Optimizing Moving Average Calculation on ARM Cortex-M7 Using UMAAL Instruction

ARM Cortex-M7 DSP Moving Average Implementation Challenges

The ARM Cortex-M7 processor, with its advanced DSP capabilities, is often employed in applications requiring high-performance signal processing. One common operation in such applications is the calculation of a moving average, which is used to smooth data streams and reduce noise. The moving average algorithm typically involves maintaining a sum of the most recent values in a window, updating this sum by adding the newest value and subtracting the oldest value, and then dividing by the window size to obtain the average.

The UMAAL (Unsigned Multiply Accumulate Accumulate Long) instruction is a powerful tool in the ARM Cortex-M7’s instruction set that can be leveraged to optimize this operation. UMAAL performs a 32×32-bit unsigned multiplication and accumulates the result into two 32-bit registers, effectively allowing for a 64-bit accumulation. This is particularly useful in scenarios where the sum of products can exceed the 32-bit limit, which is often the case in moving average calculations over large data sets.

However, implementing a moving average using UMAAL on the Cortex-M7 is not straightforward. The primary challenge lies in the fact that the UMAAL instruction is not directly exposed through the CMSIS (Cortex Microcontroller Software Interface Standard) library, which is the standard software interface for ARM Cortex-M processors. This absence necessitates a deeper understanding of the instruction’s behavior and the use of inline assembly or compiler intrinsics to access it.

CMSIS Intrinsic Limitations and UMAAL Instruction Details

The CMSIS library provides a set of standardized APIs and intrinsic functions that abstract the underlying hardware, making it easier for developers to write portable and efficient code for ARM Cortex-M processors. However, CMSIS does not provide intrinsic functions for every instruction in the ARM instruction set. Specifically, the UMAAL instruction is not included in the CMSIS headers, which means developers cannot directly call it using a high-level function.

The UMAAL instruction performs the following operation:

[ \text{RdLo} = \text{RdLo} + (\text{Rn} \times \text{Rm}) + \text{RdHi} ]
[ \text{RdHi} = \text{RdHi} + \text{carry} ]

Here, RdLo and RdHi are the lower and upper 32-bit parts of a 64-bit accumulator, and Rn and Rm are the 32-bit operands being multiplied. The result of the multiplication is added to the 64-bit accumulator, and the carry from the addition is propagated to the upper 32 bits.

The absence of a UMAAL intrinsic in CMSIS means that developers must either rely on inline assembly or create their own intrinsic function. Inline assembly allows developers to embed assembly code directly within C/C++ code, providing direct access to the UMAAL instruction. However, inline assembly can be error-prone and less portable across different compilers and architectures.

Alternatively, developers can define their own intrinsic function for UMAAL. This involves writing a function that uses inline assembly to perform the UMAAL operation and then wrapping it in a high-level function that can be called from C/C++ code. This approach provides a balance between performance and portability, as the intrinsic function can be reused across different projects and compilers.

Implementing UMAAL for Moving Average Calculation

To implement a moving average calculation using the UMAAL instruction, developers must first understand how to structure the data and the algorithm to take advantage of UMAAL’s capabilities. The moving average algorithm involves maintaining a sum of the most recent values in a window, updating this sum by adding the newest value and subtracting the oldest value, and then dividing by the window size to obtain the average.

The UMAAL instruction can be used to efficiently update the sum by performing the multiplication and accumulation in a single step. However, care must be taken to ensure that the data is correctly aligned and that the 64-bit accumulator is properly managed. The following steps outline the process of implementing a moving average using UMAAL:

1. Data Structure Definition: Define a data structure to hold the sum, the newest value, and the oldest value. The sum should be stored as a 64-bit integer to accommodate the accumulation of large values.

2. UMAAL Intrinsic Implementation: Implement the UMAAL intrinsic function using inline assembly. This function should take the 64-bit accumulator and the two 32-bit operands as inputs and return the updated 64-bit accumulator.

3. Moving Average Algorithm: Implement the moving average algorithm using the UMAAL intrinsic function. The algorithm should update the sum by adding the newest value and subtracting the oldest value, and then divide the sum by the window size to obtain the average.

4. Testing and Validation: Test the implementation to ensure that it produces correct results and performs efficiently. This may involve comparing the results with a reference implementation and profiling the code to identify any performance bottlenecks.

The following code snippet demonstrates how to implement the UMAAL intrinsic function and use it in a moving average calculation:

#include <stdint.h>

// Define the UMAAL intrinsic function
__STATIC_FORCEINLINE uint64_t __UMAAL(uint64_t acc, uint32_t rn, uint32_t rm) {
    uint32_t lo, hi;
    lo = acc;
    hi = acc >> 32;
    __ASM volatile ("umaal %0, %1, %2, %3"
                    : "+r" (lo), "+r" (hi)
                    : "r" (rn), "r" (rm));
    acc = hi;
    acc <<= 32;
    acc |= lo;
    return acc;
}

// Moving average calculation using UMAAL
uint32_t moving_average(uint32_t *values, uint32_t window_size, uint32_t new_value) {
    static uint64_t sum = 0;
    static uint32_t index = 0;
    static uint32_t oldest_value = 0;

    // Update the sum using UMAAL
    sum = __UMAAL(sum, new_value, 1);  // Multiply new_value by 1 and add to sum
    sum -= oldest_value;               // Subtract the oldest value

    // Update the oldest value
    oldest_value = values[index];
    values[index] = new_value;
    index = (index + 1) % window_size;

    // Calculate the average
    return (uint32_t)(sum / window_size);
}

In this implementation, the __UMAAL function is defined using inline assembly to perform the UMAAL operation. The moving_average function uses this intrinsic to update the sum and calculate the moving average. The values array holds the most recent values in the window, and the index variable is used to keep track of the oldest value.

By following these steps and using the UMAAL instruction, developers can achieve a highly efficient moving average calculation on the ARM Cortex-M7 processor. This approach leverages the processor’s DSP capabilities while maintaining the flexibility and portability of high-level code.