How to do parallel operation with if condition in Neon intrinsics? - arm

I have asked a question for vclt_s8 comparation.
Does anybody know how to use Neon intrinsics uint8x8_t vclt_s8 (int8x8_t, int8x8_t)
However, if we have such code:
if(a > b + c) {
a = b + c;
} else if(a < b - c) {
a = b - c;
}
How can I transform it to Neon intrinsics? It seems that we can not do 8 operator parallel operation in such case. Isn't it?

Obviously you can't do branching with SIMD, so you have to look at how do implement this kind of logic in a branchless way, using masks. I'll just give pseudo code, so you get the general idea - coding this should be fairly straightforward:
bc = b + c ; get `(b + c)` in a vector register
mask = a > bc ; use compare instruction to generate mask (-1 = true, 0 = false)
bc = bc & mask ; use bitwise AND to zero out elements of `(b + c)` which we do not want
a = a & ~mask ; use bitwise ANDC to zero out elements of `a` which we do not want
a = a | bc ; combine required elements into `a` using bitwise OR
bc = b - c ; get `(b - c)` in a vector register
mask = a < bc ; use compare instruction to generate mask (-1 = true, 0 = false)
bc = bc & mask ; use bitwise AND to zero out elements of `(b - c)` which we do not want
a = a & ~mask ; use bitwise ANDC to zero out elements of `a` which we do not want
a = a | bc ; combine required elements into `a` using bitwise OR
Note that I've cheated a little here and omitted the else from your scalar code (assuming that the two branches are mutually exclusive) so what I've implemented is actually equivalent to:
if (a > b + c) {
a = b + c;
}
if (a < b - c) {
a = b - c;
}
If this is a bad assumption then you'll need to do some additional bitwise operations to implement the logical else.

Related

Solving a large system of linear equations over the finite field F2

I have 10163 equations and 9000 unknowns, all over finite fields, like this style:
Of course my equation will be much larger than this, I have 10163 rows and 9000 different x.
Presented in the form of a matrix is AX=B. A is a 10163x9000 coefficient matrix and it may be sparse, X is a 9000x1 unknown vector, B is the result of their multiplication and mod 2.
Because of the large number of unknowns that need to be solved for, it can be time consuming. I'm looking for a faster way to solve this system of equations using C language.
I tried to use Gaussian elimination method to solve this equation, In order to make the elimination between rows more efficient, I store the matrix A in a 64-bit two-dimensional array, and let the last column of the array store the value of B, so that the XOR operation may reduce the calculating time.
The code I am using is as follows:
uint8_t guss_x_main[R_BITS] = {0};
uint64_t tmp_guss[guss_j_num];
for(uint16_t guss_j = 0; guss_j < x_weight; guss_j++)
{
uint64_t mask_1 = 1;
uint64_t mask_guss = (mask_1 << (guss_j % GUSS_BLOCK));
uint16_t eq_j = guss_j / GUSS_BLOCK;
for(uint16_t guss_i = guss_j; guss_i < R_BITS; guss_i++)
{
if((mask_guss & equations_guss_byte[guss_i][eq_j]) != 0)
{
if(guss_x_main[guss_j] == 0)
{
guss_x_main[guss_j] = 1;
for(uint16_t change_i = 0; change_i < guss_j_num; change_i++)
{
tmp_guss[change_i] = equations_guss_byte[guss_j][change_i];
equations_guss_byte[guss_j][change_i] =
equations_guss_byte[guss_i][change_i];
equations_guss_byte[guss_i][change_i] = tmp_guss[change_i];
}
}
else
{
GUARD(xor_64(equations_guss_byte[guss_i], equations_guss_byte[guss_i],
equations_guss_byte[guss_j], guss_j_num));
}
}
}
for(uint16_t guss_i = 0; guss_i < guss_j; guss_i++)
{
if((mask_guss & equations_guss_byte[guss_i][eq_j]) != 0)
{
GUARD(xor_64(equations_guss_byte[guss_i], equations_guss_byte[guss_i],
equations_guss_byte[guss_j], guss_j_num));
}
}
}
R_BIT = 10163, x_weight = 9000, GUSS_BLOCK = 64, guss_j_num = x_weight / GUSS_BLOCK + 1; equations_guss_byte is a two-dimensional array of uint64, where x_weight / GUSS_BLOCK column stores the matrix A and the latter column stores the vector B, xor_64() is used to XOR two arrays, GUARD() is used to check the correctness of function operation.
