Bug in OpenGL? Identical float computation leads to different results - opengl

Question

The "minimial example" is quite long unfortunately as the bug disappears if I drop too much seamingly irrelevant code.
Here is the C++ code:
#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <vector>
#include <math.h>
#include <time.h>
#include <fstream>
#include <sstream>
//OpenGL includes
#include <GL/glew.h> //OpenGL Extension Wrangler
#include <GL/freeglut.h> //Free OpenGL Utility Toolkit (includes gl.h and glu.h)
void fPressEnter(){
std::cout << "Press enter to exit.";
std::cin.get();
}
void fCompileShaderFromString(const std::string& Source, const GLuint ShaderId){
const char* Code = Source.c_str();
glShaderSource(ShaderId, 1, &Code, NULL);
glCompileShader(ShaderId);
int Status;
glGetShaderiv(ShaderId, GL_COMPILE_STATUS, &Status);
if(Status == GL_FALSE){
int Length = 0;
glGetShaderiv(ShaderId, GL_INFO_LOG_LENGTH, &Length);
if(Length > 0){
char* Log = new char[Length];
int Written = 0;
glGetShaderInfoLog(ShaderId, Length, &Written, Log);
std::cout << Log << std::endl;
delete[] Log;
}
}
}
void fCompileShaderFromFile(const char* FileName, const GLuint ShaderId){
std::ifstream InFile(FileName, std::ios::in);
std::ostringstream Code;
while(InFile.good()){
int TI = InFile.get();
if(!InFile.eof()) Code << (char) TI;
}
InFile.close();
fCompileShaderFromString(Code.str(), ShaderId);
}
void fLinkProgram(const GLuint ProgramId){
glLinkProgram(ProgramId);
int Status;
glGetProgramiv(ProgramId, GL_LINK_STATUS, &Status);
if(Status == GL_FALSE){
int Length = 0;
glGetProgramiv(ProgramId, GL_INFO_LOG_LENGTH, &Length);
if(Length > 0){
char* Log = new char[Length];
int Written = 0;
glGetProgramInfoLog(ProgramId, Length, &Written, Log);
std::cout << Log << std::endl;
delete[] Log;
}
}
}
int main(){
//OpenGL setup
//Glut
int argc = 1;
char* argv[1] = {(char*) ""};
glutInit(&argc, argv);
glutInitWindowPosition((glutGet(GLUT_SCREEN_WIDTH) - 256) / 2, (glutGet(GLUT_SCREEN_HEIGHT) - 256) / 2);
glutInitWindowSize(256, 256);
glutInitDisplayMode(GLUT_RGB);
glutCreateWindow("Bug");
glutHideWindow();
//Glew
GLenum glew_ok = glewInit();
if(glew_ok != GLEW_OK){fprintf(stderr, "Glew error: '%s'\n", glewGetErrorString(glew_ok)); fPressEnter(); return(1);}
//Main program
//Auxiliary variables
GLuint ShaderId, ProgramId, BufferId;
float* BufferPointer;
float* Data = new float[32 * 32 * 2];
float dsup, esup;
//Compile shader program and create buffer in graphics card memory
ShaderId = glCreateShader(GL_COMPUTE_SHADER);
fCompileShaderFromFile("Shader.txt", ShaderId);
ProgramId = glCreateProgram();
glAttachShader(ProgramId, ShaderId);
fLinkProgram(ProgramId);
glDetachShader(ProgramId, ShaderId);
glDeleteShader(ShaderId);
glUseProgram(ProgramId);
glGenBuffers(1, &BufferId);
glBindBufferBase(GL_SHADER_STORAGE_BUFFER, 0, BufferId);
glBufferData(GL_SHADER_STORAGE_BUFFER, 32 * 32 * 2 * sizeof(float), NULL, GL_STREAM_READ);
glBindBuffer(GL_SHADER_STORAGE_BUFFER, 0);
//Actual computation
std::cout << "Starting computation" << std::endl << std::endl << std::flush;
dsup = 0.f;
esup = 0.f;
glUniform1i(0, 0);
glUniform1i(1, 0);
glDispatchCompute(4, 4, 1);
glMemoryBarrier(GL_ALL_BARRIER_BITS);
glFinish();
glBindBufferBase(GL_SHADER_STORAGE_BUFFER, 0, BufferId);
BufferPointer = (float*) glMapBuffer(GL_SHADER_STORAGE_BUFFER, GL_READ_ONLY);
memcpy(Data, BufferPointer, 32 * 32 * 2 * sizeof(float));
