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我在其他系统中运行此示例。在Intel i7-3630QM，Intel HD4000和Radeon HD 7630M上，所有结果都是一样的。对于i7-4700MQ / 4800MQ，当使用32位gcc的OpenCL或64位gcc时，CPU的结果会有所不同。这是64位gcc和OpenCl默认使用SSE而32位gcc使用387数学运算的结果，至少64位gcc在设置-mfpmath = 387时产生相同的结果。所以我必须阅读更多内容并尝试使用x86浮点。谢谢大家的答案。

我从＆＃34;编程CUDA和OpenCL运行Lorenz系统示例：使用现代C ++库的案例研究＆＃34;对于不同的OpenCL设备上的十个系统，我得到的结果不同：

Quadro K1100M（NVIDIA CUDA）

R =＆gt; x y z
0.100000 =＆gt; -0.000000 -0.000000 0.000000
5.644444 =＆gt; -3.519254 -3.519250 4.644452
11.188890 =＆gt; 5.212534 5.212530 10.188904
16.733334 =＆gt; 6.477303 6.477297 15.733333



22.277779 =＆gt; 3.178553 2.579687 17.946903
    27.822224 =＆gt; 5.008720 7.753564 16.377680
    33.366669 =＆gt; -13.381100 -15.252210 36.107887
    38.911114 =＆gt; 4.256534 6.813675 23.838787
    44.455555 =＆gt; -11.083726 0.691549 53.632290
    50.000000 =＆gt; -8.624105 -15.728293 32.516193
英特尔（R）HD Graphics 4600（英特尔（R）OpenCL）

R =＆gt; x y z
0.100000 =＆gt; -0.000000 -0.000000 0.000000
5.644444 =＆gt; -3.519253 -3.519250 4.644451
11.188890 =＆gt; 5.212531 5.212538 10.188890
16.733334 =＆gt; 6.477320 6.477326 15.733339



22.277779 =＆gt; 7.246771 7.398651 20.735369
    27.822224 =＆gt; -6.295782 -10.615027 14.646572
    33.366669 =＆gt; -4.132523 -7.773201 14.292910
    38.911114 =＆gt; 14.183139 19.582197 37.943520
    44.455555 =＆gt; -3.129006 7.564254 45.736408
    50.000000 =＆gt; -9.146419 -17.006729 32.976696
Intel（R）Core（TM）i7-4800MQ CPU @ 2.70GHz（英特尔（R）OpenCL）

R =＆gt; x y z
0.100000 =＆gt; -0.000000 -0.000000 0.000000
5.644444 =＆gt; -3.519254 -3.519251 4.644453
11.188890 =＆gt; 5.212513 5.212507 10.188900
16.733334 =＆gt; 6.477303 6.477296 15.733332



22.277779 =＆gt; -8.295195 -8.198518 22.271002
    27.822224 =＆gt; -4.329878 -4.022876 22.573458
    33.366669 =＆gt; 9.702943 3.997370 38.659538
    38.911114 =＆gt; 16.105495 14.401397 48.537579
    44.455555 =＆gt; -12.551083 -9.239071 49.378693
    50.000000 =＆gt; 7.377638 3.447747 47.542763

正如您所看到的，这三个设备同意R = 16.733334的值，然后开始分歧。

我在没有VexCL的情况下使用odeint运行相同的区域，并且在CPU运行时得到的结果接近OpenCL的结果：

Vanilla odeint：

R => x y z
16.733334 => 6.47731 6.47731 15.7333
22.277779 =>  -8.55303 -6.72512 24.7049
27.822224 => 3.88874 3.72254 21.8227

示例代码可在此处找到：https://github.com/ddemidov/gpgpu_with_modern_cpp/blob/master/src/lorenz_ensemble/vexcl_lorenz_ensemble.cpp

我不确定我在这看到的是什么？由于CPU结果彼此如此接近，它看起来像GPU的问题，但由于我是一个OpenCL新手，我需要一些指示如何找到这个的根本原因。

Answer 1

您必须了解GPU的精度低于CPU。这是常见的，因为GPU专为游戏而设计，其中精确值不是设计目标。

通常GPU精度为32位。虽然CPU内部具有48或64位精度数学运算，但即使结果被切割为32位存储。

您运行的操作在很大程度上取决于这些小差异，为每个设备创建不同的结果。例如，此操作也会根据准确度创建非常不同的结果：

a=1/(b-c); 
a=1/(b-c); //b = 1.00001, c = 1.00002  -> a = -100000
a=1/(b-c); //b = 1.0000098, c = 1.000021  -> a = -89285.71428

