized for active data mode...."); // Initialize device for active mode read of acclerometer, gyroscope, and temperature
      
      // Read the WHO_AM_I register of the magnetometer, this is a good test of communication
      byte d = readByte(AK8963_ADDRESS, WHO_AM_I_AK8963);  // Read WHO_AM_I register for AK8963
      Serial.print("AK8963 "); Serial.print("I AM "); Serial.print(d, HEX); Serial.print(" I should be "); Serial.println(0x48, HEX);
      display.clearDisplay();
      display.setCursor(20,0); display.print("AK8963");
      display.setCursor(0,10); display.print("I AM");
      display.setCursor(0,20); display.print(d, HEX);  
      display.setCursor(0,30); display.print("I Should Be");
      display.setCursor(0,40); display.print(0x48, HEX);  
      display.display();
      delay(1000); 
      
      // Get magnetometer calibration from AK8963 ROM
      initAK8963(magCalibration); Serial.println("AK8963 initialized for active data mode...."); // Initialize device for active mode read of magnetometer
      
      if(SerialDebug) {
    ////  Serial.println("Calibration values: ");
    //  Serial.print("X-Axis sensitivity adjustment value "); Serial.println(magCalibration[0], 2);
     // Serial.print("Y-Axis sensitivity adjustment value "); Serial.println(magCalibration[1], 2);
     // Serial.print("Z-Axis sensitivity adjustment value "); Serial.println(magCalibration[2], 2);
      }
      
      display.clearDisplay();
      display.setCursor(20,0); display.print("AK8963");
      display.setCursor(0,10); display.print("ASAX "); display.setCursor(50,10); display.print(magCalibration[0], 2);
      display.setCursor(0,20); display.print("ASAY "); display.setCursor(50,20); display.print(magCalibration[1], 2);
      display.setCursor(0,30); display.print("ASAZ "); display.setCursor(50,30); display.print(magCalibration[2], 2);
      display.display();
      delay(1000);  
      }
      else
      {
        Serial.print("Could not connect to MPU9250: 0x");
        Serial.println(c, HEX);
        while(1) ; // Loop forever if communication doesn't happen
      }
    }
    
    void loop()
    {  
      // If intPin goes high, all data registers have new data
      if (readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01) {  // On interrupt, check if data ready interrupt
        readAccelData(accelCount);  // Read the x/y/z adc values
        getAres();
        
        // Now we'll calculate the accleration value into actual g's
        ax = (float)accelCount[0]*aRes - accelBias[0];  // get actual g value, this depends on scale being set
        ay = (float)accelCount[1]*aRes - accelBias[1];   
        az = (float)accelCount[2]*aRes - accelBias[2];  
       
        readGyroData(gyroCount);  // Read the x/y/z adc values
        getGres();
     
        // Calculate the gyro value into actual degrees per second
        gx = (float)gyroCount[0]*gRes;  // get actual gyro value, this depends on scale being set
        gy = (float)gyroCount[1]*gRes;  
        gz = (float)gyroCount[2]*gRes;   
      
        readMagData(magCount);  // Read the x/y/z adc values
        getMres();
        magbias[0] = +470.;  // User environmental x-axis correction in milliGauss, should be automatically calculated
        magbias[1] = +120.;  // User environmental x-axis correction in milliGauss
        magbias[2] = +125.;  // User environmental x-axis correction in milliGauss
        
        // Calculate the magnetometer values in milliGauss
        // Include factory calibration per data sheet and user environmental corrections
        mx = (float)magCount[0]*mRes*magCalibration[0] - magbias[0];  // get actual magnetometer value, this depends on scale being set
        my = (float)magCount[1]*mRes*magCalibration[1] - magbias[1];  
        mz = (float)magCount[2]*mRes*magCalibration[2] - magbias[2];   
      }
      
      Now = micros();
      deltat = ((Now - lastUpdate)/1000000.0f); // set integration time by time elapsed since last filter update
      lastUpdate = Now;
    
      sum += deltat; // sum for averaging filter update rate
      sumCount++;
      
      // Sensors x (y)-axis of the accelerometer is aligned with the y (x)-axis of the magnetometer;
      // the magnetometer z-axis (+ down) is opposite to z-axis (+ up) of accelerometer and gyro!
      // We have to make some allowance for this orientationmismatch in feeding the output to the quaternion filter.
      // For the MPU-9250, we have chosen a magnetic rotation that keeps the sensor forward along the x-axis just like
      // in the LSM9DS0 sensor. This rotation can be modified to allow any convenient orientation convention.
      // This is ok by aircraft orientation standards!  
      // Pass gyro rate as rad/s
      MadgwickQuaternionUpdate(ax, ay, az, gx*PI/180.0f, gy*PI/180.0f, gz*PI/180.0f,  my,  mx, mz);
    //  MahonyQuaternionUpdate(ax, ay, az, gx*PI/180.0f, gy*PI/180.0f, gz*PI/180.0f, my, mx, mz);
    
    
        if (!AHRS) {
        delt_t = millis() - count;
        if(delt_t > 500) {
    
        if(SerialDebug) {
        // Print acceleration values in milligs!
        Serial.print("X-acceleration: "); Serial.print(1000*ax); Serial.print(" mg ");
        Serial.print("Y-acceleration: "); Serial.print(1000*ay); Serial.print(" mg ");
        Serial.print("Z-acceleration: "); Serial.print(1000*az); Serial.println(" mg ");
     
        // Print gyro values in degree/sec
        Serial.print("X-gyro rate: "); Serial.print(gx, 3); Serial.print(" degrees/sec "); 
        Serial.print("Y-gyro rate: "); Serial.print(gy, 3); Serial.print(" degrees/sec "); 
        Serial.print("Z-gyro rate: "); Serial.print(gz, 3); Serial.println(" degrees/sec"); 
        