glUnmapBuffer(GL_SHADER_STORAGE_BUFFER);
glBindBuffer(GL_SHADER_STORAGE_BUFFER, 0);
for(int z2 = 0; z2 < 32; z2++) for(int z3 = 0; z3 < 32; z3++){
if(Data[z2 * 32 * 2 + z3 * 2 + 0] > dsup) dsup = Data[z2 * 32 * 2 + z3 * 2 + 0];
if(Data[z2 * 32 * 2 + z3 * 2 + 1] > esup) esup = Data[z2 * 32 * 2 + z3 * 2 + 1];
}
std::cout << std::setprecision(8) << dsup << ", " << std::setprecision(8) << esup << std::endl;
//Cleanup
delete[] Data;
glDeleteBuffers(1, &BufferId);
glDeleteProgram(ProgramId);
fPressEnter();
return(0);
}
and here is the shader:
#version 430 core
const uint mg = 2048;
const uint mb = 512;
const uint my = 128;
layout(local_size_x = 8, local_size_y = 8, local_size_z = 1) in;
layout(binding = 0) buffer OutputBlock{
float Data[32][32][2];
} Output;
layout(location = 0) uniform int goffset;
layout(location = 1) uniform int boffset;
vec2 fe(float x){return(vec2(cos(6.2831853e0f * x), sin(6.2831853e0f * x)));}
vec2 fComplexTimes(const vec2 A, const vec2 B){return(vec2(A.x * B.x - A.y * B.y, A.x * B.y + A.y * B.x));}
vec2 fComplexTimesI(const vec2 A){return(vec2(-A.y, A.x));}
vec2 fComplexTimesMinusI(const vec2 A){return(vec2(A.y, -A.x));}
float dsup, esup;
void fDESupTaylor_a10_w3_d2(){
const vec2 one = vec2(1.f, 0.f);
uint q, zg, zb, zy, n;
float fq, fb, fg, fys, fymb, fmg, fmb, fatmy;
float dsum, esum, dsummandsup, esummandsup, dabs, eabs;
float t;
vec2 td, te;
vec2 Di_0_, Di_0_y, Di_0_yy, Di_1_, Di_1_g, Di_1_b, Di_1_y, Di_1_gg, Di_1_gb, Di_1_gy, Di_1_bg, Di_1_bb, Di_1_by, Di_1_yg, Di_1_yb, Di_1_yy, Di_2_, Di_2_g, Di_2_b, Di_2_y, Di_2_gg, Di_2_gb, Di_2_gy, Di_2_bg, Di_2_bb, Di_2_by, Di_2_yg, Di_2_yb, Di_2_yy;
vec2 Ei_0_, Ei_0_y, Ei_0_yy, Ei_1_, Ei_1_g, Ei_1_b, Ei_1_y, Ei_1_gg, Ei_1_gb, Ei_1_gy, Ei_1_bg, Ei_1_bb, Ei_1_by, Ei_1_yg, Ei_1_yb, Ei_1_yy, Ei_2_, Ei_2_g, Ei_2_b, Ei_2_y, Ei_2_gg, Ei_2_gb, Ei_2_gy, Ei_2_bg, Ei_2_bb, Ei_2_by, Ei_2_yg, Ei_2_yb, Ei_2_yy;
vec2 D_2_, D_2_g, D_2_b, D_2_y, D_2_gg, D_2_gb, D_2_gy, D_2_bg, D_2_bb, D_2_by, D_2_yg, D_2_yb, D_2_yy, D_3_, D_3_g, D_3_b, D_3_y, D_3_gg, D_3_gb, D_3_gy, D_3_bg, D_3_bb, D_3_by, D_3_yg, D_3_yb, D_3_yy;
vec2 E_2_, E_2_g, E_2_b, E_2_y, E_2_gg, E_2_gb, E_2_gy, E_2_bg, E_2_bb, E_2_by, E_2_yg, E_2_yb, E_2_yy, E_3_, E_3_g, E_3_b, E_3_y, E_3_gg, E_3_gb, E_3_gy, E_3_bg, E_3_bb, E_3_by, E_3_yg, E_3_yb, E_3_yy;
float R_g, R_b, R_y, R_gg, R_gb, R_gy, R_bg, R_bb, R_by, R_yg, R_yb, R_yy;
fmg = float(mg);
fmb = float(mb);
fatmy = 10.f * float(my);
R_g = 2.f * fmg;
R_b = 2.f * fmb;
R_y = 2.f * fatmy;
R_gg = 8.f * pow(fmg, 2.f);
R_gb = 8.f * fmg * fmb;
R_gy = 8.f * fmg * fatmy;
R_bg = 8.f * fmg * fmb;
R_bb = 8.f * pow(fmb, 2.f);
R_by = 8.f * fmb * fatmy;
R_yg = 8.f * fmg * fatmy;
R_yb = 8.f * fmb * fatmy;
R_yy = 8.f * pow(fatmy, 2.f);
dsup = 0.f;
esup = 0.f;
zg = goffset + gl_GlobalInvocationID.x;
fg = float(zg) / fmg;
zb = boffset + gl_GlobalInvocationID.y;
fb = float(zb) / fmb;
for(q = 0; q < 10; q++){
fq = float(q);
dsum = 0.f;
esum = 0.f;
for(n = 0; n <= 1031; n++){
dsummandsup = 0.f;
esummandsup = 0.f;
fys = float(n) / 10.f;
for(zy = 0; zy <= my; zy++){
fymb = fys + float(zy) / fatmy - fb;
t = fb + fymb;
Di_0_ = one + fe(1.e-1f * fq + t) + fe(2.e-1f * fq + 2.f * t) + fe(3.e-1f * fq + 3.f * t) + fe(4.e-1f * fq + 4.f * t) + fe(5.e-1f * fq + 5.f * t) + fe(6.e-1f * fq + 6.f * t) + fe(7.e-1f * fq + 7.f * t) + fe(8.e-1f * fq + 8.f * t) + fe(9.e-1f * fq + 9.f * t);
