Quickly find whether a value is present in a C array?

Question

I have an embedded application with a time-critical ISR that needs to iterate through an array of size 256 (preferably 1024, but 256 is the minimum) and check if a value matches the arrays contents. A bool will be set to true is this is the case.

The microcontroller is an NXP LPC4357, ARM Cortex M4 core, and the compiler is GCC. I already have combined optimisation level 2 (3 is slower) and placing the function in RAM instead of flash. I also use pointer arithmetic and a for loop, which does down-counting instead of up (checking if i!=0 is faster than checking if i<256). All in all, I end up with a duration of 12.5 µs which has to be reduced drastically to be feasible. This is the (pseudo) code I use now:

uint32_t i;
uint32_t *array_ptr = &theArray[0];
uint32_t compareVal = 0x1234ABCD;
bool validFlag = false;

for (i=256; i!=0; i--)
{
    if (compareVal == *array_ptr++)
    {
         validFlag = true;
         break;
     }
}

What would be the absolute fastest way to do this? Using inline assembly is allowed. Other 'less elegant' tricks are also allowed.

Answer 1

In situations where performance is of utmost importance, the C compiler will most likely not produce the fastest code compared to what you can do with hand tuned assembly language. I tend to take the path of least resistance - for small routines like this, I just write asm code and have a good idea how many cycles it will take to execute. You may be able to fiddle with the C code and get the compiler to generate good output, but you may end up wasting lots of time tuning the output that way. Compilers (especially from Microsoft) have come a long way in the last few years, but they are still not as smart as the compiler between your ears because you're working on your specific situation and not just a general case. The compiler may not make use of certain instructions (e.g. LDM) that can speed this up, and it's unlikely to be smart enough to unroll the loop. Here's a way to do it which incorporates the 3 ideas I mentioned in my comment: Loop unrolling, cache prefetch and making use of the multiple load (ldm) instruction. The instruction cycle count comes out to about 3 clocks per array element, but this doesn't take into account memory delays.

Theory of operation: ARM's CPU design executes most instructions in one clock cycle, but the instructions are executed in a pipeline. C compilers will try to eliminate the pipeline delays by interleaving other instructions in between. When presented with a tight loop like the original C code, the compiler will have a hard time hiding the delays because the value read from memory must be immediately compared. My code below alternates between 2 sets of 4 registers to significantly reduce the delays of the memory itself and the pipeline fetching the data. In general, when working with large data sets and your code doesn't make use of most or all of the available registers, then you're not getting maximum performance.

; r0 = count, r1 = source ptr, r2 = comparison value

   stmfd sp!,{r4-r11}   ; save non-volatile registers
   mov r3,r0,LSR #3     ; loop count = total count / 8
   pld [r1,#128]
   ldmia r1!,{r4-r7}    ; pre load first set
loop_top:
   pld [r1,#128]
   ldmia r1!,{r8-r11}   ; pre load second set
   cmp r4,r2            ; search for match
   cmpne r5,r2          ; use conditional execution to avoid extra branch instructions
   cmpne r6,r2
   cmpne r7,r2
   beq found_it
   ldmia r1!,{r4-r7}    ; use 2 sets of registers to hide load delays
   cmp r8,r2
   cmpne r9,r2
   cmpne r10,r2
   cmpne r11,r2
   beq found_it
   subs r3,r3,#1        ; decrement loop count
   bne loop_top
   mov r0,#0            ; return value = false (not found)
   ldmia sp!,{r4-r11}   ; restore non-volatile registers
   bx lr                ; return
found_it:
   mov r0,#1            ; return true
   ldmia sp!,{r4-r11}
   bx lr

Update: There are a lot of skeptics in the comments who think that my experience is anecdotal/worthless and require proof. I used GCC 4.8 (from the Android NDK 9C) to generate the following output with optimization -O2 (all optimizations turned on including loop unrolling). I compiled the original C code presented in the question above. Here's what GCC produced:

.L9: cmp r3, r0
     beq .L8
.L3: ldr r2, [r3, #4]!
     cmp r2, r1
     bne .L9
     mov r0, #1
.L2: add sp, sp, #1024
     bx  lr
.L8: mov r0, #0
     b .L2

GCC's output not only doesn't unroll the loop, but also wastes a clock on a stall after the LDR. It requires at least 8 clocks per array element. It does a good job of using the address to know when to exit the loop, but all of the magical things compilers are capable of doing are nowhere to be found in this code. I haven't run the code on the target platform (I don't own one), but anyone experienced in ARM code performance can see that my code is faster.

