spark-instrumented-optimizer/licenses-binary/LICENSE-blas.txt
Ludovic Henry 5b77ebb57b [SPARK-35150][ML] Accelerate fallback BLAS with dev.ludovic.netlib
### What changes were proposed in this pull request?

Following https://github.com/apache/spark/pull/30810, I've continued looking for ways to accelerate the usage of BLAS in Spark. With this PR, I integrate work done in the [`dev.ludovic.netlib`](https://github.com/luhenry/netlib/) Maven package.

The `dev.ludovic.netlib` library wraps the original `com.github.fommil.netlib` library and focus on accelerating the linear algebra routines in use in Spark. When running the `org.apache.spark.ml.linalg.BLASBenchmark` benchmarking suite, I get the results at [1] on an Intel machine. Moreover, this library is thoroughly tested to return the exact same results as the reference implementation.

Under the hood, it reimplements the necessary algorithms in pure autovectorization-friendly Java 8, as well as takes advantage of the Vector API and Foreign Linker API introduced in JDK 16 when available.

A table summarising which version gets loaded in which case:

```
|                       | BLAS.nativeBLAS                                    | BLAS.javaBLAS                                      |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
| with -Pnetlib-lgpl    | 1. dev.ludovic.netlib.blas.NetlibNativeBLAS, a     | 1. dev.ludovic.netlib.blas.VectorizedBLAS          |
|                       |     wrapper for com.github.fommil:all              |    (JDK16+, relies on the Vector API, requires     |
|                       | 2. dev.ludovic.netlib.blas.ForeignBLAS (JDK16+,    |     `--add-modules=jdk.incubator.vector` on JDK16) |
|                       |    relies on the Foreign Linker API, requires      | 2. dev.ludovic.netlib.blas.Java11BLAS (JDK11+)     |
|                       |    `--add-modules=jdk.incubator.foreign            | 3. dev.ludovic.netlib.blas.JavaBLAS                |
|                       |     -Dforeign.restricted=warn`)                    | 4. dev.ludovic.netlib.blas.NetlibF2jBLAS, a        |
|                       | 3. fails to load, falls back to BLAS.javaBLAS in   |     wrapper for com.github.fommil:core             |
|                       |     org.apache.spark.ml.linalg.BLAS                |                                                    |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
| without -Pnetlib-lgpl | 1. dev.ludovic.netlib.blas.ForeignBLAS (JDK16+,    | 1. dev.ludovic.netlib.blas.VectorizedBLAS          |
|                       |    relies on the Foreign Linker API, requires      |    (JDK16+, relies on the Vector API, requires     |
|                       |    `--add-modules=jdk.incubator.foreign            |     `--add-modules=jdk.incubator.vector` on JDK16) |
|                       |     -Dforeign.restricted=warn`)                    | 2. dev.ludovic.netlib.blas.Java11BLAS (JDK11+)     |
|                       | 2. fails to load, falls back to BLAS.javaBLAS in   | 3. dev.ludovic.netlib.blas.JavaBLAS                |
|                       |     org.apache.spark.ml.linalg.BLAS                | 4. dev.ludovic.netlib.blas.NetlibF2jBLAS, a        |
|                       |                                                    |     wrapper for com.github.fommil:core             |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
```

### Why are the changes needed?

Accelerates linear algebra operations when the pure-java fallback method is in use. Transparently falls back to native implementation (OpenBLAS, MKL) when available.

### Does this PR introduce _any_ user-facing change?

No, all changes are transparent to the user.

### How was this patch tested?

The `dev.ludovic.netlib` library has its own test suite [2]. It has also been validated by running the Spark test suite and benchmarking suite.