Using this method takes about 8 seconds to run on my machine. Is there a better way to speed up the calculation?

Efficient C vectors for generic SIMD (SSE, AVX, NEON) test for zero matches. (find FP max absolute value and index)

I want to see if it's possible to write some generic SIMD code that can compile efficiently. Mostly for SSE, AVX, and NEON. A simplified version of the problem is: Find the maximum absolute value of an array of floating point numbers and return both the value and the index. It is the last part, the index of the maximum, that causes the problem. There doesn't seem to be a very good way to write code that has a branch.
See update at end for finished code using some of the suggested answers.
Here's a sample implementation (more complete version on godbolt):
#define VLEN 8
typedef float vNs __attribute__((vector_size(VLEN*sizeof(float))));
typedef int vNb __attribute__((vector_size(VLEN*sizeof(int))));
#define SWAP128 4,5,6,7, 0,1,2,3
#define SWAP64 2,3, 0,1, 6,7, 4,5
#define SWAP32 1, 0, 3, 2, 5, 4, 7, 6
static bool any(vNb x) {
x = x | __builtin_shufflevector(x,x, SWAP128);
x = x | __builtin_shufflevector(x,x, SWAP64);
x = x | __builtin_shufflevector(x,x, SWAP32);
return x[0];
}
float maxabs(float* __attribute__((aligned(32))) data, unsigned n, unsigned *index) {
vNs max = {0,0,0,0,0,0,0,0};
vNs tmax;
unsigned imax = 0;
for (unsigned i = 0 ; i < n; i += VLEN) {
vNs t = *(vNs*)(data + i);
t = -t < t ? t : -t; // Absolute value
vNb cmp = t > max;
if (any(cmp)) {
tmax = t; imax = i;
// broadcast horizontal max of t into every element of max
vNs tswap128 = __builtin_shufflevector(t,t, SWAP128);
t = t < tswap128 ? tswap128 : t;
vNs tswap64 = __builtin_shufflevector(t,t, SWAP64);
t = t < tswap64 ? tswap64 : t;
vNs tswap32 = __builtin_shufflevector(t,t, SWAP32);
max = t < tswap32 ? tswap32 : t;
}
}
// To simplify example, ignore finding index of true value in tmax==max
*index = imax; // + which(tmax == max);
return max[0];
}
Code on godbolt allows changing VLEN to 8 or 4.
This mostly works very well. For AVX/SSE the absolute value becomes t & 0x7fffffff using a (v)andps, i.e. clear the sign bit. For NEON it's done with vneg + fmaxnm. The block to find and broadcast the horizontal max becomes an efficient sequence of permute and max instructions. gcc is able to use NEON fabs for absolute value.
The 8 element vector on the 4 element SSE/NEON targets works well on clang. It uses a pair of instructions on two sets of registers and for the SWAP128 horizontal op will max or or the two registers without any unnecessary permute. gcc on the other hand really can't handle this and produces mostly non-SIMD code. If we reduce the vector length to 4, gcc works fine for SSE and NEON.
But there's a problem with if (any(cmp)). For clang + SSE/AVX, it works well, vcmpltps + vptest, with an orps to go from 8->4 on SSE.
But gcc and clang on NEON do all the permutes and ORs, then move the result to a gp register to test.
Is there some bit of code, other than architecture specific intrinsics, to get ptest with gcc and vmaxvq with clang/gcc and NEON?
