simd

Vectorized Math Functions

This library contains a set of vectorized mathematical functions which were auto-vectorized using clang compiler and translated into PLAN9 assembly code for Go. Generic version is also provided for CPUs where vectorization is not available, or for which this library doesn't have a generated code.

It currently supports only AVX2, but AVX512 and SVE (for ARM) should be easy enough to generate. Most of the code in this library is auto-generated, which helps with maintenance.

Usage

Usage of this library is very straightforward, it simply exposes a set of non-opinionated functions. For example, if you want to sum up a slice of floating point numbers, you can use SumFloat32s([]float32) float32 function to do so.

sum := simd.SumFloat32s([]float32{1, 2, 3, 4, 5})

Benchmarks

goos: windows
goarch: amd64
pkg: github.com/kelindar/simd
cpu: Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz

   TYPE    OP    SIZE     RATE        SPEEDUP
float32   sum     256     8.86 ns/op   20.54x
float32   min     256    27.57 ns/op    4.15x
float32   max     256    27.65 ns/op    4.07x
float32   add     256    15.35 ns/op    7.43x
float32   sub     256    15.31 ns/op    7.44x
float32   mul     256    15.39 ns/op    7.39x
float32   div     256    27.60 ns/op    5.90x
float32   sum    4096   107.74 ns/op   31.65x
float32   min    4096   133.08 ns/op   12.89x
float32   max    4096   140.77 ns/op   12.26x
float32   add    4096   373.34 ns/op    4.71x
float32   sub    4096   389.79 ns/op    4.40x
float32   mul    4096   369.63 ns/op    4.69x
float32   div    4096   457.12 ns/op    5.65x
float32   sum   16384   466.87 ns/op   29.47x
float32   min   16384   504.66 ns/op   13.64x
float32   max   16384   515.63 ns/op   13.33x
float32   add   16384  1422.20 ns/op    4.88x
float32   sub   16384  1414.59 ns/op    4.86x
float32   mul   16384  1426.91 ns/op    4.84x
float32   div   16384  1847.74 ns/op    5.54x

   TYPE    OP    SIZE     RATE        SPEEDUP
float64   sum     256    14.28 ns/op   13.01x
float64   min     256    24.58 ns/op    4.73x
float64   max     256    24.28 ns/op    3.77x
float64   add     256    25.44 ns/op    4.50x
float64   sub     256    25.40 ns/op    4.44x
float64   mul     256    25.66 ns/op    4.47x
float64   div     256   107.58 ns/op    2.01x
float64   sum    4096   217.11 ns/op   15.64x
float64   min    4096   237.68 ns/op    7.21x
float64   max    4096   238.10 ns/op    5.68x
float64   add    4096   779.90 ns/op    2.33x
float64   sub    4096   752.78 ns/op    2.31x
float64   mul    4096   737.30 ns/op    2.43x
float64   div    4096  1735.34 ns/op    1.98x
float64   sum   16384   922.49 ns/op   15.07x
float64   min   16384   989.75 ns/op    6.98x
float64   max   16384  1017.51 ns/op    5.42x
float64   add   16384  5987.32 ns/op    1.42x
float64   sub   16384  5383.73 ns/op    1.50x
float64   mul   16384  5674.55 ns/op    1.44x
float64   div   16384  7063.43 ns/op    2.00x

   TYPE    OP    SIZE     RATE        SPEEDUP
  uint8   sum     100    35.63 ns/op    1.02x
  uint8   min     100    23.77 ns/op    2.17x
  uint8   max     100    29.69 ns/op    1.59x
  uint8   add     100    37.46 ns/op    1.41x
  uint8   sub     100    36.63 ns/op    1.45x
  uint8   mul     100     9.42 ns/op    8.03x
  uint8   div     100   193.95 ns/op    1.14x