Update 2: I gave Microsoft's Visual Studio 2013 SP2 a chance to do better with the code. It was able to use NEON instructions to vectorize my array initialization, but the linear value search as written by the OP came out similar to what GCC generated (I renamed the labels to make it more readable):

loop_top:
   ldr  r3,[r1],#4  
   cmp  r3,r2  
   beq  true_exit
   subs r0,r0,#1 
   bne  loop_top
false_exit: xxx
   bx   lr
true_exit: xxx
   bx   lr

As I said, I don't own the OP's exact hardware, but I will be testing the performance on an nVidia Tegra 3 and Tegra 4 of the 3 different versions and post the results here soon.

Update 3: I ran my code and Microsoft's compiled ARM code on a Tegra 3 and Tegra 4 (Surface RT, Surface RT 2). I ran 1000000 iterations of a loop which fails to find a match so that everything is in cache and it's easy to measure.

             My Code       MS Code
Surface RT    297ns         562ns
Surface RT 2  172ns         296ns  

In both cases my code runs almost twice as fast. Most modern ARM CPUs will probably give similar results.

Answer 2

There's a trick for optimizing it (I was asked this on a job-interview once):

• If the last entry in the array holds the value that you're looking for, then return true
• Write the value that you're looking for into the last entry in the array
• Iterate the array until you encounter the value that you're looking for
• If you've encountered it before the last entry in the array, then return true
• Return false

---

bool check(uint32_t theArray[], uint32_t compareVal)
{
    uint32_t i;
    uint32_t x = theArray[SIZE-1];
    if (x == compareVal)
        return true;
    theArray[SIZE-1] = compareVal;
    for (i = 0; theArray[i] != compareVal; i++);
    theArray[SIZE-1] = x;
    return i != SIZE-1;
}

This yields one branch per iteration instead of two branches per iteration.

---

UPDATE:

If you're allowed to allocate the array to SIZE+1, then you can get rid of the "last entry swapping" part:

bool check(uint32_t theArray[], uint32_t compareVal)
{
    uint32_t i;
    theArray[SIZE] = compareVal;
    for (i = 0; theArray[i] != compareVal; i++);
    return i != SIZE;
}

You can also get rid of the additional arithmetic embedded in theArray[i], using the following instead:

bool check(uint32_t theArray[], uint32_t compareVal)
{
    uint32_t *arrayPtr;
    theArray[SIZE] = compareVal;
    for (arrayPtr = theArray; *arrayPtr != compareVal; arrayPtr++);
    return arrayPtr != theArray+SIZE;
}

If the compiler doesn't already apply it, then this function will do so for sure. On the other hand, it might make it harder on the optimizer to unroll the loop, so you will have to verify that in the generated assembly code...

Answer 3

You're asking for help with optimising your algorithm, which may push you to assembler. But your algorithm (a linear search) is not so clever, so you should consider changing your algorithm. E.g.:

• perfect hash function
• binary search

Perfect hash function

If your 256 "valid" values are static and known at compile time, then you can use a perfect hash function. You need to find a hash function that maps your input value to a value in the range 0..n, where there are no collisions for all the valid values you care about. That is, no two "valid" values hash to the same output value. When searching for a good hash function, you aim to:

• Keep the hash function reasonably fast.
• Minimise n. The smallest you can get is 256 (minimal perfect hash function), but that's probably hard to achieve, depending on the data.

Note for efficient hash functions, n is often a power of 2, which is equivalent to a bitwise mask of low bits (AND operation). Example hash functions:

• CRC of input bytes, modulo n.
• ((x << i) ^ (x >> j) ^ (x << k) ^ ...) % n (picking as many i, j, k, ... as needed, with left or right shifts)

Then you make a fixed table of n entries, where the hash maps the input values to an index i into the table. For valid values, table entry i contains the valid value. For all other table entries, ensure that each entry of index i contains some other invalid value which doesn't hash to i.

Then in your interrupt routine, with input x:

1. Hash x to index i (which is in the range 0..n)
2. Look up entry i in the table and see if it contains the value x.

This will be much faster than a linear search of 256 or 1024 values.

I've written some Python code to find reasonable hash functions.

Binary search

If you sort your array of 256 "valid" values, then you can do a binary search, rather than a linear search. That means you should be able to search 256-entry table in only 8 steps (log2(256)), or a 1024-entry table in 10 steps. Again, this will be much faster than a linear search of 256 or 1024 values.

