Optimizing Bit Reversal in Embedded Systems: Time vs Memory Trade-offs

In embedded systems development, there are many situations where bit manipulations are of great importance, whether you are writing some device driver, calculating checksums, reversing bits, or packing/unpacking data. However, there is often a trade-off between memory and time efficiency in embedded systems.

In this article, we will explore two common approaches to solving the problem of bit reversal and examine how each approach balances the trade-offs between time latency and memory consumption.

Problem statement:

Let's say we need to reverse the bits of a 32-bit integer in an embedded system. For instance, given a number like 0x2941E9C (which is 00000010100101000001111010011100 in binary), we want to reverse its bit order. The problem created above might seem trivial, but in embedded systems, where performance and memory are often constrained, how we solve this problem can make a big difference.

Approach 1: Lookup Table:

A lookup table (LUT) is a precomputed array that stores the results of all possible values for a given operation—in this case, the reversed bits for all 256 possible byte values (since each byte can have a maximum of 8 bits).

How does it work?

A lookup table of 256 entries (one for each possible byte value) is created in memory.

For each byte in the 32-bit number, we simply use the lookup table to find the reversed bits of that byte and combine the results.

uint8_t lookupTable[256] = 
{ 0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0, 0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8, 0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4, 0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC, 0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2, 0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA, 0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6, 0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE, 0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1, 0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9, 0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5, 0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD, 0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3, 0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB, 0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7, 0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF
};

uint32_t reverseBitsUsingLookUp(uint32_t num) 
{
    return (lookupTable[num & 0xFF] << 24) | 
           (lookupTable[(num >> 8) & 0xFF] << 16) |
           (lookupTable[(num >> 16) & 0xFF] << 8) |
           (lookupTable[(num >> 24) & 0xFF]);
}        

Benefits:

• Time Efficiency: The bit reversal operation becomes a simple array lookup for each byte, which is extremely fast (constant time O(1) for each byte).
• Optimized for Performance: This method is ideal in applications where speed is critical, such as high-performance systems or real-time processing.

Drawbacks:

• Memory Usage: The lookup table requires 256 bytes of memory (for 256 possible 8-bit values). While this is manageable in many systems, it can be a significant overhead in memory-constrained environments like embedded systems, where every byte matters.
• Precomputation: It requires time to precompute the lookup table, and the table must be stored in memory during runtime.

Approach 2: Bitwise Operations (Iterative Method):

In this approach, we reverse the bits of the 32-bit number without using any lookup table. Instead, we perform bitwise shifts and logical operations (AND, OR) directly on each bit.

uint32_t reverseBits(uint32_t number)
{ 
    uint32_t reversednumber = 0;
    for(int i = 0; i < 32; i++)
    {
        reversednumber |= ((((number >> i) & 1) << (31 - i)));
    }
    return reversednumber;
}        

Benefits:

• Memory Efficiency: No extra memory is required, and we only use a few variables to store intermediate results. This approach is ideal for embedded systems with limited memory.
• No Precomputation: This method doesn't require precomputing and storing a lookup table, so it’s suitable for systems where memory usage is a higher priority than speed.

Drawbacks:

• Time Complexity: The time complexity is O(32) (linear time), as we need to process each of the 32 bits one by one. While this is still efficient, it’s slower than the constant-time lookup table approach, especially when dealing with a large number of bit reversals.

Conclusion:

When optimizing embedded systems, there is no one size-fits-all solution. The choice between using a lookup table or bitwise operations ultimately depends on the system's specific requirements:

The above example problem shows that often there are some cases in which an embedded developer has to decide in which direction he/she can go to write the most efficient code possible, considering time and memory constraints.

Call to Action:

Feel free to share your experiences or any alternative techniques you have used to tackle similar challenges in embedded systems development. Let's continue to learn from each other!