Page 6 PROCESSOR PROCESSOR FRAGMENT FRAGMENT. texy[1] texx. texy[1] texx. texy[0] texy[0]

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1 This lecture is based on GPGPU::Basic Math Tutorial, Dominik Goeddeke, Winter 2009 CMPE A linear algebra application GPGPU: SAXPY stands for (single-precision) Scalar Alpha X Plus Y. A linear algebra application: saxpy() We want to perform many iterations, as in 15 3 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas y i+1 = ff x + y i ffl A linear algebra application: saxpy() ffl ffl Floating-point precision on the GPU 15 1 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas A linear algebra application: saxpy() Where x and y are two vectors. y = ffx + y Page 1 Page 1 Page 2

2 PACK, LINPACK). is part of BLAS, the Basic Linear SAXPY Subprograms. First published in Algebra 1979, are used to build larger packages (LA- file saxpy.f file daxpy.f for y = a*x + y for y = a*x + y for y = a*x + y Reading and writing textures ffl Unlike the CPU, the GPU cannot perform a read-modify-write operation ffl Need two Y textures: an old" one to read from, and a new" one to write ffl For multiple iterations, their role switches every time CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas A linear algebra application: saxpy() BLAS prec single prec double file caxpy.f prec complex file zaxpy.f for y = a*x + y prec doublecomplex 15 4 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas GPU concept: we cannot use the same texture for reading Important writing at the same time. and that will update vector Y. to. Page 3 Page 2 Page 4

3 Ping-pong technique GL_COLOR_ATTACHMENT0_EXT GL_COLOR_ATTACHMENT1_EXT GL_COLOR_ATTACHMENT2_EXT GL_COLOR_ATTACHMENT3_EXT writetex = 0 readtex = 1 GL_COLOR_ATTACHMENT0_EXT GL_COLOR_ATTACHMENT1_EXT GL_COLOR_ATTACHMENT2_EXT GL_COLOR_ATTACHMENT3_EXT writetex = 1 readtex = 0 texy[0] texy[1] texx texy[0] texy[1] texx FRAGMENT PROCESSOR α x + y FRAGMENT PROCESSOR α x + y 1. Input parameters, set input variables: texsize, alpha, datax, datay, 5. For iterations times perform the main loop 4. Load and bind the Cg program 7. Read back the values from the GPU 8. Compare the performance and the values Program structure 6. Perform the same computation on the CPU for comparison 2. Setup OpenGL and GPU: initialize GLUT, GLEW, FBO, and CG. 3. Generate three textures: texx, texy[0], and texy[1]. texy[0] and 15 7 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas datayold, dataynew, and iterations CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas texy[1] will switch the role of new" Y (writetex) and old" Y, (readtex). 9. Clean up Page 5 Page 3 Page 6

4 Structure of the main loop iterations times: For Set the render destination (the write" texture) ffl Set the source destination (the read" texture) ffl Draw a quad to perform the computation ffl Swap the texture read/write roles ffl Input parameters create vector Ynew test data and initialize it (GPU only) input alpha create vector X test data and initialize it printf(" n*** out of memory allocating datax *** n"); NOTE: the amount of data is texsize * texsize * 4 if((datax = (float*)malloc(4*texsize*texsize*sizeof(float))) == NULL) 15 9 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas input texsize input iterations for(i = 0; i < texsize*texsize*4; i++) create vector Y test data and initialize it (used by CPU only) create vector Yold test data and initialize it like the CPU's (GPU only) 15 8 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas return(2); datax[i] = (float)i; Page 7 Page 4 Page 8

5 Setup OpenGL and GPU int err; glewinit return value void initglut(int ac, char *av[]) void initglew() glutinit(&ac, av); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas /* */ initglut and initglew printf((char *)glewgeterrorstring(err)); glutcreatewindow("saxpy on GPU with Ping-Pong (D. Goeddeke, ADB)"); init GLEW, obtain function pointers. NOTE that it doesn't check if all the extensions used are actually available. the functions' entry points will be NULL if unavailable. = glewinit(); err!= GLEW_OK) if(err initglut(ac, av); initglew(); initfbo(); initcg(); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas exit(3); Page 9 Page 5 Page 10

