Data Types {#dev_guide_data_types}
==================================

oneDNN functionality supports a number of numerical
data types. IEEE single precision floating-point (fp32) is considered
to be the golden standard in deep learning applications and is supported
in all the library functions. The purpose of low precision data types
support is to improve performance of compute intensive operations, such as
convolutions, inner product, and recurrent neural network cells
in comparison to fp32.

| Data type | Description                                                                                                                                                                             |
|:----------|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| f32       | [IEEE single precision floating-point](https://en.wikipedia.org/wiki/Single-precision_floating-point_format#IEEE_754_single-precision_binary_floating-point_format:_binary32)           |
| bf16      | [non-IEEE 16-bit floating-point](https://www.intel.com/content/dam/develop/external/us/en/documents/bf16-hardware-numerics-definition-white-paper.pdf)                                  |
| f16       | [IEEE half precision floating-point](https://en.wikipedia.org/wiki/Half-precision_floating-point_format#IEEE_754_half-precision_binary_floating-point_format:_binary16)                 |
| s8/u8     | signed/unsigned 8-bit integer                                                                                                                                                           |
| s4/u4     | signed/unsigned 4-bit integer                                                                                                                                                           |
| f64       | [IEEE double precision floating-point](https://en.wikipedia.org/wiki/Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64)           |
| boolean   | bool (size is C++ implementation defined)                                                                                                                                               |
| f8\_e5m2  | [OFP8 standard 8-bit floating-point](https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf) with 5 exponent and 2 mantissa bits |
| f8\_e4m3  | [OFP8 standard 8-bit floating-point](https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf) with 4 exponent and 3 mantissa bits |
| e8m0      | [MX standard 8-bit scaling type](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf)                                                                 |
| f4\_e2m1  | [MX standard 4-bit floating-point](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf) with 2 exponent and 1 mantissa bits                           |
| f4\_e3m0  | 4-bit floating-point with 3 exponent bits and no mantissa bit                                                                                                                           |


## Inference and Training

oneDNN supports training and inference with the following data types:

| Usage mode | CPU                                                                          | GPU                                           |
|:-----------|:-----------------------------------------------------------------------------|:----------------------------------------------|
| Inference  | f32, bf16, f16, f8\_e5m2/f8\_e4m3, f4\_e2m1, f4\_e3m0, s8/u8, s4/u4, boolean | f32, bf16, f16, f8\_e5m2/f8\_e4m3, s8/u8, f64 |
| Training   | f32, bf16, f16, f8\_e5m2/f8\_e4m3                                            | f32, bf16, f16, f8\_e5m2/f8\_e4m3, f64        |

@note
    Using lower precision arithmetic may require changes in the deep learning
    model implementation.

@note
    f64 is supported only for matmul, convolution, reorder, layer normalization, and
    pooling primitives on the GPU engine.

@note
    s4/u4 data types are only supported as a storage data type for weights argument
    in case of weights decompression. For more details, refer to
    [Matmul Tutorial: weights decompression](@ref weights_decompression_matmul_cpp).

See topics for the corresponding data types details:
 * @ref dev_guide_inference_int8
 * @ref dev_guide_attributes_quantization
 * @ref dev_guide_training_bf16
 * @ref dev_guide_attributes_fpmath_mode
 * @ref weights_decompression_matmul_cpp

Individual primitives may have additional limitations with respect to data type
by each primitive is included in the corresponding sections of the developer
guide.