        // Print mag values in degree/sec
        Serial.print("X-mag field: "); Serial.print(mx); Serial.print(" mG "); 
        Serial.print("Y-mag field: "); Serial.print(my); Serial.print(" mG "); 
        Serial.print("Z-mag field: "); Serial.print(mz); Serial.println(" mG"); 
     
        tempCount = readTempData();  // Read the adc values
        temperature = ((float) tempCount) / 333.87 + 21.0; // Temperature in degrees Centigrade
       // Print temperature in degrees Centigrade      
        Serial.print("Temperature is ");  Serial.print(temperature, 1);  Serial.println(" degrees C"); // Print T values to tenths of s degree C
        }
       
        display.clearDisplay();     
        display.setCursor(0, 0); display.print("MPU9250/AK8963");
        display.setCursor(0, 8); display.print(" x   y   z  ");
    
        display.setCursor(0,  16); display.print((int)(1000*ax)); 
        display.setCursor(24, 16); display.print((int)(1000*ay)); 
        display.setCursor(48, 16); display.print((int)(1000*az)); 
        display.setCursor(72, 16); display.print("mg");
        
        display.setCursor(0,  24); display.print((int)(gx)); 
        display.setCursor(24, 24); display.print((int)(gy)); 
        display.setCursor(48, 24); display.print((int)(gz)); 
        display.setCursor(66, 24); display.print("o/s");    
            
        display.setCursor(0,  32); display.print((int)(mx)); 
        display.setCursor(24, 32); display.print((int)(my)); 
        display.setCursor(48, 32); display.print((int)(mz)); 
        display.setCursor(72, 32); display.print("mG");   
       
        display.setCursor(0,  40); display.print("Gyro T "); 
        display.setCursor(50,  40); display.print(temperature, 1); display.print(" C");
        display.display();
        
        count = millis();
        }
        }
        else {
          
        // Serial print and/or display at 0.5 s rate independent of data rates
        delt_t = millis() - count;
        if (delt_t > 500) { // update LCD once per half-second independent of read rate
    /*
        if(SerialDebug) {
        Serial.print("ax = "); Serial.print((int)1000*ax);  
        Serial.print(" ay = "); Serial.print((int)1000*ay); 
        Serial.print(" az = "); Serial.print((int)1000*az); Serial.println(" mg");
        Serial.print("gx = "); Serial.print( gx, 2); 
        Serial.print(" gy = "); Serial.print( gy, 2); 
        Serial.print(" gz = "); Serial.print( gz, 2); Serial.println(" deg/s");
        Serial.print("mx = "); Serial.print( (int)mx ); 
        Serial.print(" my = "); Serial.print( (int)my ); 
        Serial.print(" mz = "); Serial.print( (int)mz ); Serial.println(" mG");
        
        Serial.print("q0 = "); Serial.print(q[0]);
        Serial.print(" qx = "); Serial.print(q[1]); 
        Serial.print(" qy = "); Serial.print(q[2]); 
        Serial.print(" qz = "); Serial.println(q[3]); 
        }               
    */    
      // Define output variables from updated quaternion---these are Tait-Bryan angles, commonly used in aircraft orientation.
      // In this coordinate system, the positive z-axis is down toward Earth. 
      // Yaw is the angle between Sensor x-axis and Earth magnetic North (or true North if corrected for local declination, looking down on the sensor positive yaw is counterclockwise.
      // Pitch is angle between sensor x-axis and Earth ground plane, toward the Earth is positive, up toward the sky is negative.
      // Roll is angle between sensor y-axis and Earth ground plane, y-axis up is positive roll.
      // These arise from the definition of the homogeneous rotation matrix constructed from quaternions.
      // Tait-Bryan angles as well as Euler angles are non-commutative; that is, the get the correct orientation the rotations must be
      // applied in the correct order which for this configuration is yaw, pitch, and then roll.
      // For more see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles which has additional links.
        yaw   = atan2(2.0f * (q[1] * q[2] + q[0] * q[3]), q[0] * q[0] + q[1] * q[1] - q[2] * q[2] - q[3] * q[3]);   
        pitch = -asin(2.0f * (q[1] * q[3] - q[0] * q[2]));
        roll  = atan2(2.0f * (q[0] * q[1] + q[2] * q[3]), q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3]);
        pitch *= 180.0f / PI;
        yaw   *= 180.0f / PI; 
        yaw   -= 13.8; // Declination at Danville, California is 13 degrees 48 minutes and 47 seconds on 2014-04-04
        roll  *= 180.0f / PI;
         
        if(SerialDebug) {
    //    Serial.print("Yaw, Pitch, Roll: ");
        Serial.print(yaw, 2);
        Serial.print(", ");
        Serial.print(pitch, 2);
        Serial.print(", ");
        Serial.println(roll, 2);
        
    //    Serial.print("rate = "); Serial.print((float)sumCount/sum, 2); Serial.println(" Hz");
        }
       
        display.clearDisplay();    
     
        display.setCursor(0, 0); display.print(" x   y   z  ");
    
        display.setCursor(0,  8); display.print((int)(1000*ax)); 
        display.setCursor(24, 8); display.print((int)(1000*ay)); 
        display.setCursor(48, 8); display.print((int)(1000*az)); 
        display.setCursor(72, 8); display.print("mg");
        
        display.setCursor(0,  16); display.print((int)(gx)); 
        display.setCursor(24, 16); display.print((int)(gy)); 
        display.setCursor(48, 16); display.print((int)(gz)); 
        display.setCursor(66, 16); display.print("o/s");    
    
        display.setCursor(0,  24); display.print((int)(mx)); 
        display.setCursor(24, 24); display.print((int)(my)); 
        display.setCursor(48, 24); display.print((int)(mz)); 
        display.setCursor(72, 24); display.print("mG");    
     
        display.setCursor(0,  32); display.print((int)(yaw)); 
        display.setCursor(24, 32); display.print((int)(pitch)); 
        display.setCursor(48, 32); display.print((int)(roll)); 
        display.setCursor(66, 32); display.print("ypr");  
      
        // With these settings the filter is updating at a ~145 Hz rate using the Madgwick scheme and 
        // >200 Hz using the Mahony scheme even though the display refreshes at only 2 Hz.
        // The filter update rate is determined mostly by the mathematical steps in the respective algorithms, 
        // the processor speed (8 MHz for the 3.3V Pro Mini), and the magnetometer ODR:
        // an ODR of 10 Hz for the magnetometer produce the above rates, maximum magnetometer ODR of 100 Hz produces
        // filter update rates of 36 - 145 and ~38 Hz for the Madgwick and Mahony schemes, respectively. 
        // This is presumably because the magnetometer read takes longer than the gyro or accelerometer reads.
        // This filter update rate should be fast enough to maintain accurate platform orientation for 
        // stabilization control of a fast-moving robot or quadcopter. Compare to the update rate of 200 Hz
        // produced by the on-board Digital Motion Processor of Invensense's MPU6050 6 DoF and MPU9150 9DoF sensors.
        // The 3.3 V 8 MHz Pro Mini is doing pretty well!
        display.setCursor(0, 40); display.print("rt: "); display.print((float) sumCount / sum, 2); display.print(" Hz"); 
        display.display();
    
        count = millis(); 
        sumCount = 0;
        sum = 0;    
        }
        }
    
