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When the number of cols is large, split each row across multiple workgroups. There are three phases that communicate partial results through temp buffers:
(1) compute max partials
(2) take max of partials, compute sum(exp(x-max)) partials
(3) sum partials, compute scaled result

a84dfd3 added a similar optimization for ggml-cuda, I guess this is needed to sample probabilities above a threshold.

Perf on 5090:

before:
  SOFT_MAX(type=f32,ne=[4096,4096,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                2340 runs -   435.67 us/run -   655360 kB/run - 1448.37 GB/s
  SOFT_MAX(type=f32,ne=[12888,256,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               13050 runs -    77.94 us/run -   128880 kB/run - 1579.94 GB/s
  SOFT_MAX(type=f32,ne=[77,4096,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 87168 runs -    11.50 us/run -    12320 kB/run - 1021.67 GB/s
  SOFT_MAX(type=f32,ne=[1024,1024,10,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):              33620 runs -    29.91 us/run -    81920 kB/run - 2615.38 GB/s
  SOFT_MAX(type=f32,ne=[77,1024,10,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               152544 runs -     6.62 us/run -     6160 kB/run -  887.36 GB/s
  SOFT_MAX(type=f32,ne=[256,256,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               213005 runs -     4.76 us/run -    10240 kB/run - 2051.83 GB/s
  SOFT_MAX(type=f32,ne=[64,64,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 466887 runs -     2.15 us/run -      640 kB/run -  284.24 GB/s
  SOFT_MAX(type=f32,ne=[77,64,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 450505 runs -     2.25 us/run -      770 kB/run -  326.02 GB/s
  SOFT_MAX(type=f32,ne=[8192,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 262112 runs -     3.85 us/run -       64 kB/run -   15.86 GB/s
  SOFT_MAX(type=f32,ne=[8192,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 253921 runs -     3.98 us/run -      256 kB/run -   61.28 GB/s
  SOFT_MAX(type=f32,ne=[8192,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                253921 runs -     4.07 us/run -     1024 kB/run -  240.14 GB/s
  SOFT_MAX(type=f32,ne=[16384,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                163820 runs -     6.36 us/run -      128 kB/run -   19.19 GB/s
  SOFT_MAX(type=f32,ne=[16384,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                155629 runs -     6.67 us/run -      512 kB/run -   73.23 GB/s
  SOFT_MAX(type=f32,ne=[16384,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               155629 runs -     6.69 us/run -     2048 kB/run -  292.13 GB/s
  SOFT_MAX(type=f32,ne=[32768,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 40955 runs -    27.26 us/run -      256 kB/run -    8.96 GB/s
  SOFT_MAX(type=f32,ne=[32768,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 40955 runs -    27.97 us/run -     1024 kB/run -   34.91 GB/s
  SOFT_MAX(type=f32,ne=[32768,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                40955 runs -    28.44 us/run -     4096 kB/run -  137.34 GB/s
  SOFT_MAX(type=f32,ne=[65536,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 24573 runs -    57.37 us/run -      512 kB/run -    8.51 GB/s
  SOFT_MAX(type=f32,ne=[65536,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 24573 runs -    59.17 us/run -     2048 kB/run -   33.01 GB/s
  SOFT_MAX(type=f32,ne=[65536,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                16388 runs -    61.50 us/run -     8192 kB/run -  127.04 GB/s
  SOFT_MAX(type=f32,ne=[131072,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                16382 runs -   114.85 us/run -     1024 kB/run -    8.50 GB/s
  SOFT_MAX(type=f32,ne=[131072,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                16382 runs -   118.04 us/run -     4096 kB/run -   33.10 GB/s
  SOFT_MAX(type=f32,ne=[131072,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               10245 runs -   119.02 us/run -    16384 kB/run -  131.31 GB/s
  SOFT_MAX(type=f32,ne=[262144,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 8191 runs -   229.78 us/run -     2048 kB/run -    8.50 GB/s
  SOFT_MAX(type=f32,ne=[262144,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 8194 runs -   238.03 us/run -     8192 kB/run -   32.82 GB/s
  SOFT_MAX(type=f32,ne=[262144,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                5125 runs -   240.39 us/run -    32768 kB/run -  130.06 GB/s
  SOFT_MAX(type=f32,ne=[524288,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 8191 runs -   459.77 us/run -     4096 kB/run -    8.50 GB/s
  SOFT_MAX(type=f32,ne=[524288,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 4098 runs -   476.72 us/run -    16384 kB/run -   32.78 GB/s
  SOFT_MAX(type=f32,ne=[524288,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                2565 runs -   481.95 us/run -    65536 kB/run -  129.81 GB/s

