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Single-precision `sum()` over certain axes sometimes deviates from NumPy's outcome

See original GitHub issue

When using single-precision floating numbers (float32 and complex64) and summing over a particular axis set (axis=(0, 1) for ndim=3; other possible axis combinations work fine), the result of sum(axis=axis) in CuPy is not the same (within tolerance) as that of NumPy.

Not sure how this can be fixed – most likely it’s due to a combination insufficient numerical precision and the order of operation on GPU, as this only happens randomly (depending on input). I believe CuPy’s ufunc implementation is correct, because this also happened with my experimental CUB support for sum(axis=axis) (see https://github.com/cupy/cupy/issues/2519#issuecomment-544531651), which does not use ufunc at all.

The test below is verified and reproducible on two different GPU machines with different environment setups.

Conditions (you can just paste the output of python -c 'import cupy; cupy.show_config()')

CuPy Version          : 7.0.0b4
CUDA Root             : /usr/local/cuda
CUDA Build Version    : 9010
CUDA Driver Version   : 9010
CUDA Runtime Version  : 9010
cuDNN Build Version   : None
cuDNN Version         : None
NCCL Build Version    : 2115
NCCL Runtime Version  : (unknown)

Code to reproduce:

import cupy as cp
from contextlib import contextmanager


@contextmanager
def sync_time(name):
    start = cp.cuda.Event()
    end = cp.cuda.Event()
    start.record()
    #start.synchronize()
    yield
    end.record()
    end.synchronize()
    t = cp.cuda.get_elapsed_time(start, end)
    print("{} : {} ms".format(name, t/N))


N = 100
shape = (400, 326, 287)
axis = (0, 1)

for dtype in (cp.float32, cp.complex64):
    if dtype is cp.float32:
        x = cp.random.random(shape, dtype=dtype)
    else:
        x = cp.random.random(shape).astype(dtype) + 1j * cp.random.random(shape).astype(dtype)
    x_np = cp.asnumpy(x) #move to cpu

    for func in ('sum',): #, 'max', 'min'):
        for keepdims in (False, True):
            print("testing", axis, "+", str(dtype), "+", "keepdims=", keepdims, "+", func, "...")

            y = None
            with sync_time("cupy"):
                for i in range(N):
                    y = getattr(x, func)(axis=axis, keepdims=keepdims)

            z = None
            with sync_time("numpy"):
                for i in range(N):
                    z = getattr(x_np, func)(axis=axis, keepdims=keepdims)

            try:
                assert cp.allclose(y, z)
            except AssertionError:
                print(y, z)

output:

testing (0, 1) + <class 'numpy.float32'> + keepdims= False + sum ...
cupy : 3.833934326171875 ms
numpy : 42.49509765625 ms
[65107.914 65282.875 65074.527 65245.703 65266.44  65286.04  65184.78
 65211.15  65307.42  65170.098 65158.305 65215.14  65141.066 65230.62
 65214.22  65119.094 65190.766 65161.977 65225.023 65134.875 65121.
 65294.008 65219.695 65240.64  65227.52  65444.656 65345.46  65153.312
 65024.04  65165.46  65223.586 65127.492 65289.99  65319.332 65268.336
 65325.74  65189.03  65193.254 65242.39  65374.28  65318.742 65159.24
 65151.15  65243.89  65171.    65236.367 65152.68  65242.    65187.816
 65183.47  65174.17  65066.973 65166.8   65240.254 65223.773 65232.934
 65282.848 65228.38  65221.734 65076.96  65212.434 64956.46  65161.156
 65248.61  64932.22  65230.9   65164.832 65301.64  65013.23  65292.457
 65153.93  65129.562 65159.97  65012.523 65105.11  65071.92  65223.633
 65228.176 65221.07  65147.34  65090.316 65007.17  65244.207 65090.633
 65204.258 65141.383 65109.605 65303.438 65145.023 65118.5   65162.703
 65051.19  65089.703 65132.79  65378.133 65325.844 65010.87  65214.14
 65181.883 65265.    65044.297 65202.914 65191.93  65093.992 65233.688
 65149.426 65034.61  65178.35  65255.484 65171.543 65185.45  65369.926
 65241.508 64994.617 65123.93  65361.902 65289.72  65063.234 65058.094
 65194.844 65137.633 65108.223 65169.094 65072.94  65245.15  65164.867
 65404.664 65034.87  65113.027 65195.656 65082.4   65249.93  65176.285
 65166.11  65156.22  65109.6   65119.69  65287.516 65305.855 65116.85
 65218.93  65180.117 65183.926 65069.03  65383.156 65127.586 65154.977
 65192.246 65270.613 65190.4   65234.477 65188.23  65082.664 65173.89
 65179.63  65081.54  65258.586 65239.27  65104.59  65188.19  65377.164
 65340.33  65277.566 65273.84  65360.4   64913.676 65230.035 65189.375
 65176.19  65145.055 65183.42  65287.6   65153.863 65253.086 65128.656
 65256.68  65142.11  65116.05  65289.883 65257.78  65202.5   65010.203
 65319.85  65172.47  65108.16  65154.11  65435.27  65155.46  65141.5
 65285.22  65269.426 65190.023 65073.77  65000.266 65048.54  65464.414
 65240.625 65199.78  65292.383 65203.21  65205.5   65174.68  65245.395
 65301.176 65377.043 65446.344 65074.4   65330.777 65270.45  65111.32
 65142.703 65242.203 65285.64  65023.3   65301.727 65062.633 65216.176
 65172.117 65168.15  65238.742 65212.816 65256.156 65153.105 65220.883
 65219.938 65346.453 65209.484 65186.78  65160.312 65279.64  65152.035
 65138.812 65313.457 65147.242 65368.098 65161.125 65293.492 65032.4
 65404.8   65326.9   65241.727 65219.797 64880.03  64901.67  65310.965
 65246.652 65217.465 65131.83  65206.484 65153.176 65250.65  65174.85
 65114.11  65147.35  65187.47  65149.758 65234.58  65211.24  65109.348
 65302.438 65206.617 65236.13  65377.47  65212.79  65493.26  65375.695
 65239.36  65135.438 65318.344 65170.797 65088.64  65204.184 65294.945
 65204.234 65475.164 65355.15  65273.21  65380.145 65257.37  65063.953
 65370.555 65265.113 65043.758 65127.53  65282.516 65243.234 65364.777] [65107.883 65282.35  65074.676 65245.32  65266.36  65285.984 65184.547
 65210.523 65307.855 65169.52  65158.074 65215.074 65141.355 65230.176
 65213.965 65118.953 65190.574 65161.617 65224.723 65135.094 65120.688
 65294.02  65220.082 65240.156 65227.957 65444.742 65345.457 65152.65
 65023.844 65165.258 65223.34  65127.523 65290.13  65319.445 65268.605
 65325.27  65189.066 65192.637 65242.312 65374.68  65319.023 65159.426
 65151.062 65243.945 65171.39  65236.027 65152.574 65242.484 65187.957
 65183.805 65174.535 65067.7   65166.684 65239.785 65223.03  65233.3
 65282.434 65229.223 65221.227 65076.523 65212.336 64956.53  65160.83
 65249.09  64931.848 65230.945 65164.914 65301.65  65012.566 65292.695
 65153.793 65129.68  65160.086 65012.527 65104.84  65071.867 65223.832
 65228.16  65221.77  65147.316 65090.176 65007.08  65243.695 65091.16
 65204.414 65141.598 65109.734 65303.777 65144.87  65118.312 65162.863