    }
    
    //===================================================================================================================
    //====== Set of useful function to access acceleration. gyroscope, magnetometer, and temperature data
    //===================================================================================================================
    
    void getMres() {
      switch (Mscale)
      {
     	// Possible magnetometer scales (and their register bit settings) are:
    	// 14 bit resolution (0) and 16 bit resolution (1)
        case MFS_14BITS:
              mRes = 10.*4219./8190.; // Proper scale to return milliGauss
              break;
        case MFS_16BITS:
              mRes = 10.*4219./32760.0; // Proper scale to return milliGauss
              break;
      }
    }
    
    void getGres() {
      switch (Gscale)
      {
     	// Possible gyro scales (and their register bit settings) are:
    	// 250 DPS (00), 500 DPS (01), 1000 DPS (10), and 2000 DPS  (11). 
            // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
        case GFS_250DPS:
              gRes = 250.0/32768.0;
              break;
        case GFS_500DPS:
              gRes = 500.0/32768.0;
              break;
        case GFS_1000DPS:
              gRes = 1000.0/32768.0;
              break;
        case GFS_2000DPS:
              gRes = 2000.0/32768.0;
              break;
      }
    }
    
    void getAres() {
      switch (Ascale)
      {
     	// Possible accelerometer scales (and their register bit settings) are:
    	// 2 Gs (00), 4 Gs (01), 8 Gs (10), and 16 Gs  (11). 
            // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
        case AFS_2G:
              aRes = 2.0/32768.0;
              break;
        case AFS_4G:
              aRes = 4.0/32768.0;
              break;
        case AFS_8G:
              aRes = 8.0/32768.0;
              break;
        case AFS_16G:
              aRes = 16.0/32768.0;
              break;
      }
    }
    
    
    void readAccelData(int16_t * destination)
    {
      uint8_t rawData[6];  // x/y/z accel register data stored here
      readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers into data array
      destination[0] = ((int16_t)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a signed 16-bit value
      destination[1] = ((int16_t)rawData[2] << 8) | rawData[3] ;  
      destination[2] = ((int16_t)rawData[4] << 8) | rawData[5] ; 
    }
    
    
    void readGyroData(int16_t * destination)
    {
      uint8_t rawData[6];  // x/y/z gyro register data stored here
      readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers sequentially into data array
      destination[0] = ((int16_t)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a signed 16-bit value
      destination[1] = ((int16_t)rawData[2] << 8) | rawData[3] ;  
      destination[2] = ((int16_t)rawData[4] << 8) | rawData[5] ; 
    }
    
    void readMagData(int16_t * destination)
    {
      uint8_t rawData[7];  // x/y/z gyro register data, ST2 register stored here, must read ST2 at end of data acquisition
      if(readByte(AK8963_ADDRESS, AK8963_ST1) & 0x01) { // wait for magnetometer data ready bit to be set
      readBytes(AK8963_ADDRESS, AK8963_XOUT_L, 7, &rawData[0]);  // Read the six raw data and ST2 registers sequentially into data array
      uint8_t c = rawData[6]; // End data read by reading ST2 register
        if(!(c & 0x08)) { // Check if magnetic sensor overflow set, if not then report data
        destination[0] = ((int16_t)rawData[1] << 8) | rawData[0] ;  // Turn the MSB and LSB into a signed 16-bit value
        destination[1] = ((int16_t)rawData[3] << 8) | rawData[2] ;  // Data stored as little Endian
        destination[2] = ((int16_t)rawData[5] << 8) | rawData[4] ; 
       }
      }
    }
    
    int16_t readTempData()
    {
      uint8_t rawData[2];  // x/y/z gyro register data stored here
      readBytes(MPU9250_ADDRESS, TEMP_OUT_H, 2, &rawData[0]);  // Read the two raw data registers sequentially into data array 
      return ((int16_t)rawData[0] << 8) | rawData[1] ;  // Turn the MSB and LSB into a 16-bit value
    }
           
    void initAK8963(float * destination)
    {
      // First extract the factory calibration for each magnetometer axis
      uint8_t rawData[3];  // x/y/z gyro calibration data stored here
      writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer  
      delay(10);
      writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F); // Enter Fuse ROM access mode
      delay(10);
      readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]);  // Read the x-, y-, and z-axis calibration values
      destination[0] =  (float)(rawData[0] - 128)/256. + 1.;   // Return x-axis sensitivity adjustment values, etc.
      destination[1] =  (float)(rawData[1] - 128)/256. + 1.;  
      destination[2] =  (float)(rawData[2] - 128)/256. + 1.; 
      writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer  
      delay(10);
      // Configure the magnetometer for continuous read and highest resolution
      // set Mscale bit 4 to 1 (0) to enable 16 (14) bit resolution in CNTL register,
      // and enable continuous mode data acquisition Mmode (bits [3:0]), 0010 for 8 Hz and 0110 for 100 Hz sample rates
      writeByte(AK8963_ADDRESS, AK8963_CNTL, Mscale << 4 | Mmode); // Set magnetometer data resolution and sample ODR
      delay(10);
    }
    
    
    void initMPU9250()
    {  
     // wake up device
      writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors 
      delay(100); // Wait for all registers to reset 
    
     // get stable time source
      writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  // Auto select clock source to be PLL gyroscope reference if ready else
      delay(200); 
      
     // Configure Gyro and Thermometer
     // Disable FSYNC and set thermometer and gyro bandwidth to 41 and 42 Hz, respectively; 
     // minimum delay time for this setting is 5.9 ms, which means sensor fusion update rates cannot
     // be higher than 1 / 0.0059 = 170 Hz
     // DLPF_CFG = bits 2:0 = 011; this limits the sample rate to 1000 Hz for both
     // With the MPU9250, it is possible to get gyro sample rates of 32 kHz (!), 8 kHz, or 1 kHz
      writeByte(MPU9250_ADDRESS, CONFIG, 0x03);  
    
     // Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
      writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x04);  // Use a 200 Hz rate; a rate consistent with the filter update rate 
                                        // determined inset in CONFIG above
     
     // Set gyroscope full scale range
     // Range selects FS_SEL and AFS_SEL are 0 - 3, so 2-bit values are left-shifted into positions 4:3
      uint8_t c = readByte(MPU9250_ADDRESS, GYRO_CONFIG);
    //  writeRegister(GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5] 
      writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x02); // Clear Fchoice bits [1:0] 
      writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
      writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c | Gscale << 3); // Set full scale range for the gyro
     // writeRegister(GYRO_CONFIG, c | 0x00); // Set Fchoice for the gyro to 11 by writing its inverse to bits 1:0 of GYRO_CONFIG
      
     // Set accelerometer full-scale range configuration
      c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG);
    //  writeRegister(ACCEL_CONFIG, c & ~0xE0); // Clear self-test bits [7:5] 
      writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
      writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c | Ascale << 3); // Set full scale range for the accelerometer 
    
