Compute bit parity in CUDA - cuda

CUDA has popcount intrinsics for 32-bit and 64-bit types: __popc() and __popcll().
Does CUDA also have intrinsics to get the parity of 32-bit and 64-bit types?
(The parity refers to whether an integer has an even or odd amount of 1-bits.)
For example, GCC has __builtin_parityl() for 64-bit integers.
And here's a C function that does the same thing:
inline uint parity64(uint64 n){
n ^= n >> 1;
n ^= n >> 2;
n = (n & 0x1111111111111111lu) * 0x1111111111111111lu;
return (n >> 60) & 1;
}

I'm not aware of a parity intrinsic for CUDA.
However you should be able to create a fairly simple function to do it using either the __popc() (32-bit unsigned case) or __popcll() (64-bit unsigned case) intrinsics.
For example, the following function should indicate whether the number of 1 bits in a 64-bit unsigned quantity is odd (true) or even (false):
__device__ bool my_parity(unsigned long long d){
return (__popcll(d) & 1);}

Related

CUDA shared vs global memory, possible speedup

I believe my CUDA application could potentially benefit from shared memory, in order to keep the data near the GPU cores. Right now, I have a single kernel to which I pass a pointer to a previously allocated chunk of device memory, and some constants. After the kernel has finished, the device memory includes the result, which is copied to host memory. This scheme works perfectly and is cross-checked with the same algorithm run on the CPU.
The docs make it quite clear that global memory is much slower and has higher access latency than shared memory, but either way to get the best performance you should make your threads coalesce and align any access. My GPU has Compute Capability 6.1 "Pascal", has 48 kiB of shared memory per thread block and 2 GiB DRAM. If I refactor my code to use shared memory, how do I make sure to avoid bank conflicts?
Shared memory is organized in 32 banks, so that 32 threads from the same block each may simultaneously access a different bank without having to wait. Let's say I take the kernel from above, launch a kernel configuration with one block and 32 threads in that block, and statically allocate 48 kiB of shared memory outside the kernel. Also, each thread will only ever read from and write to the same single memory location in (shared) memory, which is specific to the algorithm I am working on. Given this, I would access those 32 shared memory locations with on offset of 48 kiB / 32 banks / sizeof(double) which equals 192:
__shared__ double cache[6144];
__global__ void kernel(double *buf_out, double a, double b, double c)
{
for(...)
{
// Perform calculation on shared memory
cache[threadIdx.x * 192] = ...
}
// Write result to global memory
buf_out[threadIdx.x] = cache[threadIdx.x * 192];
}
My reasoning: while threadIdx.x runs from 0 to 31, the offset together with cache being a double make sure that each thread will access the first element of a different bank, at the same time. I haven't gotten around to modify and test the code, but is this the right way to align access for the SM?
MWE added:
This is the naive CPU-to-CUDA port of the algorithm, using global memory only. Visual Profiler reports a kernel execution time of 10.3 seconds.
Environment: Win10, MSVC 2019, x64 Release Build, CUDA v11.2.
#include "cuda_runtime.h"
#include <iostream>
#include <stdio.h>
#define _USE_MATH_DEFINES
#include <math.h>
__global__ void kernel(double *buf, double SCREEN_STEP_SIZE, double APERTURE_RADIUS,
double APERTURE_STEP_SIZE, double SCREEN_DIST, double WAVE_NUMBER)
{
double z, y, y_max;
unsigned int tid = threadIdx.x/* + blockIdx.x * blockDim.x*/;
double Z = tid * SCREEN_STEP_SIZE, Y = 0;
double temp = WAVE_NUMBER / SCREEN_DIST;
// Make sure the per-thread accumulator is zero before we begin
buf[tid] = 0;
for (z = -APERTURE_RADIUS; z <= APERTURE_RADIUS; z += APERTURE_STEP_SIZE)
{
y_max = sqrt(APERTURE_RADIUS * APERTURE_RADIUS - z * z);
for (y = -y_max; y <= y_max; y += APERTURE_STEP_SIZE)
{
buf[tid] += cos(temp * (Y * y + Z * z));
}
}
}
int main(void)
{
double *dev_mem;
double *buf = NULL;
cudaError_t cudaStatus;
unsigned int screen_elems = 1000;
if ((buf = (double*)malloc(screen_elems * sizeof(double))) == NULL)
{
printf("Could not allocate memory...");
return -1;
}
memset(buf, 0, screen_elems * sizeof(double));
if ((cudaStatus = cudaMalloc((void**)&dev_mem, screen_elems * sizeof(double))) != cudaSuccess)
{
printf("cudaMalloc failed with code %u", cudaStatus);
return cudaStatus;
}
kernel<<<1, 1000>>>(dev_mem, 1e-3, 5e-5, 50e-9, 10.0, 2 * M_PI / 5e-7);
cudaDeviceSynchronize();
if ((cudaStatus = cudaMemcpy(buf, dev_mem, screen_elems * sizeof(double), cudaMemcpyDeviceToHost)) != cudaSuccess)
{
printf("cudaMemcpy failed with code %u", cudaStatus);
return cudaStatus;
}
cudaFree(dev_mem);
cudaDeviceReset();
free(buf);
return 0;
}
The kernel below uses shared memory instead and takes approximately 10.6 seconds to execute, again measured in Visual Profiler:
__shared__ double cache[1000];
__global__ void kernel(double *buf, double SCREEN_STEP_SIZE, double APERTURE_RADIUS,
double APERTURE_STEP_SIZE, double SCREEN_DIST, double WAVE_NUMBER)
{
double z, y, y_max;
unsigned int tid = threadIdx.x + blockIdx.x * blockDim.x;
double Z = tid * SCREEN_STEP_SIZE, Y = 0;
double temp = WAVE_NUMBER / SCREEN_DIST;
// Make sure the per-thread accumulator is zero before we begin
cache[tid] = 0;
for (z = -APERTURE_RADIUS; z <= APERTURE_RADIUS; z += APERTURE_STEP_SIZE)
{
y_max = sqrt(APERTURE_RADIUS * APERTURE_RADIUS - z * z);
for (y = -y_max; y <= y_max; y += APERTURE_STEP_SIZE)
{
cache[tid] += cos(temp * (Y * y + Z * z));
}
}
buf[tid] = cache[tid];
}
The innermost line inside the loops is typically executed several million times, depending on the five constants passed to the kernel. So instead of thrashing the off-chip global memory, I expected the on-chip shared-memory version to be much faster, but apparently it is not - what am I missing?
Let's say... each thread will only ever read from and write to the same single memory location in (shared) memory, which is specific to the algorithm I am working on.
In that case, it does not make sense to use shared memory. The whole point of shared memory is the sharing... among all threads in a block. Under your assumptions, you should keep your element in a register, not in shared memory. Indeed, in your "MWE Added" kernel - that's probably what you should do.
If your threads were to share information - then the pattern of this sharing would determine how best to utilize shared memory.
Also remember that if you don't read data repeatedly, or from multiple threads, it is much less likely that shared memory will help you - as you always have to read from global memory at least once and write to shared memory at least once to have your data in shared memory.