I tried some other methods, like if (x[0] || x[1] || ... x[7]) but they were worse.
Update
I've created an updated example that shows two different implementations, both the original and "indices in a vector" method as suggested by chtz and shown in Aki Suihkonen's answer. One can see the resulting SSE and NEON output.
While some might be skeptical, the compiler does produce very good code from the generic SIMD (not auto-vectorization!) C++ code. On SSE/AVX, I see very little room to improve the code in the loop. The NEON version still troubled by a sub-optimal implementation of "any()".
Unless the data is usually in ascending order, or nearly so, my original version is still fastest on SSE/AVX. I haven't tested on NEON. This is because most loop iterations do not find a new max value and it's best to optimize for that case. The "indices in a vector" method produces a tighter loop and the compiler does a better job too, but the common case is just a bit slower on SSE/AVX. The common case might be equal or faster on NEON.
Some notes on writing generic SIMD code.
The absolute value of a vector of floats can be found with the following. It produces optimal code on SSE/AVX (and with a mask that clears the sign bit) and on NEON (the fabs instruction).
static vNs vabs(vNs x) {
return -x < x ? x : -x;
}
This will do a vertical max efficiently on SSE/AVX/NEON. It doesn't do a compare; it produces the architecture's "max' instruction. On NEON, changing it to use > instead of < causes the compiler to produce very bad scalar code. Something with denormals or exceptions I guess.
template <typename v> // Deduce vector type (float, unsigned, etc.)
static v vmax(v a, v b) {
return a < b ? b : a; // compiles best with "<" as compare op
}
This code will broadcast the horizontal max across a register. It compiles very well on SSE/AVX. On NEON, it would probably be better if the compiler could use a horizontal max instruction and then broadcast the result. I was impressed to see that if one uses 8 element vectors on SSE/NEON, which have only 4 element registers, the compiler is smart enough to use just one register for the broadcasted result, since the top 4 and bottom 4 elements are the same.
template <typename v>
static v hmax(v x) {
if (VLEN >= 8)
x = vmax(x, __builtin_shufflevector(x,x, SWAP128));
x = vmax(x, __builtin_shufflevector(x,x, SWAP64));
return vmax(x, __builtin_shufflevector(x,x, SWAP32));
}
This is the best "any()" I found. It is optimal on SSE/AVX, using a single ptest instruction. On NEON it does the permutes and ORs, instead of a horizontal max instruction, but I haven't found a way to get anything better on NEON.
static bool any(vNb x) {
if (VLEN >= 8)
x |= __builtin_shufflevector(x,x, SWAP128);
x |= __builtin_shufflevector(x,x, SWAP64);
x |= __builtin_shufflevector(x,x, SWAP32);
return x[0];
}
Also interesting, on AVX the code i = i + 1 will be compiled to vpsubd ymmI, ymmI, ymmNegativeOne, i.e. subtract -1. Why? Because a vector of -1s is produced with vpcmpeqd ymm0, ymm0, ymm0 and that's faster than broadcasting a vector of 1s.
Here is the best which() I've come up with. This gives you the index of the 1st true value in a vector of booleans (0 = false, -1 = true). One can do somewhat better on AVX with movemask. I don't know about the best NEON.