 65051.41  65089.12  65133.07  65378.387 65325.887 65010.406 65213.996
 65181.633 65265.008 65043.87  65202.887 65192.117 65094.37  65234.113
 65149.832 65034.445 65178.18  65256.18  65171.2   65185.23  65370.367
 65241.44  64995.    65124.    65361.87  65289.363 65063.07  65058.508
 65194.895 65137.32  65107.72  65168.406 65072.844 65245.445 65165.215
 65404.582 65035.41  65113.227 65194.934 65082.617 65249.785 65176.043
 65165.84  65156.496 65109.457 65119.06  65287.992 65305.613 65116.598
 65219.16  65180.02  65184.242 65069.168 65382.902 65127.887 65155.1
 65192.094 65270.625 65190.67  65234.94  65187.965 65082.875 65173.992
 65179.65  65081.84  65258.31  65239.793 65104.5   65188.242 65377.598
 65340.195 65278.08  65273.973 65360.434 64913.477 65230.684 65189.582
 65176.19  65145.11  65183.605 65287.656 65153.957 65252.758 65128.547
 65256.523 65141.965 65116.035 65289.574 65258.137 65202.562 65010.098
 65319.91  65172.297 65107.92  65154.008 65435.32  65155.812 65141.53
 65284.86  65269.76  65190.688 65074.094 65000.547 65048.11  65464.383
 65241.01  65200.184 65292.582 65203.15  65205.684 65175.008 65245.504
 65301.74  65377.395 65446.73  65074.125 65331.113 65270.33  65111.53
 65142.87  65242.605 65286.273 65023.305 65301.617 65062.543 65216.664
 65172.35  65167.938 65239.844 65212.58  65256.137 65152.88  65220.562
 65220.293 65346.58  65209.445 65186.72  65160.38  65279.92  65152.734
 65138.57  65312.75  65147.273 65367.734 65160.633 65293.766 65032.246
 65404.46  65326.59  65241.44  65219.594 64880.023 64901.617 65310.84
 65246.285 65217.363 65131.59  65206.41  65153.504 65250.973 65175.016
 65113.754 65146.875 65188.035 65149.98  65234.703 65211.105 65109.586
 65302.21  65206.832 65235.777 65377.594 65212.49  65493.37  65376.066
 65239.453 65135.81  65318.477 65171.047 65088.65  65204.316 65294.867
 65204.11  65474.746 65354.977 65273.64  65380.465 65257.703 65063.902
 65370.445 65265.04  65043.586 65127.348 65282.49  65242.777 65365.195]
testing (0, 1) + <class 'numpy.float32'> + keepdims= True + sum ...
cupy : 3.8184237670898438 ms
numpy : 42.4822802734375 ms
[[[65107.914 65282.875 65074.527 65245.703 65266.44  65286.04  65184.78
   65211.15  65307.42  65170.098 65158.305 65215.14  65141.066 65230.62
   65214.22  65119.094 65190.766 65161.977 65225.023 65134.875 65121.
   65294.008 65219.695 65240.64  65227.52  65444.656 65345.46  65153.312
   65024.04  65165.46  65223.586 65127.492 65289.99  65319.332 65268.336
   65325.74  65189.03  65193.254 65242.39  65374.28  65318.742 65159.24
   65151.15  65243.89  65171.    65236.367 65152.68  65242.    65187.816
   65183.47  65174.17  65066.973 65166.8   65240.254 65223.773 65232.934
   65282.848 65228.38  65221.734 65076.96  65212.434 64956.46  65161.156
   65248.61  64932.22  65230.9   65164.832 65301.64  65013.23  65292.457
   65153.93  65129.562 65159.97  65012.523 65105.11  65071.92  65223.633
   65228.176 65221.07  65147.34  65090.316 65007.17  65244.207 65090.633
   65204.258 65141.383 65109.605 65303.438 65145.023 65118.5   65162.703
   65051.19  65089.703 65132.79  65378.133 65325.844 65010.87  65214.14
   65181.883 65265.    65044.297 65202.914 65191.93  65093.992 65233.688
   65149.426 65034.61  65178.35  65255.484 65171.543 65185.45  65369.926
   65241.508 64994.617 65123.93  65361.902 65289.72  65063.234 65058.094
   65194.844 65137.633 65108.223 65169.094 65072.94  65245.15  65164.867
   65404.664 65034.87  65113.027 65195.656 65082.4   65249.93  65176.285
   65166.11  65156.22  65109.6   65119.69  65287.516 65305.855 65116.85
   65218.93  65180.117 65183.926 65069.03  65383.156 65127.586 65154.977
   65192.246 65270.613 65190.4   65234.477 65188.23  65082.664 65173.89
   65179.63  65081.54  65258.586 65239.27  65104.59  65188.19  65377.164
   65340.33  65277.566 65273.84  65360.4   64913.676 65230.035 65189.375
   65176.19  65145.055 65183.42  65287.6   65153.863 65253.086 65128.656