   TYPE    OP    SIZE     RATE        SPEEDUP
 uint16   sum     256     6.24 ns/op   13.95x
 uint16   min     256    29.83 ns/op    5.49x
 uint16   max     256    43.57 ns/op    2.54x
 uint16   add     256    10.30 ns/op   17.19x
 uint16   sub     256    10.29 ns/op   16.14x
 uint16   mul     256    10.36 ns/op   16.57x
 uint16   div     256   440.84 ns/op    1.27x
 uint16   sum    4096    42.39 ns/op   30.41x
 uint16   min    4096    79.48 ns/op   32.70x
 uint16   max    4096    95.83 ns/op   18.66x
 uint16   add    4096    90.78 ns/op   29.94x
 uint16   sub    4096    87.41 ns/op   29.95x
 uint16   mul    4096    86.62 ns/op   29.73x
 uint16   div    4096  6867.75 ns/op    1.28x
 uint16   sum   16384   155.46 ns/op   32.00x
 uint16   min   16384   246.67 ns/op   42.19x
 uint16   max   16384   262.69 ns/op   26.06x
 uint16   add   16384   739.30 ns/op   14.01x
 uint16   sub   16384   721.78 ns/op   14.33x
 uint16   mul   16384   787.84 ns/op   12.89x
 uint16   div   16384 26838.80 ns/op    1.28x

   TYPE    OP    SIZE     RATE        SPEEDUP
 uint32   sum     256     7.94 ns/op   10.47x
 uint32   min     256    22.62 ns/op    6.96x
 uint32   max     256    25.75 ns/op    4.20x
 uint32   add     256    14.72 ns/op    8.31x
 uint32   sub     256    14.80 ns/op    8.32x
 uint32   mul     256    15.93 ns/op    7.52x
 uint32   div     256   419.09 ns/op    1.30x
 uint32   sum    4096    74.25 ns/op   16.59x
 uint32   min    4096   119.60 ns/op   21.61x
 uint32   max    4096   125.50 ns/op   13.67x
 uint32   add    4096   382.51 ns/op    5.09x
 uint32   sub    4096   369.66 ns/op    5.27x
 uint32   mul    4096   376.69 ns/op    4.82x
 uint32   div    4096  6611.42 ns/op    1.30x
 uint32   sum   16384   470.78 ns/op   10.45x
 uint32   min   16384   509.34 ns/op   20.05x
 uint32   max   16384   509.63 ns/op   14.20x
 uint32   add   16384  1430.07 ns/op    5.62x
 uint32   sub   16384  1470.22 ns/op    5.37x
 uint32   mul   16384  1469.16 ns/op    5.45x
 uint32   div   16384 26749.18 ns/op    1.31x

   TYPE    OP    SIZE     RATE        SPEEDUP
 uint64   sum     256    12.16 ns/op    9.29x
 uint64   min     256    41.61 ns/op    3.80x
 uint64   max     256    44.33 ns/op    2.59x
 uint64   add     256    24.87 ns/op    4.95x
 uint64   sub     256    24.85 ns/op    4.95x
 uint64   mul     256    50.84 ns/op    2.35x
 uint64   div     256  1241.17 ns/op    1.21x
 uint64   sum    4096   142.52 ns/op   11.94x
 uint64   min    4096   502.09 ns/op    5.15x
 uint64   max    4096   501.85 ns/op    3.43x
 uint64   add    4096   736.55 ns/op    2.66x
 uint64   sub    4096   768.94 ns/op    2.59x
 uint64   mul    4096   899.77 ns/op    2.24x
 uint64   div    4096 19940.91 ns/op    1.21x
 uint64   sum   16384   976.09 ns/op    7.30x
 uint64   min   16384  2107.63 ns/op    5.02x
 uint64   max   16384  2123.41 ns/op    3.33x
 uint64   add   16384  5605.09 ns/op    1.53x
 uint64   sub   16384  5382.83 ns/op    1.57x
 uint64   mul   16384  5934.57 ns/op    1.43x
 uint64   div   16384 79974.54 ns/op    1.18x

   TYPE    OP    SIZE     RATE        SPEEDUP
   int8   sum     100    35.60 ns/op    1.01x
   int8   min     100    24.12 ns/op    2.10x
   int8   max     100    24.06 ns/op    1.96x
   int8   add     100    35.74 ns/op    1.45x
   int8   sub     100    36.45 ns/op    1.43x
   int8   mul     100     9.42 ns/op    7.55x
   int8   div     100   203.37 ns/op    1.46x