// vector of signed ints
typedef int vNi __attribute__((vector_size(VLEN*sizeof(int))));
// vector of bytes, same number of elements, 1/4 the size
typedef unsigned char vNb __attribute__((vector_size(VLEN*sizeof(unsigned char))));
// scalar type the same size as the byte vector
using sNb = std::conditional_t<VLEN == 4, uint32_t, uint64_t>;
static int which(vNi x) {
vNb cidx = __builtin_convertvector(x, vNb);
return __builtin_ctzll((sNb)cidx) / 8u;
}
As commented by chtz, the most generic and typical method is to have another mask to gather indices:
Vec8s indices = { 0,1,2,3,4,5,6,7};
Vec8s max_idx = indices;
Vec8f max_abs = abs(load8(ptr));
for (auto i = 8; i + 8 <= vec_length; i+=8) {
Vec8s data = abs(load8(ptr[i]));
auto mask = is_greater(data, max_abs);
max_idx = bitselect(mask, indices, max_idx);
max_abs = max(max_abs, data);
indices = indices + 8;
}
Another option is to interleave the values and indices:
auto data = load8s(ptr) & 0x7fffffff; // can load data as int32_t
auto idx = vec8s{0,1,2,3,4,5,6,7};
auto lo = zip_lo(idx, data);
auto hi = zip_hi(idx, data);
for (int i = 8; i + 8 <= size; i+=8) {
idx = idx + 8;
auto d1 = load8s(ptr + i) & 0x7fffffff;
auto lo1 = zip_lo(idx, d1);
auto hi1 = zip_hi(idx, d1);
lo = max_u64(lo, lo1);
hi = max_u64(hi, hi1);
}
This method is especially lucrative, if the range of inputs is small enough to shift the input left, while appending a few bits from the index to the LSB bits of the same word.
Even in this case we can repurpose 1 bit in the float allowing us to save one half of the bit/index selection operations.
auto data0 = load8u(ptr) << 1; // take abs by shifting left
auto data1 = (load8u(ptr + 8) << 1) + 1; // encode odd index to data
auto mx = max_u32(data0, data1); // the LSB contains one bit of index
Looks like one can use double as the storage, since even SSE2 supports _mm_max_pd (some attention needs to be given to Inf/Nan handling, which don't encode as Inf/Nan any more when reinterpreted as the high part of 64-bit double).
UPD: the no-aligning issue is fixed now, all the examples on godbolt use aligned reads.
UPD: MISSED THE ABS
Terribly sorry about that, I missed the absolute value from the definition.
I do not have the measurements, but here are all 3 functions vectorised:
max value with abs: https://godbolt.org/z/6Wznrc5qq
find with abs: https://godbolt.org/z/61r9Efxvn
one pass with abs: https://godbolt.org/z/EvdbfnWjb
Asm stashed in a gist
On the method
The way to do max element with simd is to first find the value and then find the index.
Alternatively you have to keep a register of indexes and blend the indexes.
This requires keeping indexes, doing more operations and the problem of the overflow needs to be addressed.
Here are my timings on avx2 by type (char, short and int) for 10'000 bytes of data
The min_element is my implementation of keeping the index.
reduce(min) + find is doing two loops - first get the value, then find where.
For ints (should behave like floats), performance is 25% faster for the two loops solution, at least on my measurements.
For completeness, comparisons against scalar for both methods - this is definitely an operation that should be vectorized.
How to do it
finding the maximum value is auto-vectorised across all platforms if you write it as reduce
if (!arr.size()) return {};
// std::reduce is also ok, just showing for more C ppl
float res = arr[0];
for (int i = 1; i != (int)arr.size(); ++i) {
res = res > arr[i] ? res : arr[i];
}
return res;
https://godbolt.org/z/EsazWf1vT
Now the find portion is trickier, non of the compilers I know autovectorize find
We have eve library that provides you with find algorithm: https://godbolt.org/z/93a98x6Tj
Or I explain how to implement find in this talk if you want to do it yourself.
UPD:
UPD2: changed the blend to max
#Peter Cordes in the comments said that there is maybe a point to doing the one pass solution in case of bigger data.
I have no evidence of this - my measurements point to reduce + find.