Answer 4

Keep the table in sorted order, and use Bentley's unrolled binary search:

i = 0;
if (key >= a[i+512]) i += 512;
if (key >= a[i+256]) i += 256;
if (key >= a[i+128]) i += 128;
if (key >= a[i+ 64]) i +=  64;
if (key >= a[i+ 32]) i +=  32;
if (key >= a[i+ 16]) i +=  16;
if (key >= a[i+  8]) i +=   8;
if (key >= a[i+  4]) i +=   4;
if (key >= a[i+  2]) i +=   2;
if (key >= a[i+  1]) i +=   1;
return (key == a[i]);

The point is,

• if you know how big the table is, then you know how many iterations there will be, so you can fully unroll it.
• Then, there's no point testing for the == case on each iteration because, except on the last iteration, the probability of that case is too low to justify spending time testing for it.**
• Finally, by expanding the table to a power of 2, you add at most one comparison, and at most a factor of two storage.

** If you're not used to thinking in terms of probabilities, every decision point has an entropy, which is the average information you learn by executing it. For the >= tests, the probability of each branch is about 0.5, and -log2(0.5) is 1, so that means if you take one branch you learn 1 bit, and if you take the other branch you learn one bit, and the average is just the sum of what you learn on each branch times the probability of that branch. So 1*0.5 + 1*0.5 = 1, so the entropy of the >= test is 1. Since you have 10 bits to learn, it takes 10 branches. That's why it's fast!

On the other hand, what if your first test is if (key == a[i+512)? The probability of being true is 1/1024, while the probability of false is 1023/1024. So if it's true you learn all 10 bits! But if it's false you learn -log2(1023/1024) = .00141 bits, practically nothing! So the average amount you learn from that test is 10/1024 + .00141*1023/1024 = .0098 + .00141 = .0112 bits. About one hundredth of a bit. That test is not carrying its weight!

Answer 5

If the set of constants in your table is known in advance, you can use perfect hashing to ensure that only one access is made to the table. Perfect hashing determines a hash function that maps every interesting key to a unique slot (that table isn't always dense, but you can decide how un-dense a table you can afford, with less dense tables typically leading to simpler hashing functions).

Usually, the perfect hash function for the specific set of keys is relatively easy to compute; you don't want that to be long and complicated because that competes for time perhaps better spent doing multiple probes.

Perfect hashing is a "1-probe max" scheme. One can generalize the idea, with the thought that one should trade simplicity of computing the hash code with the time it takes to make k probes. After all, the goal is "least total time to look up", not fewest probes or simplest hash function. However, I've never seen anybody build a k-probes-max hashing algorithm. I suspect one can do it, but that's likely research.

One other thought: if your processor is extremely fast, the one probe to memory from a perfect hash probably dominates the execution time. If the processor is not very fast, than k>1 probes might be practical.

Answer 6

Use a hash set. It will give O(1) lookup time.

The following code assumes that you can reserve value 0 as an 'empty' value, i.e. not occurring in actual data. The solution can be expanded for a situation where this is not the case.

#define HASH(x) (((x >> 16) ^ x) & 1023)
#define HASH_LEN 1024
uint32_t my_hash[HASH_LEN];

int lookup(uint32_t value)
{
    int i = HASH(value);
    while (my_hash[i] != 0 && my_hash[i] != value) i = (i + 1) % HASH_LEN;
    return i;
}

void store(uint32_t value)
{
    int i = lookup(value);
    if (my_hash[i] == 0)
       my_hash[i] = value;
}

bool contains(uint32_t value)
{
    return (my_hash[lookup(value)] == value);
}

In this example implementation, the lookup time will typically be very low, but at the worst case can be up to the number of entries stored. For a realtime application, you can consider also an implementation using binary trees, which will have a more predictable lookup time.

Answer 7

In this case, it might be worthwhile investigating Bloom filters. They're capable of quickly establishing that a value is not present, which is a good thing since most of the 2^32 possible values are not in that 1024 element array. However, there are some false positives that will need an extra check.

Since your table is apparently static, you can determine which false positives exist for your Bloom filter and put those in a perfect hash.

Answer 8

Assuming your processor runs at 204 MHz which seems to be the maximum for the LPC4357, and also assuming your timing result reflects the average case (half of the array traversed), we get:

• CPU frequency: 204 MHz
• Cycle period: 4.9 ns
• Duration in cycles: 12.5 µs / 4.9 ns = 2551 cycles
• Cycles per iteration: 2551 / 128 = 19.9

So, your search loop spends around 20 cycles per iteration. That doesn't sound awful, but I guess that in order to make it faster you need to look at the assembly.