Ei_0_ = fe(10.f * t);
td = fe(1.e-1f * fq + t) + 2.f * fe(2.e-1f * fq + 2.f * t) + 3.f * fe(3.e-1f * fq + 3.f * t) + 4.f * fe(4.e-1f * fq + 4.f * t) + 5.f * fe(5.e-1f * fq + 5.f * t) + 6.f * fe(6.e-1f * fq + 6.f * t) + 7.f * fe(7.e-1f * fq + 7.f * t) + 8.f * fe(8.e-1f * fq + 8.f * t) + 9.f * fe(9.e-1f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_0_y = 6.2831853e0f * td; Ei_0_y = 6.2831853e1f * te;
td = fe(1.e-1f * fq + t) + 4.f * fe(2.e-1f * fq + 2.f * t) + 9.f * fe(3.e-1f * fq + 3.f * t) + 16.f * fe(4.e-1f * fq + 4.f * t) + 25.f * fe(5.e-1f * fq + 5.f * t) + 36.f * fe(6.e-1f * fq + 6.f * t) + 49.f * fe(7.e-1f * fq + 7.f * t) + 64.f * fe(8.e-1f * fq + 8.f * t) + 81.f * fe(9.e-1f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_0_yy = 3.9478418e1f * td; Ei_0_yy = 3.9478418e3f * te;
t = fg + fb + 9.9019514e-2f * fymb;
Di_1_ = one + fe(-fq + t) + fe(-2.f * fq + 2.f * t) + fe(-3.f * fq + 3.f * t) + fe(-4.f * fq + 4.f * t) + fe(-5.f * fq + 5.f * t) + fe(-6.f * fq + 6.f * t) + fe(-7.f * fq + 7.f * t) + fe(-8.f * fq + 8.f * t) + fe(-9.f * fq + 9.f * t);
Ei_1_ = fe(10.f * t);
td = fe(-fq + t) + 2.f * fe(-2.f * fq + 2.f * t) + 3.f * fe(-3.f * fq + 3.f * t) + 4.f * fe(-4.f * fq + 4.f * t) + 5.f * fe(-5.f * fq + 5.f * t) + 6.f * fe(-6.f * fq + 6.f * t) + 7.f * fe(-7.f * fq + 7.f * t) + 8.f * fe(-8.f * fq + 8.f * t) + 9.f * fe(-9.f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_1_g = 6.2831853e0f * td; Ei_1_g = 6.2831853e1f * te;
Di_1_b = 5.6610274e0f * td; Ei_1_b = 5.6610274e1f * te;
Di_1_y = 6.2215795e-1f * td; Ei_1_y = 6.2215795e0f * te;
td = fe(-fq + t) + 4.f * fe(-2.f * fq + 2.f * t) + 9.f * fe(-3.f * fq + 3.f * t) + 16.f * fe(-4.f * fq + 4.f * t) + 25.f * fe(-5.f * fq + 5.f * t) + 36.f * fe(-6.f * fq + 6.f * t) + 49.f * fe(-7.f * fq + 7.f * t) + 64.f * fe(-8.f * fq + 8.f * t) + 81.f * fe(-9.f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_1_gg = 3.9478418e1f * td; Ei_1_gg = 3.9478418e3f * te;
Di_1_gb = 3.5569284e1f * td; Ei_1_gb = 3.5569284e3f * te;
Di_1_gy = 3.9091337e0f * td; Ei_1_gy = 3.9091337e2f * te;
Di_1_bg = 3.5569284e1f * td; Ei_1_bg = 3.5569284e3f * te;
Di_1_bb = 3.2047231e1f * td; Ei_1_bb = 3.2047231e3f * te;
Di_1_by = 3.5220532e0f * td; Ei_1_by = 3.5220532e2f * te;
Di_1_yg = 3.9091337e0f * td; Ei_1_yg = 3.9091337e2f * te;
Di_1_yb = 3.5220532e0f * td; Ei_1_yb = 3.5220532e2f * te;
Di_1_yy = 3.8708052e-1f * td; Ei_1_yy = 3.8708052e1f * te;
t = -10.f * fg + fb + 9.8048641e-3f * fymb;
Di_2_ = one + fe(1.01e1f * fq + t) + fe(2.02e1f * fq + 2.f * t) + fe(3.03e1f * fq + 3.f * t) + fe(4.04e1f * fq + 4.f * t) + fe(5.05e1f * fq + 5.f * t) + fe(6.06e1f * fq + 6.f * t) + fe(7.07e1f * fq + 7.f * t) + fe(8.08e1f * fq + 8.f * t) + fe(9.09e1f * fq + 9.f * t);
Ei_2_ = fe(10.f * t);
td = fe(1.01e1f * fq + t) + 2.f * fe(2.02e1f * fq + 2.f * t) + 3.f * fe(3.03e1f * fq + 3.f * t) + 4.f * fe(4.04e1f * fq + 4.f * t) + 5.f * fe(5.05e1f * fq + 5.f * t) + 6.f * fe(6.06e1f * fq + 6.f * t) + 7.f * fe(7.07e1f * fq + 7.f * t) + 8.f * fe(8.08e1f * fq + 8.f * t) + 9.f * fe(9.09e1f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_2_g = -6.2831853e1f * td; Ei_2_g = -6.2831853e2f * te;
Di_2_b = 6.2215795e0f * td; Ei_2_b = 6.2215795e1f * te;
Di_2_y = 6.1605778e-2f * td; Ei_2_y = 6.1605778e-1f * te;