CUDA float precision not matching CPU implementation

I am using CUDA 5.5 compute 3.5 on GTX 1080Ti and want to compute this formula:
y = a * a * b / 64 + c * c
Suppose I have these parameters:
a = 5876
b = 0.4474222958088
c = 664
I am computing this both via GPU and on the CPU and they give me different inexact answers:
h_data[0] = 6.822759375000e+05,
h_ref[0] = 6.822760000000e+05,
difference = -6.250000000000e-02
h_data is the CUDA answer, h_ref is the CPU answer. When I plug these into my calculator the GPU answer is closer to the exact answer, and I suspect this has to do with floating point precision. My question now is, how can I get the CUDA solution to match the precision/roundoff of CPU version? If I offset the a parameter by +/-1 the solutions match, but if I offset say the c parameter I still get a difference of 1/16
Here's the working code:
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
__global__ void test_func(float a, float b, int c, int nz, float * __restrict__ d_out)
{
float *fdes_out = d_out + blockIdx.x * nz;
float roffout2 = a * a / 64.f;
//float tmp = fma(roffout2,vel,index*index);
for (int tid = threadIdx.x; tid < nz; tid += blockDim.x) {
fdes_out[tid] = roffout2 * b + c * c;
}
}
int main (int argc, char **argv)
{
// parameters
float a = 5876.0f, b = 0.4474222958088f;
int c = 664;
int nz = 1;
float *d_data, *h_data, *h_ref;
h_data = (float*)malloc(nz*sizeof(float));
h_ref = (float*)malloc(nz*sizeof(float));
// CUDA
cudaMalloc((void**)&d_data, sizeof(float)*nz);
dim3 nb(1,1,1); dim3 nt(64,1,1);
test_func <<<nb,nt>>> (a,b,c,nz,d_data);
cudaMemcpy(h_data, d_data, sizeof(float)*nz, cudaMemcpyDeviceToHost);
// Reference
float roffout2 = a * a / 64.f;
h_ref[0] = roffout2*b + c*c;
// Compare
printf("h_data[0] = %1.12e,\nh_ref[0] = %1.12e,\ndifference = %1.12e\n",
h_data[0],h_ref[0],h_data[0]-h_ref[0]);
// Free
free(h_data); free(h_ref);
cudaFree(d_data);
return 0;
}
I'm compiling only with the-O3 flag.
This small numerical difference of one single-precision ulp occurs because the CUDA compiler applies FMA-merging by default, whereas the host compiler does not do that. FMA-merging can be turned off by adding the command line flag -fmad=false to the invocation of the CUDA compiler driver nvcc.
FMA-merging is a compiler optimization in which an FMUL and a dependent FADD are transformed into a single fused multiply-add, or FMA, instruction. An FMA instruction computes a*b+c such that the full unrounded product a*b enters into the addition with c before a final rounding is applied to produce the final result.
Usually, this has performance advantages, since a single FMA instruction is executed instead of two instructions FMUL, FADD, and all the instructions have similar latency. Usually, this also has accuracy advantages as the use of FMA eliminates one rounding step and guards against subtractive cancellation when a*c and c have opposite signs.
In this case, as noted by OP, the GPU result computed with FMA is slightly more accurate than the host result computed without FMA. Using a higher precision reference, I find that the relative error in the GPU result is -4.21e-8, while the relative error in the host result is 4.95e-8.