I would recommend dropping the index and using a pointer comparison instead, and making all the pointers const.

bool arrayContains(const uint32_t *array, size_t length)
{
  const uint32_t * const end = array + length;
  while(array != end)
  {
    if(*array++ == 0x1234ABCD)
      return true;
  }
  return false;
}

That's at least worth testing.

Answer 9

Other people have suggested reorganizing your table, adding a sentinel value at the end, or sorting it in order to provide a binary search.

You state "I also use pointer arithmetic and a for loop, which does down-counting instead of up (checking if i != 0 is faster than checking if i < 256)."

My first advice is: get rid of the pointer arithmetic and the downcounting. Stuff like

for (i=0; i<256; i++)
{
    if (compareVal == the_array[i])
    {
       [...]
    }
}

tends to be idiomatic to the compiler. The loop is idiomatic, and the indexing of an array over a loop variable is idiomatic. Juggling with pointer arithmetic and pointers will tend to obfuscate the idioms to the compiler and make it generate code related to what you wrote rather than what the compiler writer decided to be the best course for the general task.

For example, the above code might be compiled into a loop running from -256 or -255 to zero, indexing off &the_array[256]. Possibly stuff that is not even expressible in valid C but matches the architecture of the machine you are generating for.

So don't microoptimize. You are just throwing spanners into the works of your optimizer. If you want to be clever, work on the data structures and algorithms but don't microoptimize their expression. It will just come back to bite you, if not on the current compiler/architecture, then on the next.

In particular using pointer arithmetic instead of arrays and indexes is poison for the compiler being fully aware of alignments, storage locations, aliasing considerations and other stuff, and for doing optimizations like strength reduction in the way best suited to the machine architecture.

Answer 10

Vectorization can be used here, as it is often is in implementations of memchr. You use the following algorithm:

1. Create a mask of your query repeating, equal in length to your OS'es bit count (64-bit, 32-bit, etc.). On a 64-bit system you would repeat the 32-bit query twice.

2. Process the list as a list of multiple pieces of data at once, simply by casting the list to a list of a larger data type and pulling values out. For each chunk, XOR it with the mask, then XOR with 0b0111...1, then add 1, then & with a mask of 0b1000...0 repeating. If the result is 0, there is definitely not a match. Otherwise, there may (usually with very high probability) be a match, so search the chunk normally.

Example implementation: https://sourceware.org/cgi-bin/cvsweb.cgi/src/newlib/libc/string/memchr.c?rev=1.3&content-type=text/x-cvsweb-markup&cvsroot=src

Answer 11

If you can accommodate the domain of your values with the amount of memory that's available to your application, then, the fastest solution would be to represent your array as an array of bits:

bool theArray[MAX_VALUE]; // of which 1024 values are true, the rest false
uint32_t compareVal = 0x1234ABCD;
bool validFlag = theArray[compareVal];

EDIT

I'm astounded by the number of critics. The title of this thread is "How do I quickly find whether a value is present in a C array?" for which I will stand by my answer because it answers precisely that. I could argue that this has the most speed efficient hash function (since address === value). I've read the comments and I'm aware of the obvious caveats. Undoubtedly those caveats limit the range of problems this can be used to solve, but, for those problems that it does solve, it solves very efficiently.

Rather than reject this answer outright, consider it as the optimal starting point for which you can evolve by using hash functions to achieve a better balance between speed and performance.

Answer 12

I'm sorry if my answer was already answered - just I'm a lazy reader. Feel you free to downvote then ))

1) you could remove counter 'i' at all - just compare pointers, ie

for (ptr = &the_array[0]; ptr < the_array+1024; ptr++)
{
    if (compareVal == *ptr)
    {
       break;
    }
}
... compare ptr and the_array+1024 here - you do not need validFlag at all.

all that won't give any significant improvement though, such optimization probably could be achieved by the compiler itself.