td = fe(1.01e1f * fq + t) + 4.f * fe(2.02e1f * fq + 2.f * t) + 9.f * fe(3.03e1f * fq + 3.f * t) + 16.f * fe(4.04e1f * fq + 4.f * t) + 25.f * fe(5.05e1f * fq + 5.f * t) + 36.f * fe(6.06e1f * fq + 6.f * t) + 49.f * fe(7.07e1f * fq + 7.f * t) + 64.f * fe(8.08e1f * fq + 8.f * t) + 81.f * fe(9.09e1f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_2_gg = 3.9478418e3f * td; Ei_2_gg = 3.9478418e5f * te;
Di_2_gb = -3.9091337e2f * td; Ei_2_gb = -3.9091337e4f * te;
Di_2_gy = -3.8708052e0f * td; Ei_2_gy = -3.8708052e2f * te;
Di_2_bg = -3.9091337e2f * td; Ei_2_bg = -3.9091337e4f * te;
Di_2_bb = 3.8708052e1f * td; Ei_2_bb = 3.8708052e3f * te;
Di_2_by = 3.8328525e-1f * td; Ei_2_by = 3.8328525e1f * te;
Di_2_yg = -3.8708052e0f * td; Ei_2_yg = -3.8708052e2f * te;
Di_2_yb = 3.8328525e-1f * td; Ei_2_yb = 3.8328525e1f * te;
Di_2_yy = 3.7952719e-3f * td; Ei_2_yy = 3.7952719e-1f * te;
D_2_ = fComplexTimes(Di_0_, Di_1_) + Ei_0_;
D_2_g = fComplexTimes(Di_0_, Di_1_g);
D_2_b = fComplexTimes(Di_0_, Di_1_b);
D_2_y = fComplexTimes(Di_0_y, Di_1_) + fComplexTimes(Di_0_, Di_1_y) + Ei_0_y;
D_2_gg = fComplexTimes(Di_0_, Di_1_gg);
D_2_gb = fComplexTimes(Di_0_, Di_1_gb);
D_2_gy = fComplexTimes(Di_0_y, Di_1_g) + fComplexTimes(Di_0_, Di_1_gy);
D_2_bg = fComplexTimes(Di_0_, Di_1_bg);
D_2_bb = fComplexTimes(Di_0_, Di_1_bb);
D_2_by = fComplexTimes(Di_0_y, Di_1_b) + fComplexTimes(Di_0_, Di_1_by);
D_2_yg = fComplexTimes(Di_0_y, Di_1_g) + fComplexTimes(Di_0_, Di_1_yg);
D_2_yb = fComplexTimes(Di_0_y, Di_1_b) + fComplexTimes(Di_0_, Di_1_yb);
D_2_yy = fComplexTimes(Di_0_yy, Di_1_) + fComplexTimes(Di_0_y, Di_1_y) + fComplexTimes(Di_0_y, Di_1_y) + fComplexTimes(Di_0_, Di_1_yy) + Ei_0_yy;
E_2_ = fComplexTimes(Di_0_, Ei_1_);
E_2_g = fComplexTimes(Di_0_, Ei_1_g);
E_2_b = fComplexTimes(Di_0_, Ei_1_b);
E_2_y = fComplexTimes(Di_0_y, Ei_1_) + fComplexTimes(Di_0_, Ei_1_y);
E_2_gg = fComplexTimes(Di_0_, Ei_1_gg);
E_2_gb = fComplexTimes(Di_0_, Ei_1_gb);
E_2_gy = fComplexTimes(Di_0_y, Ei_1_g) + fComplexTimes(Di_0_, Ei_1_gy);
E_2_bg = fComplexTimes(Di_0_, Ei_1_bg);
E_2_bb = fComplexTimes(Di_0_, Ei_1_bb);
E_2_by = fComplexTimes(Di_0_y, Ei_1_b) + fComplexTimes(Di_0_, Ei_1_by);
E_2_yg = fComplexTimes(Di_0_y, Ei_1_g) + fComplexTimes(Di_0_, Ei_1_yg);
E_2_yb = fComplexTimes(Di_0_y, Ei_1_b) + fComplexTimes(Di_0_, Ei_1_yb);
E_2_yy = fComplexTimes(Di_0_yy, Ei_1_) + fComplexTimes(Di_0_y, Ei_1_y) + fComplexTimes(Di_0_y, Ei_1_y) + fComplexTimes(Di_0_, Ei_1_yy);
D_3_ = fComplexTimes(D_2_, Di_2_) + E_2_;
D_3_g = fComplexTimes(D_2_g, Di_2_) + fComplexTimes(D_2_, Di_2_g) + E_2_g;
D_3_b = fComplexTimes(D_2_b, Di_2_) + fComplexTimes(D_2_, Di_2_b) + E_2_b;
D_3_y = fComplexTimes(D_2_y, Di_2_) + fComplexTimes(D_2_, Di_2_y) + E_2_y;
D_3_gg = fComplexTimes(D_2_gg, Di_2_) + fComplexTimes(D_2_g, Di_2_g) + fComplexTimes(D_2_g, Di_2_g) + fComplexTimes(D_2_, Di_2_gg) + E_2_gg;
D_3_gb = fComplexTimes(D_2_gb, Di_2_) + fComplexTimes(D_2_g, Di_2_b) + fComplexTimes(D_2_b, Di_2_g) + fComplexTimes(D_2_, Di_2_gb) + E_2_gb;
D_3_gy = fComplexTimes(D_2_gy, Di_2_) + fComplexTimes(D_2_g, Di_2_y) + fComplexTimes(D_2_y, Di_2_g) + fComplexTimes(D_2_, Di_2_gy) + E_2_gy;
D_3_bg = fComplexTimes(D_2_bg, Di_2_) + fComplexTimes(D_2_b, Di_2_g) + fComplexTimes(D_2_g, Di_2_b) + fComplexTimes(D_2_, Di_2_bg) + E_2_bg;
D_3_bb = fComplexTimes(D_2_bb, Di_2_) + fComplexTimes(D_2_b, Di_2_b) + fComplexTimes(D_2_b, Di_2_b) + fComplexTimes(D_2_, Di_2_bb) + E_2_bb;
D_3_by = fComplexTimes(D_2_by, Di_2_) + fComplexTimes(D_2_b, Di_2_y) + fComplexTimes(D_2_y, Di_2_b) + fComplexTimes(D_2_, Di_2_by) + E_2_by;