   TYPE    OP    SIZE     RATE        SPEEDUP
  int16   sum     256     6.11 ns/op   13.56x
  int16   min     256    30.70 ns/op    3.43x
  int16   max     256    29.39 ns/op    3.66x
  int16   add     256     9.81 ns/op   17.06x
  int16   sub     256     9.84 ns/op   17.05x
  int16   mul     256    10.21 ns/op   16.58x
  int16   div     256   489.38 ns/op    1.55x
  int16   sum    4096    37.85 ns/op   32.80x
  int16   min    4096    79.82 ns/op   21.40x
  int16   max    4096    78.70 ns/op   21.86x
  int16   add    4096    85.27 ns/op   30.57x
  int16   sub    4096    84.76 ns/op   30.43x
  int16   mul    4096    88.35 ns/op   29.32x
  int16   div    4096  7896.65 ns/op    1.51x
  int16   sum   16384   152.95 ns/op   32.75x
  int16   min   16384   243.98 ns/op   28.40x
  int16   max   16384   245.85 ns/op   27.93x
  int16   add   16384   783.82 ns/op   13.01x
  int16   sub   16384   740.70 ns/op   14.02x
  int16   mul   16384   736.79 ns/op   14.00x
  int16   div   16384 31574.74 ns/op    1.53x

   TYPE    OP    SIZE     RATE        SPEEDUP
  int32   sum     256     7.92 ns/op   10.50x
  int32   min     256    21.82 ns/op    4.82x
  int32   max     256    22.71 ns/op    4.65x
  int32   add     256    14.98 ns/op    8.25x
  int32   sub     256    14.91 ns/op    8.22x
  int32   mul     256    15.95 ns/op    7.54x
  int32   div     256   488.63 ns/op    1.38x
  int32   sum    4096    74.84 ns/op   16.85x
  int32   min    4096   119.84 ns/op   14.27x
  int32   max    4096   119.55 ns/op   14.33x
  int32   add    4096   383.44 ns/op    5.07x
  int32   sub    4096   373.52 ns/op    5.20x
  int32   mul    4096   373.64 ns/op    4.76x
  int32   div    4096  7791.16 ns/op    1.37x
  int32   sum   16384   468.25 ns/op   10.68x
  int32   min   16384   483.94 ns/op   14.19x
  int32   max   16384   485.43 ns/op   14.13x
  int32   add   16384  1411.90 ns/op    5.57x
  int32   sub   16384  1401.61 ns/op    5.55x
  int32   mul   16384  1422.65 ns/op    5.40x
  int32   div   16384 31080.74 ns/op    1.37x

   TYPE    OP    SIZE     RATE        SPEEDUP
  int64   sum     256    12.01 ns/op    6.79x
  int64   min     256    29.99 ns/op    3.47x
  int64   max     256    29.96 ns/op    3.53x
  int64   add     256    24.87 ns/op    4.96x
  int64   sub     256    24.83 ns/op    4.94x
  int64   mul     256    50.67 ns/op    2.34x
  int64   div     256  1546.44 ns/op    1.15x
  int64   sum    4096   148.93 ns/op    8.48x
  int64   min    4096   323.19 ns/op    5.27x
  int64   max    4096   322.25 ns/op    5.35x
  int64   add    4096   721.78 ns/op    2.72x
  int64   sub    4096   725.84 ns/op    2.71x
  int64   mul    4096   901.09 ns/op    2.10x
  int64   div    4096 24406.86 ns/op    1.17x
  int64   sum   16384   930.98 ns/op    5.64x
  int64   min   16384  1427.03 ns/op    4.78x
  int64   max   16384  1429.45 ns/op    4.78x
  int64   add   16384  5703.49 ns/op    1.48x
  int64   sub   16384  5103.69 ns/op    1.64x
  int64   mul   16384  6019.09 ns/op    1.42x
  int64   div   16384 98294.20 ns/op    1.15x

Acknowledgements

This library was originally inspired by the work of Valery Carey & Adrian Witas in viant/vec package, but instead of hand-rolled assembly and intrinsics I opted for using auto-vectorization for maintainability reasons.