cpp_extensions.py

# Copyright (c) 2022-2024, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# See LICENSE for license information.
"""JAX te custom call"""
from abc import ABCMeta, abstractmethod
from dataclasses import dataclass
from typing import Tuple
from functools import partial, reduce
import operator
import os
import warnings

import numpy as np
import jax.numpy as jnp
from jax.lib import xla_client
from jax import core, dtypes
from jax.interpreters import xla, mlir
from jax.experimental.custom_partitioning import custom_partitioning
from jax.interpreters.mlir import ir, dtype_to_ir_type
from jax.sharding import PartitionSpec, NamedSharding
from jax._src.interpreters import batching
from jax._src import dispatch

import transformer_engine_jax
from transformer_engine_jax import DType as TEDType
from transformer_engine_jax import NVTE_Bias_Type
from transformer_engine_jax import NVTE_Mask_Type
from transformer_engine_jax import NVTE_QKV_Layout
from transformer_engine_jax import NVTE_Fused_Attn_Backend

from .sharding import all_reduce_max_along_all_axes_except_PP
from .sharding import all_reduce_sum_along_dp_fsdp
from .sharding import get_all_mesh_axes, num_of_devices
from .sharding import get_padded_spec as te_get_padded_spec

try:
    from jaxlib.hlo_helpers import custom_call
except ImportError:
    # Newer JAX changed its API. But we want to support a few JAX
    # version, so we still need this import.
    pass

for _name, _value in transformer_engine_jax.registrations().items():
    xla_client.register_custom_call_target(_name, _value, platform="CUDA")


def te_dtype_to_jax_dtype(te_dtype):
    """
    convert TE dtype to jax dtype
    """
    assert isinstance(te_dtype, TEDType)

    converter = {
        TEDType.kFloat32: jnp.float32,
        TEDType.kFloat16: jnp.float16,
        TEDType.kBFloat16: jnp.bfloat16,
        TEDType.kInt32: jnp.int32,
        TEDType.kInt64: jnp.int64,
        TEDType.kFloat8E4M3: jnp.float8_e4m3fn,
        TEDType.kFloat8E5M2: jnp.float8_e5m2,
        TEDType.kByte: jnp.uint8
    }

    if te_dtype not in converter:
        raise ValueError(f"Unsupported {te_dtype=}")

    return converter.get(te_dtype)


def te_dtype_to_ir_dtype(te_dtype):
    """
    convert TE dtype to MLIR dtype
    """
    return dtype_to_ir_type(np.dtype(te_dtype_to_jax_dtype(te_dtype)))


def jax_dtype_to_ir_dtype(jax_dtype):
    """
    convert Jax dtype to MLIR dtype
    """
    return dtype_to_ir_type(np.dtype(jax_dtype))


def jax_dtype_to_te_dtype(jax_dtype):
    """
    convert jax dtype to TE dtype
    """
    jax_dtype = dtypes.canonicalize_dtype(jax_dtype)

    converter = {
        jnp.float32.dtype: TEDType.kFloat32,
        jnp.float16.dtype: TEDType.kFloat16,
        jnp.bfloat16.dtype: TEDType.kBFloat16,
        jnp.int32.dtype: TEDType.kInt32,
        jnp.int64.dtype: TEDType.kInt64,
        jnp.float8_e4m3fn.dtype: TEDType.kFloat8E4M3,
        jnp.float8_e5m2.dtype: TEDType.kFloat8E5M2,
        jnp.uint8.dtype: TEDType.kByte,
    }

    if jax_dtype not in converter:
        raise ValueError(f"Unsupported {jax_dtype=}")

    return converter.get(jax_dtype)


def get_padded_spec(arg_info):
    """
    Get padded spec for partitioning from arguments' information
    """
    if arg_info.sharding is None:
        return te_get_padded_spec(None, arg_info.ndim)
    ndim, spec = arg_info.ndim, arg_info.sharding.spec
    return te_get_padded_spec(spec, ndim)


def _check_valid_batch_dims(bdims):
    """
    Assert out non-supported bath dims
    """
    for dim in bdims:
        assert dim in [0, None], \
            "Currently only support batch_dim in [0, None], " \
            f"but got {dim=}"


class BasePrimitive(metaclass=ABCMeta):
    """
    jax primitive
    """

