# C++: Can this be optimized?

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Greetings, I'm working on an AES implementation (http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf). It works fine and I'm using it in the implementation of some other signal processing. Now, I'm trying to optimize the most cycle intesive parts of it. It boils down to the polynomial multiplication that's eating up over half of all my cycles for my entire signal processing. Here's the code snippet:
uint8_t Aes::Mult(uint8_t inputA, uint8_t inputB)
{
uint16_t temp = 0;

// Polynomial multiplication.
for (uint16_t bitCnt = 0; bitCnt < 8; bitCnt++)
{
if ((inputA >> bitCnt) & 0x01)
{
temp ^= (inputB << bitCnt);
}
}

// Modulo reduction.
for (uint16_t bitCnt = 15; bitCnt > 7; bitCnt--)
{
if ((temp >> bitCnt) & 0x01)
{
temp ^= (m_IrreduciblePolynomial << (bitCnt - 8));
}
}

// Result should now fit within a byte after the modulo reduction.
return static_cast<uint8_t>(temp);
}

I can't come up with any other tricks. The compiler (for an embedded platform) must be doing a pretty decent job, because anything I try just makes it worse. Any insights would be appreciated. Thanks!

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Use a lookup table that maps every number in the range 0-255 to a list of integers in the range 0-7. The numbers in this list represent positions of 1-bits. So, take the number 147. This is 10010011. So your lookup table for entry 147 would contain the following array: {0, 1, 4, 7}. This comes from the fact that entries 0, 1, 4, and 7 contain 1 bits. (For the record, I'm amazed that the positions of 1 bits are spell out the number in decimal. What a strange coincidence!)

Then the loop becomes the following.

int* indices = mapping[inputA];for (int i=0; i < listlength; ++i){   temp ^= (inputB << indices[i]);}

Of course we need to know how many items are in the list since it's different for every number. So make a *second* array that maps each integer in the range 0-255 to a single integer that is the number of 1 bits. This way in your multi-dimensional array all the inner arrays can have exactly 8 items so it's rectangular. The code then becomes this:

int length = lengths[inputA];int* indices = mapping[inputA];for (int i=0; i < length; ++i){   temp ^= (inputB << mapping[i]);}

This removes one of the conditionals, but still has another conditional in it (the loop termination test), that is executed for every item in the list. We'd like to remove that. For this you can use a switch statement with a fallthrough. In a more general case you'd use Duff's Device, but since there's only a max of 8 possible values of listlength, it's easier.

int length = lengths[inputA];int* indices = mapping[inputA];switch (length){case 8:   temp ^= (inputB << *indices++);case 7:   temp ^= (inputB << *indices++);case 6:   temp ^= (inputB << *indices++);case 5:   temp ^= (inputB << *indices++);case 4:   temp ^= (inputB << *indices++);case 3:   temp ^= (inputB << *indices++);case 2:   temp ^= (inputB << *indices++);case 1:   temp ^= (inputB << *indices++);}

This is basically just an unrolled loop. Now you've gotten the entire loop, which previously had 16 conditionals, down to a single conditional just to determine where in the switch statement to jump to.

Do the same thing for the other loop.

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unsigned char FFMul(unsigned char a, unsigned char b) {   unsigned char aa = a, bb = b, r = 0, t;   while (aa != 0) {      if ((aa & 1) != 0)         r = r ^ bb;      t = bb & 0x80;      bb = bb << 1;      if (t != 0)         bb = bb ^ 0x1b;      aa = aa >> 1;    }   return r;}

Source.

On a PC, this version takes half the time. Anything more is impossible to compare, branch and memory performance between PC and embedded platforms simply differ too much.

Also, depending on memory - if speed really is at premium, consider making a pre-calculated table. It's 64kilobytes, but then multiplication will be just a memory access - 'mult = tab[a][b];'

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Depending on your target platform/compiler, doing arithmetic on 8/16 bit integers will cause lots of useless masking and sign extension. If the platform has 32 bit registers, use 32 bit ints for all internal operations even if member variables/parameters want to be 8/16 bit.

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Can't you just precompute a 64-Kbyte table with all the results? I doubt you can do faster than that.

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Quote:
 Original post by alvaroCan't you just precompute a 64-Kbyte table with all the results? I doubt you can do faster than that.

Since it's an embedded environment, this probably wouldn't be possible. I'd be surprised if the method I gave above wasn't significantly faster though. Precomputing the whole table is obviously the fastest though if possible.

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Precomputing a 64kB table would be prohibitive. The system only has 1MB internal memory which is divided into cache (256kB), BIOS/drivers, and general use (about 650kB). Putting the table into internal memory would eat up 10% of available resources, and putting it in external memory could trash what little (and very precious) cache I have.

