- Important Change from v1.2.0
- Why do we need this MBED_RP2040_Slow_PWM library
- Changelog
- Prerequisites
- Installation
- HOWTO Fix
Multiple DefinitionsLinker Error - More useful Information
- Usage
- Examples
- Example ISR_16_PWMs_Array_Complex
- Debug Terminal Output Samples
- Debug
- Troubleshooting
- Issues
- TO DO
- DONE
- Contributions and Thanks
- Contributing
- License
- Copyright
Please have a look at HOWTO Fix Multiple Definitions Linker Error
As more complex calculation and check inside ISR are introduced from v1.2.0, there is possibly some crash depending on use-case.
You can modify to use larger HW_TIMER_INTERVAL_US, (from current 20uS), according to your board and use-case if crash happens.
// Current 20uS #define HW_TIMER_INTERVAL_US 20LWhy do we need this MBED_RP2040_Slow_PWM library
This library enables you to use Hardware Timers on RP2040-based boards to create and output PWM to pins. Because this library doesn't use the powerful hardware-controlled PWM with limitations, the maximum PWM frequency is currently limited at 1000Hz, which is still suitable for many real-life applications. Now you can also modify PWM settings on-the-fly.
This library enables you to use Interrupt from Hardware Timers on RP2040-based boards to create and output PWM to pins. It now supports 16 ISR-based synchronized PWM channels, while consuming only 1 Hardware Timer. PWM interval can be very long (uint32_t millisecs). The most important feature is they're ISR-based PWM channels. Therefore, their executions are not blocked by bad-behaving functions or tasks. This important feature is absolutely necessary for mission-critical tasks. These hardware PWM channels, using interrupt, still work even if other functions are blocking. Moreover, they are much more precise (certainly depending on clock frequency accuracy) than other software PWM using millis() or micros(). That's necessary if you need to measure some data requiring better accuracy.
As Hardware Timers are rare, and very precious assets of any board, this library now enables you to use up to 16 ISR-based synchronized PWM channels, while consuming only 1 Hardware Timer. Timers' interval is very long (ulong millisecs).
Now with these new 16 ISR-based PWM-channels, the maximum interval is practically unlimited (limited only by unsigned long milliseconds) while the accuracy is nearly perfect compared to software PWM channels.
The most important feature is they're ISR-based PWM channels. Therefore, their executions are not blocked by bad-behaving functions / tasks. This important feature is absolutely necessary for mission-critical tasks.
The ISR_16_PWMs_Array_Complex example will demonstrate the nearly perfect accuracy, compared to software PWM, by printing the actual period / duty-cycle in microsecs of each of PWM-channels.
Being ISR-based PWM, their executions are not blocked by bad-behaving functions / tasks, such as connecting to WiFi, Internet or Blynk services. You can also have many (up to 16) PWM channels to use.
This non-being-blocked important feature is absolutely necessary for mission-critical tasks.
You'll see software-based SimpleTimer is blocked while system is connecting to WiFi / Internet / Blynk, as well as by blocking task in loop(), using delay() function as an example. The elapsed time then is very unaccurate
Imagine you have a system with a mission-critical function, measuring water level and control the sump pump or doing something much more important. You normally use a software timer to poll, or even place the function in loop(). But what if another function is blocking the loop() or setup().
So your function might not be executed, and the result would be disastrous.
You'd prefer to have your function called, no matter what happening with other functions (busy loop, bug, etc.).
The correct choice is to use a Hardware Timer with Interrupt to call your function.
These hardware PWM channels, using interrupt, still work even if other functions are blocking. Moreover, they are much more precise (certainly depending on clock frequency accuracy) than other software PWM channels using millis() or micros(). That's necessary if you need to measure some data requiring better accuracy.
Functions using normal software PWM channels, relying on loop() and calling millis(), won't work if the loop() or setup() is blocked by certain operation. For example, certain function is blocking while it's connecting to WiFi or some services.
The catch is your function is now part of an ISR (Interrupt Service Routine), and must be lean / mean, and follow certain rules. More to read on:
- RP2040-based boards such as Nano_RP2040_Connect, RaspberryPi Pico, etc., using ArduinoCore-mbed mbed_nano or mbed_rp2040 core
-
Inside the attached function, delay() won’t work and the value returned by millis() will not increment. Serial data received while in the function may be lost. You should declare as volatile any variables that you modify within the attached function.