However, I hacked together roughly how keeping the index looks (there is an aligning issue at the moment, we should definitely align reads here)
https://godbolt.org/z/djrzobEj4
AVX2 main loop:
.L6:
vmovups ymm6, YMMWORD PTR [rdx]
add rdx, 32
vcmpps ymm3, ymm6, ymm0, 30
vmaxps ymm0, ymm6, ymm0
vpblendvb ymm3, ymm2, ymm1, ymm3
vpaddd ymm1, ymm5, ymm1
vmovdqa ymm2, ymm3
cmp rcx, rdx
jne .L6
ARM-64 main loop:
.L6:
ldr q3, [x0], 16
fcmgt v4.4s, v3.4s, v0.4s
fmax v0.4s, v3.4s, v0.4s
bit v1.16b, v2.16b, v4.16b
add v2.4s, v2.4s, v5.4s
cmp x0, x1
bne .L6
Links to ASM if godbolt becomes stale: https://gist.github.com/DenisYaroshevskiy/56d82c8cf4a4dd5bf91d58b053ea80f2
I don’t believe that’s possible. Compilers aren’t smart enough to do that efficiently.
Compare the other answer (which uses NEON-like pseudocode) with the SSE version below:
// Compare vector absolute value with aa, if greater update both aa and maxIdx
inline void updateMax( __m128 vec, __m128i idx, __m128& aa, __m128& maxIdx )
{
vec = _mm_andnot_ps( _mm_set1_ps( -0.0f ), vec );
const __m128 greater = _mm_cmpgt_ps( vec, aa );
aa = _mm_max_ps( vec, aa );
// If you don't have SSE4, emulate with bitwise ops: and, andnot, or
maxIdx = _mm_blendv_ps( maxIdx, _mm_castsi128_ps( idx ), greater );
}
float maxabs_sse4( const float* rsi, size_t length, size_t& index )
{
// Initialize things
const float* const end = rsi + length;
const float* const endAligned = rsi + ( ( length / 4 ) * 4 );
__m128 aa = _mm_set1_ps( -1 );
__m128 maxIdx = _mm_setzero_ps();
__m128i idx = _mm_setr_epi32( 0, 1, 2, 3 );
// Main vectorized portion
while( rsi < endAligned )
{
__m128 vec = _mm_loadu_ps( rsi );
rsi += 4;
updateMax( vec, idx, aa, maxIdx );
idx = _mm_add_epi32( idx, _mm_set1_epi32( 4 ) );
}
// Handle the remainder, if present
if( rsi < end )
{
__m128 vec;
if( length > 4 )
{
// The source has at least 5 elements
// Offset the source pointer + index back, by a few elements
const int offset = (int)( 4 - ( length % 4 ) );
rsi -= offset;
idx = _mm_sub_epi32( idx, _mm_set1_epi32( offset ) );
vec = _mm_loadu_ps( rsi );
}
else
{
// The source was smaller than 4 elements, copy them into temporary buffer and load vector from there
alignas( 16 ) float buff[ 4 ];
_mm_store_ps( buff, _mm_setzero_ps() );
for( size_t i = 0; i < length; i++ )
buff[ i ] = rsi[ i ];
vec = _mm_load_ps( buff );
}
updateMax( vec, idx, aa, maxIdx );
}
// Reduce to scalar
__m128 tmpMax = _mm_movehl_ps( aa, aa );
__m128 tmpMaxIdx = _mm_movehl_ps( maxIdx, maxIdx );
__m128 greater = _mm_cmpgt_ps( tmpMax, aa );
aa = _mm_max_ps( tmpMax, aa );
maxIdx = _mm_blendv_ps( maxIdx, tmpMaxIdx, greater );
// SSE3 has 100% market penetration in 2022
tmpMax = _mm_movehdup_ps( tmpMax );
tmpMaxIdx = _mm_movehdup_ps( tmpMaxIdx );
greater = _mm_cmpgt_ss( tmpMax, aa );
aa = _mm_max_ss( tmpMax, aa );
maxIdx = _mm_blendv_ps( maxIdx, tmpMaxIdx, greater );
index = (size_t)_mm_cvtsi128_si32( _mm_castps_si128( maxIdx ) );
return _mm_cvtss_f32( aa );
}
As you see, pretty much everything is completely different. Not just the boilerplate about remainder and final reduction, the main loop is very different too.