@ Antheus: very nice link. I'll have to see what the compiler does with that. Also, your link has a second solution, FFMulFast(), that uses two 256 byte lookup tables and a couple conditional checks.
uint8_t FFMulFast(uint8_t a, uint8_t b){   uint16_t t = 0;   if (a == 0 || b == 0) return 0;   t = L[a] + L[b];   if (t > 255) t = t - 255;   return E[t];}

Where L and E are the two 256 byte LUTs. That should prove to be even better. I can easily support tables that size.

I'll try the various methods tomorrow and let you guys know what happens. Thanks everyone!

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I implemented three versions of this multiplication under MSVC2008.
Version 1 - my original implementation
Version 2 - Antheus version
Version 3 - second method provided by the link Antheus posted (uses 2, 256-byte LUTs)

Here are the results:

DEBUG
-----
Correctness Test: Same = 65536, Different = 0

Performance Test (10000000 iterations):
Method 1: Output (ignore) = 10, Duration = 2.56581 seconds.
Method 2: Output (ignore) = 130, Duration = 1.91427 seconds.
Method 3: Output (ignore) = 84, Duration = 0.785167 seconds.

RELEASE
-------
Correctness Test: Same = 65536, Different = 0

Performance Test (10000000 iterations):
Method 1: Output (ignore) = 172, Duration = 1.44255 seconds.
Method 2: Output (ignore) = 25, Duration = 1.04715 seconds.
Method 3: Output (ignore) = 21, Duration = 0.388543 seconds.

The first pass, the Correctness Test, makes sure that for all inputs A (0-255) and B (0-255), the outputs of all three methods are the same. The performance tests iterate through each method 10,000,000 times. Each method has a unique set of input and output vectors (10 million A and B inputs for each method). To keep the optimizer from cheating, I output a random selection from each output vector (the "Output (ignore)" in the print status).

Built and ran the tests under both Debug and Release builds (standard Debug and Release settings, nothing changed from the default MSVC2008 settings for those).