Can CUDA branch divergence help me in this case?

This is little more than a thought experiment right now, but I want to check my understanding of the CUDA execution model. Consider the following case:
I am running on a GPU with poor double-precision performance (a non-Tesla card).
I have a kernel that needs to calculate a value using double precision. That value is a constant for the rest of the runtime of the kernel, and it is also constant across a warp.
Is something like the following pseudocode advantageous?
// value that we use later in the kernel; this is constant across all threads
// in a warp
int constant_value;
// check to see if this is the first thread in a warp
enum { warp_size = 32 };
if (!(threadIdx.x & (warp_size - 1))
{
// only do the double-precision math in one thread
constant_value = (int) round(double_precision_calculation());
}
// broadcast constant_value to all threads in the warp
constant_value = __shfl(v, 0);
// go on to use constant_value as needed later in the kernel
The reason why I considered doing this is my (possibly wrong) understanding of how double-precision resources are made available on each multiprocessor. From what I understand, there are simply 1/32 as many double-precision ALUs as single-precision ones on recent Geforce cards. Does this mean that if the other threads in a warp diverge, I can work around this lack of resources, and still get decent performance, as long as the double-precision values that I want can be broadcast to all threads in a warp?
Does this mean that if the other threads in a warp diverge, I can work around this lack of resources, and still get decent performance, as long as the double-precision values that I want can be broadcast to all threads in a warp?
No, you can't.
An instruction issue always occurs at the warp level, even in a warp-diverged scenario. Since it is issued at the warp level, it will require/use/schedule enough execution resources for the warp, even for inactive threads.
Therefore a computation done on only one thread will still use the same resources/scheduling slot as a computation done on all 32 threads in the warp.
For example, a floating point multiply will require 32 instances of usage of a floating point ALU. The exact scheduling of this will vary based on the specific GPU, but you cannot reduce the 32 instance usage to a lower number through warp divergence or any other mechanism.
Based on a question in the comments, here's a worked example on CUDA 7.5, Fedora 20, GT640 (GK208 - has 1/24 ratio of DP to SP units):
$ cat t1241.cu
#include <stdio.h>
#include <time.h>
#include <sys/time.h>
#define USECPSEC 1000000ULL
unsigned long long dtime_usec(unsigned long long start){
timeval tv;
gettimeofday(&tv, 0);
return ((tv.tv_sec*USECPSEC)+tv.tv_usec)-start;
}
const int nTPB = 32;
const int nBLK = 1;
const int rows = 1048576;
const int nSD = 128;
typedef double mytype;
template <bool use_warp>
__global__ void mpy_k(const mytype * in, mytype * out){
__shared__ mytype sdata[nTPB*nSD];
int idx = threadIdx.x + blockDim.x*blockIdx.x;
mytype accum = in[idx];
#pragma unroll 128
for (int i = 0; i < rows; i++)
if (use_warp)
accum += accum*sdata[threadIdx.x+(i&(nSD-1))*nTPB];
else
if (threadIdx.x == 0)
accum += accum*sdata[threadIdx.x+(i&(nSD-1))*nTPB];
out[idx] = accum;
}
int main(){
mytype *din, *dout;
cudaMalloc(&din, nTPB*nBLK*rows*sizeof(mytype));
cudaMalloc(&dout, nTPB*nBLK*sizeof(mytype));
cudaMemset(din, 0, nTPB*nBLK*rows*sizeof(mytype));
cudaMemset(dout, 0, nTPB*nBLK*sizeof(mytype));
mpy_k<true><<<nBLK, nTPB>>>(din, dout); // warm-up
cudaDeviceSynchronize();
unsigned long long dt = dtime_usec(0);
mpy_k<true><<<nBLK, nTPB>>>(din, dout);
cudaDeviceSynchronize();
dt = dtime_usec(dt);
printf("full warp elapsed time: %f\n", dt/(float)USECPSEC);
mpy_k<false><<<nBLK, nTPB>>>(din, dout); //warm up
cudaDeviceSynchronize();
dt = dtime_usec(0);
mpy_k<false><<<nBLK, nTPB>>>(din, dout);
cudaDeviceSynchronize();
dt = dtime_usec(dt);
printf("one thread elapsed time: %f\n", dt/(float)USECPSEC);
cudaError_t res = cudaGetLastError();
if (res != cudaSuccess) printf("CUDA runtime failure %s\n", cudaGetErrorString(res));
return 0;
}
$ nvcc -arch=sm_35 -o t1241 t1241.cu
$ CUDA_VISIBLE_DEVICES="1" ./t1241
full warp elapsed time: 0.034346
one thread elapsed time: 0.049174
$
It is not faster to use just one thread in the warp for a floating-point multiply