    @staticmethod
    @abstractmethod
    def abstract():
        """
        to describe computing graph
        """
        return NotImplemented

    @classmethod
    def outer_abstract(cls, *args, **kwargs):
        """
        optional abstract wrapper to eliminate workspace tensors
        """
        return cls.abstract(*args, **kwargs)

    @staticmethod
    @abstractmethod
    def lowering():
        """
        to describe MLIR
        """
        return NotImplemented

    @staticmethod
    @abstractmethod
    def impl():
        """
        to describe implementation
        """
        return NotImplemented

    @staticmethod
    @abstractmethod
    def batcher():
        """
        to describe batch rules for vmap
        """
        return NotImplemented

    @staticmethod
    @abstractmethod
    def infer_sharding_from_operands():
        """
        to describe infer_sharding_from_operands for custom_partitioning
        """
        return NotImplemented

    @staticmethod
    @abstractmethod
    def partition():
        """
        to describe partition for custom_partitioning
        """
        return NotImplemented


def register_primitive(cls):
    """
    register jax primitive
    """

    def name_of_wrapper_p():
        return cls.name + "_wrapper"

    inner_p = core.Primitive(cls.name)
    dispatch.prim_requires_devices_during_lowering.add(inner_p)
    inner_p.multiple_results = cls.multiple_results
    inner_p.def_impl(partial(xla.apply_primitive, inner_p))
    inner_p.def_abstract_eval(cls.abstract)
    mlir.register_lowering(inner_p, cls.lowering, platform='cuda')
    cls.inner_primitive = inner_p

    outer_p = core.Primitive(name_of_wrapper_p())
    dispatch.prim_requires_devices_during_lowering.add(outer_p)
    outer_p.multiple_results = cls.multiple_results
    outer_p.def_impl(cls.impl)
    outer_p.def_abstract_eval(cls.outer_abstract)
    batching.primitive_batchers[outer_p] = cls.batcher
    outer_p_lower = custom_partitioning(cls.impl, static_argnums=cls.impl_static_args)
    outer_p_lower.def_partition(infer_sharding_from_operands=cls.infer_sharding_from_operands,
                                partition=cls.partition)
    mlir.register_lowering(outer_p,
                           mlir.lower_fun(outer_p_lower, multiple_results=cls.multiple_results))
    cls.outer_primitive = outer_p


@dataclass
class CustomCallArgsWrapper:
    """
    wrapper of XLA custom call args
    """

    def __init__(self,
                 output_types,
                 operands,
                 operand_shapes,
                 operand_specific_layouts=None,
                 output_specific_layouts=None):
        self.output_types = output_types
        self.operands = operands
        self.operand_layouts = CustomCallArgsWrapper.generate_layouts(operand_shapes,
                                                                      operand_specific_layouts)
        output_shapes = [x.shape for x in output_types]
        self.output_layouts = CustomCallArgsWrapper.generate_layouts(output_shapes,
                                                                     output_specific_layouts)

    @staticmethod
    def generate_layouts(shapes, specific_layouts):
        """
        setup layouts for XLA custom call
        """

        def default_layout(shape):
            return range(len(shape) - 1, -1, -1)

        if specific_layouts is None:
            specific_layouts = {}

        layouts = []
        for idx, shape in enumerate(shapes):
            if idx in specific_layouts:
                layouts.append(specific_layouts[idx])
            else:
                layouts.append(default_layout(shape))
        return layouts


def custom_caller(name, args, opaque, has_side_effect, **kwargs):
    """
    XLA custom call warpper
    """
    if hasattr(mlir, "custom_call"):
        out = mlir.custom_call(name,
                               result_types=args.output_types,
                               operands=args.operands,
                               operand_layouts=args.operand_layouts,
                               result_layouts=args.output_layouts,
                               backend_config=opaque,
                               has_side_effect=has_side_effect,
                               **kwargs).results
    else:
        # Need to disable one pylint error as the second function
        # parameter name recenctly in JAX. Otherwise we won't be
        # compatible with multiple JAX version.
        out = custom_call(    # pylint: disable=too-many-function-args
            name,
            args.output_types,
            operands=args.operands,
            operand_layouts=args.operand_layouts,
            result_layouts=args.output_layouts,
            backend_config=opaque,
            has_side_effect=has_side_effect,
            **kwargs)
    return out


class LayerNormFwdPrimitive(BasePrimitive):
    """
    Layer Normalization Forward Primitive
    """
    name = "te_layernorm_forward"
    multiple_results = True
    impl_static_args = (3, 4)    # zero_centered_gamma, epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, gamma_aval, beta_aval, **kwargs):
        """
        LayerNorm fwd inner primitive abstract
        """
        x_dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert x_dtype in [jnp.float32, jnp.float16, jnp.bfloat16]

        mu_rsigama_dtype = jnp.float32

        out_aval = core.raise_to_shaped(x_aval)
        mu_aval = rsigma_aval = out_aval.update(shape=out_aval.shape[:-1], dtype=mu_rsigama_dtype)

        assert gamma_aval.size == beta_aval.size
        hidden_size = gamma_aval.size
        assert x_aval.size % hidden_size == 0

        wkspace_info, barrier_info = transformer_engine_jax.get_layernorm_fwd_workspace_sizes(
            x_aval.size // hidden_size,    # batch size
            hidden_size,
            jax_dtype_to_te_dtype(x_aval.dtype),    # in te_dtype
            jax_dtype_to_te_dtype(gamma_aval.dtype),    # weight te_dtype
            jax_dtype_to_te_dtype(x_aval.dtype),    # out te_dtype (same as input for Fp16/Bf16)
            True,
            kwargs['zero_centered_gamma'],
            kwargs['epsilon'])
        wkspace_aval = out_aval.update(shape=wkspace_info[0],
                                       dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = out_aval.update(shape=barrier_info[0],
                                       dtype=te_dtype_to_jax_dtype(barrier_info[1]))

        return out_aval, mu_aval, rsigma_aval, wkspace_aval, barrier_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        LayerNorm fwd outer primitive abstract
        """
        out_aval, mu_aval, rsigma_aval, _, _ = \
            LayerNormFwdPrimitive.abstract(*args, **kwargs)
        return out_aval, mu_aval, rsigma_aval

    @staticmethod
    def lowering(ctx, x, gamma, beta, *, zero_centered_gamma, epsilon):
        """
        LayerNorm fwd lowering rules
        """
        x_aval, gamma_aval, beta_aval = ctx.avals_in
        assert gamma_aval.dtype == beta_aval.dtype
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape
        b_type = ir.RankedTensorType(beta.type)
        b_shape = b_type.shape

        assert g_type == b_type
        assert g_shape == b_shape

        # Output shape is same as the input shape, but the output type is same as the weight type.
        # See ln_api.cpp
        output_type = g_type.element_type
        ir_mu_dtype = ir.F32Type.get()
        ir_rsigma_dtype = ir.F32Type.get()

        out_shape = x_shape
        hidden_size = reduce(operator.mul, g_shape)
        batch_shape = out_shape[:-1]
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        wkspace_aval, barrier_aval = ctx.avals_out[-2:]

        out_types = [
            ir.RankedTensorType.get(out_shape, output_type),
            ir.RankedTensorType.get(batch_shape, ir_mu_dtype),
            ir.RankedTensorType.get(batch_shape, ir_rsigma_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
            ir.RankedTensorType.get(barrier_aval.shape, jax_dtype_to_ir_dtype(barrier_aval.dtype))
        ]
        operands = [x, gamma, beta]
        operand_shapes = [x_shape, g_shape, b_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_FWD_LAYERNORM_SM_MARGIN", "0"))

        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            (0,),    # no dgamma_part in FWD pass
            (0,),    # no dbeta_part in BWD pass
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            TEDType.kByte,    # dummy dgamma_part te_dtype
            TEDType.kByte,    # dummy dbeta_part te_dtype
            zero_centered_gamma,
            epsilon,
            sm_margin,
        )

        out = custom_caller(LayerNormFwdPrimitive.name, args, opaque, False)

        return out

    @staticmethod
    def impl(x, gamma, beta, zero_centered_gamma, epsilon):
        """
        to describe implementation
        """
        assert LayerNormFwdPrimitive.inner_primitive is not None
        out, mu, rsigma, _, _ = LayerNormFwdPrimitive.inner_primitive.bind(
            x, gamma, beta, zero_centered_gamma=zero_centered_gamma, epsilon=epsilon)
        return out, mu, rsigma

    @staticmethod
    def batcher(batched_args, batch_dims, *, zero_centered_gamma, epsilon):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert LayerNormFwdPrimitive.outer_primitive is not None
        x, gamma, beta = batched_args
        x_bdim, _, _ = batch_dims

        out_bdims = x_bdim, x_bdim, x_bdim
        return LayerNormFwdPrimitive.outer_primitive.bind(x,
                                                          gamma,
                                                          beta,
                                                          zero_centered_gamma=zero_centered_gamma,
                                                          epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(zero_centered_gamma, epsilon, mesh, arg_infos, result_infos):
        del zero_centered_gamma, epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormFwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        mu_sharding = rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        return (out_sharding, mu_sharding, rsigma_sharding)

    @staticmethod
    def partition(zero_centered_gamma, epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec, g_spec, b_spec = map(get_padded_spec, arg_infos)
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormFwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        if g_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormFwdPrimitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        if b_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormFwdPrimitive.name} does not support sharding of parameter beta " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )

        x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        g_sharding = NamedSharding(mesh, PartitionSpec(None))
        b_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_sharding = x_sharding
        mu_sharding = rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))

        arg_shardings = (x_sharding, g_sharding, b_sharding)
        out_shardings = (out_sharding, mu_sharding, rsigma_sharding)
        impl = partial(LayerNormFwdPrimitive.impl,
                       zero_centered_gamma=zero_centered_gamma,
                       epsilon=epsilon)
        return mesh, impl, out_shardings, arg_shardings


register_primitive(LayerNormFwdPrimitive)


def layernorm_fwd(x: jnp.ndarray, gamma: jnp.ndarray, beta: jnp.ndarray, zero_centered_gamma: bool,
                  epsilon: float):
    """
    Wrapper for TE layernorm fwd
    """
    return LayerNormFwdPrimitive.outer_primitive.bind(x,
                                                      gamma,
                                                      beta,
                                                      zero_centered_gamma=zero_centered_gamma,
                                                      epsilon=epsilon)


class LayerNormBwdPrimitive(BasePrimitive):
    """
    Layer Normalization Backward Primitive
    """
    name = "te_layernorm_backward"
    multiple_results = True
    impl_static_args = (5, 6)    # zero_centered_gamma, epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, mu_aval, rsigma_aval, gamma_aval, **kwargs):
        """
        Layernorm bwd inner primitive abstract
        """
        w_dtype = dtypes.canonicalize_dtype(gamma_aval.dtype)
        mu_dtype = dtypes.canonicalize_dtype(mu_aval.dtype)
        rsigma_dtype = dtypes.canonicalize_dtype(rsigma_aval.dtype)

        assert dtypes.canonicalize_dtype(dz_aval.dtype) == w_dtype
        assert dz_aval.shape == x_aval.shape
        assert mu_aval.shape == rsigma_aval.shape == x_aval.shape[:-1]
        assert mu_dtype == rsigma_dtype == jnp.float32

        dx_aval = core.raise_to_shaped(dz_aval)
        dgamma_aval = dbeta_aval = core.raise_to_shaped(gamma_aval)

        wkspace_info, barrier_info, dgamma_part_info, dbeta_part_info = \
            transformer_engine_jax.get_layernorm_bwd_workspace_sizes(
                x_aval.size // gamma_aval.size,           # batch size
                gamma_aval.size,                          # hidden size
                jax_dtype_to_te_dtype(x_aval.dtype),      # input te_dtype
                jax_dtype_to_te_dtype(gamma_aval.dtype),  # weight te_dtype
                True, kwargs['zero_centered_gamma'], kwargs['epsilon']
            )
        wkspace_aval = dx_aval.update(shape=wkspace_info[0],
                                      dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = dx_aval.update(shape=barrier_info[0],
                                      dtype=te_dtype_to_jax_dtype(barrier_info[1]))
        dgamma_part_aval = dgamma_aval.update(shape=dgamma_part_info[0],
                                              dtype=te_dtype_to_jax_dtype(dgamma_part_info[1]))
        dbeta_part_aval = dbeta_aval.update(shape=dbeta_part_info[0],
                                            dtype=te_dtype_to_jax_dtype(dbeta_part_info[1]))

        return dx_aval, dgamma_aval, dbeta_aval, wkspace_aval, barrier_aval, \
               dgamma_part_aval, dbeta_part_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        LayerNorm bwd outer primitive abstract
        """
        dx_aval, dgamma_aval, dbeta_aval, _, _, _, _ = \
            LayerNormBwdPrimitive.abstract(*args, **kwargs)
        return dx_aval, dgamma_aval, dbeta_aval

    @staticmethod
    def lowering(ctx, dz, x, mu, rsigma, gamma, *, zero_centered_gamma, epsilon):
        """
        Layernorm bwd lowering rules
        """
        _, x_aval, _, _, gamma_aval = ctx.avals_in
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape
        b_type = ir.RankedTensorType(gamma.type)
        b_shape = b_type.shape
        assert g_type == b_type
        assert g_shape == b_shape

        dz_shape = ir.RankedTensorType(dz.type).shape
        mu_shape = ir.RankedTensorType(mu.type).shape
        rsigma_shape = ir.RankedTensorType(rsigma.type).shape

        hidden_size = reduce(operator.mul, g_shape)
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        out_types = [
            ir.RankedTensorType.get(output.shape, mlir.dtype_to_ir_type(output.dtype))
            for output in ctx.avals_out
        ]

        operands = [dz, mu, rsigma, x, gamma]
        operand_shapes = [dz_shape, mu_shape, rsigma_shape, x_shape, g_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_BWD_LAYERNORM_SM_MARGIN", "0"))

        wkspace_aval, barrier_aval, dgamma_part_aval, dbeta_part_aval = ctx.avals_out[-4:]
        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            dgamma_part_aval.shape,
            dbeta_part_aval.shape,
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            jax_dtype_to_te_dtype(dgamma_part_aval.dtype),
            jax_dtype_to_te_dtype(dbeta_part_aval.dtype),
            zero_centered_gamma,
            epsilon,
            sm_margin,
        )

        out = custom_caller(LayerNormBwdPrimitive.name, args, opaque, False)

        return out

    @staticmethod
    def impl(dz, x, mu, rsigma, gamma, zero_centered_gamma, epsilon):
        assert LayerNormBwdPrimitive.inner_primitive is not None
        dx, dgamma, dbeta, _, _, _, _ = LayerNormBwdPrimitive.inner_primitive.bind(
            dz, x, mu, rsigma, gamma, zero_centered_gamma=zero_centered_gamma, epsilon=epsilon)
        return dx, dgamma, dbeta

    @staticmethod
    def batcher(batched_args, batch_dims, *, zero_centered_gamma, epsilon):
        _check_valid_batch_dims(batch_dims)
        assert LayerNormBwdPrimitive.outer_primitive is not None
        dz, x, mu, rsigma, gamma = batched_args
        _, x_bdim, _, _, gamma_bdim = batch_dims

        out_bdims = x_bdim, gamma_bdim, gamma_bdim
        return LayerNormBwdPrimitive.outer_primitive.bind(dz,
                                                          x,
                                                          mu,
                                                          rsigma,
                                                          gamma,
                                                          zero_centered_gamma=zero_centered_gamma,
                                                          epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(zero_centered_gamma, epsilon, mesh, arg_infos, result_infos):
        del zero_centered_gamma, epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormBwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        g_b_spec = get_padded_spec(arg_infos[4])
        if g_b_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormBwdPrimitive.name} does not support sharding of gradients " \
                f"of gamma and beta of Layernorm " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )

        dx_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        dgamma_sharding = dbeta_sharding = NamedSharding(mesh, PartitionSpec(None))
        return dx_sharding, dgamma_sharding, dbeta_sharding

    @staticmethod
    def partition(zero_centered_gamma, epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormBwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        g_b_spec = get_padded_spec(arg_infos[4])
        if g_b_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormBwdPrimitive.name} does not support sharding of gradients " \
                f"of gamma and beta of Layernorm " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )

        dx_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        dgamma_sharding = dbeta_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_shardings = dx_sharding, dgamma_sharding, dbeta_sharding
        x_shardings = (dx_sharding,) * 2    # dz and x should have the same sharding.
        mu_shardings = (NamedSharding(mesh, PartitionSpec(*x_spec[:-1])),) * 2
        arg_shardings = (*x_shardings, *mu_shardings, NamedSharding(mesh, PartitionSpec(None)))

        def sharded_impl(dz, x, mu, rsigma, gamma):
            local_dx, local_dgamma, local_dbeta = \
                LayerNormBwdPrimitive.impl(dz, x, mu, rsigma, gamma,
                     zero_centered_gamma=zero_centered_gamma,
                     epsilon=epsilon)
            global_dgamma = all_reduce_sum_along_dp_fsdp(local_dgamma)
            global_dbeta = all_reduce_sum_along_dp_fsdp(local_dbeta)
            return local_dx, global_dgamma, global_dbeta

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(LayerNormBwdPrimitive)


def layernorm_bwd(dz: jnp.ndarray, x: jnp.ndarray, mu: jnp.ndarray, rsigma: jnp.ndarray,
                  gamma: jnp.ndarray, zero_centered_gamma: bool, epsilon: float):
    """
    Wrapper for TE layernorm bwd
    """
    return LayerNormBwdPrimitive.outer_primitive.bind(dz,
                                                      x,
                                                      mu,
                                                      rsigma,
                                                      gamma,
                                                      zero_centered_gamma=zero_centered_gamma,
                                                      epsilon=epsilon)


class RmsNormFwdPrimitive(BasePrimitive):
    """
    RMS Normalization Forward Primitive
    """
    name = "te_rmsnorm_forward"
    multiple_results = True
    impl_static_args = (2,)    # epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, gamma_aval, **kwargs):
        """
        RMSNorm fwd inner primitive abstract
        """
        x_dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert x_dtype in [jnp.float32, jnp.float16, jnp.bfloat16]

        rsigama_dtype = jnp.float32

        out_aval = core.raise_to_shaped(x_aval)
        rsigma_aval = out_aval.update(shape=out_aval.shape[:-1], dtype=rsigama_dtype)

        hidden_size = gamma_aval.size
        assert x_aval.size % hidden_size == 0

        wkspace_info, barrier_info = transformer_engine_jax.get_layernorm_fwd_workspace_sizes(
            x_aval.size // hidden_size,    # batch size
            hidden_size,
            jax_dtype_to_te_dtype(x_aval.dtype),    # in te_dtype
            jax_dtype_to_te_dtype(gamma_aval.dtype),    # weight te_dtype
            jax_dtype_to_te_dtype(x_aval.dtype),    # out te_dtype (same as input for Fp16/Bf16)
            False,
            False,
            kwargs['epsilon'])
        wkspace_aval = out_aval.update(shape=wkspace_info[0],
                                       dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = out_aval.update(shape=barrier_info[0],
                                       dtype=te_dtype_to_jax_dtype(barrier_info[1]))

        return out_aval, rsigma_aval, wkspace_aval, barrier_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        RMSNorm fwd outer primitive abstract
        """
        out_aval, rsigma_aval, _, _ = RmsNormFwdPrimitive.abstract(*args, **kwargs)
        return out_aval, rsigma_aval