I'll do these same tests under my embedded environment and post what I get there. Here's the sample code I used under MSVC2008.
#include "stdafx.h"#include "windows.h"#include <ctime>#include <iostream>unsigned short m_IrreduciblePolynomial = 0x011b;unsigned char Exp[256] = {0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff, 0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35,0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4, 0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa, 0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26, 0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31, 0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc, 0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd, 0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7, 0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88, 0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f, 0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a, 0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0, 0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3, 0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec, 0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0, 0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2, 0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41, 0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0, 0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75, 0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e, 0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80, 0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf, 0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54, 0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09, 0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca, 0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91, 0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e, 0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c, 0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17, 0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd, 0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6, 0x01};unsigned char Log[256] = {0x00, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1a, 0xc6, 0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee, 0xdf, 0x03, 0x64, 0x04, 0xe0, 0x0e, 0x34, 0x8d, 0x81, 0xef, 0x4c, 0x71, 0x08, 0xc8, 0xf8, 0x69, 0x1c, 0xc1, 0x7d, 0xc2, 0x1d, 0xb5, 0xf9, 0xb9, 0x27, 0x6a, 0x4d, 0xe4, 0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78, 0x65, 0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24, 0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda, 0x8e, 0x96, 0x8f, 0xdb, 0xbd, 0x36, 0xd0, 0xce, 0x94, 0x13, 0x5c, 0xd2, 0xf1, 0x40, 0x46, 0x83, 0x38, 0x66, 0xdd, 0xfd, 0x30, 0xbf, 0x06, 0x8b, 0x62, 0xb3, 0x25, 0xe2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7e, 0x6e, 0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42, 0x3a, 0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba, 0x2b, 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e, 0xca, 0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73, 0xa7, 0x57, 0xaf, 0x58, 0xa8, 0x50, 0xf4, 0xea, 0xd6, 0x74, 0x4f, 0xae, 0xe9, 0xd5, 0xe7, 0xe6, 0xad, 0xe8, 0x2c, 0xd7, 0x75, 0x7a, 0xeb, 0x16, 0x0b, 0xf5, 0x59, 0xcb, 0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0, 0x7f, 0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec, 0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b, 0xb7, 0xcc, 0xbb, 0x3e, 0x5a, 0xfb, 0x60, 0xb1, 0x86, 0x3b, 0x52, 0xa1, 0x6c, 0xaa, 0x55, 0x29, 0x9d, 0x97, 0xb2, 0x87, 0x90, 0x61, 0xbe, 0xdc, 0xfc, 0xbc, 0x95, 0xcf, 0xcd, 0x37, 0x3f, 0x5b, 0xd1, 0x53, 0x39, 0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47, 0x14, 0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab, 0x44, 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e, 0x89, 0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99, 0xe3, 0xa5, 0x67, 0x4a, 0xed, 0xde, 0xc5, 0x31, 0xfe, 0x18, 0x0d, 0x63, 0x8c, 0x80, 0xc0, 0xf7, 0x70, 0x07};unsigned char Mult1(unsigned char inputA, unsigned char inputB){    //////////////	// Method 1 //	//////////////	unsigned short temp = 0;    // Polynomial multiplication.    for (unsigned short bitCnt = 0; bitCnt < 8; bitCnt++)    {        if ((inputA >> bitCnt) & 0x01)        {            temp ^= (inputB << bitCnt);        }    }    // Modulo reduction.    for (unsigned short bitCnt = 15; bitCnt > 7; bitCnt--)    {        if ((temp >> bitCnt) & 0x01)        {            temp ^= (m_IrreduciblePolynomial << (bitCnt - 8));        }    }    // Result should now fit within a byte after the modulo reduction.    return static_cast<unsigned char>(temp);}unsigned char Mult2(unsigned char inputA, unsigned char inputB){    //////////////	// Method 2 //	//////////////	unsigned char aa = inputA, bb = inputB, r = 0, t;		while (aa != 0)	{		if ((aa & 1) != 0)			r = r ^ bb;		t = bb & 0x80;		bb = bb << 1;		if (t != 0)			bb = bb ^ 0x1b;				aa = aa >> 1;    }   	return r;}unsigned char Mult3(unsigned char inputA, unsigned char inputB){    //////////////	// Method 3 //	//////////////	unsigned short t = 0;	if (inputA == 0 || inputB == 0)		return 0;	t = Log[inputA] + Log[inputB];	if (t > 255)		t = t - 255;	return Exp[t];}int _tmain(int argc, _TCHAR* argv[]){	LARGE_INTEGER proc_freq;	QueryPerformanceFrequency(&proc_freq);	double frequency = (1.0 / static_cast<double>(proc_freq.QuadPart));		LARGE_INTEGER start;	LARGE_INTEGER stop;	double diff;	unsigned char output1;	unsigned char output2;	unsigned char output3;	int same = 0;	int different = 0;	int iterations = 10000000;	unsigned char* inputArrayA1 = new unsigned char[iterations];	unsigned char* inputArrayA2 = new unsigned char[iterations];	unsigned char* inputArrayA3 = new unsigned char[iterations];	unsigned char* inputArrayB1 = new unsigned char[iterations];	unsigned char* inputArrayB2 = new unsigned char[iterations];	unsigned char* inputArrayB3 = new unsigned char[iterations];	unsigned char* outputArray1 = new unsigned char[iterations];	unsigned char* outputArray2 = new unsigned char[iterations];	unsigned char* outputArray3 = new unsigned char[iterations];	srand(static_cast<unsigned int>(time(NULL)));	for (int i = 0; i < iterations; i++)	{		inputArrayA1[i] = rand();		inputArrayA2[i] = rand();		inputArrayA3[i] = rand();		inputArrayB1[i] = rand();		inputArrayB2[i] = rand();		inputArrayB3[i] = rand();	}		// Correctness test.	for (int i = 0; i < 256; i++)	{		for (int j = 0; j < 256; j++)		{			output1 = Mult1(static_cast<unsigned char>(i), static_cast<unsigned char>(j));			output2 = Mult2(static_cast<unsigned char>(i), static_cast<unsigned char>(j));			output3 = Mult3(static_cast<unsigned char>(i), static_cast<unsigned char>(j));			if ((output1 == output2) && (output2 == output3))			{				same++;			}			else			{				different++;			}		}	}	std::cout << "Correctness Test: Same = " << same << ", Different = " << different << std::endl << std::endl;			// Performance test.	std::cout << "Performance Test (" << iterations << " iterations):" << std::endl;	QueryPerformanceCounter(&start);	for (int i = 0; i < iterations; i++)	{		outputArray1[i] = Mult1(inputArrayA1[i], inputArrayB1[i]);	}	QueryPerformanceCounter(&stop);	diff = (stop.QuadPart - start.QuadPart) * frequency;	std::cout << "Method 1: Output (ignore) = " << static_cast<unsigned short>(outputArray1[rand() % iterations]) << ", Duration = " << diff << " seconds." << std::endl;	QueryPerformanceCounter(&start);	for (int i = 0; i < iterations; i++)	{		outputArray2[i] = Mult2(inputArrayA2[i], inputArrayB2[i]);	}	QueryPerformanceCounter(&stop);	diff = (stop.QuadPart - start.QuadPart) * frequency;	std::cout << "Method 2: Output (ignore) = " << static_cast<unsigned short>(outputArray2[rand() % iterations]) << ", Duration = " << diff << " seconds." << std::endl;	QueryPerformanceCounter(&start);	for (int i = 0; i < iterations; i++)	{		outputArray3[i] = Mult3(inputArrayA3[i], inputArrayB3[i]);	}	QueryPerformanceCounter(&stop);	diff = (stop.QuadPart - start.QuadPart) * frequency;	std::cout << "Method 3: Output (ignore) = " << static_cast<unsigned short>(outputArray3[rand() % iterations]) << ", Duration = " << diff << " seconds." << std::endl;	delete[] outputArray1;	delete[] outputArray2;	delete[] outputArray3;	delete[] inputArrayA1;	delete[] inputArrayA2;	delete[] inputArrayA3;	delete[] inputArrayB1;	delete[] inputArrayB2;	delete[] inputArrayB3;	return 0;}