2) As it was already mentioned by other answers, almost all modern CPU are RISC-based, for example ARM. Even modern Intel X86 CPUs use RISC cores inside, as far as I know (compiling from X86 on fly). Major optimization for RISC is pipeline optimization (and for Intel and other CPU as well), minimizing code jumps. One type of such optimization (probably a major one), is "cycle rollback" one. It's incredibly stupid, and efficient, even Intel compiler can do that AFAIK. It looks like:

if (compareVal == the_array[0]) { validFlag = true; goto end_of_compare; }
if (compareVal == the_array[1]) { validFlag = true; goto end_of_compare; }
...and so on...
end_of_compare:

This way the optimization is that the pipeline is not broken for the worst case (if compareVal is absent in the array), so it is as fast as possible (of course not counting algorithm optimizations such as hash tables, sorted arrays and so on, mentioned in other answers, which may give better results depending on array size. Cycles Rollback approach can be applied there as well by the way. I'm writing here about that I think I didn't see in others)

The second part of this optimization is that that array item is taken by direct address (calculated at compiling stage, make sure you use a static array), and do not need additional ADD op to calculate pointer from array's base address. This optimization may not have significant effect, since AFAIK ARM architecture has special features to speed up arrays addressing. But anyway it's always better to know that you did all the best just in C code directly, right?

Cycle Rollback may look awkward due to waste of ROM (yep, you did right placing it to fast part of RAM, if your board supports this feature), but actually it's a fair pay for speed, being based on RISC concept. This is just a general point of calculation optimization - you sacrifice space for sake of speed, and vice versa, depending on your requirements.

If you think that rollback for array of 1024 elements is too large sacrifice for your case, you can consider 'partial rollback', for example dividing the array into 2 parts of 512 items each, or 4x256, and so on.

3) modern CPU often support SIMD ops, for example ARM NEON instruction set - it allows to execute the same ops in parallel. Frankly speaking I do not remember if it is suitable for comparison ops, but I feel it may be, you should check that. Googling shows that there may be some tricks as well, to get max speed, see https://stackoverflow.com/a/5734019/1028256

I hope it can give you some new ideas.

Answer 13

This is more like an addendum than an answer.

I've had a similar case in the past, but my array was constant over a considerable number of searches.

In half of them, the searched value was NOT present in array. Then I realized I could apply a "filter" before doing any search.

This "filter" is just a simple integer number, calculated ONCE and used in each search.

It's in Java, but it's pretty simple:

binaryfilter = 0;
for (int i = 0; i < array.length; i++)
{
    // just apply "Binary OR Operator" over values.
    binaryfilter = binaryfilter | array[i];
}

So, before do a binary search, I check binaryfilter:

// Check binaryfilter vs value with a "Binary AND Operator"
if ((binaryfilter & valuetosearch) != valuetosearch)
{
    // valuetosearch is not in the array!
    return false;
}
else
{
    // valuetosearch MAYBE in the array, so let's check it out
    // ... do binary search stuff ...

}

You can use a 'better' hash algorithm, but this can be very fast, specially for large numbers. May be this could save you even more cycles.

Answer 14

Make sure the instructions ("the pseudo code") and the data ("theArray") are in separate (RAM) memories so CM4 Harvard architecture is utilized to its full potential. From the user manual:

To optimize the CPU performance, the ARM Cortex-M4 has three buses for Instruction (code) (I) access, Data (D) access, and System (S) access. When instructions and data are kept in separate memories, then code and data accesses can be done in parallel in one cycle. When code and data are kept in the same memory, then instructions that load or store data may take two cycles.

Following this guideline I observed ~30% speed increase (FFT calculation in my case).

Answer 15

I'm a great fan of hashing. The problem of course is to find an efficient algorithm that is both fast and uses a minimum amount of memory (especially on an embedded processor).

If you know beforehand the values that may occur you can create a program that runs through a multitude of algorithms to find the best one - or, rather, the best parameters for your data.

I created such a program that you can read about in this post and achieved some very fast results. 16000 entries translates roughly to 2^14 or an average of 14 comparisons to find the value using a binary search. I explicitly aimed for very fast lookups - on average finding the value in <=1.5 lookups - which resulted in greater RAM requirements. I believe that with a more conservative average value (say <=3) a lot of memory could be saved. By comparison the average case for a binary search on your 256 or 1024 entries would result in an average number of comparisons of 8 and 10, respectively.

My average lookup required around 60 cycles (on a laptop with an intel i5) with a generic algorithm (utilizing one division by a variable) and 40-45 cycles with a specialized (probably utilizing a multiplication). This should translate into sub-microsecond lookup times on your MCU, depending of course on the clock frequency it executes at.

It can be real-life-tweaked further if the entry array keeps track of how many times an entry was accessed. If the entry array is sorted from most to least accessed before the indeces are computed then it'll find the most commonly occuring values with a single comparison.