     // Set accelerometer sample rate configuration
     // It is possible to get a 4 kHz sample rate from the accelerometer by choosing 1 for
     // accel_fchoice_b bit [3]; in this case the bandwidth is 1.13 kHz
      c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG2);
      writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c & ~0x0F); // Clear accel_fchoice_b (bit 3) and A_DLPFG (bits [2:0])  
      writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c | 0x03); // Set accelerometer rate to 1 kHz and bandwidth to 41 Hz
    
     // The accelerometer, gyro, and thermometer are set to 1 kHz sample rates, 
     // but all these rates are further reduced by a factor of 5 to 200 Hz because of the SMPLRT_DIV setting
    
      // Configure Interrupts and Bypass Enable
      // Set interrupt pin active high, push-pull, hold interrupt pin level HIGH until interrupt cleared,
      // clear on read of INT_STATUS, and enable I2C_BYPASS_EN so additional chips 
      // can join the I2C bus and all can be controlled by the Arduino as master
       writeByte(MPU9250_ADDRESS, INT_PIN_CFG, 0x22);    
       writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x01);  // Enable data ready (bit 0) interrupt
       delay(100);
    }
    
    
    // Function which accumulates gyro and accelerometer data after device initialization. It calculates the average
    // of the at-rest readings and then loads the resulting offsets into accelerometer and gyro bias registers.
    void calibrateMPU9250(float * dest1, float * dest2)
    {  
      uint8_t data[12]; // data array to hold accelerometer and gyro x, y, z, data
      uint16_t ii, packet_count, fifo_count;
      int32_t gyro_bias[3]  = {0, 0, 0}, accel_bias[3] = {0, 0, 0};
      
     // reset device
      writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
      delay(100);
       
     // get stable time source; Auto select clock source to be PLL gyroscope reference if ready 
     // else use the internal oscillator, bits 2:0 = 001
      writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);  
      writeByte(MPU9250_ADDRESS, PWR_MGMT_2, 0x00);
      delay(200);                                    
    
    // Configure device for bias calculation
      writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x00);   // Disable all interrupts
      writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);      // Disable FIFO
      writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00);   // Turn on internal clock source
      writeByte(MPU9250_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
      writeByte(MPU9250_ADDRESS, USER_CTRL, 0x00);    // Disable FIFO and I2C master modes
      writeByte(MPU9250_ADDRESS, USER_CTRL, 0x0C);    // Reset FIFO and DMP
      delay(15);
      
    // Configure MPU6050 gyro and accelerometer for bias calculation
      writeByte(MPU9250_ADDRESS, CONFIG, 0x01);      // Set low-pass filter to 188 Hz
      writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00);  // Set sample rate to 1 kHz
      writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);  // Set gyro full-scale to 250 degrees per second, maximum sensitivity
      writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00); // Set accelerometer full-scale to 2 g, maximum sensitivity
     
      uint16_t  gyrosensitivity  = 131;   // = 131 LSB/degrees/sec
      uint16_t  accelsensitivity = 16384;  // = 16384 LSB/g
    
        // Configure FIFO to capture accelerometer and gyro data for bias calculation
      writeByte(MPU9250_ADDRESS, USER_CTRL, 0x40);   // Enable FIFO  
      writeByte(MPU9250_ADDRESS, FIFO_EN, 0x78);     // Enable gyro and accelerometer sensors for FIFO  (max size 512 bytes in MPU-9150)
      delay(40); // accumulate 40 samples in 40 milliseconds = 480 bytes
    
    // At end of sample accumulation, turn off FIFO sensor read
      writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00);        // Disable gyro and accelerometer sensors for FIFO
      readBytes(MPU9250_ADDRESS, FIFO_COUNTH, 2, &data[0]); // read FIFO sample count
      fifo_count = ((uint16_t)data[0] << 8) | data[1];
      packet_count = fifo_count/12;// How many sets of full gyro and accelerometer data for averaging
      
      for (ii = 0; ii < packet_count; ii++) {
        int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
        readBytes(MPU9250_ADDRESS, FIFO_R_W, 12, &data[0]); // read data for averaging
        accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1]  ) ;  // Form signed 16-bit integer for each sample in FIFO
        accel_temp[1] = (int16_t) (((int16_t)data[2] << 8) | data[3]  ) ;
        accel_temp[2] = (int16_t) (((int16_t)data[4] << 8) | data[5]  ) ;    
        gyro_temp[0]  = (int16_t) (((int16_t)data[6] << 8) | data[7]  ) ;
        gyro_temp[1]  = (int16_t) (((int16_t)data[8] << 8) | data[9]  ) ;
        gyro_temp[2]  = (int16_t) (((int16_t)data[10] << 8) | data[11]) ;
        
        accel_bias[0] += (int32_t) accel_temp[0]; // Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
        accel_bias[1] += (int32_t) accel_temp[1];
        accel_bias[2] += (int32_t) accel_temp[2];
        gyro_bias[0]  += (int32_t) gyro_temp[0];
        gyro_bias[1]  += (int32_t) gyro_temp[1];
        gyro_bias[2]  += (int32_t) gyro_temp[2];
                
    }
        accel_bias[0] /= (int32_t) packet_count; // Normalize sums to get average count biases
        accel_bias[1] /= (int32_t) packet_count;
        accel_bias[2] /= (int32_t) packet_count;
        gyro_bias[0]  /= (int32_t) packet_count;
        gyro_bias[1]  /= (int32_t) packet_count;
        gyro_bias[2]  /= (int32_t) packet_count;
        
      if(accel_bias[2] > 0L) {accel_bias[2] -= (int32_t) accelsensitivity;}  // Remove gravity from the z-axis accelerometer bias calculation
      else {accel_bias[2] += (int32_t) accelsensitivity;}
       
    // Construct the gyro biases for push to the hardware gyro bias registers, which are reset to zero upon device startup
      data[0] = (-gyro_bias[0]/4  >> 8) & 0xFF; // Divide by 4 to get 32.9 LSB per deg/s to conform to expected bias input format
      data[1] = (-gyro_bias[0]/4)       & 0xFF; // Biases are additive, so change sign on calculated average gyro biases
      data[2] = (-gyro_bias[1]/4  >> 8) & 0xFF;
      data[3] = (-gyro_bias[1]/4)       & 0xFF;
      data[4] = (-gyro_bias[2]/4  >> 8) & 0xFF;
      data[5] = (-gyro_bias[2]/4)       & 0xFF;
      
    // Push gyro biases to hardware registers
      writeByte(MPU9250_ADDRESS, XG_OFFSET_H, data[0]);
      writeByte(MPU9250_ADDRESS, XG_OFFSET_L, data[1]);
      writeByte(MPU9250_ADDRESS, YG_OFFSET_H, data[2]);
      writeByte(MPU9250_ADDRESS, YG_OFFSET_L, data[3]);
      writeByte(MPU9250_ADDRESS, ZG_OFFSET_H, data[4]);
      writeByte(MPU9250_ADDRESS, ZG_OFFSET_L, data[5]);
      
    // Output scaled gyro biases for display in the main program
      dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity;  
      dest1[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
      dest1[2] = (float) gyro_bias[2]/(float) gyrosensitivity;
    
    // Construct the accelerometer biases for push to the hardware accelerometer bias registers. These registers contain
    // factory trim values which must be added to the calculated accelerometer biases; on boot up these registers will hold
    // non-zero values. In addition, bit 0 of the lower byte must be preserved since it is used for temperature
    // compensation calculations. Accelerometer bias registers expect bias input as 2048 LSB per g, so that
    // the accelerometer biases calculated above must be divided by 8.
    
      int32_t accel_bias_reg[3] = {0, 0, 0}; // A place to hold the factory accelerometer trim biases
      readBytes(MPU9250_ADDRESS, XA_OFFSET_H, 2, &data[0]); // Read factory accelerometer trim values
      accel_bias_reg[0] = (int32_t) (((int16_t)data[0] << 8) | data[1]);
      readBytes(MPU9250_ADDRESS, YA_OFFSET_H, 2, &data[0]);
      accel_bias_reg[1] = (int32_t) (((int16_t)data[0] << 8) | data[1]);
      readBytes(MPU9250_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
      accel_bias_reg[2] = (int32_t) (((int16_t)data[0] << 8) | data[1]);
      
      uint32_t mask = 1uL; // Define mask for temperature compensation bit 0 of lower byte of accelerometer bias registers
      uint8_t mask_bit[3] = {0, 0, 0}; // Define array to hold mask bit for each accelerometer bias axis
      
      for(ii = 0; ii < 3; ii++) {
        if((accel_bias_reg[ii] & mask)) mask_bit[ii] = 0x01; // If temperature compensation bit is set, record that fact in mask_bit
      }
      
      // Construct total accelerometer bias, including calculated average accelerometer bias from above
      accel_bias_reg[0] -= (accel_bias[0]/8); // Subtract calculated averaged accelerometer bias scaled to 2048 LSB/g (16 g full scale)
      accel_bias_reg[1] -= (accel_bias[1]/8);
      accel_bias_reg[2] -= (accel_bias[2]/8);
      
      data[0] = (accel_bias_reg[0] >> 8) & 0xFF;
      data[1] = (accel_bias_reg[0])      & 0xFF;
      data[1] = data[1] | mask_bit[0]; // preserve temperature compensation bit when writing back to accelerometer bias registers
      data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
      data[3] = (accel_bias_reg[1])      & 0xFF;
      data[3] = data[3] | mask_bit[1]; // preserve temperature compensation bit when writing back to accelerometer bias registers
      data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
      data[5] = (accel_bias_reg[2])      & 0xFF;
      data[5] = data[5] | mask_bit[2]; // preserve temperature compensation bit when writing back to accelerometer bias registers
     
    // Apparently this is not working for the acceleration biases in the MPU-9250
    // Are we handling the temperature correction bit properly?
    // Push accelerometer biases to hardware registers
    //  writeByte(MPU9250_ADDRESS, XA_OFFSET_H, data[0]);
    //  writeByte(MPU9250_ADDRESS, XA_OFFSET_L, data[1]);
    //  writeByte(MPU9250_ADDRESS, YA_OFFSET_H, data[2]);
    //  writeByte(MPU9250_ADDRESS, YA_OFFSET_L, data[3]);
    //  writeByte(MPU9250_ADDRESS, ZA_OFFSET_H, data[4]);
    //  writeByte(MPU9250_ADDRESS, ZA_OFFSET_L, data[5]);
    
    // Output scaled accelerometer biases for display in the main program
       dest2[0] = (float)accel_bias[0]/(float)accelsensitivity; 
       dest2[1] = (float)accel_bias[1]/(float)accelsensitivity;
       dest2[2] = (float)accel_bias[2]/(float)accelsensitivity;
    }
    
    // Accelerometer and gyroscope self test; check calibration wrt factory settings
    void MPU9250SelfTest(float * destination) // Should return percent deviation from factory trim values, +/- 14 or less deviation is a pass
    {
       uint8_t rawData[4];
       uint8_t selfTest[6];
       float factoryTrim[6];
       
       // Configure the accelerometer for self-test
       writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0xF0); // Enable self test on all three axes and set accelerometer range to +/- 8 g
       writeByte(MPU9250_ADDRESS, GYRO_CONFIG,  0xE0); // Enable self test on all three axes and set gyro range to +/- 250 degrees/s
       delay(250);  // Delay a while to let the device execute the self-test
       rawData[0] = readByte(MPU9250_ADDRESS, SELF_TEST_X_ACCEL); // X-axis self-test results
       rawData[1] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_ACCEL); // Y-axis self-test results
       rawData[2] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_ACCEL); // Z-axis self-test results
       // Extract the acceleration test results first
       selfTest[0] = (rawData[0] >> 3) | (rawData[3] & 0x30) >> 4 ; // XA_TEST result is a five-bit unsigned integer
       selfTest[1] = (rawData[1] >> 3) | (rawData[3] & 0x0C) >> 4 ; // YA_TEST result is a five-bit unsigned integer
       selfTest[2] = (rawData[2] >> 3) | (rawData[3] & 0x03) >> 4 ; // ZA_TEST result is a five-bit unsigned integer
       // Extract the gyration test results first
       selfTest[3] = rawData[0]  & 0xD0 ; // XG_TEST result is a five-bit unsigned integer
       selfTest[4] = rawData[1]  & 0xD0 ; // YG_TEST result is a five-bit unsigned integer
       selfTest[5] = rawData[2]  & 0xD0 ; // ZG_TEST result is a five-bit unsigned integer   
       // Process results to allow final comparison with factory set values
       factoryTrim[0] = (4096.0*0.34)*(pow( (0.92/0.34) , (((float)selfTest[0] - 1.0)/30.0))); // FT[Xa] factory trim calculation
       factoryTrim[1] = (4096.0*0.34)*(pow( (0.92/0.34) , (((float)selfTest[1] - 1.0)/30.0))); // FT[Ya] factory trim calculation
       factoryTrim[2] = (4096.0*0.34)*(pow( (0.92/0.34) , (((float)selfTest[2] - 1.0)/30.0))); // FT[Za] factory trim calculation
       factoryTrim[3] =  ( 25.0*131.0)*(pow( 1.046 , ((float)selfTest[3] - 1.0) ));             // FT[Xg] factory trim calculation
       factoryTrim[4] =  (-25.0*131.0)*(pow( 1.046 , ((float)selfTest[4] - 1.0) ));             // FT[Yg] factory trim calculation
       factoryTrim[5] =  ( 25.0*131.0)*(pow( 1.046 , ((float)selfTest[5] - 1.0) ));             // FT[Zg] factory trim calculation
       