//The bug occurs here: Use one of the two following semantically identical lines to get different results
D_3_yg = fComplexTimes(D_2_gy, Di_2_) + fComplexTimes(D_2_g, Di_2_y) + fComplexTimes(D_2_y, Di_2_g) + fComplexTimes(D_2_, Di_2_gy) + E_2_gy;
//D_3_yg = D_3_gy;
D_3_yb = fComplexTimes(D_2_yb, Di_2_) + fComplexTimes(D_2_y, Di_2_b) + fComplexTimes(D_2_b, Di_2_y) + fComplexTimes(D_2_, Di_2_yb) + E_2_yb;
D_3_yy = fComplexTimes(D_2_yy, Di_2_) + fComplexTimes(D_2_y, Di_2_y) + fComplexTimes(D_2_y, Di_2_y) + fComplexTimes(D_2_, Di_2_yy) + E_2_yy;
dabs = length(D_3_) + length(D_3_g) / R_g + length(D_3_b) / R_b + length(D_3_y) / R_y + length(D_3_gg) / R_gg + length(D_3_gb) / R_gb + length(D_3_gy) / R_gy + length(D_3_bg) / R_bg + length(D_3_bb) / R_bb + length(D_3_by) / R_by + length(D_3_yg) / R_yg + length(D_3_yb) / R_yb + length(D_3_yy) / R_yy;
dsummandsup = max(dsummandsup, dabs);
E_3_ = fComplexTimes(D_2_, Ei_2_);
E_3_g = fComplexTimes(D_2_g, Ei_2_) + fComplexTimes(D_2_, Ei_2_g);
E_3_b = fComplexTimes(D_2_b, Ei_2_) + fComplexTimes(D_2_, Ei_2_b);
E_3_y = fComplexTimes(D_2_y, Ei_2_) + fComplexTimes(D_2_, Ei_2_y);
E_3_gg = fComplexTimes(D_2_gg, Ei_2_) + fComplexTimes(D_2_g, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gg);
E_3_gb = fComplexTimes(D_2_gb, Ei_2_) + fComplexTimes(D_2_g, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gb);
E_3_gy = fComplexTimes(D_2_gy, Ei_2_) + fComplexTimes(D_2_g, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gy);
E_3_bg = fComplexTimes(D_2_bg, Ei_2_) + fComplexTimes(D_2_b, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_b) + fComplexTimes(D_2_, Ei_2_bg);
E_3_bb = fComplexTimes(D_2_bb, Ei_2_) + fComplexTimes(D_2_b, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_b) + fComplexTimes(D_2_, Ei_2_bb);
E_3_by = fComplexTimes(D_2_by, Ei_2_) + fComplexTimes(D_2_b, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_b) + fComplexTimes(D_2_, Ei_2_by);
E_3_yg = fComplexTimes(D_2_yg, Ei_2_) + fComplexTimes(D_2_y, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yg);
E_3_yb = fComplexTimes(D_2_yb, Ei_2_) + fComplexTimes(D_2_y, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yb);
E_3_yy = fComplexTimes(D_2_yy, Ei_2_) + fComplexTimes(D_2_y, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yy);
eabs = length(E_3_) + length(E_3_g) / R_g + length(E_3_b) / R_b + length(E_3_y) / R_y + length(E_3_gg) / R_gg + length(E_3_gb) / R_gb + length(E_3_gy) / R_gy + length(E_3_bg) / R_bg + length(E_3_bb) / R_bb + length(E_3_by) / R_by + length(E_3_yg) / R_yg + length(E_3_yb) / R_yb + length(E_3_yy) / R_yy;
esummandsup = max(esummandsup, eabs);
}
dsum += dsummandsup;
esum += esummandsup;
}
for(n = 1032; n <= 10402; n++){
dsummandsup = 0.f;
esummandsup = 0.f;
fys = float(n) / 10.f;
for(zy = 0; zy <= my; zy++){
fymb = fys + float(zy) / fatmy - fb;
t = fb + fymb;
Di_0_ = one + fe(1.e-1f * fq + t) + fe(2.e-1f * fq + 2.f * t) + fe(3.e-1f * fq + 3.f * t) + fe(4.e-1f * fq + 4.f * t) + fe(5.e-1f * fq + 5.f * t) + fe(6.e-1f * fq + 6.f * t) + fe(7.e-1f * fq + 7.f * t) + fe(8.e-1f * fq + 8.f * t) + fe(9.e-1f * fq + 9.f * t);
Ei_0_ = fe(10.f * t);
td = fe(1.e-1f * fq + t) + 2.f * fe(2.e-1f * fq + 2.f * t) + 3.f * fe(3.e-1f * fq + 3.f * t) + 4.f * fe(4.e-1f * fq + 4.f * t) + 5.f * fe(5.e-1f * fq + 5.f * t) + 6.f * fe(6.e-1f * fq + 6.f * t) + 7.f * fe(7.e-1f * fq + 7.f * t) + 8.f * fe(8.e-1f * fq + 8.f * t) + 9.f * fe(9.e-1f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_0_y = 6.2831853e0f * td; Ei_0_y = 6.2831853e1f * te;