## General numerical behavior of the oneDNN library

During a primitive computation, oneDNN can use different datatypes
than those of the inputs/outputs. In particular, oneDNN uses wider
accumulator datatypes (s32 for integral computations, and f32/f64 for
floating-point computations), and converts intermediate results to f32
before applying post-ops (f64 configuration does not support
post-ops).  The following formula governs the datatypes dynamic during
a primitive computation:

\f[
\operatorname{convert_{dst\_dt}} ( \operatorname{zp_{dst}} + 1/\operatorname{scale_{dst}} * \operatorname{postops_{f32}} (\operatorname{convert_{f32}} (\operatorname{Op}(\operatorname{src_{src\_dt}}, \operatorname{weights_{wei\_dt}}, ...))))
\f]

The `Op` output datatype depends on the datatype of its inputs:
- if `src`, `weights`, ... are floating-point datatype (f32, f16,
  bf16, f8\_e5m2, f8\_e4m3, f4\_e2m1, f4\_e3m0), then the `Op` outputs f32 elements.
- if `src`, `weights`, ... are integral datatypes (s8, u8, s32), then
  the `Op` outputs s32 elements.
- if the primitive allows to mix input datatypes, the `Op` outputs
  datatype will be s32 if its weights are an integral datatype, or f32
  otherwise.

The accumulation datatype used during `Op` computation is governed by
the `accumulation_mode` attribute of the primitive. By default, f32 is
used for floating-point primitives (or f64 for f64 primitives) and s32
is used for integral primitives.

No downconversions are allowed by default, but can be enabled using
the floating-point math controls described in @ref
dev_guide_attributes_fpmath_mode.

The \f$convert_{dst\_dt}\f$ conversion is guaranteed to be faithfully
rounded but not guaranteed to be correctly rounded (the returned value
is not always the closest one but one of the two closest representable
value). In particular, some hardware platforms have no direct
conversion instructions from f32 data type to low-precision data types
such as fp8 or fp4, and will perform conversion through an
intermediate data type (for example f16 or bf16), which may result in
[double
rounding](https://en.wikipedia.org/wiki/Rounding#Double_rounding).

### Rounding mode and denormal handling

oneDNN floating-point computation behavior follows the floating-point
environment for the given device runtime by default. In particular,
the floating-point environment can control:
- the rounding mode. It is set to round-to-nearest tie-even by default
  on x64 systems as well as devices running on SYCL and openCL runtime.
- the handling of denormal values. Computation on denormals are not
  flushed to zero by default. Note denormal handling can negatively
  impact performance on x64 systems.

@note
  For CPU devices, the default floating-point environment is defined by
  the C and C++ standards in the following header:
~~~cpp
#include <fenv.h>
~~~
  Rounding mode can be changed globally using the `fesetround()` C function.

@note
  Most DNN applications do not require precise computations with denormal
  numbers and flushing these denormals to zero can improve performance.
  On x64 systems, the floating-point environment can be updated to allow
  flushing denormals to zero as follow:
~~~cpp
#include <xmmintrin.h>
_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
~~~

@note
  On some hardware architectures, low-precision datatype acceleration
  ignores floating-point environment and will flush denormal outputs
  to zero (FTZ). In particular this is the case for Intel AMX
  instruction set.

oneDNN also exposes non-standard stochastic rounding through the
`rounding_mode` primitive attribute. More details on this attribute
can be found in @ref dev_guide_attributes_rounding_mode.

## Hardware Limitations

While all the platforms oneDNN supports have hardware acceleration for
fp32 arithmetics, that is not the case for other data types. Support
for low precision data types may not be available for older
platforms. The next sections explain limitations that exist for low
precision data types for Intel(R) Architecture processors, Intel
Processor Graphics and Xe Architecture graphics.

### Intel(R) Architecture Processors

oneDNN performance optimizations for Intel Architecture Processors are
specialized based on Instruction Set Architecture (ISA).
The following ISA have specialized optimizations in the library:
* Intel Streaming SIMD Extensions 4.1 (Intel SSE4.1)
* Intel Advanced Vector Extensions (Intel AVX)
* Intel Advanced Vector Extensions 2 (Intel AVX2)
* Intel Advanced Vector Extensions 512 (Intel AVX-512)
* Intel Deep Learning Boost (Intel DL Boost)
* Intel Advanced Matrix Extensions (Intel AMX)

The following table indicates the minimal supported ISA for each of the data
types that oneDNN recognizes.
| Data type          | Minimal supported ISA                |
|:-------------------|:-------------------------------------|
| f32                | Intel SSE4.1                         |
| s8, u8             | Intel AVX2                           |
| bf16               | Intel DL Boost with bfloat16 support |
| f16                | Intel AVX512-FP16                    |
| boolean            | Intel AVX2                           |
| f8\_e5m2, f8\_e4m3 | Intel AVX512-FP16                    |
| f4\_e2m1, f4\_e3m0 | TBA                                  |

@note
  See @ref dev_guide_int8_computations in the Developer Guide for additional
  limitations related to int8 arithmetic.

@note
  The library has functional bfloat16 support on processors with
  Intel AVX-512 Byte and Word Instructions (AVX512BW) support for validation
  purposes. The performance of bfloat16 primitives on platforms without
  hardware acceleration for bfloat16 is 3-4x lower in comparison to
  the same operations on the fp32 data type.

@note
  The Intel AMX instructions ignore the floating-point environment
  flag and always round to nearest tie-even and flush denormals to
  zero.

@note
  f64 configuration is not available for the CPU engine.

@note
  The current f16 CPU instructions accumulate to f16. To avoid overflow, the f16
  primitives might up-convert the data to f32 before performing math operations.
  This can lead to scenarios where a f16 primitive may perform slower than
  similar f32 primitive.

### Intel(R) Processor Graphics and Xe Architecture graphics
oneDNN performance optimizations for Intel Processor graphics and
Xe Architecture graphics are specialized based on device microarchitecture (uArch).
The following uArchs and associated devices have specialized optimizations in the 
library:
 * Xe-LP (accelerated u8, s8 support via DP4A)
   * Intel(R) UHD Graphics for 11th-14th Gen Intel(R) Processors
   * Intel(R) Iris(R) Xe Graphics
   * Intel(R) Iris(R) Xe MAX Graphics (formerly DG1)
 * Xe-HPG (accelerated f16, bf16, u8, and s8 support via Intel(R) Xe Matrix Extensions (Intel(R) XMX), aka DPAS)
   * Intel(R) Arc(TM) Graphics (formerly Achemist)
   * Intel(R) Data Center GPU Flex Series (formerly Arctic Sound)
 * Xe-HPC (accelerated f16, bf16, u8, and s8 support via DPAS and f64 support via MAD)
   * Intel(R) Data Center GPU Max Series (formerly Ponte Vecchio)
 * Xe2-LPG
   * Intel(R) Graphics for Intel(R) Core(TM) Ultra processors (Series 2) (formerly Lunar Lake)
 * Xe2-HPG
   * Intel(R) Arc(TM) B-Series Graphics (formerly Battlemage)

The following table indicates the data types with performant compute primitives
for each uArch supported by oneDNN. Unless otherwise noted, all data types have 
reference support on all architectures.

| uArch   | Supported Data types                                                |
|:--------|:--------------------------------------------------------------------|
| Xe-LP   | f32, f16, s8, u8                                                    |
| Xe-HPG  | f32, f16, bf16, s8, u8                                              |
| Xe-HPC  | f64, f32, bf16, f16, s8, u8                                         |
| Xe2-LPG | f64, f32, bf16, f16, s8, u8                                         |
| Xe2-HPG | f64, f32, bf16, f16, s8, u8                                         |
| TBA     | f64, f32, bf16, f16, s8, u8, f8\_e5m2, f8\_e4m3, f4\_e2m1, f4\_e3m0 |


@note
  f64 configurations are only supported on GPU engines with HW capability for
  double-precision floating-point.

@note
  f8\_e5m2 and f8\_e4m3 compute operations have limited performance through upconversion on
  Xe-HPC and Xe2 GPUs.

@note
  f16 operations may be faster with f16 accumulation on GPU architectures older
  than Xe-HPC. Newer architectures accumulate to f32.