   65256.68  65142.11  65116.05  65289.883 65257.78  65202.5   65010.203
   65319.85  65172.47  65108.16  65154.11  65435.27  65155.46  65141.5
   65285.22  65269.426 65190.023 65073.77  65000.266 65048.54  65464.414
   65240.625 65199.78  65292.383 65203.21  65205.5   65174.68  65245.395
   65301.176 65377.043 65446.344 65074.4   65330.777 65270.45  65111.32
   65142.703 65242.203 65285.64  65023.3   65301.727 65062.633 65216.176
   65172.117 65168.15  65238.742 65212.816 65256.156 65153.105 65220.883
   65219.938 65346.453 65209.484 65186.78  65160.312 65279.64  65152.035
   65138.812 65313.457 65147.242 65368.098 65161.125 65293.492 65032.4
   65404.8   65326.9   65241.727 65219.797 64880.03  64901.67  65310.965
   65246.652 65217.465 65131.83  65206.484 65153.176 65250.65  65174.85
   65114.11  65147.35  65187.47  65149.758 65234.58  65211.24  65109.348
   65302.438 65206.617 65236.13  65377.47  65212.79  65493.26  65375.695
   65239.36  65135.438 65318.344 65170.797 65088.64  65204.184 65294.945
   65204.234 65475.164 65355.15  65273.21  65380.145 65257.37  65063.953
   65370.555 65265.113 65043.758 65127.53  65282.516 65243.234 65364.777]]] [[[65107.883 65282.35  65074.676 65245.32  65266.36  65285.984 65184.547
   65210.523 65307.855 65169.52  65158.074 65215.074 65141.355 65230.176
   65213.965 65118.953 65190.574 65161.617 65224.723 65135.094 65120.688
   65294.02  65220.082 65240.156 65227.957 65444.742 65345.457 65152.65
   65023.844 65165.258 65223.34  65127.523 65290.13  65319.445 65268.605
   65325.27  65189.066 65192.637 65242.312 65374.68  65319.023 65159.426
   65151.062 65243.945 65171.39  65236.027 65152.574 65242.484 65187.957
   65183.805 65174.535 65067.7   65166.684 65239.785 65223.03  65233.3
   65282.434 65229.223 65221.227 65076.523 65212.336 64956.53  65160.83
   65249.09  64931.848 65230.945 65164.914 65301.65  65012.566 65292.695
   65153.793 65129.68  65160.086 65012.527 65104.84  65071.867 65223.832
   65228.16  65221.77  65147.316 65090.176 65007.08  65243.695 65091.16
   65204.414 65141.598 65109.734 65303.777 65144.87  65118.312 65162.863
   65051.41  65089.12  65133.07  65378.387 65325.887 65010.406 65213.996
   65181.633 65265.008 65043.87  65202.887 65192.117 65094.37  65234.113
   65149.832 65034.445 65178.18  65256.18  65171.2   65185.23  65370.367
   65241.44  64995.    65124.    65361.87  65289.363 65063.07  65058.508
   65194.895 65137.32  65107.72  65168.406 65072.844 65245.445 65165.215
   65404.582 65035.41  65113.227 65194.934 65082.617 65249.785 65176.043
   65165.84  65156.496 65109.457 65119.06  65287.992 65305.613 65116.598
   65219.16  65180.02  65184.242 65069.168 65382.902 65127.887 65155.1
   65192.094 65270.625 65190.67  65234.94  65187.965 65082.875 65173.992
   65179.65  65081.84  65258.31  65239.793 65104.5   65188.242 65377.598
   65340.195 65278.08  65273.973 65360.434 64913.477 65230.684 65189.582
   65176.19  65145.11  65183.605 65287.656 65153.957 65252.758 65128.547
   65256.523 65141.965 65116.035 65289.574 65258.137 65202.562 65010.098
   65319.91  65172.297 65107.92  65154.008 65435.32  65155.812 65141.53
   65284.86  65269.76  65190.688 65074.094 65000.547 65048.11  65464.383
   65241.01  65200.184 65292.582 65203.15  65205.684 65175.008 65245.504
   65301.74  65377.395 65446.73  65074.125 65331.113 65270.33  65111.53
   65142.87  65242.605 65286.273 65023.305 65301.617 65062.543 65216.664
   65172.35  65167.938 65239.844 65212.58  65256.137 65152.88  65220.562
   65220.293 65346.58  65209.445 65186.72  65160.38  65279.92  65152.734
   65138.57  65312.75  65147.273 65367.734 65160.633 65293.766 65032.246
   65404.46  65326.59  65241.44  65219.594 64880.023 64901.617 65310.84
   65246.285 65217.363 65131.59  65206.41  65153.504 65250.973 65175.016
   65113.754 65146.875 65188.035 65149.98  65234.703 65211.105 65109.586
   65302.21  65206.832 65235.777 65377.594 65212.49  65493.37  65376.066
   65239.453 65135.81  65318.477 65171.047 65088.65  65204.316 65294.867