td = fe(1.e-1f * fq + t) + 4.f * fe(2.e-1f * fq + 2.f * t) + 9.f * fe(3.e-1f * fq + 3.f * t) + 16.f * fe(4.e-1f * fq + 4.f * t) + 25.f * fe(5.e-1f * fq + 5.f * t) + 36.f * fe(6.e-1f * fq + 6.f * t) + 49.f * fe(7.e-1f * fq + 7.f * t) + 64.f * fe(8.e-1f * fq + 8.f * t) + 81.f * fe(9.e-1f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_0_yy = 3.9478418e1f * td; Ei_0_yy = 3.9478418e3f * te;
t = fg + fb + 9.9019514e-2f * fymb;
Di_1_ = one + fe(-fq + t) + fe(-2.f * fq + 2.f * t) + fe(-3.f * fq + 3.f * t) + fe(-4.f * fq + 4.f * t) + fe(-5.f * fq + 5.f * t) + fe(-6.f * fq + 6.f * t) + fe(-7.f * fq + 7.f * t) + fe(-8.f * fq + 8.f * t) + fe(-9.f * fq + 9.f * t);
Ei_1_ = fe(10.f * t);
td = fe(-fq + t) + 2.f * fe(-2.f * fq + 2.f * t) + 3.f * fe(-3.f * fq + 3.f * t) + 4.f * fe(-4.f * fq + 4.f * t) + 5.f * fe(-5.f * fq + 5.f * t) + 6.f * fe(-6.f * fq + 6.f * t) + 7.f * fe(-7.f * fq + 7.f * t) + 8.f * fe(-8.f * fq + 8.f * t) + 9.f * fe(-9.f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_1_g = 6.2831853e0f * td; Ei_1_g = 6.2831853e1f * te;
Di_1_b = 5.6610274e0f * td; Ei_1_b = 5.6610274e1f * te;
Di_1_y = 6.2215795e-1f * td; Ei_1_y = 6.2215795e0f * te;
td = fe(-fq + t) + 4.f * fe(-2.f * fq + 2.f * t) + 9.f * fe(-3.f * fq + 3.f * t) + 16.f * fe(-4.f * fq + 4.f * t) + 25.f * fe(-5.f * fq + 5.f * t) + 36.f * fe(-6.f * fq + 6.f * t) + 49.f * fe(-7.f * fq + 7.f * t) + 64.f * fe(-8.f * fq + 8.f * t) + 81.f * fe(-9.f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_1_gg = 3.9478418e1f * td; Ei_1_gg = 3.9478418e3f * te;
Di_1_gb = 3.5569284e1f * td; Ei_1_gb = 3.5569284e3f * te;
Di_1_gy = 3.9091337e0f * td; Ei_1_gy = 3.9091337e2f * te;
Di_1_bg = 3.5569284e1f * td; Ei_1_bg = 3.5569284e3f * te;
Di_1_bb = 3.2047231e1f * td; Ei_1_bb = 3.2047231e3f * te;
Di_1_by = 3.5220532e0f * td; Ei_1_by = 3.5220532e2f * te;
Di_1_yg = 3.9091337e0f * td; Ei_1_yg = 3.9091337e2f * te;
Di_1_yb = 3.5220532e0f * td; Ei_1_yb = 3.5220532e2f * te;
Di_1_yy = 3.8708052e-1f * td; Ei_1_yy = 3.8708052e1f * te;
t = -10.f * fg + fb + 9.8048641e-3f * fymb;
Di_2_ = one + fe(1.01e1f * fq + t) + fe(2.02e1f * fq + 2.f * t) + fe(3.03e1f * fq + 3.f * t) + fe(4.04e1f * fq + 4.f * t) + fe(5.05e1f * fq + 5.f * t) + fe(6.06e1f * fq + 6.f * t) + fe(7.07e1f * fq + 7.f * t) + fe(8.08e1f * fq + 8.f * t) + fe(9.09e1f * fq + 9.f * t);
Ei_2_ = fe(10.f * t);
td = fe(1.01e1f * fq + t) + 2.f * fe(2.02e1f * fq + 2.f * t) + 3.f * fe(3.03e1f * fq + 3.f * t) + 4.f * fe(4.04e1f * fq + 4.f * t) + 5.f * fe(5.05e1f * fq + 5.f * t) + 6.f * fe(6.06e1f * fq + 6.f * t) + 7.f * fe(7.07e1f * fq + 7.f * t) + 8.f * fe(8.08e1f * fq + 8.f * t) + 9.f * fe(9.09e1f * fq + 9.f * t); td = fComplexTimesI(td);
te = fe(10.f * t); te = fComplexTimesI(te);
Di_2_g = -6.2831853e1f * td; Ei_2_g = -6.2831853e2f * te;
Di_2_b = 6.2215795e0f * td; Ei_2_b = 6.2215795e1f * te;
Di_2_y = 6.1605778e-2f * td; Ei_2_y = 6.1605778e-1f * te;
td = fe(1.01e1f * fq + t) + 4.f * fe(2.02e1f * fq + 2.f * t) + 9.f * fe(3.03e1f * fq + 3.f * t) + 16.f * fe(4.04e1f * fq + 4.f * t) + 25.f * fe(5.05e1f * fq + 5.f * t) + 36.f * fe(6.06e1f * fq + 6.f * t) + 49.f * fe(7.07e1f * fq + 7.f * t) + 64.f * fe(8.08e1f * fq + 8.f * t) + 81.f * fe(9.09e1f * fq + 9.f * t); td = -td;
te = fe(10.f * t); te = -te;