     //  Output self-test results and factory trim calculation if desired
     //  Serial.println(selfTest[0]); Serial.println(selfTest[1]); Serial.println(selfTest[2]);
     //  Serial.println(selfTest[3]); Serial.println(selfTest[4]); Serial.println(selfTest[5]);
     //  Serial.println(factoryTrim[0]); Serial.println(factoryTrim[1]); Serial.println(factoryTrim[2]);
     //  Serial.println(factoryTrim[3]); Serial.println(factoryTrim[4]); Serial.println(factoryTrim[5]);
    
     // Report results as a ratio of (STR - FT)/FT; the change from Factory Trim of the Self-Test Response
     // To get to percent, must multiply by 100 and subtract result from 100
       for (int i = 0; i < 6; i++) {
         destination[i] = 100.0 + 100.0*((float)selfTest[i] - factoryTrim[i])/factoryTrim[i]; // Report percent differences
       }
       
    }
    
            
    
            void writeByte(uint8_t address, uint8_t subAddress, uint8_t data)
    {
    	Wire.beginTransmission(address);  // Initialize the Tx buffer
    	Wire.write(subAddress);           // Put slave register address in Tx buffer
    	Wire.write(data);                 // Put data in Tx buffer
    	Wire.endTransmission();           // Send the Tx buffer
    }
    
            uint8_t readByte(uint8_t address, uint8_t subAddress)
    {
    	uint8_t data; // `data` will store the register data	 
    	Wire.beginTransmission(address);         // Initialize the Tx buffer
    	Wire.write(subAddress);	                 // Put slave register address in Tx buffer
    	Wire.endTransmission(I2C_NOSTOP);        // Send the Tx buffer, but send a restart to keep connection alive
    //	Wire.endTransmission(false);             // Send the Tx buffer, but send a restart to keep connection alive
    //	Wire.requestFrom(address, 1);  // Read one byte from slave register address 
    	Wire.requestFrom(address, (size_t) 1);  // Read one byte from slave register address 
    	data = Wire.read();                      // Fill Rx buffer with result
    	return data;                             // Return data read from slave register
    }
    
            void readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest)
    {  
    	Wire.beginTransmission(address);   // Initialize the Tx buffer
    	Wire.write(subAddress);            // Put slave register address in Tx buffer
    	Wire.endTransmission(I2C_NOSTOP);  // Send the Tx buffer, but send a restart to keep connection alive
    //	Wire.endTransmission(false);       // Send the Tx buffer, but send a restart to keep connection alive
    	uint8_t i = 0;
    //        Wire.requestFrom(address, count);  // Read bytes from slave register address 
            Wire.requestFrom(address, (size_t) count);  // Read bytes from slave register address 
    	while (Wire.available()) {
            dest[i++] = Wire.read(); }         // Put read results in the Rx buffer
    }
    Which requires this library function:

    Code:
    // Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
    // (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
    // which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
    // device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
    // The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
    // but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
            void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
            {
                float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
                float norm;
                float hx, hy, _2bx, _2bz;
                float s1, s2, s3, s4;
                float qDot1, qDot2, qDot3, qDot4;
    
                // Auxiliary variables to avoid repeated arithmetic
                float _2q1mx;
                float _2q1my;
                float _2q1mz;
                float _2q2mx;
                float _4bx;
                float _4bz;
                float _2q1 = 2.0f * q1;
                float _2q2 = 2.0f * q2;
                float _2q3 = 2.0f * q3;
                float _2q4 = 2.0f * q4;
                float _2q1q3 = 2.0f * q1 * q3;
                float _2q3q4 = 2.0f * q3 * q4;
                float q1q1 = q1 * q1;
                float q1q2 = q1 * q2;
                float q1q3 = q1 * q3;
                float q1q4 = q1 * q4;
                float q2q2 = q2 * q2;
                float q2q3 = q2 * q3;
                float q2q4 = q2 * q4;
                float q3q3 = q3 * q3;
                float q3q4 = q3 * q4;
                float q4q4 = q4 * q4;
    
                // Normalise accelerometer measurement
                norm = sqrt(ax * ax + ay * ay + az * az);
                if (norm == 0.0f) return; // handle NaN
                norm = 1.0f/norm;
                ax *= norm;
                ay *= norm;
                az *= norm;
    
                // Normalise magnetometer measurement
                norm = sqrt(mx * mx + my * my + mz * mz);
                if (norm == 0.0f) return; // handle NaN
                norm = 1.0f/norm;
                mx *= norm;
                my *= norm;
                mz *= norm;
    
                // Reference direction of Earth's magnetic field
                _2q1mx = 2.0f * q1 * mx;
                _2q1my = 2.0f * q1 * my;
                _2q1mz = 2.0f * q1 * mz;
                _2q2mx = 2.0f * q2 * mx;
                hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
                hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
                _2bx = sqrt(hx * hx + hy * hy);
                _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
                _4bx = 2.0f * _2bx;
                _4bz = 2.0f * _2bz;
    
                // Gradient decent algorithm corrective step
                s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
                s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
                s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
                s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
                norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
                norm = 1.0f/norm;
                s1 *= norm;
                s2 *= norm;
                s3 *= norm;
                s4 *= norm;
    
                // Compute rate of change of quaternion
                qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
                qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
                qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
                qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
    
                // Integrate to yield quaternion
                q1 += qDot1 * deltat;
                q2 += qDot2 * deltat;
                q3 += qDot3 * deltat;
                q4 += qDot4 * deltat;
                norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
                norm = 1.0f/norm;
                q[0] = q1 * norm;
                q[1] = q2 * norm;
                q[2] = q3 * norm;
                q[3] = q4 * norm;
    
            }
      
      
      
     // Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
     // measured ones. 
                void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
            {
                float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
                float norm;
                float hx, hy, bx, bz;
                float vx, vy, vz, wx, wy, wz;
                float ex, ey, ez;
                float pa, pb, pc;
    
                // Auxiliary variables to avoid repeated arithmetic
                float q1q1 = q1 * q1;
                float q1q2 = q1 * q2;
                float q1q3 = q1 * q3;
                float q1q4 = q1 * q4;
                float q2q2 = q2 * q2;
                float q2q3 = q2 * q3;
                float q2q4 = q2 * q4;
                float q3q3 = q3 * q3;
                float q3q4 = q3 * q4;
                float q4q4 = q4 * q4;   
    
                // Normalise accelerometer measurement
                norm = sqrt(ax * ax + ay * ay + az * az);
                if (norm == 0.0f) return; // handle NaN
                norm = 1.0f / norm;        // use reciprocal for division
                ax *= norm;
                ay *= norm;
                az *= norm;
    
                // Normalise magnetometer measurement
                norm = sqrt(mx * mx + my * my + mz * mz);
                if (norm == 0.0f) return; // handle NaN
                norm = 1.0f / norm;        // use reciprocal for division
                mx *= norm;
                my *= norm;
                mz *= norm;
    
                // Reference direction of Earth's magnetic field
                hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
                hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
                bx = sqrt((hx * hx) + (hy * hy));
                bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
    
                // Estimated direction of gravity and magnetic field
                vx = 2.0f * (q2q4 - q1q3);
                vy = 2.0f * (q1q2 + q3q4);
                vz = q1q1 - q2q2 - q3q3 + q4q4;
                wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
                wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
                wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);  
    
                // Error is cross product between estimated direction and measured direction of gravity
                ex = (ay * vz - az * vy) + (my * wz - mz * wy);
                ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
                ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
                if (Ki > 0.0f)
                {
                    eInt[0] += ex;      // accumulate integral error
                    eInt[1] += ey;
                    eInt[2] += ez;
                }
                else
                {
                    eInt[0] = 0.0f;     // prevent integral wind up
                    eInt[1] = 0.0f;
                    eInt[2] = 0.0f;
                }
    
                // Apply feedback terms
                gx = gx + Kp * ex + Ki * eInt[0];
                gy = gy + Kp * ey + Ki * eInt[1];
                gz = gz + Kp * ez + Ki * eInt[2];
    
                // Integrate rate of change of quaternion
                pa = q2;
                pb = q3;
                pc = q4;
                q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
                q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
                q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
                q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
    
                // Normalise quaternion
                norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
                norm = 1.0f / norm;
                q[0] = q1 * norm;
                q[1] = q2 * norm;
                q[2] = q3 * norm;
                q[3] = q4 * norm;
     
            }

  9. #9
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    onehorse, where did you install the libraries needed for that sketch? If you put them inside your sketches/libraries then they will be available for all installs of Arduino (assuming they all use the same sketch location). On the other hand if you put them in the Arduino/TeensyDuino libraries folder, you need to do that for each new version you install.

    I find its best to install Teensyduino with the "all" libraries option so you have all the standard ones, and put any others under sketches/libraries

  10. #10
    Senior Member onehorse's Avatar
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    I just migrated to a new laptop (Windows 7) and I've been having some trouble getting everything set up the way I like it and working as it used to. This is one such case. I can see the i2c_t3.h library in the Sketch/Import Library pull down in the contributed category. When I installed the 1.20 version of teensyduino I did indeed check the 'all' box. I just checked on my old laptop; the sketch above works fine with the i2c_t3 library under the old version 1.18; I never upgraded to 1.19. It's more than likely I did something stupid when I installed version 1.20. Still, can anyone confirm that i2c_t3.h works with version 1.20?

  11. #11
    Senior Member onehorse's Avatar
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    I reinstalled Arduino v.1.05-r2 and Teensyduino 1.20 and i2c_t3.v6b, in that order, and I can now compile usin i2c_t3 without complaint. I think I inadvertently downloaded the first i2c_t3 file in the list the first time, which turns out to be the earliest version, which apparently isn't compatible with the latest syntax. Pilot error, but at least I'm consistent!

  12. #12
    Senior Member PaulStoffregen's Avatar
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    Quote Originally Posted by onehorse View Post
    I noticed that now there are a greater variety of clock speeds available. Does 'no USB' mean that one cannot use the USB in a program at these low clock speeds
    Yes. The USB port does not function when the clock is below 24 MHz.

    or that one cannot enter a new program through the USB at these low clock speed settings?
    The automatic reboot, when you click Upload in Arduino, also does not work, because the USB isn't active.

    You will need to press the pushbutton to initiate update. After you release the pushbutton, the Mini54 takes control and reconfigures the MK20 to 24 MHz for the duration of the upload.

    Could you comment on this increase in clock speed setting choices? Thanks.
    For about half a year after releasing Teensy 3.1, the software only supported 24, 48 and 96 MHz, even though the chip is rated by Freescale for up to 72 MHz.

    Inside the chip, the are 3 main clocks, for the CPU, peripherals and flash memory. Originally, Teensyduino used either 48 MHz when the CPU was 48 or 96 MHz, or 24 MHz, for peripherals. Most peripherals have some sort of prescaler in powers of 2, so code supporting 48 MHz and half of that speed was fairly simple.

    72 MHz CPU speed resulted in a 36 MHz peripheral clock. I suspect many less ambitious software developers would have simply used 24 MHz instead of 36 MHz, but not me. Instead, I waited several months, so when I did support 72 MHz, I could spend some time to really work on editing the many places that depend on this clock. I usually prefer to spend more time to really do something well...

    People also started to play with hacking even higher overclocking, and even slower clocks for low power applications. While editing the code, I expanded the list from only 2 peripheral speeds, 48 & 24, to 8 speeds: 60, 56, 48, 36, 24, 16, 8, 4, 2 MHz. The idea is that there are many places to edit to add any new peripheral speed, so I wanted to expand the list to a wide range that will (hopefully) cover all the speeds Teensyduino will support for quite a long time.

    For extremely low power, the 2 MHz speed is special. The chip has a VLPR mode where the hardware internally plays tricks with the power supply voltage, which dramatically reduces the current consumed, but it only works up to 2 MHz. That's the reason why the speeds go all the way down to 2 MHz.

  13. #13
    Senior Member onehorse's Avatar
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    Thanks for the detailed reply. I am particularly interested in the VLP applications of the Teensy for the motion sensing and BLE add-ons I am designing. This new (to me) capability keeps Teensy in the running for such VLP applications against other worthy competitors like the STM32F401 ARM microprocessor I have been playing with.

    Edit: There must be something more to running at 2 MHz; I just tried setting the 2 MHz speed on the sketch above and encountered this error:

    C:\Users\Pesky Products\Documents\Arduino\libraries\i2c_t3\i2c_t3 .cpp:263:10: error: #error "F_BUS must be 48 MHz or 24 MHz"

    Is the clock speed hardwired into the i2C_t3 library? I have run this sketch with this i2c_t3 library at 24, 48, and 96 MHz. What's the trick to running with the lower clock speeds?
    Last edited by onehorse; 07-05-2014 at 07:43 AM.

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    I've been following the thread related with this change "Fix ARM toolchain linker & zlib issue (thanks to Andrew Kroll)", so with 1.20 I was expecting my sketch to be much smaller (both flash and RAM), but it haven't seems to make a difference at all, it's still compiling all the usb_* classes that I don't use, the audio class, the ipaddress class, etc etc. Does I'm missing something ?