[1] Results for `org.apache.spark.ml.linalg.BLASBenchmark`:
#### JDK8:
```
[info] OpenJDK 64-Bit Server VM 1.8.0_292-b10 on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.Java8BLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.Java8BLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 223            232           8        448.0           2.2       1.0X
[info] java                                                221            228           7        453.0           2.2       1.0X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 122            128           4        821.2           1.2       1.0X
[info] java                                                122            128           4        822.3           1.2       1.0X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 109            112           2        921.4           1.1       1.0X
[info] java                                                 70             74           3       1423.5           0.7       1.5X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             98           2       1046.1           1.0       1.0X
[info] java                                                 47             49           2       2121.7           0.5       2.0X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 184            195           8        544.3           1.8       1.0X
[info] java                                                185            196           7        539.5           1.9       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  99            104           4       1011.9           1.0       1.0X
[info] java                                                 99            104           4       1010.4           1.0       1.0X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        947.2           1.1       1.0X
[info] java                                                  0              0           0       1584.8           0.6       1.7X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        867.4           1.2       1.0X
[info] java                                                  1              1           0        865.0           1.2       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        485.9           2.1       1.0X
[info] java                                                  1              1           0        486.8           2.1       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1843.0           0.5       1.0X
[info] java                                                  0              0           0       2690.6           0.4       1.5X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1214.7           0.8       1.0X
[info] java                                                  0              0           0       2536.8           0.4       2.1X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1895.9           0.5       1.0X
[info] java                                                  0              0           0       2961.1           0.3       1.6X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1223.4           0.8       1.0X
[info] java                                                  0              0           0       3091.4           0.3       2.5X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 560            575          20       1787.1           0.6       1.0X
[info] java                                                226            232           5       4432.4           0.2       2.5X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 570            586          23       1755.2           0.6       1.0X
[info] java                                                227            232           4       4410.1           0.2       2.5X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 863            879          17       1158.4           0.9       1.0X
[info] java                                                227            231           3       4407.9           0.2       3.8X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1282           1305          23        780.0           1.3       1.0X
[info] java                                                227            232           4       4413.4           0.2       5.7X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 538            548           8       1858.6           0.5       1.0X
[info] java                                                221            226           3       4521.1           0.2       2.4X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 549            558          10       1819.9           0.5       1.0X
[info] java                                                222            229           7       4503.5           0.2       2.5X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 838            852          12       1193.0           0.8       1.0X
[info] java                                                222            229           5       4500.5           0.2       3.8X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 905            919          18       1104.8           0.9       1.0X
[info] java                                                221            228           5       4521.3           0.2       4.1X
```

#### JDK11:
```
[info] OpenJDK 64-Bit Server VM 11.0.11+9-LTS on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.Java11BLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.Java11BLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 195            204          10        512.7           2.0       1.0X
[info] java                                                195            202           7        512.4           2.0       1.0X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 108            113           4        923.3           1.1       1.0X
[info] java                                                102            107           4        984.4           1.0       1.1X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 107            110           3        938.1           1.1       1.0X
[info] java                                                 69             72           3       1447.1           0.7       1.5X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             98           2       1046.5           1.0       1.0X
[info] java                                                 43             45           2       2317.1           0.4       2.2X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 155            168           8        644.2           1.6       1.0X
[info] java                                                158            169           8        632.8           1.6       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  85             90           4       1178.1           0.8       1.0X
[info] java                                                 86             90           4       1167.7           0.9       1.0X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       1182.1           0.8       1.0X
[info] java                                                  0              0           0       1432.1           0.7       1.2X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        898.7           1.1       1.0X
[info] java                                                  1              1           0        891.5           1.1       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        495.4           2.0       1.0X
[info] java                                                  1              1           0        495.7           2.0       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2271.6           0.4       1.0X
[info] java                                                  0              0           0       3648.1           0.3       1.6X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1229.3           0.8       1.0X
[info] java                                                  0              0           0       2711.3           0.4       2.2X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2677.5           0.4       1.0X
[info] java                                                  0              0           0       3288.2           0.3       1.2X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1233.0           0.8       1.0X
[info] java                                                  0              0           0       2766.3           0.4       2.2X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 520            536          16       1923.6           0.5       1.0X
[info] java                                                214            221           7       4669.5           0.2       2.4X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 593            612          17       1686.5           0.6       1.0X
[info] java                                                215            219           3       4643.3           0.2       2.8X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 853            870          16       1172.8           0.9       1.0X
[info] java                                                215            218           3       4659.7           0.2       4.0X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1350           1370          23        740.8           1.3       1.0X
[info] java                                                215            219           4       4656.6           0.2       6.3X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 460            468           6       2173.2           0.5       1.0X
[info] java                                                210            213           2       4752.7           0.2       2.2X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 535            544           8       1869.3           0.5       1.0X
[info] java                                                210            215           5       4761.8           0.2       2.5X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 843            853          11       1186.8           0.8       1.0X
[info] java                                                209            214           4       4793.4           0.2       4.0X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 891            904          15       1122.0           0.9       1.0X
[info] java                                                209            214           4       4777.2           0.2       4.3X
```

