mirror of
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Reverted docs/*.md links to relative paths.
Details:
- Within the documents in docs/*.md, reverted links to other local
documents to relative paths.
- Fixed some links/documents that did not yet have the '.md' suffix.
- Testing whether we can use relative links ('docs/BLISTypedAPI.md')
from within README.md.
This commit is contained in:
Field G. Van Zee
@@ -87,17 +87,17 @@ Kernels marked with a "1" for a given level-2 operation are preferred for optimi
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## BLIS kernels reference
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This section seeks to provide developers with a complete reference for each of the following BLIS kernels, including function prototypes, parameter descriptions, implementation notes, and diagrams:
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* [Level-3 micro-kernels](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#level-3-micro-kernels)
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* [gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemm-micro-kernel)
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* [trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#trsm-micro-kernels)
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* [gemmtrsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemmtrsm-micro-kernels)
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* [Level-1f kernels](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#level-1f-kernels)
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* [Level-3 micro-kernels](KernelsHowTo.md#level-3-micro-kernels)
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* [gemm](KernelsHowTo.md#gemm-micro-kernel)
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* [trsm](KernelsHowTo.md#trsm-micro-kernels)
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* [gemmtrsm](KernelsHowTo.md#gemmtrsm-micro-kernels)
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* [Level-1f kernels](KernelsHowTo.md#level-1f-kernels)
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* axpy2v
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* dotaxpyv
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* axpyf
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* dotxf
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* dotxaxpyf
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* [Level-1v kernels](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#level-1v-kernels)
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* [Level-1v kernels](KernelsHowTo.md#level-1v-kernels)
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* axpyv
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* dotv
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* dotxv
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@@ -113,9 +113,9 @@ The function prototypes in this section follow the same guidelines as those list
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### Level-3 micro-kernels
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This section describes in detail the various level-3 micro-kernels supported by BLIS:
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* [gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemm-micro-kernel)
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* [trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#trsm_micro-kernels)
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* [gemmtrsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemmtrsm-micro-kernels)
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* [gemm](KernelsHowTo.md#gemm-micro-kernel)
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* [trsm](KernelsHowTo.md#trsm_micro-kernels)
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* [gemmtrsm](KernelsHowTo.md#gemmtrsm-micro-kernels)
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#### gemm micro-kernel
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@@ -164,13 +164,13 @@ Parameters:
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* `k`: The number of columns of `A1` and rows of `B1`.
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* `alpha`: The address of a scalar to the `A1 * B1` product.
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* `a1`: The address of a micro-panel of matrix `A` of dimension _MR x k_, stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.)
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* `b1`: The address of a micro-panel of matrix `B` of dimension _k x NR_, stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `a1`: The address of a micro-panel of matrix `A` of dimension _MR x k_, stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.)
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* `b1`: The address of a micro-panel of matrix `B` of dimension _k x NR_, stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `beta`: The address of a scalar to the input value of matrix `C11`.
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* `c11`: The address of a matrix `C11` of dimension _MR x NR_, stored according to `rsc` and `csc`.
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* `rsc`: The row stride of matrix `C11` (ie: the distance to the next row, in units of matrix elements).
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* `csc`: The column stride of matrix `C11` (ie: the distance to the next column, in units of matrix elements).
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `gemm` micro-kernel implementation. (See [Using the auxinfo\_t object](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`.)
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `gemm` micro-kernel implementation. (See [Using the auxinfo\_t object](KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`.)
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* `cntx`: The address of the runtime context. The context can be queried for implementation-specific values such as cache and register blocksizes. However, most micro-kernels intrinsically "know" these values already, and thus the `cntx` argument usually can be safely ignored.
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#### Diagram for gemm
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@@ -206,7 +206,7 @@ The diagram below shows the packed micro-panel operands and how elements of each
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#### Using the auxinfo\_t object
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Each micro-kernel ([gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemm-micro-kernel), [trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#trsm_micro-kernels), and [gemmtrsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemmtrsm-micro-kernels)) takes as its last argument a pointer of type `auxinfo_t`. This BLIS-defined type is defined as a `struct` whose fields contain auxiliary values that may be useful to some micro-kernel authors, particularly when implementing certain optimization techniques. BLIS provides kernel authors access to the fields of the `auxinfo_t` object via the following function-like preprocessor macros. Each macro takes a single argument, the `auxinfo_t` pointer, and returns one of the values stored within the object.
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Each micro-kernel ([gemm](KernelsHowTo.md#gemm-micro-kernel), [trsm](KernelsHowTo.md#trsm_micro-kernels), and [gemmtrsm](KernelsHowTo.md#gemmtrsm-micro-kernels)) takes as its last argument a pointer of type `auxinfo_t`. This BLIS-defined type is defined as a `struct` whose fields contain auxiliary values that may be useful to some micro-kernel authors, particularly when implementing certain optimization techniques. BLIS provides kernel authors access to the fields of the `auxinfo_t` object via the following function-like preprocessor macros. Each macro takes a single argument, the `auxinfo_t` pointer, and returns one of the values stored within the object.
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* `bli_auxinfo_next_a()`. Returns the address (`void*`) of the micro-panel of `A` that will be used the next time the micro-kernel will be called.
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* `bli_auxinfo_next_b()`. Returns the address (`void*`) of the micro-panel of `B` that will be used the next time the micro-kernel will be called.
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@@ -288,23 +288,23 @@ _MR_ and _NR_ are the register blocksizes associated with the micro-kernel. They
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Parameters:
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* `a11`: The address of `A11`, which is the _MR x MR_ lower (`trsm_l`) or upper (`trsm_u`) triangular submatrix within the packed micro-panel of matrix `A`. `A11` is stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.) Note that `A11` contains elements in both triangles, though elements in the unstored triangle are not guaranteed to be zero and thus should not be referenced.
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* `b11`: The address of `B11`, which is an _MR x NR_ submatrix of the packed micro-panel of `B`. `B11` is stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `a11`: The address of `A11`, which is the _MR x MR_ lower (`trsm_l`) or upper (`trsm_u`) triangular submatrix within the packed micro-panel of matrix `A`. `A11` is stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.) Note that `A11` contains elements in both triangles, though elements in the unstored triangle are not guaranteed to be zero and thus should not be referenced.
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* `b11`: The address of `B11`, which is an _MR x NR_ submatrix of the packed micro-panel of `B`. `B11` is stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `c11`: The address of `C11`, which is an _MR x NR_ submatrix of matrix `C`, stored according to `rsc` and `csc`. `C11` is the submatrix within `C` that corresponds to the elements which were packed into `B11`. Thus, `C` is the original input matrix `B` to the overall `trsm` operation.
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* `rsc`: The row stride of matrix `C11` (ie: the distance to the next row, in units of matrix elements).
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* `csc`: The column stride of matrix `C11` (ie: the distance to the next column, in units of matrix elements).
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `trsm` micro-kernel implementation. (See [Using the auxinfo\_t object](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`, and also [Implementation Notes for trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-trsm) for caveats.)
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `trsm` micro-kernel implementation. (See [Using the auxinfo\_t object](KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`, and also [Implementation Notes for trsm](KernelsHowTo.md#implementation-notes-for-trsm) for caveats.)
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* `cntx`: The address of the runtime context. The context can be queried for implementation-specific values such as cache and register blocksizes. However, most micro-kernels intrinsically "know" these values already, and thus the `cntx` argument usually can be safely ignored.
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#### Diagrams for trsm
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Please see the diagram for [gemmtrsm\_l](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#diagram-for-gemmtrsm-l) and [gemmtrsm\_u](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#diagram-for-gemmtrsm-u) to see depictions of the `trsm_l` and `trsm_u` micro-kernel operations and where they fit in with their preceding `gemm` subproblems.
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Please see the diagram for [gemmtrsm\_l](KernelsHowTo.md#diagram-for-gemmtrsm-l) and [gemmtrsm\_u](KernelsHowTo.md#diagram-for-gemmtrsm-u) to see depictions of the `trsm_l` and `trsm_u` micro-kernel operations and where they fit in with their preceding `gemm` subproblems.
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#### Implementation Notes for trsm
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* **Register blocksizes.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Leading dimensions of `a11` and `b11`: _PACKMR_ and _PACKNR_.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Edge cases in _MR_, _NR_ dimensions.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Register blocksizes.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Leading dimensions of `a11` and `b11`: _PACKMR_ and _PACKNR_.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Edge cases in _MR_, _NR_ dimensions.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Alignment of `a11` and `b11`.** The addresses `a11` and `b11` are aligned according to `PACKMR * sizeof(type)` and `PACKNR * sizeof(type)`, respectively.
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* **Unrolling loops.** Most optimized implementations should unroll all three loops within the `trsm` micro-kernel.
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* **Prefetching next micro-panels of `A` and `B`.** We advise against using the `bli_auxinfo_next_a()` and `bli_auxinfo_next_b()` macros from within the `trsm_l` and `trsm_u` micro-kernels, since the values returned usually only make sense in the context of the overall `gemmtrsm` subproblem.
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@@ -410,14 +410,14 @@ Parameters:
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* `k`: The number of columns of `A10` and rows of `B01` (`trsm_l`); the number of columns of `A12` and rows of `B21` (`trsm_u`).
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* `alpha`: The address of a scalar to be applied to `B11`.
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* `a10`, `a12`: The address of `A10` or `A12`, which is the _MR x k_ submatrix of the packed micro-panel of `A` that is situated to the left (`trsm_l`) or right (`trsm_u`) of the _MR x MR_ triangular submatrix `A11`. `A10` and `A12` are stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.)
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* `a11`: The address of `A11`, which is the _MR x MR_ lower (`trsm_l`) or upper (`trsm_u`) triangular submatrix within the packed micro-panel of matrix `A` that is situated to the right of `A10` (`trsm_l`) or the left of `A12` (`trsm_u`). `A11` is stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.) Note that `A11` contains elements in both triangles, though elements in the unstored triangle are not guaranteed to be zero and thus should not be referenced.
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* `b01`, `b21`: The address of `B01` and `B21`, which is the _k x NR_ submatrix of the packed micro-panel of `B` that is situated above (`trsm_l`) or below (`trsm_u`) the _MR x NR_ block `B11`. `B01` and `B21` are stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `b11`: The address of `B11`, which is the _MR x NR_ submatrix of the packed micro-panel of `B`, situated below `B01` (`trsm_l`) or above `B21` (`trsm_u`). `B11` is stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `a10`, `a12`: The address of `A10` or `A12`, which is the _MR x k_ submatrix of the packed micro-panel of `A` that is situated to the left (`trsm_l`) or right (`trsm_u`) of the _MR x MR_ triangular submatrix `A11`. `A10` and `A12` are stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.)
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* `a11`: The address of `A11`, which is the _MR x MR_ lower (`trsm_l`) or upper (`trsm_u`) triangular submatrix within the packed micro-panel of matrix `A` that is situated to the right of `A10` (`trsm_l`) or the left of `A12` (`trsm_u`). `A11` is stored by columns with leading dimension _PACKMR_, where typically _PACKMR_ = _MR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKMR_.) Note that `A11` contains elements in both triangles, though elements in the unstored triangle are not guaranteed to be zero and thus should not be referenced.
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* `b01`, `b21`: The address of `B01` and `B21`, which is the _k x NR_ submatrix of the packed micro-panel of `B` that is situated above (`trsm_l`) or below (`trsm_u`) the _MR x NR_ block `B11`. `B01` and `B21` are stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `b11`: The address of `B11`, which is the _MR x NR_ submatrix of the packed micro-panel of `B`, situated below `B01` (`trsm_l`) or above `B21` (`trsm_u`). `B11` is stored by rows with leading dimension _PACKNR_, where typically _PACKNR_ = _NR_. (See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for a discussion of _PACKNR_.)
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* `c11`: The address of `C11`, which is an _MR x NR_ submatrix of matrix `C`, stored according to `rsc` and `csc`. `C11` is the submatrix within `C` that corresponds to the elements which were packed into `B11`. Thus, `C` is the original input matrix `B` to the overall `trsm` operation.
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* `rsc`: The row stride of matrix `C11` (ie: the distance to the next row, in units of matrix elements).
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* `csc`: The column stride of matrix `C11` (ie: the distance to the next column, in units of matrix elements).
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `gemmtrsm` micro-kernel implementation. (See [Using the auxinfo\_t object](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`, and also [Implementation Notes for gemmtrsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemmtrsm) for caveats.)
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* `data`: The address of an `auxinfo_t` object that contains auxiliary information that may be useful when optimizing the `gemmtrsm` micro-kernel implementation. (See [Using the auxinfo\_t object](KernelsHowTo.md#Using_the_auxinfo_t_object) for a discussion of the kinds of values available via `auxinfo_t`, and also [Implementation Notes for gemmtrsm](KernelsHowTo.md#implementation-notes-for-gemmtrsm) for caveats.)
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* `cntx`: The address of the runtime context. The context can be queried for implementation-specific values such as cache and register blocksizes. However, most micro-kernels intrinsically "know" these values already, and thus the `cntx` argument usually can be safely ignored.
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#### Diagram for gemmtrsm\_l
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@@ -469,18 +469,18 @@ The diagram below shows the packed micro-panel operands for `trsm_u` and how ele
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#### Implementation Notes for gemmtrsm
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* **Register blocksizes.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Leading dimensions of `a1` and `b1`: _PACKMR_ and _PACKNR_.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Edge cases in _MR_, _NR_ dimensions.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Alignment of `a1` and `b1`.** See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm).
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* **Unrolling loops.** Most optimized implementations should unroll all three loops within the `trsm` subproblem of `gemmtrsm`. See [Implementation Notes for gemm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-gemm) for remarks on unrolling the `gemm` subproblem.
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* **Register blocksizes.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Leading dimensions of `a1` and `b1`: _PACKMR_ and _PACKNR_.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Edge cases in _MR_, _NR_ dimensions.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Alignment of `a1` and `b1`.** See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm).
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* **Unrolling loops.** Most optimized implementations should unroll all three loops within the `trsm` subproblem of `gemmtrsm`. See [Implementation Notes for gemm](KernelsHowTo.md#implementation-notes-for-gemm) for remarks on unrolling the `gemm` subproblem.
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* **Prefetching next micro-panels of `A` and `B`.** When invoked from within a `gemmtrsm_l` micro-kernel, the addresses accessible via `bli_auxinfo_next_a()` and `bli_auxinfo_next_b()` refer to the next invocation's `a10` and `b01`, respectively, while in `gemmtrsm_u`, the `_next_a()` and `_next_b()` macros return the addresses of the next invocation's `a11` and `b11` (since those submatrices precede `a12` and `b21`).
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* **Zero `alpha`.** The micro-kernel can safely assume that `alpha` is non-zero; "alpha equals zero" handling is performed at a much higher level, which means that, in such a scenario, the micro-kernel will never get called.
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* **Diagonal elements of `A11`.** See [Implementation Notes for trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-trsm).
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* **Zero elements of `A11`.** See [Implementation Notes for trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-trsm).
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* **Output.** See [Implementation Notes for trsm](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#implementation-notes-for-trsm).
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* **Optimization.** Let's assume that the [gemm micro-kernel](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#gemm-micro-kernel) has already been optimized. You have two options with regard to optimizing the fused `gemmtrsm` micro-kernels:
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1. Optimize only the [trsm micro-kernels](https://github.com/flame/blis/blob/master/docs/KernelsHowTo.md#trsm-micro-kernels). This will result in the `gemm` and `trsm_l` micro-kernels being called in sequence. (Likewise for `gemm` and `trsm_u`.)
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* **Diagonal elements of `A11`.** See [Implementation Notes for trsm](KernelsHowTo.md#implementation-notes-for-trsm).
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* **Zero elements of `A11`.** See [Implementation Notes for trsm](KernelsHowTo.md#implementation-notes-for-trsm).
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* **Output.** See [Implementation Notes for trsm](KernelsHowTo.md#implementation-notes-for-trsm).
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* **Optimization.** Let's assume that the [gemm micro-kernel](KernelsHowTo.md#gemm-micro-kernel) has already been optimized. You have two options with regard to optimizing the fused `gemmtrsm` micro-kernels:
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1. Optimize only the [trsm micro-kernels](KernelsHowTo.md#trsm-micro-kernels). This will result in the `gemm` and `trsm_l` micro-kernels being called in sequence. (Likewise for `gemm` and `trsm_u`.)
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1. Fuse the implementation of the `gemm` micro-kernel with that of the `trsm` micro-kernels by inlining both into the `gemmtrsm_l` and `gemmtrsm_u` micro-kernel definitions. This option is more labor-intensive, but also more likely to yield higher performance because it avoids redundant memory operations on the packed _MR x NR_ submatrix `B11`.
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Reference in New Issue
Block a user