   65204.11  65474.746 65354.977 65273.64  65380.465 65257.703 65063.902
   65370.445 65265.04  65043.586 65127.348 65282.49  65242.777 65365.195]]]
testing (0, 1) + <class 'numpy.complex64'> + keepdims= False + sum ...
cupy : 3.869806213378906 ms
numpy : 63.1233447265625 ms
[65186.426+65182.477j 65242.88 +65049.57j  65206.117+65214.55j
 65048.14 +65278.664j 65197.906+65209.71j  65135.867+65215.363j
 65327.36 +65208.02j  65108.22 +65141.016j 65333.676+65136.883j
 65342.   +65213.28j  65342.848+65298.93j  65177.773+65312.83j
 65148.21 +65119.227j 65293.832+65267.695j 65199.023+65202.207j
 65269.957+65003.875j 65027.14 +65102.934j 65293.555+65337.57j
 65036.09 +65326.45j  65069.555+65122.21j  65170.188+65182.14j
 65086.773+65204.25j  65245.074+65350.133j 65278.77 +65176.047j
 65383.12 +65328.25j  65372.785+65076.875j 65340.812+65295.15j
 65258.914+65019.492j 65179.637+65094.973j 65114.742+65139.965j
 65228.574+65214.1j   65028.324+65035.492j 65158.71 +65270.234j
 65299.96 +65310.32j  65314.164+65216.145j 65152.445+65163.82j
 64984.176+65205.04j  65325.242+65244.406j 65308.74 +65173.617j
 65165.5  +65330.65j  65126.445+65090.18j  65136.22 +65150.49j
 65072.883+65090.805j 65156.95 +65377.67j  65243.934+65084.496j
 65335.4  +65139.293j 65354.574+65371.266j 65277.297+65176.633j
 65213.723+65281.656j 65096.094+65255.336j 65214.305+65097.867j
 65304.68 +65323.668j 65336.617+65143.016j 65109.906+65269.316j
 65259.906+65267.74j  65062.758+65238.457j 65106.82 +65017.633j
 65121.54 +65096.45j  65187.688+65272.53j  65071.33 +65308.246j
 64950.973+65187.082j 65391.445+65345.008j 64989.47 +65234.906j
 65107.72 +65159.03j  65278.68 +65234.58j  65301.086+65031.836j
 65155.4  +65310.01j  65247.79 +65235.55j  65272.406+65041.395j
 65176.75 +65342.47j  65235.73 +65273.438j 65082.28 +65235.61j
 65384.97 +65267.312j 65182.273+65253.41j  64940.703+65254.39j
 65218.484+65367.008j 65279.703+65307.156j 65180.89 +65182.312j
 65345.543+65134.254j 65168.86 +65003.234j 65209.777+65194.227j
 65188.15 +65257.156j 65191.836+65144.566j 65330.88 +65215.676j
 65241.883+65340.89j  65280.305+65152.39j  65297.39 +65284.293j
 65348.71 +65193.9j   64999.133+65260.25j  65156.867+65223.32j
 65131.63 +65199.j    65172.418+64953.39j  65135.727+65222.703j
 65380.312+65251.58j  65325.17 +64980.1j   65282.47 +65105.555j
 65455.387+65341.54j  65183.01 +65014.965j 65267.117+65139.87j
 65088.547+65313.78j  65362.477+65227.875j 65148.18 +65164.008j
 65254.21 +65241.027j 65168.984+65253.984j 65015.96 +65285.254j
 65027.53 +64951.78j  65211.297+65116.21j  65158.47 +65244.29j
 65213.37 +65143.49j  65220.664+65484.926j 64716.637+65213.066j
 65112.074+65131.67j  65283.23 +65231.72j  65198.812+65132.902j
 65300.664+65246.043j 65212.797+65223.035j 65311.69 +65423.25j
 65248.95 +65294.04j  65215.062+65093.79j  65100.785+65147.414j
 65112.848+65067.598j 65221.78 +65091.434j 65397.516+65159.254j
 65271.918+65186.727j 65224.195+65424.516j 65287.332+65154.57j
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testing (0, 1) + <class 'numpy.complex64'> + keepdims= True + sum ...
cupy : 3.859105224609375 ms
numpy : 63.1188671875 ms
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Issue Analytics

State:
Created 4 years ago
Comments:5 (5 by maintainers)

Top GitHub Comments

1reaction

grlee77commented, Oct 21, 2019

I think NumPy does pairwise summation to improve accuracy in some cases. They describe it in the notes section here. It sounds like your case when providing axes=(0, 1) would fall under one of the cases where it is NOT used, though. Unfortunately I won’t have time to look into this in the immediate future, but I think it is a potential starting point for looking into any discrepancy.

0reactions

leofangcommented, Oct 21, 2020

Yes I think. It’s hard to match the behavior. Maybe at most we can do is to document this observation?

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