-
Typically global variables are used to pass data between an ISR and the main program. To make sure variables shared between an ISR and the main program are updated correctly, declare them as volatile.
Arduino IDE 1.8.19+for Arduino.Arduino mbed_rp2040 core 3.4.1+for Arduino (Use Arduino Board Manager) RP2040-based boards, such as Arduino Nano RP2040 Connect, RASPBERRY_PI_PICO, etc..- To use with certain example
SimpleTimer libraryfor ISR_Timers_Array_Simple and ISR_16_Timers_Array_Complex examples.
The best and easiest way is to use Arduino Library Manager. Search for MBED_RP2040_Slow_PWM, then select / install the latest version. You can also use this link for more detailed instructions.
Another way to install is to:
- Navigate to MBED_RP2040_Slow_PWM page.
- Download the latest release
MBED_RP2040_Slow_PWM-main.zip. - Extract the zip file to
MBED_RP2040_Slow_PWM-maindirectory - Copy whole
MBED_RP2040_Slow_PWM-mainfolder to Arduino libraries' directory such as~/Arduino/libraries/.
- Install VS Code
- Install PlatformIO
- Install MBED_RP2040_Slow_PWM library by using Library Manager. Search for MBED_RP2040_Slow_PWM in Platform.io Author's Libraries
- Use included platformio.ini file from examples to ensure that all dependent libraries will installed automatically. Please visit documentation for the other options and examples at Project Configuration File
The current library implementation, using xyz-Impl.h instead of standard xyz.cpp, possibly creates certain Multiple Definitions Linker error in certain use cases.
You can include this .hpp file
// Can be included as many times as necessary, without `Multiple Definitions` Linker Error #include "MBED_RP2040_Slow_PWM.hpp" //https://github.com/khoih-prog/MBED_RP2040_Slow_PWMin many files. But be sure to use the following .h file in just 1 .h, .cpp or .ino file, which must not be included in any other file, to avoid Multiple Definitions Linker Error
// To be included only in main(), .ino with setup() to avoid `Multiple Definitions` Linker Error #include "MBED_RP2040_Slow_PWM.h" //https://github.com/khoih-prog/MBED_RP2040_Slow_PWMCheck the new multiFileProject example for a HOWTO demo.
Have a look at the discussion in Different behaviour using the src_cpp or src_h lib #80
The RP2040-based system timer peripheral provides a global microsecond timebase for the system, and generates interrupts based on this timebase. It supports the following features:
• A single 64-bit counter, incrementing once per microsecond • This counter can be read from a pair of latching registers, for race-free reads over a 32-bit bus. • Four alarms: match on the lower 32 bits of counter, IRQ on match: TIMER_IRQ_0-TIMER_IRQ_3
Now with these new 16 ISR-based PWM channels (while consuming only 1 hardware timer), the maximum interval is practically unlimited (limited only by unsigned long milliseconds). The accuracy is nearly perfect compared to software PWM channels. The most important feature is they're ISR-based PWM channels Therefore, their executions are not blocked by bad-behaving functions / tasks. This important feature is absolutely necessary for mission-critical tasks.
The ISR_16_PWMs_Array_Complex example will demonstrate the nearly perfect accuracy compared to software PWM channels by printing the actual elapsed microsecs / millisecs of each type of PWM channels.
Being ISR-based PWM channels, their executions are not blocked by bad-behaving functions / tasks, such as connecting to WiFi, Internet and Blynk services. You can also have many (up to 16) PWM channels to use. This non-being-blocked important feature is absolutely necessary for mission-critical tasks. You'll see blynkTimer Software is blocked while system is connecting to WiFi / Internet / Blynk, as well as by blocking task in loop(), using delay() function as an example. The elapsed time then is very unaccurate
Before using any Timer, you have to make sure the Timer has not been used by any other purpose. TIMER_IRQ_0, TIMER_IRQ_1, TIMER_IRQ_2 and TIMER_IRQ_3 are supported for RP2040-based boards.
// Init MBED_RPI_PICO_Timer MBED_RP2040_Timer ITimer(0);; // Init MBED_RP2040_Slow_PWM, each can service 16 different ISR-based PWM channels MBED_RP2040_Slow_PWM ISR_PWM;void irqCallbackStartFunc() { } void irqCallbackStopFunc() { } void setup() { .... // You can use this with PWM_Freq in Hz ISR_PWM.setPWM(PWM_Pin, PWM_Freq, PWM_DutyCycle, irqCallbackStartFunc, irqCallbackStopFunc); .... } - ISR_16_PWMs_Array
- ISR_16_PWMs_Array_Complex
- ISR_16_PWMs_Array_Simple
- ISR_Changing_PWM
- ISR_Modify_PWM
- multiFileProject New
Example ISR_16_PWMs_Array_Complex
The following is the sample terminal output when running example ISR_16_PWMs_Array_Complex to demonstrate how to use multiple PWM channels with complex callback functions, the accuracy of ISR Hardware PWM-channels, especially when system is very busy. The ISR PWM-channels is running exactly according to corresponding programmed periods and duty-cycles
Starting ISR_16_PWMs_Array_Complex on RaspberryPi Pico MBED_RP2040_Slow_PWM v1.3.0 [PWM] _timerNo = 0 , Clock (Hz) = 1000000.00 , _fre (Hz) = 50000.00 [PWM] _count = 0 - 20 [PWM] hardware_alarm_set_target, uS = 20 Starting ITimer OK, micros() = 3320077 Channel : 0 Period : 1000000OnTime : 50000Start_Time : 3321325 Channel : 1 Period : 500000OnTime : 50000Start_Time : 3322698 Channel : 2 Period : 333333OnTime : 66666Start_Time : 3323943 Channel : 3 Period : 250000OnTime : 75000Start_Time : 3325097 Channel : 4 Period : 200000OnTime : 80000Start_Time : 3326457 Channel : 5 Period : 166666OnTime : 74999Start_Time : 3327632 Channel : 6 Period : 142857OnTime : 71428Start_Time : 3328874 Channel : 7 Period : 125000OnTime : 68750Start_Time : 3330002 Channel : 8 Period : 111111OnTime : 66666Start_Time : 3331139 Channel : 9 Period : 100000OnTime : 65000Start_Time : 3332396 Channel : 10 Period : 66666OnTime : 46666Start_Time : 3333625 Channel : 11 Period : 50000OnTime : 37500Start_Time : 3334912 Channel : 12 Period : 40000OnTime : 32000Start_Time : 3336165 Channel : 13 Period : 33333OnTime : 28333Start_Time : 3337497 Channel : 14 Period : 25000OnTime : 22500Start_Time : 3338945 Channel : 15 Period : 20000OnTime : 19000Start_Time : 3340266 SimpleTimer (ms): 2000, us : 13341250, Dus : 10020493 PWM Channel : 0, programmed Period (us): 1000000.00, actual : 1000000, programmed DutyCycle : 5.00, actual : 5.00 PWM Channel : 1, programmed Period (us): 500000.00, actual : 499999, programmed DutyCycle : 10.00, actual : 10.00 PWM Channel : 2, programmed Period (us): 333333.34, actual : 333339, programmed DutyCycle : 20.00, actual : 20.00 PWM Channel : 3, programmed Period (us): 250000.00, actual : 250000, programmed DutyCycle : 30.00, actual : 30.00 PWM Channel : 4, programmed Period (us): 200000.00, actual : 200000, programmed DutyCycle : 40.00, actual : 40.00 PWM Channel : 5, programmed Period (us): 166666.67, actual : 166680, programmed DutyCycle : 45.00, actual : 44.99 PWM Channel : 6, programmed Period (us): 142857.14, actual : 142859, programmed DutyCycle : 50.00, actual : 49.99 PWM Channel : 7, programmed Period (us): 125000.00, actual : 124999, programmed DutyCycle : 55.00, actual : 54.99 PWM Channel : 8, programmed Period (us): 111111.11, actual : 111120, programmed DutyCycle : 60.00, actual : 59.99 PWM Channel : 9, programmed Period (us): 100000.00, actual : 100000, programmed DutyCycle : 65.00, actual : 65.00 PWM Channel : 10, programmed Period (us): 66666.66, actual : 66680, programmed DutyCycle : 70.00, actual : 69.98 PWM Channel : 11, programmed Period (us): 50000.00, actual : 49999, programmed DutyCycle : 75.00, actual : 75.00 PWM Channel : 12, programmed Period (us): 40000.00, actual : 39999, programmed DutyCycle : 80.00, actual : 79.97 PWM Channel : 13, programmed Period (us): 33333.33, actual : 33340, programmed DutyCycle : 85.00, actual : 84.98 PWM Channel : 14, programmed Period (us): 25000.00, actual : 25012, programmed DutyCycle : 90.00, actual : 89.93 PWM Channel : 15, programmed Period (us): 20000.00, actual : 20034, programmed DutyCycle : 95.00, actual : 94.76 SimpleTimer (ms): 2000, us : 23380221, Dus : 10038971 PWM Channel : 0, programmed Period (us): 1000000.00, actual : 1000002, programmed DutyCycle : 5.00, actual : 5.00 PWM Channel : 1, programmed Period (us): 500000.00, actual : 500001, programmed DutyCycle : 10.00, actual : 10.00 PWM Channel : 2, programmed Period (us): 333333.34, actual : 333340, programmed DutyCycle : 20.00, actual : 20.00 PWM Channel : 3, programmed Period (us): 250000.00, actual : 250001, programmed DutyCycle : 30.00, actual : 29.99 PWM Channel : 4, programmed Period (us): 200000.00, actual : 200001, programmed DutyCycle : 40.00, actual : 39.99 PWM Channel : 5, programmed Period (us): 166666.67, actual : 166680, programmed DutyCycle : 45.00, actual : 44.98 PWM Channel : 6, programmed Period (us): 142857.14, actual : 142860, programmed DutyCycle : 50.00, actual : 49.99 PWM Channel : 7, programmed Period (us): 125000.00, actual : 125001, programmed DutyCycle : 55.00, actual : 55.00 PWM Channel : 8, programmed Period (us): 111111.11, actual : 111120, programmed DutyCycle : 60.00, actual : 59.99 PWM Channel : 9, programmed Period (us): 100000.00, actual : 99999, programmed DutyCycle : 65.00, actual : 64.99 PWM Channel : 10, programmed Period (us): 66666.66, actual : 66670, programmed DutyCycle : 70.00, actual : 69.99 PWM Channel : 11, programmed Period (us): 50000.00, actual : 50029, programmed DutyCycle : 75.00, actual : 74.96 PWM Channel : 12, programmed Period (us): 40000.00, actual : 40001, programmed DutyCycle : 80.00, actual : 80.02 PWM Channel : 13, programmed Period (us): 33333.33, actual : 33341, programmed DutyCycle : 85.00, actual : 84.98 PWM Channel : 14, programmed Period (us): 25000.00, actual : 25009, programmed DutyCycle : 90.00, actual : 89.90 PWM Channel : 15, programmed Period (us): 20000.00, actual : 19994, programmed DutyCycle : 95.00, actual : 94.93 SimpleTimer (ms): 2000, us : 33419214, Dus : 10038993 PWM Channel : 0, programmed Period (us): 1000000.00, actual : 1000001, programmed DutyCycle : 5.00, actual : 5.00 PWM Channel : 1, programmed Period (us): 500000.00, actual : 500000, programmed DutyCycle : 10.00, actual : 10.00 PWM Channel : 2, programmed Period (us): 333333.34, actual : 333341, programmed DutyCycle : 20.00, actual : 20.00 PWM Channel : 3, programmed Period (us): 250000.00, actual : 249999, programmed DutyCycle : 30.00, actual : 30.00 PWM Channel : 4, programmed Period (us): 200000.00, actual : 200000, programmed DutyCycle : 40.00, actual : 40.00 PWM Channel : 5, programmed Period (us): 166666.67, actual : 166679, programmed DutyCycle : 45.00, actual : 44.99 PWM Channel : 6, programmed Period (us): 142857.14, actual : 142860, programmed DutyCycle : 50.00, actual : 49.99 PWM Channel : 7, programmed Period (us): 125000.00, actual : 125000, programmed DutyCycle : 55.00, actual : 54.99 PWM Channel : 8, programmed Period (us): 111111.11, actual : 111120, programmed DutyCycle : 60.00, actual : 59.99 PWM Channel : 9, programmed Period (us): 100000.00, actual : 100014, programmed DutyCycle : 65.00, actual : 64.99 PWM Channel : 10, programmed Period (us): 66666.66, actual : 66681, programmed DutyCycle : 70.00, actual : 69.97 PWM Channel : 11, programmed Period (us): 50000.00, actual : 50028, programmed DutyCycle : 75.00, actual : 74.94 PWM Channel : 12, programmed Period (us): 40000.00, actual : 40000, programmed DutyCycle : 80.00, actual : 79.97 PWM Channel : 13, programmed Period (us): 33333.33, actual : 33343, programmed DutyCycle : 85.00, actual : 84.94 PWM Channel : 14, programmed Period (us): 25000.00, actual : 25021, programmed DutyCycle : 90.00, actual : 89.90 PWM Channel : 15, programmed Period (us): 20000.00, actual : 20003, programmed DutyCycle : 95.00, actual : 94.94The following is the sample terminal output when running example ISR_16_PWMs_Array on RP2040-based RaspberryPi Pico to demonstrate how to use multiple PWM channels with simple callback functions.