    @staticmethod
    def lowering(ctx, x, gamma, *, epsilon):
        """
        RMSNorm fwd lowering rules
        """
        x_aval, gamma_aval = ctx.avals_in
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape
        rsigma_element_type = ir.F32Type.get()

        out_shape = x_shape
        hidden_size = reduce(operator.mul, g_shape)
        batch_shape = out_shape[:-1]
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        wkspace_aval, barrier_aval = ctx.avals_out[-2:]

        out_types = [
            ir.RankedTensorType.get(out_shape, x_type.element_type),
            ir.RankedTensorType.get(batch_shape, rsigma_element_type),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
            ir.RankedTensorType.get(barrier_aval.shape, jax_dtype_to_ir_dtype(barrier_aval.dtype))
        ]
        operands = [x, gamma]
        operand_shapes = [x_shape, g_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_FWD_LAYERNORM_SM_MARGIN", "0"))

        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            (0,),    # no dgamma_part in FWD pass
            (0,),    # no dbeta_part in BWD pass
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            TEDType.kByte,    # dummy dgamma_part te_dtype
            TEDType.kByte,    # dummy dbeta_part te_dtype
            False,    # RMSNorm doesn't support zero_centered_gamma
            epsilon,
            sm_margin,
        )

        out = custom_caller(RmsNormFwdPrimitive.name, args, opaque, False)

        return out

    @staticmethod
    def impl(x, gamma, epsilon):
        """
        to describe implementation
        """
        assert RmsNormFwdPrimitive.inner_primitive is not None
        out, rsigma, _, _ = RmsNormFwdPrimitive.inner_primitive.bind(x, gamma, epsilon=epsilon)
        return out, rsigma

    @staticmethod
    def batcher(batched_args, batch_dims, *, epsilon):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert RmsNormFwdPrimitive.outer_primitive is not None
        x, gamma = batched_args
        x_bdim, _ = batch_dims

        out_bdims = x_bdim, x_bdim
        return RmsNormFwdPrimitive.outer_primitive.bind(x, gamma, epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(epsilon, mesh, arg_infos, result_infos):
        del epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormFwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        return (out_sharding, rsigma_sharding)

    @staticmethod
    def partition(epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec, g_spec = map(get_padded_spec, arg_infos)
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormFwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        if g_spec[-1] is not None:
            warnings.warn(
                f"{RmsNormFwdPrimitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )

        x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        g_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_sharding = x_sharding
        rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        arg_shardings = (x_sharding, g_sharding)
        out_shardings = (out_sharding, rsigma_sharding)
        impl = partial(RmsNormFwdPrimitive.impl, epsilon=epsilon)
        return mesh, impl, out_shardings, arg_shardings


register_primitive(RmsNormFwdPrimitive)


def rmsnorm_fwd(x: jnp.ndarray, gamma: jnp.ndarray, epsilon: float):
    """
    Wrapper for TE rmsnorm fwd
    """
    return RmsNormFwdPrimitive.outer_primitive.bind(x, gamma, epsilon=epsilon)


class RmsNormBwdPrimitive(BasePrimitive):
    """
    RMS Normalization Backward Primitive
    """
    name = "te_rmsnorm_backward"
    multiple_results = True
    impl_static_args = (4,)    # epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, rsigma_aval, gamma_aval, **kwargs):
        """
        RMSNorm bwd inner primitive abstract
        """
        w_dtype = dtypes.canonicalize_dtype(gamma_aval.dtype)
        rsigma_dtype = dtypes.canonicalize_dtype(rsigma_aval.dtype)

        assert dtypes.canonicalize_dtype(dz_aval.dtype) == w_dtype
        assert dz_aval.shape == x_aval.shape
        assert rsigma_aval.shape == x_aval.shape[:-1]
        assert rsigma_dtype == jnp.float32

        dx_aval = core.raise_to_shaped(dz_aval)
        dgamma_aval = core.raise_to_shaped(gamma_aval)

