Triton MX4 Quantize Rounding Mode Support. (#2821)

Summary:
Pull Request resolved: #2821

X-link: facebookresearch/FBGEMM#22

This diff adds the `rounding_mode` argument to triton quantize. We support all the rounding described in the [best practices doc](https://docs.google.com/document/d/156Du0hBRH6umG_i-OrYC574XhpQMUU5SJYG0RTS2tTg/edit#heading=h.akfcp7xpg8cr).

Reviewed By: summerdengfb

Differential Revision: D59562029

fbgemm_gpu/fbgemm_gpu/quantize/__init__.py

@@ -49,7 +49,8 @@ def op_registeration(
             int elem_ebits,
             int elem_mbits,
             float elem_max_norm,
-            int mx_group_size
+            int mx_group_size,
+            int rounding_mode
         ) -> Tensor
         """
     )

fbgemm_gpu/fbgemm_gpu/quantize/quantize_ops.py

@@ -4,11 +4,12 @@
 # This source code is licensed under the BSD-style license found in the
 # LICENSE file in the root directory of this source tree.
 
-# # pyre-unsafe
+# pyre-unsafe
+from typing import Union
 
 import torch
 
-from fbgemm_gpu.quantize_utils import fp32_to_mx4, mx4_to_fp32
+from fbgemm_gpu.quantize_utils import fp32_to_mx4, mx4_to_fp32, RoundingMode
 
 
 def quantize_mx(
@@ -18,6 +19,7 @@ def quantize_mx(
     elem_mbits: int = 3,
     elem_max_norm: float = 6.0,
     mx_group_size: int = 32,
+    rounding_mode: Union[RoundingMode, int] = RoundingMode.even,
 ) -> torch.Tensor:
     """
     Registered quantize_mx ops for E2E comm.
@@ -31,14 +33,17 @@ def quantize_mx(
                     i.e., 3 for MX4 e2m1)
         elem_max_norm: max value of the float (i.e., 6.0 for MX4 e2m1)
         mx_group_size: num elements that share the max shared_exponent
+        rounding_mode: Which type of rounding to use when calculating shared exponent.
 
     Return:
         output: MX4 tensor packed into int8 values with size
                 (total_elems / 2 + total_elems / groupsize)
                 the shared exponent of each group is stored at the last byte
                 of output of each group
     """
-    return fp32_to_mx4(input, mx_group_size, use_triton=True)
+    return fp32_to_mx4(
+        input, mx_group_size, rounding_mode=rounding_mode, use_triton=True
+    )
 
 
 def dequantize_mx(

fbgemm_gpu/fbgemm_gpu/quantize_utils.py

@@ -11,7 +11,7 @@
 
 import torch
 
-from fbgemm_gpu.triton import dequantize_mx4, quantize_mx4
+from fbgemm_gpu.triton import dequantize_mx4, quantize_mx4, RoundingMode
 from fbgemm_gpu.triton.quantize_ref import py_dequantize_mx4, py_quantize_mx4
 
 logger: logging.Logger = logging.getLogger()
@@ -31,13 +31,18 @@
 
 
 def fp32_to_mx4(
-    tensor: torch.Tensor, group_size: int = 32, use_triton: bool = True
+    tensor: torch.Tensor,
+    group_size: int = 32,
+    rounding_mode: Union[RoundingMode, int] = RoundingMode.even,
+    use_triton: bool = True,
 ) -> torch.Tensor:
     """Quantize an FP32 tensor to MX4 with triton or native cuda impl.
 
     Args:
         tensor (torch.Tensor): FP32 tensor to quantize with M total elements.
         group_size (int): Compute scale in chunks of group_size.
+        rounding_mode (RoundingMode or int): Which type of rounding to use when computing exponent.
+        Only supported with use_triton=True.
         use_triton (bool): If set, use triton quantization, otherwise cuda.
 
     Return:
@@ -48,10 +53,10 @@ def fp32_to_mx4(
     input = tensor.flatten()
 
     if not tensor.is_cuda:
-        return py_quantize_mx4(input, group_size)
+        return py_quantize_mx4(input, group_size, rounding_mode=rounding_mode)
 
     if use_triton:
-        return quantize_mx4(input, group_size)
+        return quantize_mx4(input, group_size, rounding_mode=rounding_mode)
     else:
         out = torch.ops.fbgemm.quantize_mx_cuda(
             input,

fbgemm_gpu/fbgemm_gpu/triton/__init__.py

@@ -10,11 +10,13 @@
 # Attempt to import triton kernels, fallback to reference if we cannot.
 try:
     from .quantize import (
+        RoundingMode,
         triton_dequantize_mx4 as dequantize_mx4,
         triton_quantize_mx4 as quantize_mx4,
     )
 except ImportError:
     from .quantize_ref import (  # noqa: F401, E402
         py_dequantize_mx4 as dequantize_mx4,
         py_quantize_mx4 as quantize_mx4,
+        RoundingMode,
     )

fbgemm_gpu/fbgemm_gpu/triton/quantize.py

@@ -7,6 +7,8 @@
 
 # pyre-unsafe
 import math
+from enum import IntEnum
+from typing import Union
 
 import torch
 import triton  # @manual
@@ -15,6 +17,81 @@
 from triton import Config  # @manual
 
 
+class RoundingMode(IntEnum):
+    nearest = 0
+    floor = 1
+    even = 2
+    stochastic = 3
+    ceil = 4
+
+
+@triton.jit
+def _floor_log2(x):
+    """Helper function to efficiently compute floor(log2(x))
+
+    Args:
+        x (Tensor): FP32 Input tensor to operate on.
+
+    Returns:
+        Tensor: Floor of log2(x).
+    """
+    # Helpful bit constants.
+    FP32_EXP_MASK: tl.constexpr = 0x7F800000  # type: ignore[Incompatible variable type]
+    FP32_EXP_OFFSET: tl.constexpr = 23  # type: ignore[Incompatible variable type]
+    FP32_EXP_BIAS: tl.constexpr = 127  # type: ignore[Incompatible variable type]
+
+    # View x as an integer and extract its exponent.
+    x = x.to(tl.int32, bitcast=True) & FP32_EXP_MASK
+    # Shift exponent down to bottom bits.
+    x = x >> FP32_EXP_OFFSET
+    # Remove FP32 exponent bias and return.
+    return (x - FP32_EXP_BIAS).to(tl.float32)
+
+
+@triton.jit
+def _compute_exp(
+    group_max,
+    rounding_mode,
+    rand_bits,
+):
+    """Compute shared exponent of group using specified rounding mode.
+
+    Args:
+        group_max (Tensor): Group of values to compute exponent of.
+        rounding_mode (int or RoundingMode): Which rounding mode to use.
+        rand_bits (int): Random integer values used for stochastic rounding.
+
+    Returns:
+        Tensor: Shared exponent of group.
+    """
+    # TODO(jwfromm) Enable hip libdevice support as well.
+    # Nearest rounding mode.
+    if rounding_mode == 0:
+        return tl.extra.cuda.libdevice.round(tl.log2(group_max))
+    # Floor rounding mode. This can be done with fast bit ops.
+    if rounding_mode == 1:
+        return _floor_log2(group_max)
+    # Even pre-rounding mode.
+    elif rounding_mode == 2:
+        # First round to nearest even integer.
+        group_max = tl.extra.cuda.libdevice.rint(group_max)
+        # Then perform floor rounding of log.
+        return _floor_log2(group_max)
+    # Stochastic rounding mode.
+    elif rounding_mode == 3:
+        # Define constants needed for stochastic rounding.
+        MBITS_FP32: tl.constexpr = 23  # type: ignore[Incompatible variable type]
+        MBITS_E2M1: tl.constexpr = 1  # type: ignore[Incompatible variable type]
+        RAND_MASK: tl.constexpr = 1 << (MBITS_FP32 - MBITS_E2M1) - 1  # type: ignore[Incompatible variable type]
+        # Use random bits to add noise to mantissa that would otherwise
+        # be rounded away.
+        group_max = group_max.to(tl.int32, bitcast=True) + (RAND_MASK & rand_bits)
+        # Now compute log and truncate.
+        return _floor_log2(group_max)
+    else:
+        return tl.ceil(tl.log2(group_max))
+
+
 @triton.autotune(
     configs=[
         Config({"GROUP_LOAD": 1}),
@@ -31,6 +108,8 @@ def _kernel_quantize_mx4(
     out,
     M,
     K,
+    rand_bits,
+    ROUNDING_MODE: tl.constexpr,
     GROUP_SIZE: tl.constexpr,
     GROUP_LOAD: tl.constexpr,
 ) -> None:
@@ -42,6 +121,8 @@ def _kernel_quantize_mx4(
         out (Tensor): [M / 2 + M / GROUP_SIZE] output containing packed mx4 values.
         M (int): Total number of elements.
         K (int): Number of elements to process in each thread.
+        rand_bits (Optional Tensor): [M, K / 2] random integers used for stochastic rounding.
+        ROUNDING_MODE (int): Which rounding method to use when calculating shared exponent.
         GROUP_SIZE (int): Size of chunks that use the same shared exponent.
         GROUP_LOAD (int): Number of groups to process simultaneously.
     """
@@ -73,6 +154,7 @@ def _kernel_quantize_mx4(
     # Initiate offset ranges used in kernel.
     input_offset = tl.arange(0, GROUP_LOAD * GROUP_SIZE) + input_start
     output_offset = tl.arange(0, GROUP_LOAD * (GROUP_SIZE // 2))
+    rand_bits_offset = tl.arange(0, GROUP_LOAD) + pid * K // GROUP_SIZE
     # We need to shift output offsets to make space for shared exponent storage.
     output_offset += output_offset // (GROUP_SIZE // 2) + output_start
     # Now create offsets for writing the shared exponent.
@@ -97,9 +179,18 @@ def _kernel_quantize_mx4(
         group_max = tl.max(tl.abs(a_groups), axis=1)
         # Prevent infinite values in log.
         group_max = tl.where(group_max == 0, FP32_MIN_NORMAL, group_max)
-        # Convert max to exponent via direct log computation and ceiling
-        # rounding to minimize errors.
-        group_exp = tl.ceil(tl.log2(group_max))
+        # Load relevant random values if doing stochastic rounding.
+        if ROUNDING_MODE == 3:
+            group_rand_bits = tl.load(
+                rand_bits + rand_bits_offset,
+                mask=rand_bits_offset < K // GROUP_SIZE,
+                other=0,
+            )
+            rand_bits_offset += GROUP_LOAD
+        else:
+            group_rand_bits = None
+        # Compute shared exponent using specified rounding mode.
+        group_exp = _compute_exp(group_max, ROUNDING_MODE, group_rand_bits)
         # Subtract largest exponent in target datatype and remove bias.
         group_exp = group_exp - 2
         # Make sure exponent is in valid range.
@@ -204,13 +295,19 @@ def _kernel_quantize_mx4(
         output_offset += GROUP_LOAD * PACKED_GROUP_SIZE
 
 
-def triton_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
+def triton_quantize_mx4(
+    a: torch.Tensor,
+    group_size: int = 32,
+    rounding_mode: Union[RoundingMode, int] = RoundingMode.even,
+) -> torch.Tensor:
     """
     Quantize a tensor to mx4 format using efficient triton kernels.
 
     Args:
         a (Tensor): [M] higher precision input tensor.
         group_size (int): Size of chunks that will use the same shared exponent.
+        rounding_mode (Union[RoundingMode, int]): Which type of rounding to use
+        when calculating shared exponent. Defaults to pre-rounding to nearest even int.
 