6 void initfbo() GLint param; glgenframebuffersext(1, &fb); glmatrixmode(gl_projection); generate FBO (offscreen buffer) and bind it fb); glbindframebufferext(gl_framebuffer_ext, set viewport for 1:1 pixel to texel mapping gluortho2d(0.0, (float)texsize, 0.0, (float)texsize); the FBO is incomplete at this time: misses attachment void initcg() fragmentprogram = cgcreateprogramfromfile(mycgcontext, register error callback right away set optimal implicit compiler options cgglsetoptimaloptions(fragmentprofile); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas assert(fragmentprofile!= CG_PROFILE_UNKNOWN); check that profiles are detected properly fragmentprofile = cgglgetlatestprofile(cg_gl_fragment); reports both compiler and runtime errors cgseterrorcallback(myerrorcallback); create cg context and get profiles = cgcreatecontext(); mycgcontext initfbo glloadidentity(); glmatrixmode(gl_modelview); glloadidentity(); glviewport(0, 0, texsize, texsize); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas initcg create fragment program CG_SOURCE, cgfragprogfile, fragmentprofile, "saxpygpupp", NULL); Page 11 Page 6 Page 12

7 Generate texture X (1/2) GL_TEXTURE_WRAP_T, GL_CLAMP); gltexparameteri(gl_texture_rectangle_arb, set texenv to replace instead of default modulate A texture environment specifies how texture values are gltexenvi(gl_texture_env, GL_TEXTURE_ENV_MODE, GL_REPLACE); interpreted when a fragment is texture Generate texture X (2/2) glteximage2d(gl_texture_rectangle_arb, gltexsubimage2d(gl_texture_rectangle_arb, CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas GL_RGBA, internal format Note: texture X doesn't need to be attached to an FBO since it's never rendered to. GL_FLOAT, format of data coming from the CPU 0); allocate only, do not initialize glgentextures(1, &texx); glbindtexture(gl_texture_rectangle_arb, texx); turn off filtering and set wrap mode gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_MIN_FILTER, GL_NEAREST); gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_MAG_FILTER, GL_NEAREST); gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_WRAP_S, GL_CLAMP); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas allocate graphics memory 0, mipmap level GL_RGBA32F_ARB, format texsize, texsize, size 0, no border transfer the data to the texture 0, 0, 0, mipmap level, x and y offset texsize, texsize, size of sub-image GL_RGBA, internal format GL_FLOAT, CPU data format datax); pointer to start of data Page 13 Page 7 Page 14

8 Same for both texy[0] and texy[1], as for texx. Generate the two Y textures (1/2) GL_TEXTURE_WRAP_T, GL_CLAMP); gltexparameteri(gl_texture_rectangle_arb, set texenv to replace instead of default modulate A texture environment specifies how texture values are gltexenvi(gl_texture_env, GL_TEXTURE_ENV_MODE, GL_REPLACE); interpreted when a fragment is textured Generate the two Y textures (2/2) CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Same for both texy[0] and texy[1], as for texx. gltexsubimage2d(gl_texture_rectangle_arb, GL_RGBA, internal format GL_FLOAT, format of data coming from the CPU allocate graphics memory and transfer the data to the texture 0); allocate only, do not initialize dataynew); pointer to start of data <-- NOTE generate the two Y textures glgentextures(2, texy); bind the texture glbindtexture(gl_texture_rectangle_arb, texy[0]); turn off filtering and set wrap mode gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_MIN_FILTER, GL_NEAREST); gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_MAG_FILTER, GL_NEAREST); gltexparameteri(gl_texture_rectangle_arb, GL_TEXTURE_WRAP_S, GL_CLAMP); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas glteximage2d(gl_texture_rectangle_arb, 0, mipmap level GL_RGBA32F_ARB, format texsize, texsize, size 0, no border 0, 0, 0, mipmap level, x and y offset texsize, texsize, size of sub-image GL_RGBA, internal format GL_FLOAT, CPU data format Page 15 Page 8 Page 16

9 Attach the two Y textures to the FBO glframebuffertexture2dext(gl_framebuffer_ext, glframebuffertexture2dext(gl_framebuffer_ext, printf(" nmain: Checking framebuffer status... "); attach both textures to different color attachments of the same FBO Loading and binding the Cg program CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas attachmentpoints[writetex], GL_TEXTURE_RECTANGLE_ARB, texy[writetex], texture 0); mipmap level attachmentpoints[readtex], GL_TEXTURE_RECTANGLE_ARB, texy[readtex], texture 0); mipmap level checkframebufferstatus(); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas loadcgfragprog(); Page 17 Page 9 Page 18