  15. #15
    Senior Member PaulStoffregen's Avatar
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    Quote Originally Posted by 3400tZ View Post
    so with 1.20 I was expecting my sketch to be much smaller (both flash and RAM)
    Please post a specific program, with the flash & ram size using both 1.19 and 1.20-rc1.

    The toolchain still compiles all the same code. The difference is only what the linker keeps in your final executable image.

  16. #16
    Senior Member onehorse's Avatar
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    I have re-read your post on clock speeds several times and I think my confusion has to do with the difference between clock speed and the speed of peripherals that are 1/2n multiples. Does the 2 MHz capability only refer to the ability to scale the 48 MHz clock speed down to 2 MHz to run the CAN bus or I2S or whatever? Is that what you mean by peripherals? Or can we somehow run the Teensy clock at 2 MHz? As I am sure you know, clock speed is important for low power applications where the current goes as something like 200 microAmp per MHz. So a 2 MHz clock speed capability for those applications that could afford the speed slowdown would save significant power. Sorry for the lame questions but I really would like to understand this better.

  17. #17
    Senior Member PaulStoffregen's Avatar
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    Quote Originally Posted by onehorse View Post
    Or can we somehow run the Teensy clock at 2 MHz?
    Yes, that's exactly what it does!

    Set Tools > CPU Speed to 2 MHz and your Teensy 3.1 will run at only 2 MHz speed.

    Really, it's that easy. You choose the speed in that menu and it changes to that speed when your uploaded code runs. It's kinda like magic.

    As I am sure you know, clock speed is important for low power applications where the current goes as something like 200 microAmp per MHz. So a 2 MHz clock speed capability for those applications that could afford the speed slowdown would save significant power.
    That's why so much work went into version 1.19 to make these extra slow speeds available.

    but I really would like to understand this better.
    Whatever you select in the CPU Speed menu causes a name to be #defined in the code. Use File > Preferences to show verbose info while compiling to make the exact compiler commands appear when you upload. The code uses that info to configure the hardware.

    To understand the hardware, you should look at chapter 5 of the reference manual. On page 156, you'll see this diagram:

    Click image for larger version. 

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    This circuitry lets the chip run from a wide variety of speeds. The system osc on Teensy is always 16 MHz, but the PLL can multiply the frequency, and those OUTDIV circuits can divide it. There are MANY different clocks inside this chip, as you can see in the huge list of section 5.4, but the 3 main ones from from those 3 OUTDIV circuits. Section 5.5 explains some of the requirements of how those 3 clocks must be related to each other. Section 5.7 explains which things in the chip run from which clocks. You'll see almost everything runs from either the system clock or bus (peripheral) clock.

    Another key piece of information is this list of clocks:

    https://github.com/PaulStoffregen/co...kinetis.h#L176

    These are the actual clock speeds for all 3, for each of the options you can set in Tools > CPU Speed. This list is merely for documentation, so other code can know which speed is in use. The actual code which configures the hardware is here:

    https://github.com/PaulStoffregen/co...20dx128.c#L414

    You can see there are many #ifdef checks, because the hardware is configured differently depending on whether the PLL is needed to increase the frequency, and of course the OUTDIV settings are different for each speed. The exact functionality of all those registers is documented in the reference manual. That PDF is huge, but you can use text search to find those names within the document to learn how each register works.

    If you want to understand how it really works, rather than just take my word for the fact that menu really does control the speed, you're going to need to really read that reference manual documentation and the source code. I've written all I can here to point to you to the places to look.

  18. #18
    Senior Member onehorse's Avatar
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    Thanks for the patient explanation Paul, you've made it easy for me to learn what I want to know.
    I'll study the reference manual so I can understand what you've done in the source code.
    Next time I'll have a more intelligent question for you!

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    Quote Originally Posted by PaulStoffregen View Post
    Please post a specific program, with the flash & ram size using both 1.19 and 1.20-rc1.

    The toolchain still compiles all the same code. The difference is only what the linker keeps in your final executable image.
    Hi Paul, code is here.

    I'm just a bit surprised because the flash / RAM usage output by the IDE are the same with 1.19 and 1.20:

    Binary sketch size: 105,964 bytes (of a 262,144 byte maximum)
    Estimated memory use: 15,492 bytes (of a 65,536 byte maximum)

    I'm mainly surprised that my code use like 40% of the flash but I guess that's possible.

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    In the ease of use department...
    In addition to the change to boards.txt requested above,

    Please change the window pop-up saying the selected board type in the IDE doesn't match the board type. This popup normally (windows 7) comes up hidden behind other windows. Confusing.
    Also when this happens, the last line displayed in the IDE says "download complete" which adds to the confusion.

  21. #21
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    Quote Originally Posted by 3400tZ View Post
    I'm just a bit surprised because the flash / RAM usage output by the IDE are the same with 1.19 and 1.20
    Its surprising they are exactly identical, since 1.20 puts the interrupt vector table in RAM so they should be slightly different in sizes even if the linker is unable to reduce size by not including stuff.

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    Quote Originally Posted by Nantonos View Post
    Its surprising they are exactly identical, since 1.20 puts the interrupt vector table in RAM so they should be slightly different in sizes even if the linker is unable to reduce size by not including stuff.
    Well, sorry, by the same, I mean similar, not EXACTLY the same.

    1.19:

    Binary sketch size: 106,248 bytes (of a 262,144 byte maximum)
    Estimated memory use: 15,004 bytes (of a 65,536 byte maximum)

    1.20:

    Binary sketch size: 105,964 bytes (of a 262,144 byte maximum)
    Estimated memory use: 15,492 bytes (of a 65,536 byte maximum)

  23. #23
    Senior Member PaulStoffregen's Avatar
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    Quote Originally Posted by 3400tZ View Post
    Well, sorry, by the same, I mean similar, not EXACTLY the same.
    If your program is actually using most of those stuff, like Serial1, Serial2 & Serial3, then the linker has to include it.

    I'm wondering if the new serialEvent stuff is forcing the linker to keep those in the code unnecessarily? Honestly, reducing memory usage is a much lower priority for me than fixing the pin 33 issue and getting SPI transaction support working and patched into the widely used SPI-based libraries. If someone else (like Andrew Kroll - who's traditionally done the most of this) looks into the issue and suggests a fix, I'll give it a try. But I'm not going to divert my limited dev hours away from fixing pin 33 and SPI compatibility.

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    Sure Paul, I'm not too worried about it, just thought I would still mention it

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    Quote Originally Posted by 3400tZ View Post
    Well, sorry, by the same, I mean similar, not EXACTLY the same.
    My reason for asking - if they were exactly the same, my next question would be to check you didn't accidentally compile twice with the same version.

    I'm seeing variable differences depending on libraries used. An SSD1306 example compiled noticeably smaller, probably because the library mixes up SPI and I2C but only actually uses one of them. Other code is, as you noted, pretty similar.

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