     Returns:
         torch.Tensor: [M / 2 + M / group_size] mx4 scaled tensor packed into in8
@@ -252,13 +349,28 @@ def triton_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
         [a.numel() // 2 + a.numel() // group_size], device=a.device, dtype=torch.uint8
     )
 
+    # If using stochastic rounding, create random noise for each group.
+    if rounding_mode == RoundingMode.stochastic:
+        # Each group will need a seed.
+        rand_bits = torch.randint(
+            low=0,
+            high=2**31 - 1,
+            size=(a.numel() // group_size,),
+            dtype=torch.int32,
+            device=a.device,
+        )
+    else:
+        rand_bits = None
+
     # Invoke triton quantization kernel over rows.
     grid = (M,)
     _kernel_quantize_mx4[grid](
         a,
         out,
         a.numel(),
         K,
+        rand_bits=rand_bits,
+        ROUNDING_MODE=rounding_mode,
         GROUP_SIZE=group_size,
     )
     # Inputs are now fully quantized and ready to return.

fbgemm_gpu/fbgemm_gpu/triton/quantize_ref.py

@@ -6,16 +6,69 @@
 # LICENSE file in the root directory of this source tree.
 
 # pyre-unsafe
+from enum import IntEnum
+from typing import Union
+
 import torch
 
 
-def py_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
+class RoundingMode(IntEnum):
+    nearest = 0
+    floor = 1
+    even = 2
+    stochastic = 3
+    ceil = 4
+
+
+def _compute_exp(
+    group_max,
+    rounding_mode,
+):
+    """Compute shared exponent of group using specified rounding mode.
+
+    Args:
+        group_max (Tensor): Group of values to compute exponent of.
+        rounding_mode (int or RoundingMode): Which rounding mode to use.
+
+    Returns:
+        Tensor: Shared exponent of group.
+    """
+    if rounding_mode == 0:
+        return torch.round(torch.log2(group_max))
+    # Floor rounding mode.
+    if rounding_mode == 1:
+        return torch.floor(torch.log2(group_max))
+    # Even pre-rounding mode.
+    elif rounding_mode == 2:
+        # First round to nearest even integer.
+        group_max = torch.round(group_max)
+        # Then perform floor rounding of log.
+        return torch.floor(torch.log2(group_max))
+    # Stochastic rounding mode.
+    elif rounding_mode == 3:
+        # Create random noise.
+        noise = torch.rand_like(group_max)
+        # Add noise to group max and round down.
+        group_max = group_max + noise
+        # Now compute log and truncate.
+        return torch.floor(torch.log2(group_max))
+    else:
+        return torch.ceil(torch.log2(group_max))
+
+
+def py_quantize_mx4(
+    a: torch.Tensor,
+    group_size: int = 32,
+    rounding_mode: Union[RoundingMode, int] = RoundingMode.even,
+) -> torch.Tensor:
     """
     Quantize a tensor to mx4 format.
 
     Args:
         a (Tensor): [M] higher precision input tensor.
         group_size (int): Size of chunks that will use the same shared exponent.
+        rounding_mode (int or RoundingMode): Which type of rounding to use when
+        calculating shared exponent.
 
     Returns:
         torch.Tensor: [M / 2 + M / group_size] mx4 scaled tensor packed into in8
@@ -43,10 +96,8 @@ def py_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
     # Replace zero values with the minimum expressible normal value.
     FP32_MIN_NORMAL = 2 ** (-126)
     shared_exp = torch.where(shared_exp == 0, FP32_MIN_NORMAL, shared_exp)
-    # Convert max into an intger exponent.
-    # Note this can be more efficient by just shifting and masking exp bits.
-    # We can even use those directly.
-    shared_exp = torch.ceil(torch.log2(shared_exp))
+    # Convert max into an integer exponent.
+    shared_exp = _compute_exp(shared_exp, rounding_mode)
     # Offset exponent by largest exponent in target datatype.
     shared_exp = shared_exp - 2
     # Restrict to range expressible as int8.