SSE doesn’t have bitselect; blendvps is not quite that, it selects 32-bit lanes based on high bit of the selector. Unlike NEON, SSE doesn’t have instructions for absolute value, need to be emulated with bitwise andnot.
The final reduction going to be completely different as well. NEON has very limited shuffles, but it has better horizontal operations, like vmaxvq_f32 which finds horizontal maximum over the complete SIMD vector.

Command to check in c >= or <= for mips

I am solving a college activity, I would like to know which command to check if one value is less than or equal to another.
I need to pass the code below c to mips
Assume that vector V is associated with the base register $ s6, and the variables a, b, c, d are associated with
registers $ s0, $ s1, $ s2, $ s3. Convert the C language statement to MIPS.
f)
if( V[8] >= 12) {
a = a + b + c;
V[8] = V[8] + a;
} else {
a = a – b – c;
V[8] = V[8] + a;
}
to check for >= and <=, you can perform a subtraction between your two values and use a BGEZ (branch on greater than or equal to zero) or BLEZ (branch on less than or equal to zero) depending on which result you want.
Example: r0 <= r1
SUB r2 r0 r1;
BLEZ r2;

How to check the number of set bits in an 8-bit unsigned char?

So I have to find the set bits (on 1) of an unsigned char variable in C?
A similar question is How to count the number of set bits in a 32-bit integer? But it uses an algorithm that's not easily adaptable to 8-bit unsigned chars (or its not apparent).
The algorithm suggested in the question How to count the number of set bits in a 32-bit integer? is trivially adapted to 8 bit:
int NumberOfSetBits( uint8_t b )
{
b = b - ((b >> 1) & 0x55);
b = (b & 0x33) + ((b >> 2) & 0x33);
return (((b + (b >> 4)) & 0x0F) * 0x01);
}
It is simply a case of shortening the constants the the least significant eight bits, and removing the final 24 bit right-shift. Equally it could be adapted for 16bit using an 8 bit shift. Note that in the case for 8 bit, the mechanical adaptation of the 32 bit algorithm results in a redundant * 0x01 which could be omitted.
The fastest approach for an 8-bit variable is using a lookup table.
Build an array of 256 values, one per 8-bit combination. Each value should contain the count of bits in its corresponding index:
int bit_count[] = {
// 00 01 02 03 04 05 06 07 08 09 0a, ... FE FF
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, ..., 7, 8
};
Getting a count of a combination is the same as looking up a value from the bit_count array. The advantage of this approach is that it is very fast.
You can generate the array using a simple program that counts bits one by one in a slow way:
for (int i = 0 ; i != 256 ; i++) {
int count = 0;
for (int p = 0 ; p != 8 ; p++) {
if (i & (1 << p)) {
count++;
}
}
printf("%d, ", count);
}
(demo that generates the table).
If you would like to trade some CPU cycles for memory, you can use a 16-byte lookup table for two 4-bit lookups:
static const char split_lookup[] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
};
int bit_count(unsigned char n) {
return split_lookup[n&0xF] + split_lookup[n>>4];
}
Demo.
I think you are looking for Hamming Weight algorithm for 8bits?
If it is true, here is the code:
unsigned char in = 22; //This is your input number
unsigned char out = 0;
in = in - ((in>>1) & 0x55);
in = (in & 0x33) + ((in>>2) & 0x33);
out = ((in + (in>>4) & 0x0F) * 0x01) ;
Counting the number of digits different than 0 is also known as a Hamming Weight. In this case, you are counting the number of 1's.
Dasblinkenlight provided you with a table driven implementation, and Olaf provided you with a software based solution. I think you have two other potential solutions. The first is to use a compiler extension, the second is to use an ASM specific instruction with inline assembly from C.
For the first alternative, see GCC's __builtin_popcount(). (Thanks to Artless Noise).