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Some interesting results on the embedded side of things. Running all three methods through my embedded testbench, I get the following:

Method 1: Mult() cycles = 8,134,008, total system run-time = 23.157ms
Method 2: Mult() cycles = 3,912,233, total system run-time = 16.124ms
Method 3: Mult() cycles = 5,823,237, total system run-time = 19.307ms

As you can see, this multiplication was taking a large portion of my total system run-time. Of the 23.157ms, Mult() was taking 13.550ms on Method 1 which is well over half the total run-time. Method 2 reduces this to 6.517ms and Method 3 reduces it to 9.700ms

On the embedded system, Method 3 is actually slower than Method 2. Looking at the generated assembly, the compiler created the same number of instructions, but was able to pipeline the instructions more for Method 2 than Method 3. A little surprising, but nice, since Method 2 uses less memory than Method 3.

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All of the new methods still use a lot of nested conditionals. I'd be interested to see how the method I posted performs, although it may no longer be a bottleneck with your new implementation and not worth testing further. The 2 lookup tables I mentioned are pretty easy to pre-compute with a simple program that counts 1-bits and spits them out. Then just copy/paste it into your source.

Also, compilers usually optimize if-then statements for the "true" case. That is, you will have more successful branch predictions if the conditions evaluate to true more often than they evaluate to false. You could profile how often they evaluate to true vs false and make sure they're written correctly. If you do a profile-guided optimization in Visual Studio, I think it will do this for you.

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@cache_hit: I've implemented your method (Method 4), replacing the first loop of Method 1 with your suggestion. I couldn't figure out how to apply it to the second loop, as the value used to check if a bit is set or not is the same value being XOR-ed, so it changes as the algorithm runs.

Here are the results. I'm re-running all of the Win32 data since I'm on a different machine now. Original machine was an Athlon 64 desktop, current machine is a Core 2 Duo laptop.

Win32
=====
DEBUG
-----
Correctness Test: Same = 65536, Different = 0

Performance Test (10000000 iterations):
Method 1: Output (ignore) = 99, Duration = 1.87773 seconds.
Method 2: Output (ignore) = 165, Duration = 1.66733 seconds.
Method 3: Output (ignore) = 137, Duration = 0.538485 seconds.
Method 4: Output (ignore) = 239, Duration = 1.56202 seconds.
Method 5: Output (ignore) = 224, Duration = 0.423876 seconds.

RELEASE
-------
Correctness Test: Same = 65536, Different = 0

Performance Test (10000000 iterations):
Method 1: Output (ignore) = 200, Duration = 1.28909 seconds.
Method 2: Output (ignore) = 69, Duration = 0.772024 seconds.
Method 3: Output (ignore) = 64, Duration = 0.0904632 seconds.
Method 4: Output (ignore) = 155, Duration = 0.798899 seconds.
Method 5: Output (ignore) = 15, Duration = 0.03105 seconds.

Embedded (release build)
========
Method 1: Mult() cycles = 8,134,008, total system run-time = 23.157ms
Method 2: Mult() cycles = 3,912,233, total system run-time = 16.124ms
Method 3: Mult() cycles = 5,823,237, total system run-time = 19.307ms
Method 4: Mult() cycles = 10,931,047, total system run-time = 27.564ms
Method 5: Mult() cycles = 4,599,964, total system run-time = 31.605ms

Under Win32, your method is on par with Method 2, winning under Debug but losing slightly under Release. Method 3 is still the clear winner under Win32.