Starting ISR_16_PWMs_Array on RaspberryPi Pico MBED_RP2040_Slow_PWM v1.3.0 [PWM] _timerNo = 0 , Clock (Hz) = 1000000.00 , _fre (Hz) = 50000.00 [PWM] _count = 0 - 20 [PWM] hardware_alarm_set_target, uS = 20 Starting ITimer OK, micros() = 3736634 Channel : 0 Period : 1000000OnTime : 50000Start_Time : 3737939 Channel : 1 Period : 500000OnTime : 50000Start_Time : 3739363 Channel : 2 Period : 333333OnTime : 66666Start_Time : 3740718 Channel : 3 Period : 250000OnTime : 75000Start_Time : 3741877 Channel : 4 Period : 200000OnTime : 80000Start_Time : 3743177 Channel : 5 Period : 166666OnTime : 74999Start_Time : 3744513 Channel : 6 Period : 142857OnTime : 71428Start_Time : 3745811 Channel : 7 Period : 125000OnTime : 68750Start_Time : 3747053 Channel : 8 Period : 111111OnTime : 66666Start_Time : 3748263 Channel : 9 Period : 100000OnTime : 65000Start_Time : 3749498 Channel : 10 Period : 66666OnTime : 46666Start_Time : 3750692 Channel : 11 Period : 50000OnTime : 37500Start_Time : 3752055 Channel : 12 Period : 40000OnTime : 32000Start_Time : 3753313 Channel : 13 Period : 33333OnTime : 28333Start_Time : 3754675 Channel : 14 Period : 25000OnTime : 22500Start_Time : 3756047 Channel : 15 Period : 20000OnTime : 19000Start_Time : 3757332The following is the sample terminal output when running example ISR_16_PWMs_Array_Simple on RP2040-based RaspberryPi Pico to demonstrate how to use multiple PWM channels.
Starting ISR_16_PWMs_Array_Simple on RaspberryPi Pico MBED_RP2040_Slow_PWM v1.3.0 [PWM] _timerNo = 0 , Clock (Hz) = 1000000.00 , _fre (Hz) = 50000.00 [PWM] _count = 0 - 20 [PWM] hardware_alarm_set_target, uS = 20 Starting ITimer OK, micros() = 3635936 Channel : 0 Period : 1000000OnTime : 50000Start_Time : 3637221 Channel : 1 Period : 500000OnTime : 50000Start_Time : 3638549 Channel : 2 Period : 333333OnTime : 66666Start_Time : 3639819 Channel : 3 Period : 250000OnTime : 75000Start_Time : 3641096 Channel : 4 Period : 200000OnTime : 80000Start_Time : 3642434 Channel : 5 Period : 166666OnTime : 74999Start_Time : 3643793 Channel : 6 Period : 142857OnTime : 71428Start_Time : 3645252 Channel : 7 Period : 125000OnTime : 68750Start_Time : 3646599 Channel : 8 Period : 111111OnTime : 66666Start_Time : 3647898 Channel : 9 Period : 100000OnTime : 65000Start_Time : 3649115 Channel : 10 Period : 66666OnTime : 46666Start_Time : 3650427 Channel : 11 Period : 50000OnTime : 37500Start_Time : 3651688 Channel : 12 Period : 40000OnTime : 32000Start_Time : 3652992 Channel : 13 Period : 33333OnTime : 28333Start_Time : 3654391 Channel : 14 Period : 25000OnTime : 22500Start_Time : 3655707 Channel : 15 Period : 20000OnTime : 19000Start_Time : 3657122The following is the sample terminal output when running example ISR_Modify_PWM on RP2040-based RaspberryPi Pico to demonstrate how to modify PWM settings on-the-fly without deleting the PWM channel