after:
  SOFT_MAX(type=f32,ne=[4096,4096,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                2340 runs -   435.44 us/run -   655360 kB/run - 1449.13 GB/s
  SOFT_MAX(type=f32,ne=[12888,256,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               12789 runs -    79.00 us/run -   128880 kB/run - 1558.70 GB/s
  SOFT_MAX(type=f32,ne=[77,4096,5,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 87168 runs -    11.54 us/run -    12320 kB/run - 1018.13 GB/s
  SOFT_MAX(type=f32,ne=[1024,1024,10,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):              33210 runs -    30.47 us/run -    81920 kB/run - 2567.02 GB/s
  SOFT_MAX(type=f32,ne=[77,1024,10,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               152544 runs -     6.69 us/run -     6160 kB/run -  878.66 GB/s
  SOFT_MAX(type=f32,ne=[256,256,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               213005 runs -     4.76 us/run -    10240 kB/run - 2051.31 GB/s
  SOFT_MAX(type=f32,ne=[64,64,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 466887 runs -     2.15 us/run -      640 kB/run -  283.47 GB/s
  SOFT_MAX(type=f32,ne=[77,64,20,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 450505 runs -     2.25 us/run -      770 kB/run -  326.24 GB/s
  SOFT_MAX(type=f32,ne=[8192,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 262112 runs -     3.85 us/run -       64 kB/run -   15.84 GB/s
  SOFT_MAX(type=f32,ne=[8192,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                 253921 runs -     4.07 us/run -      256 kB/run -   60.04 GB/s
  SOFT_MAX(type=f32,ne=[8192,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                253921 runs -     4.06 us/run -     1024 kB/run -  240.33 GB/s
  SOFT_MAX(type=f32,ne=[16384,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                163820 runs -     6.41 us/run -      128 kB/run -   19.05 GB/s
  SOFT_MAX(type=f32,ne=[16384,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                131056 runs -     8.13 us/run -      512 kB/run -   60.05 GB/s
  SOFT_MAX(type=f32,ne=[16384,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               147438 runs -     6.98 us/run -     2048 kB/run -  279.65 GB/s
  SOFT_MAX(type=f32,ne=[32768,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                163820 runs -     6.27 us/run -      256 kB/run -   38.96 GB/s
  SOFT_MAX(type=f32,ne=[32768,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                155629 runs -     6.43 us/run -     1024 kB/run -  151.91 GB/s
  SOFT_MAX(type=f32,ne=[32768,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               122865 runs -     8.27 us/run -     4096 kB/run -  472.17 GB/s
  SOFT_MAX(type=f32,ne=[65536,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                163820 runs -     6.36 us/run -      512 kB/run -   76.74 GB/s
  SOFT_MAX(type=f32,ne=[65536,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                147438 runs -     7.15 us/run -     2048 kB/run -  273.07 GB/s
  SOFT_MAX(type=f32,ne=[65536,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                94231 runs -    11.03 us/run -     8192 kB/run -  708.45 GB/s
  SOFT_MAX(type=f32,ne=[131072,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               139247 runs -     7.21 us/run -     1024 kB/run -  135.37 GB/s
  SOFT_MAX(type=f32,ne=[131072,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               114674 runs -     8.84 us/run -     4096 kB/run -  442.02 GB/s
  SOFT_MAX(type=f32,ne=[131072,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               57372 runs -    17.67 us/run -    16384 kB/run -  884.50 GB/s
  SOFT_MAX(type=f32,ne=[262144,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               122865 runs -     8.40 us/run -     2048 kB/run -  232.57 GB/s
  SOFT_MAX(type=f32,ne=[262144,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                81940 runs -    12.66 us/run -     8192 kB/run -  617.26 GB/s
  SOFT_MAX(type=f32,ne=[262144,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               30750 runs -    33.43 us/run -    32768 kB/run -  935.30 GB/s
  SOFT_MAX(type=f32,ne=[524288,1,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                90101 runs -    11.16 us/run -     4096 kB/run -  349.97 GB/s
  SOFT_MAX(type=f32,ne=[524288,4,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):                45078 runs -    23.05 us/run -    16384 kB/run -  677.95 GB/s
  SOFT_MAX(type=f32,ne=[524288,16,1,1],mask=0,sinks=0,m_prec=f32,nr23=[1,1],scale=1.000000,max_bias=0.000000,inplace=0):               14877 runs -    68.78 us/run -    65536 kB/run -  909.63 GB/s

When the number of cols is large, split each row across multiple workgroups.
There are three phases that communicate partial results through temp buffers:
(1) compute max partials
(2) take max of partials, compute sum(exp(x-max)) partials
(3) sum partials, compute scaled result
@github-actions github-actions bot added testing Everything test related Vulkan Issues specific to the Vulkan backend ggml changes relating to the ggml tensor library for machine learning labels Dec 9, 2025
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