For the second alternative, you did not specify the embedded processor, but I'm going to offer this in case its ARM based.
Some ARM processors have the VCNT instruction, which performs the count for you. So you could do it from C with inline assembly:
inline
unsigned int hamming_weight(unsigned char value) {
__asm__ __volatile__ (
"VCNT.8"
: "=value"
: "value"
);
return value;
}
Also see Fastest way to count number of 1s in a register, ARM assembly.
For completeness, here is Kernighan's bit counting algorithm:
int count_bits(int n) {
int count = 0;
while(n != 0) {
n &= (n-1);
count++;
}
return count;
}
Also see Please explain the logic behind Kernighan's bit counting algorithm.
I made an optimized version. With a 32-bit processor, utilizing multiplication, bit shifting and masking can make smaller code for the same task, especially when the input domain is small (8-bit unsigned integer).
The following two code snippets are equivalent:
unsigned int bit_count_uint8(uint8_t x)
{
uint32_t n;
n = (uint32_t)(x * 0x08040201UL);
n = (uint32_t)(((n >> 3) & 0x11111111UL) * 0x11111111UL);
/* The "& 0x0F" will be optimized out but I add it for clarity. */
return (n >> 28) & 0x0F;
}
/*
unsigned int bit_count_uint8_traditional(uint8_t x)
{
x = x - ((x >> 1) & 0x55);
x = (x & 0x33) + ((x >> 2) & 0x33);
x = ((x + (x >> 4)) & 0x0F);
return x;
}
*/
This produces smallest binary code for IA-32, x86-64 and AArch32 (without NEON instruction set) as far as I can find.
For x86-64, this doesn't use the fewest number of instructions, but the bit shifts and downcasting avoid the use of 64-bit instructions and therefore save a few bytes in the compiled binary.
Interestingly, in IA-32 and x86-64, a variant of the above algorithm using a modulo ((((uint32_t)(x * 0x08040201U) >> 3) & 0x11111111U) % 0x0F) actually generates larger code, due to a requirement to move the remainder register for return value (mov eax,edx) after the div instruction. (I tested all of these in Compiler Explorer)
Explanation
I denote the eight bits of the byte x, from MSB to LSB, as a, b, c, d, e, f, g and h.
abcdefgh
* 00001000 00000100 00000010 00000001 (make 4 copies of x
--------------------------------------- with appropriate
abc defgh0ab cdefgh0a bcdefgh0 abcdefgh bit spacing)
>> 3
---------------------------------------
000defgh 0abcdefg h0abcdef gh0abcde
& 00010001 00010001 00010001 00010001
---------------------------------------
000d000h 000c000g 000b000f 000a000e
* 00010001 00010001 00010001 00010001
---------------------------------------
000d000h 000c000g 000b000f 000a000e
... 000h000c 000g000b 000f000a 000e
... 000c000g 000b000f 000a000e
... 000g000b 000f000a 000e
... 000b000f 000a000e
... 000f000a 000e
... 000a000e
... 000e
^^^^ (Bits 31-28 will contain the sum of the bits
a, b, c, d, e, f, g and h. Extract these
bits and we are done.)
Maybe not the fastest, but straightforward:
int count = 0;
for (int i = 0; i < 8; ++i) {
unsigned char c = 1 << i;
if (yourVar & c) {
//bit n°i is set
//first bit is bit n°0
count++;
}
}
For 8/16 bit MCUs, a loop will very likely be faster than the parallel-addition approach, as these MCUs cannot shift by more than one bit per instruction, so:
size_t popcount(uint8_t val)
{
size_t cnt = 0;
do {
cnt += val & 1U; // or: if ( val & 1 ) cnt++;
} while ( val >>= 1 ) ;
return cnt;
}
For the incrementation of cnt, you might profile. If still too slow, an assember implementation might be worth a try using carry flag (if available). While I am in against using assembler optimizations in general, such algorithms are one of the few good exceptions (still just after the C version fails).