Di_2_gg = 3.9478418e3f * td; Ei_2_gg = 3.9478418e5f * te;
Di_2_gb = -3.9091337e2f * td; Ei_2_gb = -3.9091337e4f * te;
Di_2_gy = -3.8708052e0f * td; Ei_2_gy = -3.8708052e2f * te;
Di_2_bg = -3.9091337e2f * td; Ei_2_bg = -3.9091337e4f * te;
Di_2_bb = 3.8708052e1f * td; Ei_2_bb = 3.8708052e3f * te;
Di_2_by = 3.8328525e-1f * td; Ei_2_by = 3.8328525e1f * te;
Di_2_yg = -3.8708052e0f * td; Ei_2_yg = -3.8708052e2f * te;
Di_2_yb = 3.8328525e-1f * td; Ei_2_yb = 3.8328525e1f * te;
Di_2_yy = 3.7952719e-3f * td; Ei_2_yy = 3.7952719e-1f * te;
D_2_ = fComplexTimes(Di_0_, Di_1_) + Ei_0_;
D_2_g = fComplexTimes(Di_0_, Di_1_g);
D_2_b = fComplexTimes(Di_0_, Di_1_b);
D_2_y = fComplexTimes(Di_0_y, Di_1_) + fComplexTimes(Di_0_, Di_1_y) + Ei_0_y;
D_2_gg = fComplexTimes(Di_0_, Di_1_gg);
D_2_gb = fComplexTimes(Di_0_, Di_1_gb);
D_2_gy = fComplexTimes(Di_0_y, Di_1_g) + fComplexTimes(Di_0_, Di_1_gy);
D_2_bg = fComplexTimes(Di_0_, Di_1_bg);
D_2_bb = fComplexTimes(Di_0_, Di_1_bb);
D_2_by = fComplexTimes(Di_0_y, Di_1_b) + fComplexTimes(Di_0_, Di_1_by);
D_2_yg = fComplexTimes(Di_0_y, Di_1_g) + fComplexTimes(Di_0_, Di_1_yg);
D_2_yb = fComplexTimes(Di_0_y, Di_1_b) + fComplexTimes(Di_0_, Di_1_yb);
D_2_yy = fComplexTimes(Di_0_yy, Di_1_) + fComplexTimes(Di_0_y, Di_1_y) + fComplexTimes(Di_0_y, Di_1_y) + fComplexTimes(Di_0_, Di_1_yy) + Ei_0_yy;
E_2_ = fComplexTimes(Di_0_, Ei_1_);
E_2_g = fComplexTimes(Di_0_, Ei_1_g);
E_2_b = fComplexTimes(Di_0_, Ei_1_b);
E_2_y = fComplexTimes(Di_0_y, Ei_1_) + fComplexTimes(Di_0_, Ei_1_y);
E_2_gg = fComplexTimes(Di_0_, Ei_1_gg);
E_2_gb = fComplexTimes(Di_0_, Ei_1_gb);
E_2_gy = fComplexTimes(Di_0_y, Ei_1_g) + fComplexTimes(Di_0_, Ei_1_gy);
E_2_bg = fComplexTimes(Di_0_, Ei_1_bg);
E_2_bb = fComplexTimes(Di_0_, Ei_1_bb);
E_2_by = fComplexTimes(Di_0_y, Ei_1_b) + fComplexTimes(Di_0_, Ei_1_by);
E_2_yg = fComplexTimes(Di_0_y, Ei_1_g) + fComplexTimes(Di_0_, Ei_1_yg);
E_2_yb = fComplexTimes(Di_0_y, Ei_1_b) + fComplexTimes(Di_0_, Ei_1_yb);
E_2_yy = fComplexTimes(Di_0_yy, Ei_1_) + fComplexTimes(Di_0_y, Ei_1_y) + fComplexTimes(Di_0_y, Ei_1_y) + fComplexTimes(Di_0_, Ei_1_yy);
E_3_ = fComplexTimes(D_2_, Ei_2_);
E_3_g = fComplexTimes(D_2_g, Ei_2_) + fComplexTimes(D_2_, Ei_2_g);
E_3_b = fComplexTimes(D_2_b, Ei_2_) + fComplexTimes(D_2_, Ei_2_b);
E_3_y = fComplexTimes(D_2_y, Ei_2_) + fComplexTimes(D_2_, Ei_2_y);
E_3_gg = fComplexTimes(D_2_gg, Ei_2_) + fComplexTimes(D_2_g, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gg);
E_3_gb = fComplexTimes(D_2_gb, Ei_2_) + fComplexTimes(D_2_g, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gb);
E_3_gy = fComplexTimes(D_2_gy, Ei_2_) + fComplexTimes(D_2_g, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_g) + fComplexTimes(D_2_, Ei_2_gy);
E_3_bg = fComplexTimes(D_2_bg, Ei_2_) + fComplexTimes(D_2_b, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_b) + fComplexTimes(D_2_, Ei_2_bg);
E_3_bb = fComplexTimes(D_2_bb, Ei_2_) + fComplexTimes(D_2_b, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_b) + fComplexTimes(D_2_, Ei_2_bb);
E_3_by = fComplexTimes(D_2_by, Ei_2_) + fComplexTimes(D_2_b, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_b) + fComplexTimes(D_2_, Ei_2_by);
E_3_yg = fComplexTimes(D_2_yg, Ei_2_) + fComplexTimes(D_2_y, Ei_2_g) + fComplexTimes(D_2_g, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yg);
E_3_yb = fComplexTimes(D_2_yb, Ei_2_) + fComplexTimes(D_2_y, Ei_2_b) + fComplexTimes(D_2_b, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yb);