Under the embedded environment, your method seems to tank. The assembly output shows absolutely no pipelining happening during the Duff's Device switch/case fall-through code. It even throws in a couple NOPs per case. Chalk it up to a bad compiler, I guess. Method 2 still gives a great improvement over my original implementation, though.

My approach is going to be keeping all 4 methods available. A simple #define MULT_METHOD based off the build environment (WIN32_SUPPORT, EMBEDDED_SUPPORT, etc) to select which mutliplcation method to use. Win32 will use MULT_METHOD 3, embedded with use MULT_METHOD 2, etc. Each new platform the code moves to will have to check which method is best and #define the appropriate MULT_METHOD.

*EDIT: Added the 64k LUT as Method 5. Up to 3x faster than the next best under Win32 Release, but you do take the 64kB table hit. It doesn't fare as well under the embedded. Cycle count is 2nd best, but the overall time is the worste, most likely due to cache problems causing the cycle counts of other methods to increase.

[Edited by - Mantear on September 10, 2009 1:26:22 PM]

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Quote:
 Original post by MantearUnder Win32, your method is on par with Method 2, winning under Debug but losing slightly under Release. Method 3 is still the clear winner under Win32.

Why not use 64k table under Win32? Memory is not an issue, but cache might be.

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Updated previous post to include Method 5: 64k LUT.

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Quote:
 Under Win32, your method is on par with Method 2, winning under Debug but losing slightly under Release. Method 3 is still the clear winner under Win32.Under the embedded environment, your method seems to tank. The assembly output shows absolutely no pipelining happening during the Duff's Device switch/case fall-through code. It even throws in a couple NOPs per case. Chalk it up to a bad compiler, I guess. Method 2 still gives a great improvement over my original implementation, though.My approach is going to be keeping all 4 methods available. A simple #define MULT_METHOD based off the build environment (WIN32_SUPPORT, EMBEDDED_SUPPORT, etc) to select which mutliplcation method to use. Win32 will use MULT_METHOD 3, embedded with use MULT_METHOD 2, etc. Each new platform the code moves to will have to check which method is best and #define the appropriate MULT_METHOD.

Interesting results. Just goes to show the importance of profiling (as well as the fun of optimization)

I'm a bit amazed that the 64K look-up table is the slowest on the embedded build? That's weird, it should just be one instruction to fetch the result from the look up table.

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Also I just thought of another optimization. Since you said the problem was that no pipelining was happening in the implementation I proposed, it's possible to force the compiler to pipeline it.

Instead of embedding the indices into the *beginning* of the array, embed them starting from the position i=8-length. So the example I gave 0,1,4,7 there are 4 1-bits, so i=8-4=4, so you begin embedding the list 0,1,4,7 at index 4. So the indices array for the number 147 looks like {-1,-1,-1,-1,0,1,4,7}. Then your switch statement becomes:

switch (length){case 8:   temp ^= (inputB << indices[0]);case 7:   temp ^= (inputB << indices[1]);case 6:   temp ^= (inputB << indices[2]);case 5:   temp ^= (inputB << indices[3]);case 4:   temp ^= (inputB << indices[4]);case 3:   temp ^= (inputB << indices[5]);case 2:   temp ^= (inputB << indices[6]);case 1:   temp ^= (inputB << indices[7]);}

This should get pipelined more effectively.

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Quote:
 Original post by MantearUpdated previous post to include Method 5: 64k LUT.

What kind of embedded system is this? Looks like just a small L1 cache, if that at all.

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It's a TI DSP, C6416, 600MHz. It has 1MB internal memory, which can be divided several ways, and 32MB external SDRAM. 256kB of the internal memory is set as L1 Cache, several other chunks are allocated for the DSP BIOS (the 'operating system' for TI DSPs) and PCI interface buffers, etc, with the remaining 650kB left over for heap + stack. All instruction code is stored in the SDRAM and the only thing that gets cached, so it's pretty important to keep the most used execution paths loaded in the cache. Heap + stack is always at cache speeds in the remaining 650kB space.

@ cache_hit: I may give your new suggestion a try, but I doubt it'll work. It was generating zero pipelining during the switch/case fall through, and actually threw in 2 NOPs per case. Pipelining is actually shown in the generated assembly output, so it's easy to tell. Constructs like Duff's Device aren't usually usefull for signal processing, so I wouldn't be suprised if the compiler doesn't handle it well.

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Yea I guess that makes sense, it can't modify the same register with 2 different instructions at the same time. It's still doable since XOR is associative and commutative, but it would require you to use either 2 or 4 different registers and alternate which variable you're XORing into in each case label, then at the end combine them. Doubt it's worth the trouble though, the other methods are already pretty fast.

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