10 void loadcgfragprog(void) Loading and binding the Cg program load and bind program if(fragmentprogram!= NULL) enable texture X (read-only) cgglloadprogram(fragmentprogram); enable scalar alpha cgglenabletextureparameter(xparam); cgsetparameter1f(alphaparam, alpha); yparam = cggetnamedparameter(fragmentprogram, "texturey"); xparam = cggetnamedparameter(fragmentprogram, "texturex"); alphaparam = cggetnamedparameter(fragmentprogram, "alpha"); cgglsettextureparameter(xparam, texx); float4 saxpygpupp( CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas cggetnamedparameter(fragmentprogram, "texturey"); cgglsettextureparameter(xparam, texx); cgsetparameter1f(alphaparam, alpha); If texture: cgglenabletextureparameter(xparam); cgglenableprofile(fragmentprofile); cgglbindprogram(fragmentprogram); get parameter handles by name CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas uniform parameters Cg program: Cg float2 coords: TEXCOORD0, uniform samplerrect texturey, uniform samplerrect texturex, uniform float alpha): COLOR [...] If scalar: C program: CGparameter alphaparam; CGparameter xparam; CGparameter yparam; float alpha; GLuint texx; GLuint texy[2]; Page 19 Page 10 Page 20

11 int i; The fragment shader float4 saxpygpupp( uniform samplerrect texturey, uniform samplerrect texturex, uniform float alpha): COLOR result = y + alpha * x; float4 y = texrect(texturey, coords); float4 x = texrect(texturex, coords); Using non-power-of-2 textures requires using samplerrect for the sampler and texrect for the lookup function. Advanced texture lookup CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas float4 result; return(result); float2 coords: TEXCOORD0, CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Page 21 Page 11 Page 22

12 Main loop computation on the GPU for(i = 0; i < iterations; ++i) set render destination gltexcoord2f(0.0, (float)texsize); glvertex2f(0.0, (float)texsize); gltexcoord2f((float)texsize, 0.0); glvertex2f((float)texsize, 0.0); mode that can be GL POINT, GL LINE, or GL FILL (default) Example: set glpolygonmode(gl BACK, GL LINE) in rotsquare.c The glpolygonmode() function selects the polygon rasterization mode. The two parameters are: face that can be GL FRONT, GL BACK, or GL FRONT AND BACK (default) CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas gldrawbuffer(attachmentpoints[writetex]); set source Y cgglsettextureparameter(yparam, texy[readtex]); cgglenabletextureparameter(yparam); glpolygonmode(gl_front, GL_FILL); glbegin(gl_quads); gltexcoord2f(0.0, 0.0); glvertex2f(0.0, 0.0); gltexcoord2f((float)texsize, (float)texsize); glend(); swaptex(); glvertex2f((float)texsize, (float)texsize); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Polygon mode Page 23 Page 12 Page 24

13 Swapping texture roles void swaptex() = clock(); clkstart = 0; i < iterations; ++i) for(i clkend = clock(); Performing the same computation on the CPU cputime += ((double)clkend - (double)clkstart)/(double)clocks_per_sec; CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas if(readtex == 0) else readtex = 1; writetex = 0; readtex = 0; writetex = 1; CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas for(j = 0; j < texsize*texsize*4; ++j) datay[j] = alpha * datax[j] + datay[j]; Page 25 Page 13 Page 26

14 glreadbuffer(attachmentpoints[readtex]); Read back from the GPU Note: pixels are read back by rows, bottom to top and left to right: y 0,0 glreadpixels(0, 0, windows corrds of LL pixel to start reading fro texsize, texsize, width and height of pixel rectangle to read bac GL_RGBA, format of pixel data GL_FLOAT, type of pixel data dataynew); pointer to memory destination... row 1 row 0 x Compare the performance for (i = 0; i < (texsize*texsize*4); ++i) printf(" n n "); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas printf(" n max error = %13.6lf", maxerror); avgerror /= (double)(texsize*texsize*4); printf(" n avg error = %13.6lf", avgerror); printf(" n n"); double diff, sum; sum = (datay[i] + dataynew[i])/2.0; diff = fabs(datay[i]-dataynew[i]); CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas if(diff > maxerror) maxerror = diff; avgerror += diff; [...] Page 27 Page 14 Page 28

15 15 31 CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Output CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Clean up free(datax); free(datayold); free(dataynew); gldeleteframebuffersext(1,&fb); gldeletetextures(1,&texx); gldeletetextures(2,texy); cgdestroycontext(mycgcontext); Page 29 Page 15 Page 30

16 Floating-point precision on the GPU Floating-point precision on the GPU 1. Rounding 2. Denormals 3. NaNs CMPE220 Advanced Parallel Processing, Winter 2009 Andrea Di Blas Page 31 Page 16