Starting ISR_Modify_PWM on RaspberryPi Pico MBED_RP2040_Slow_PWM v1.3.0 [PWM] _timerNo = 0 , Clock (Hz) = 1000000.00 , _fre (Hz) = 50000.00 [PWM] _count = 0 - 20 [PWM] hardware_alarm_set_target, uS = 20 Starting ITimer OK, micros() = 12754395 Using PWM Freq = 200.00, PWM DutyCycle = 1.00 Channel : 0 Period : 5000OnTime : 50Start_Time : 12756541 Channel : 0 Period : 10000OnTime : 555Start_Time : 22754527 Channel : 0 Period : 5000OnTime : 50Start_Time : 32750968 Channel : 0 Period : 10000OnTime : 555Start_Time : 42758860 Channel : 0 Period : 5000OnTime : 50Start_Time : 52755360 Channel : 0 Period : 10000OnTime : 555Start_Time : 62758443The following is the sample terminal output when running example ISR_Changing_PWM on RP2040-based RaspberryPi Pico to demonstrate how to modify PWM settings on-the-fly by deleting the PWM channel and reinit the PWM channel
Starting ISR_Changing_PWM on RaspberryPi Pico MBED_RP2040_Slow_PWM v1.3.0 [PWM] _timerNo = 0 , Clock (Hz) = 1000000.00 , _fre (Hz) = 50000.00 [PWM] _count = 0 - 20 [PWM] hardware_alarm_set_target, uS = 20 Starting ITimer OK, micros() = 3336281 Using PWM Freq = 1.00, PWM DutyCycle = 50.00 Channel : 0 Period : 1000000OnTime : 500000Start_Time : 3338285 Using PWM Freq = 2.00, PWM DutyCycle = 90.00 Channel : 0 Period : 500000OnTime : 450000Start_Time : 12940431 Using PWM Freq = 1.00, PWM DutyCycle = 50.00 Channel : 0 Period : 1000000OnTime : 500000Start_Time : 22543196 Using PWM Freq = 2.00, PWM DutyCycle = 90.00 Channel : 0 Period : 500000OnTime : 450000Start_Time : 32146094 Using PWM Freq = 1.00, PWM DutyCycle = 50.00 Channel : 0 Period : 1000000OnTime : 500000Start_Time : 41747971Debug is enabled by default on Serial.
You can also change the debugging level _PWM_LOGLEVEL_ from 0 to 4
// Don't define _PWM_LOGLEVEL_ > 0. Only for special ISR debugging only. Can hang the system. #define _PWM_LOGLEVEL_ 0If you get compilation errors, more often than not, you may need to install a newer version of the core for Arduino boards.
Sometimes, the library will only work if you update the board core to the latest version because I am using newly added functions.
Submit issues to: MBED_RP2040_Slow_PWM issues
- Search for bug and improvement.
- Similar features for remaining Arduino boards
- Basic hardware multi-channel PWM for RP2040-based RaspberryPi Pico, Nano_RP2040_Connect, etc.
- Add Table of Contents
- Add functions to modify PWM settings on-the-fly
- Improve accuracy by using
float, instead ofuint32_tfordutycycle - Optimize library code by using
reference-passinginstead ofvalue-passing - DutyCycle to be optionally updated at the end current PWM period instead of immediately.
- Fix
multiple-definitionslinker error. Dropsrc_cppandsrc_hdirectories - Display informational warning only when
_PWM_LOGLEVEL_> 3 - Fix
poor-timer-accuracybug
Many thanks for everyone for bug reporting, new feature suggesting, testing and contributing to the development of this library.
- Neil Baylis to report relating issue Poor accuracy on timer interrupt frequency or interval. #4, leading to version v1.3.0 to fix
poor-timer-accuracybug
![]() Neil Baylis |
If you want to contribute to this project:
- Report bugs and errors
- Ask for enhancements
- Create issues and pull requests
- Tell other people about this library
- The library is licensed under MIT
Copyright 2021- Khoi Hoang