#### JDK16:
```
[info] OpenJDK 64-Bit Server VM 16+36 on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.VectorizedBLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.VectorizedBLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 194            199           7        515.7           1.9       1.0X
[info] java                                                181            186           3        551.1           1.8       1.1X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 109            115           4        915.0           1.1       1.0X
[info] java                                                 88             92           3       1138.8           0.9       1.2X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 108            110           2        922.6           1.1       1.0X
[info] java                                                 54             56           2       1839.2           0.5       2.0X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             97           2       1046.1           1.0       1.0X
[info] java                                                 29             30           1       3393.4           0.3       3.2X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 156            165           5        643.0           1.6       1.0X
[info] java                                                150            159           5        667.1           1.5       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  85             91           6       1171.0           0.9       1.0X
[info] java                                                 75             79           3       1340.6           0.7       1.1X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        917.0           1.1       1.0X
[info] java                                                  0              0           0       8147.2           0.1       8.9X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        859.3           1.2       1.0X
[info] java                                                  1              1           0        859.3           1.2       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        482.1           2.1       1.0X
[info] java                                                  1              1           0        482.6           2.1       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2214.2           0.5       1.0X
[info] java                                                  0              0           0       7975.8           0.1       3.6X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1231.4           0.8       1.0X
[info] java                                                  0              0           0       8680.9           0.1       7.0X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2684.3           0.4       1.0X
[info] java                                                  0              0           0      18527.1           0.1       6.9X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1235.4           0.8       1.0X
[info] java                                                  0              0           0      17347.9           0.1      14.0X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 530            552          18       1887.5           0.5       1.0X
[info] java                                                 58             64           3      17143.9           0.1       9.1X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 598            620          17       1671.1           0.6       1.0X
[info] java                                                 58             64           3      17196.6           0.1      10.3X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 834            847          14       1199.4           0.8       1.0X
[info] java                                                 57             63           4      17486.9           0.1      14.6X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1338           1366          22        747.3           1.3       1.0X
[info] java                                                 58             63           3      17356.6           0.1      23.2X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 489            501           9       2045.5           0.5       1.0X
[info] java                                                 36             38           2      27721.9           0.0      13.6X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 478            488           9       2094.0           0.5       1.0X
[info] java                                                 36             38           2      27813.2           0.0      13.3X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 825            837          10       1211.6           0.8       1.0X
[info] java                                                 35             38           2      28433.1           0.0      23.5X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 900            918          15       1111.6           0.9       1.0X
[info] java                                                 36             38           2      28073.0           0.0      25.3X
```

[2] https://github.com/luhenry/netlib/tree/master/blas/src/test/java/dev/ludovic/netlib/blas

Closes #32253 from luhenry/master.

Authored-by: Ludovic Henry <git@ludovic.dev>
Signed-off-by: Sean Owen <srowen@gmail.com>
2021-04-27 14:00:59 -05:00

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MIT License
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