在您自己的结果中，您可以看到每个设备的不同，即使是低R值：

5.644444 => -3.519254 -3.519250 4.644452
5.644444 => -3.519253 -3.519250 4.644451
5.644444 => -3.519254 -3.519251 4.644453

但是，您声明“对于低值，结果同意R=16，然后开始分歧”。嗯，这取决于，因为它们并不完全相同，即使是R=5.64。

Answer 2

我已经创建了一个stackoverflow-23805423分支来测试它。以下是不同设备的输出。请注意，CPU和AMD GPU都具有一致的结果。 Nvidia GPU也有一致的结果，只有那些不同。这个问题似乎有关：IEEE-754 standard on NVIDIA GPU (sm_13)

```

1. Intel(R) Core(TM) i7 CPU         920  @ 2.67GHz (Intel(R) OpenCL)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  9.392907e-01  1.679711e+00  1.455276e+01) (  5.351486e+00  1.051580e+01  9.403333e+00)
     6: ( -1.287673e+01 -2.096754e+01  2.790419e+01) ( -6.555650e-01 -2.142401e+00  2.721632e+01)
     8: (  2.711249e+00  2.540842e+00  3.259012e+01) ( -4.936437e+00  8.534876e-02  4.604861e+01)
}

1. Intel(R) Core(TM) i5-3570K CPU @ 3.40GHz (AMD Accelerated Parallel Processing)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  9.392907e-01  1.679711e+00  1.455276e+01) (  5.351486e+00  1.051580e+01  9.403333e+00)
     6: ( -1.287673e+01 -2.096754e+01  2.790419e+01) ( -6.555650e-01 -2.142401e+00  2.721632e+01)
     8: (  2.711249e+00  2.540842e+00  3.259012e+01) ( -4.936437e+00  8.534876e-02  4.604861e+01)
}

1. Capeverde (AMD Accelerated Parallel Processing)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  9.392907e-01  1.679711e+00  1.455276e+01) (  5.351486e+00  1.051580e+01  9.403333e+00)
     6: ( -1.287673e+01 -2.096754e+01  2.790419e+01) ( -6.555650e-01 -2.142401e+00  2.721632e+01)
     8: (  2.711249e+00  2.540842e+00  3.259012e+01) ( -4.936437e+00  8.534876e-02  4.604861e+01)
}

1. Tesla C1060 (NVIDIA CUDA)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  7.636878e+00  2.252859e+00  2.964935e+01) (  1.373357e+01  8.995382e+00  3.998563e+01)
     6: (  7.163476e+00  8.802735e+00  2.839662e+01) ( -5.536365e+00 -5.997181e+00  3.191463e+01)
     8: ( -2.762679e+00 -5.167883e+00  2.324565e+01) (  2.776211e+00  4.734162e+00  2.949507e+01)
}

1. Tesla K20c (NVIDIA CUDA)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  7.636878e+00  2.252859e+00  2.964935e+01) (  1.373357e+01  8.995382e+00  3.998563e+01)
     6: (  7.163476e+00  8.802735e+00  2.839662e+01) ( -5.536365e+00 -5.997181e+00  3.191463e+01)
     8: ( -2.762679e+00 -5.167883e+00  2.324565e+01) (  2.776211e+00  4.734162e+00  2.949507e+01)
}

1. Tesla K40c (NVIDIA CUDA)

R = {
     0:  5.000000e+00  1.000000e+01  1.500000e+01  2.000000e+01  2.500000e+01
     5:  3.000000e+01  3.500000e+01  4.000000e+01  4.500000e+01  5.000000e+01
}

X = {
     0: ( -3.265986e+00 -3.265986e+00  4.000000e+00) (  4.898979e+00  4.898979e+00  9.000000e+00)
     2: (  6.110101e+00  6.110101e+00  1.400000e+01) ( -7.118047e+00 -7.118044e+00  1.900000e+01)
     4: (  7.636878e+00  2.252859e+00  2.964935e+01) (  1.373357e+01  8.995382e+00  3.998563e+01)
     6: (  7.163476e+00  8.802735e+00  2.839662e+01) ( -5.536365e+00 -5.997181e+00  3.191463e+01)
     8: ( -2.762679e+00 -5.167883e+00  2.324565e+01) (  2.776211e+00  4.734162e+00  2.949507e+01)
}

```

使用odeint和VexCL的Lorenz示例在不同设备上产生不同的结果

2 个答案: