Add to/from E8M0 scale MX format conversion.

Implementation using bitmasking & shifting, so hopefully decently fast!

jax_scalify/core/pow2.py

@@ -4,6 +4,7 @@
 from functools import partial
 from typing import Any, Dict, Optional, Sequence, Tuple, Union
 
+import jax.numpy as jnp
 import numpy as np
 from jax import core
 from jax.interpreters import mlir
@@ -14,6 +15,9 @@
 
 # Exponent bits masking.
 _exponent_bits_mask: Dict[Any, NDArray[Any]] = {
+    np.dtype(jnp.bfloat16): np.packbits(
+        np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], dtype=np.uint8)
+    ).view(np.int16),
     np.dtype(np.float16): np.packbits(np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0], dtype=np.uint8)).view(
         np.int16
     ),
@@ -31,6 +35,24 @@
 """
 
 
+def dtype_exponent_mask(dtype: DTypeLike, sign_bit: bool = False) -> NDArray[Any]:
+    """Get the exponent mask for a given Numpy/JAX dtype.
+
+    Args:
+        dtype: Numpy/JAX dtype.
+        sign_bit: Include sign bit in the mask.
+    Returns:
+        Array mask as integer dtype.
+    """
+    mask = _exponent_bits_mask[dtype]
+    if sign_bit:
+        # Negative value to add sign.
+        intdtype = mask.dtype
+        mask = (-mask.view(dtype)).view(intdtype)
+        return mask
+    return mask
+
+
 def pow2_decompose_round_down_impl(vin: Array, scale_dtype: DTypeLike) -> Array:
     """Pow-2 decompose with rounding down.
 
@@ -42,7 +64,7 @@ def pow2_decompose_round_down_impl(vin: Array, scale_dtype: DTypeLike) -> Array:
     # NOTE: `jnp.frexp` is buggy for subnormals.
     dtype = np.dtype(np.float32)
     minval = np.finfo(dtype).smallest_normal
-    exponent_mask = _exponent_bits_mask[dtype]
+    exponent_mask = dtype_exponent_mask(dtype)
     intdtype = exponent_mask.dtype
     val = vin.astype(dtype)
     # Masking mantissa bits, keeping only the exponents ones.

jax_scalify/quantization/__init__.py

@@ -0,0 +1,2 @@
+# Copyright (c) 2024 Graphcore Ltd. All rights reserved.
+from .scale import as_e8m0  # noqa: F401

jax_scalify/quantization/scale.py

@@ -0,0 +1,62 @@
+# Copyright (c) 2024 Graphcore Ltd. All rights reserved.
+import jax.numpy as jnp
+import numpy as np
+
+from jax_scalify.core import Array, DTypeLike, get_numpy_api
+from jax_scalify.core.pow2 import dtype_exponent_mask
+
+
+def pow2_truncate(arr: Array) -> Array:
+    """Convert an Array to a power of 2, using mantissa truncation.
+
+    NOTE: all sub-normals values are flushed to zero.
+    """
+    np_api = get_numpy_api(arr)
+    # Masking mantissa & sign-bit, keeping only exponent values.
+    exponent_mask = dtype_exponent_mask(arr.dtype, sign_bit=True)
+    intdtype = exponent_mask.dtype
+    # Masking mantissa bits, keeping only the exponents ones.
+    arr_pow2 = np_api.bitwise_and(arr.view(intdtype), exponent_mask).view(arr.dtype).reshape(arr.shape)
+    return arr_pow2
+
+
+def as_e8m0(arr: Array) -> Array:
+    """Convert an Array to e8m0 format (i.e. power of two values).
+
+    This function is only implementing a truncation + saturation variant, in line with
+    the MX OCP format.
+
+    Args:
+        arr: Input array (FP16, FP32 or BF16).
+    Returns:
+        E8M0 array (as uint8).
+    """
+    np_api = get_numpy_api(arr)
+    # assert len(arr.shape) < 2
+    assert arr.dtype in {np.dtype(jnp.bfloat16), np.dtype(jnp.float32)}
+    # Saturation => negative values saturating to min value (i.e. zero bits) in E8M0.
+    arr = np_api.maximum(arr, np.array(0, arr.dtype))
+    arr = pow2_truncate(arr)
+
+    # Bit masking to extract the exponent as uint8 array.
+    arr_u8 = arr.view(np.uint8).reshape((*arr.shape, -1))
+    arr_e8m0 = np_api.bitwise_or(np_api.left_shift(arr_u8[..., -1], 1), np_api.right_shift(arr_u8[..., -2], 7))
+    return arr_e8m0
+
+
+def from_e8m0(arr: Array, dtype: DTypeLike) -> Array:
+    """Convert an Array of e8m0 values (i.e. power of two values) to a given dtype.
+
+    Args:
+        arr: E8M0 array (assuming uint8 storage dtype).
+        dtype: Output dtype. FP32 or BF16 supported.
+    Returns:
+        Converted output.
+    """
+    np_api = get_numpy_api(arr)
+    assert arr.dtype == np.uint8
+    assert np.dtype(dtype) in {np.dtype(jnp.bfloat16), np.dtype(jnp.float32)}
+    # Avoid issues with 7 mantissa bits in BF16.
+    # TODO: more efficient implementation!
+    arr = np_api.exp2(arr.astype(np.float32) - 127)
+    return arr.astype(dtype)

tests/quantization/test_scale.py

@@ -0,0 +1,58 @@
+# Copyright (c) 2024 Graphcore Ltd. All rights reserved.
+import chex
+import ml_dtypes
+import numpy as np
+import numpy.testing as npt
+from absl.testing import parameterized
+
+from jax_scalify.quantization.scale import as_e8m0, from_e8m0, pow2_truncate
+
+
+class QuantizationScaleTests(chex.TestCase):
+    @parameterized.parameters(
+        {"dtype": np.float16},
+        {"dtype": np.float32},
+        {"dtype": ml_dtypes.bfloat16},
+    )
+    def test__pow2_truncate__proper_result(self, dtype):
+        vin = np.array([-2, 0, 2, 1, 9, 15]).astype(dtype)
+        vout = pow2_truncate(vin)
+        assert vout.dtype == vin.dtype
+        npt.assert_array_equal(vout, [-2.0, 0.0, 2.0, 1.0, 8.0, 8.0])
+
+    @parameterized.parameters(
+        # {"dtype": np.float16},
+        {"dtype": np.float32},
+        {"dtype": ml_dtypes.bfloat16},
+    )
+    def test__as_e8m0__positive_values(self, dtype):
+        vin = np.array([0.6, 2, 1, 9, 15, 127]).astype(dtype).reshape((-1, 2))
+        vout = as_e8m0(vin)
+        assert vout.dtype == np.uint8
+        assert vout.shape == vin.shape
+        npt.assert_array_equal(vout, np.log2(pow2_truncate(vin)) + 127)
+
+    @parameterized.parameters(
+        # {"dtype": np.float16},
+        {"dtype": np.float32},
+        {"dtype": ml_dtypes.bfloat16},
+    )
+    def test__as_e8m0__negative_values(self, dtype):
+        vin = np.array([-0.1, -3, 0, 2**-127]).astype(dtype)
+        vout = as_e8m0(vin)
+        assert vout.dtype == np.uint8
+        # NOTE: uint8(0) is the smallest positive scale in E8M0.
+        npt.assert_array_equal(vout, np.uint8(0))
+
+    @parameterized.parameters(
+        # {"dtype": np.float16},
+        {"dtype": np.float32},
+        {"dtype": ml_dtypes.bfloat16},
+    )
+    def test__from_e8m0(self, dtype):
+        vin = np.array([2**-127, 0.25, 1, 2, 8, 2**127.0]).astype(dtype).reshape((-1, 2))
+        vin_e8m0 = as_e8m0(vin)
+        vout = from_e8m0(vin_e8m0, dtype)
+        assert vin.dtype == vout.dtype
+        assert vout.shape == vin.shape
+        npt.assert_array_equal(vout, vin)