How to write LOP3 based instructions for Maxwell and up NVIDIA Architecture?

Maxwell Architecture has introduced a new instruction in PTX assembly called LOP3 which according to the NVIDIA blog:
"Can save instructions when performing complex logic operations
on multiple inputs."
At GTC 2016, some CUDA developers managed to accelerated the atan2f function for Tegra X1 processor (Maxwell) with such instructions.
However, the below function defined within a .cu file leads to undefined definitions for __SET_LT and __LOP3_0xe2.
Do I have to define them in .ptx file instead ? if so, how ?
float atan2f(const float dy, const float dx)
{
float flag, z = 0.0f;
__SET_LT(flag, fabsf(dy), fabsf(dx));
uint32_t m, t1 = 0x80000000;
float t2 = float(M_PI) / 2.0f;
__LOP3_0x2e(m, __float_as_int(dx), t1, __float_as_int(t2));
float w = flag * __int_as_float(m) + float(M_PI)/2.0f;
float Offset = copysignf(w, dy);
float t = fminf(fabsf(dx), fabsf(dy)) / fmaxf(fabsf(dx), fabsf(dy));
uint32_t r, b = __float_as_int(flag) << 2;
uint32_t mask = __float_as_int(dx) ^ __float_as_int(dy) ^ (~b);
__LOP3_0xe2(r, mask, t1, __floast_as_int(t));
const float p = fabsf(__int_as_float(r)) - 1.0f;
return ((-0.0663f*(-p) + 0.311f) * (-p) + float(float(M_PI)/4.0)) * (*(float *)&r) + Offset;
}
Edit:
The macro defines are finally:
#define __SET_LT(D, A, B) asm("set.lt.f32.f32 %0, %1, %2;" : "=f"(D) : "f"(A), "f"(B))
#define __SET_GT(D, A, B) asm("set.gt.f32.f32 %0, %1, %2;" : "=f"(D) : "f"(A), "f"(B))
#define __LOP3_0x2e(D, A, B, C) asm("lop3.b32 %0, %1, %2, %3, 0x2e;" : "=r"(D) : "r"(A), "r"(B), "r"(C))
#define __LOP3_0xe2(D, A, B, C) asm("lop3.b32 %0, %1, %2, %3, 0xe2;" : "=r"(D) : "r"(A), "r"(B), "r"(C))
The lop3.b32 PTX instruction can perform a more-or-less arbitrary boolean (logical) operation on 3 variables A,B, and C.
In order to set the actual operation to be performed, we must provide a "lookup-table" immediate argument (immLut -- an 8-bit quantity). As indicated in the documentation, a method to compute the necessary immLut argument for a given operation F(A,B,C) is to substitute the values of 0xF0 for A, 0xCC for B, and 0xAA for C in the actual desired equation. For example suppose we want to compute:
F = (A || B) && (!C) ((A or B) and (not-C))
Then we would compute immLut argument by:
immLut = (0xF0 | 0xCC) & (~0xAA)
Note that the specified equation for F is a boolean equation, treating the arguments A,B, and C as boolean values, and producing a true/false result (F). However, the equation to compute immLut is a bitwise logical operation.
For the above example, immLut would have a computed value of 0x54
If it's desired to use a PTX instruction in ordinary CUDA C/C++ code, probably the most common (and arguably easiest) method would be to use inline PTX. Inline PTX is documented, and there are other questions discussing how to use it (such as this one), so I'll not repeat that here.
Here is a worked example of the above example case. Note that this particular PTX instruction is only available on cc5.0 and higher architectures, so be sure to compile for at least that level of target.
$ cat t1149.cu
#include <stdio.h>
const unsigned char A_or_B_and_notC=((0xF0|0xCC)&(~0xAA));
__device__ int my_LOP_0x54(int A, int B, int C){
int temp;
asm("lop3.b32 %0, %1, %2, %3, 0x54;" : "=r"(temp) : "r"(A), "r"(B), "r"(C));
return temp;
}
__global__ void testkernel(){
printf("A=true, B=false, C=true, F=%d\n", my_LOP_0x54(true, false, true));
printf("A=true, B=false, C=false, F=%d\n", my_LOP_0x54(true, false, false));
printf("A=false, B=false, C=false, F=%d\n", my_LOP_0x54(false, false, false));
}
int main(){
printf("0x%x\n", A_or_B_and_notC);
testkernel<<<1,1>>>();
cudaDeviceSynchronize();
}
$ nvcc -arch=sm_50 -o t1149 t1149.cu
$ ./t1149
0x54
A=true, B=false, C=true, F=0
A=true, B=false, C=false, F=1
A=false, B=false, C=false, F=0
$
Since immLut is an immediate constant in PTX code, I know of no way using inline PTX to pass this as a function parameter - even if templating is used. Based on your provided link, it seems that the authors of that presentation also used a separately defined function for the specific desired immediate value -- presumably 0xE2 and 0x2E in their case. Also, note that I have chosen to write my function so that it returns the result of the operation as the function return value. The authors of the presentation you linked appear to be passing the return value back via a function parameter. Either method should be workable. (In fact, it appears they have written their __LOP3... codes as functional macros rather than ordinary functions.)
Also see here for a method of understanding how the 8 bit truthtable (immLut) works for LOP3 at the source code level.