E_3_yy = fComplexTimes(D_2_yy, Ei_2_) + fComplexTimes(D_2_y, Ei_2_y) + fComplexTimes(D_2_y, Ei_2_y) + fComplexTimes(D_2_, Ei_2_yy);
eabs = length(E_3_) + length(E_3_g) / R_g + length(E_3_b) / R_b + length(E_3_y) / R_y + length(E_3_gg) / R_gg + length(E_3_gb) / R_gb + length(E_3_gy) / R_gy + length(E_3_bg) / R_bg + length(E_3_bb) / R_bb + length(E_3_by) / R_by + length(E_3_yg) / R_yg + length(E_3_yb) / R_yb + length(E_3_yy) / R_yy;
esummandsup = max(esummandsup, eabs);
}
dsum += dsummandsup;
esum += esummandsup;
}
dsup = max(dsup, dsum);
esup = max(esup, esum);
}
}
void main(void){
fDESupTaylor_a10_w3_d2();
Output.Data[gl_GlobalInvocationID.x][gl_GlobalInvocationID.y][0] = dsup;
Output.Data[gl_GlobalInvocationID.x][gl_GlobalInvocationID.y][1] = esup;
}
If I run the above program and use one of the two identical lines in the shader which I marked with a comment I get different results for the value esup (second of the printed values). If I use the first line
D_3_yg = fComplexTimes(D_2_gy, Di_2_) + fComplexTimes(D_2_g, Di_2_y) + fComplexTimes(D_2_y, Di_2_g) + fComplexTimes(D_2_, Di_2_gy) + E_2_gy;
I get esup = 85930.453 and if I use
D_3_yg = D_3_gy;
(note that this should give the same result) I get esup = 85928.164.
Also, If I change the lines
zg = goffset + gl_GlobalInvocationID.x;
fg = float(zg) / fmg;
zb = boffset + gl_GlobalInvocationID.y;
fb = float(zb) / fmb;
to
zg = gl_GlobalInvocationID.x;
fg = float(zg) / fmg;
zb = gl_GlobalInvocationID.y;
fb = float(zb) / fmb;
(note that goffset and boffset are set to 0 in C++) I get yet another result (esup = 85929.844 and esup = 85929.742 when I use the first or second lines respectively).
Another really strange aspect is that the "full bug" only seems to occur if the constant my is set to 128. For other values of my such as 64, 127, 129, or 256 changing the two lines does not change the value of esup but removing goffset and boffset still does.
Also, the value of D_3_yg (which is set by the two different lines) should actually play no role for the computation of esup but only for dsup. But dsup stays constant and esup changes.
I'm using an Nvidia Quadro M2000M and Visual Studio 2012 to compile. Any ideas what the problem could be?
Note that the program needs about 20 seconds to run and the screen freezes during that time. In Windows you need to increase your TdrDelay to, say, 60 (seconds)
https://learn.microsoft.com/en-us/windows-hardware/drivers/display/tdr-registry-keys
as Windows kills GPU computations which take longer than 2 seconds by default.

Answer 1

Your shader does a lot of float calculus. Any line operates with previous results. The precision error accumulates.
Also, the GPU may do calculations in higher precision; but each time you store the result it gets truncated. Some times the compiler can optimize it, some times it can't.
You should read
What Every Programmer Should Know About Floating-Point Arithmetic
or
What Every Computer Scientist Should Know About Floating-Point Arithmetic
Problems increase for some special, bad conditioned cases. A simple geometrical analogous issue is determinig the point of intersection between two almost parallel lines. The result can vary really a lot.
You should try to simplify those long calculations. Using double-precision types (available since OPenGL 4.0) may help, but perhaps not enough.