If you can omit the Flash, a lookup table as proposed by #dasblinkenlight is likey the fastest approach.
Just a hint: For some architectures (notably ARM and x86/64), gcc has a builtin: __builtin_popcount(), you also might want to try if available (although it takes int at least). This might use a single CPU instruction - you cannot get faster and more compact.
Allow me to post a second answer. This one is the smallest possible for ARM processors with Advanced SIMD extension (NEON). It's even smaller than __builtin_popcount() (since __builtin_popcount() is optimized for unsigned int input, not uint8_t).
#ifdef __ARM_NEON
/* ARM C Language Extensions (ACLE) recommends us to check __ARM_NEON before
including <arm_neon.h> */
#include <arm_neon.h>
unsigned int bit_count_uint8(uint8_t x)
{
/* Set all lanes at once so that the compiler won't emit instruction to
zero-initialize other lanes. */
uint8x8_t v = vdup_n_u8(x);
/* Count the number of set bits for each lane (8-bit) in the vector. */
v = vcnt_u8(v);
/* Get lane 0 and discard other lanes. */
return vget_lane_u8(v, 0);
}
#endif

SIMD code for exponentiation

I am using SIMD to compute fast exponentiation result. I compare the timing with non-simd code. The exponentiation is implemented using square and multiply algorithm.
Ordinary(non-simd) version of code:
b = 1;
for (i=WPE-1; i>=0; --i){
ew = e[i];
for(j=0; j<BPW; ++j){
b = (b * b) % p;
if (ew & 0x80000000U) b = (b * a) % p;
ew <<= 1;
}
}
SIMD version:
B.data[0] = B.data[1] = B.data[2] = B.data[3] = 1U;
P.data[0] = P.data[1] = P.data[2] = P.data[3] = p;
for (i=WPE-1; i>=0; --i) {
EW.data[0] = e1[i]; EW.data[1] = e2[i]; EW.data[2] = e3[i]; EW.data[3] = e4[i];
for (j=0; j<BPW;++j){
B.v *= B.v; B.v -= (B.v / P.v) * P.v;
EWV.v = _mm_srli_epi32(EW.v,31);
M.data[0] = (EWV.data[0]) ? a1 : 1U;
M.data[1] = (EWV.data[1]) ? a2 : 1U;
M.data[2] = (EWV.data[2]) ? a3 : 1U;
M.data[3] = (EWV.data[3]) ? a4 : 1U;
B.v *= M.v; B.v -= (B.v / P.v) * P.v;
EW.v = _mm_slli_epi32(EW.v,1);
}
}
The issue is though it is computing correctly, simd version is taking more time than non-simd version.
Please help me debug the reasons. Any suggestions on SIMD coding is also welcome.
Thanks & regards,
Anup.
All functions in the for loops should be SIMD functions, not only two. Time taking to set the arguments for your 2 functions is less optimal then your original example (which is most likely optimized by the compiler)
A SIMD loop for 32 bit int data typically looks something like this:
for (i = 0; i < N; i += 4)
{
// load input vector(s) with data at array index i..i+3
__m128 va = _mm_load_si128(&A[i]);
__m128 vb = _mm_load_si128(&B[i]);
// process vectors using SIMD instructions (i.e. no scalar code)
__m128 vc = _mm_add_epi32(va, vb);
// store result vector(s) at array index i..i+3
_mm_store_si128(&C[i], vc);
}
If you find that you need to move between scalar code and SIMD code within the loop then you probably won't gain anything from SIMD optimisation.
Much of the skill in SIMD programming comes from finding ways to make your algorithm work with the limited number of supported instructions and data types that a given SIMD architecture provides. You will often need to exploit a priori knowledge of your data set to get the best possible performance, e.g. if you know for certain that your 32 bit integer values actually have a range that fits within 16 bits then that would make the multiplication part of your algorithm a lot easier to implement.

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