atomic operation disrupting all kernels

I am running some image processing operations on GPU and I need the histogram of the output.
I have written and tested the processing kernels. Also I have tested the histogram kernel for samples of the output pictures separately. They both work fine but when I put all of them in one loop I get nothing.
This is my histogram kernel:
__global__ void histogram(int n, uchar* color, uchar* mask, int* bucket, int ch, int W, int bin)
{
unsigned int X = blockIdx.x*blockDim.x+threadIdx.x;
unsigned int Y = blockIdx.y*blockDim.y+threadIdx.y;
int l = (256%bin==0)?256/bin: 256/bin+1;
int c;
if (X+Y*W < n && mask[X+Y*W])
{
c = color[(X+Y*W)*3]/bin;
atomicAdd(&bucket[c], 1);
c = color[(X+Y*W)*3+1]/bin;
atomicAdd(&bucket[c+l], 1);
c = color[(X+Y*W)*3+2]/bin;
atomicAdd(&bucket[c+l*2], 1);
}
}
It is updating histogram vectors for red, green, and blue.('l' is the length of the vectors)
When I comment out atomicAdds it again produces the output but of course not the histogram.
Why don't they work together?
Edit:
This is the loop:
cudaMemcpy(frame_in_gpu,frame_in.data, W*H*3*sizeof(uchar),cudaMemcpyHostToDevice);
cuda_process(frame_in_gpu, frame_out_gpu, W, H, dimGrid,dimBlock);
cuda_histogram(W*H, frame_in_gpu, mask_gpu, hist, 3, W, bin, dimg_histogram, dimb_histogram);
Then I copy the output to host memory and write it to a video.
These are c codes that only call their kernels with dimGrid and dimBlock that are given as inputs. Also:
dim3 dimBlock(32,32);
dim3 dimGrid(W/32,H/32);
dim3 dimb_Histogram(16,16);
dim3 dimg_Histogram(W/16,H/16);
I changed this for histogram because it worked better with it. Does it matter?
Edit2:
I am using -arch=sm_11 option for compilation. I just read it somewhere. Could anyone tell me how I should choose it?
perhaps you should try to compile without -arch=sm_11 flag.
sm 1.1 is the first architecture which supported atomic operations on global memory while your GPU supports SM 2.0. Hence there is no reason to compile for SM 1.1 unless for backward compatibility.
One possible issue could be that SM 1.1 does not support atomic operations on 64-bit ints in global memory. So I would suggest you recompile the code without -arch option, or use
-arch=sm_20 if you like