        wkspace_info, barrier_info, dgamma_part_info, _ = \
            transformer_engine_jax.get_layernorm_bwd_workspace_sizes(
                x_aval.size // gamma_aval.size,           # batch size
                gamma_aval.size,                          # hidden size
                jax_dtype_to_te_dtype(x_aval.dtype),      # in te_dtype
                jax_dtype_to_te_dtype(gamma_aval.dtype),  # weight te_dtype
                False, False, kwargs['epsilon']
            )
        wkspace_aval = dx_aval.update(shape=wkspace_info[0],
                                      dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = dx_aval.update(shape=barrier_info[0],
                                      dtype=te_dtype_to_jax_dtype(barrier_info[1]))
        dgamma_part_aval = dgamma_aval.update(shape=dgamma_part_info[0],
                                              dtype=te_dtype_to_jax_dtype(dgamma_part_info[1]))

        return dx_aval, dgamma_aval, wkspace_aval, barrier_aval, dgamma_part_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        RMSNorm bwd outer primitive abstract
        """
        dx_aval, dgamma_aval, _, _, _ = RmsNormBwdPrimitive.abstract(*args, **kwargs)
        return dx_aval, dgamma_aval

    @staticmethod
    def lowering(ctx, dz, x, rsigma, gamma, *, epsilon):
        """
        RMSNorm bwd lowering rules
        """
        _, x_aval, _, gamma_aval = ctx.avals_in
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape
        dz_shape = ir.RankedTensorType(dz.type).shape
        rsigma_shape = ir.RankedTensorType(rsigma.type).shape

        hidden_size = reduce(operator.mul, g_shape)
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        wkspace_aval, barrier_aval, dgamma_part_aval = ctx.avals_out[-3:]

        out_types = [
            ir.RankedTensorType.get(x_shape, x_type.element_type),
            ir.RankedTensorType.get(g_shape, g_type.element_type),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
            ir.RankedTensorType.get(barrier_aval.shape, jax_dtype_to_ir_dtype(barrier_aval.dtype)),
            ir.RankedTensorType.get(dgamma_part_aval.shape,
                                    jax_dtype_to_ir_dtype(dgamma_part_aval.dtype))
        ]
        operands = [dz, rsigma, x, gamma]
        operand_shapes = [dz_shape, rsigma_shape, x_shape, g_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_BWD_LAYERNORM_SM_MARGIN", "0"))

        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            dgamma_part_aval.shape,
            (0,),    # no dbeta_part for RMSnorm
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            jax_dtype_to_te_dtype(dgamma_part_aval.dtype),
            TEDType.kByte,    # dummy dbeta_part te_dtype
            False,    # RMSNorm doesn't support zero_centered_gamma
            epsilon,
            sm_margin,
        )

        out = custom_caller(RmsNormBwdPrimitive.name, args, opaque, False)

        return out

    @staticmethod
    def impl(dz, x, rsigma, gamma, epsilon):
        assert RmsNormBwdPrimitive.inner_primitive is not None
        dx, dgamma, _, _, _ = \
            RmsNormBwdPrimitive.inner_primitive.bind(dz, x, rsigma, gamma, epsilon=epsilon)
        return dx, dgamma

    @staticmethod
    def batcher(batched_args, batch_dims, *, epsilon):
        _check_valid_batch_dims(batch_dims)
        assert RmsNormBwdPrimitive.outer_primitive is not None
        dz, x, rsigma, gamma = batched_args
        _, x_bdim, _, gamma_bdim = batch_dims

        out_bdims = x_bdim, gamma_bdim
        return RmsNormBwdPrimitive.outer_primitive.bind(dz, x, rsigma, gamma,
                                                        epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(epsilon, mesh, arg_infos, result_infos):
        del epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormBwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        g_spec = get_padded_spec(arg_infos[3])
        if g_spec[-1] is not None:
            warnings.warn(
                f"{RmsNormBwdPrimitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        dx_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        dgamma_sharding = NamedSharding(mesh, PartitionSpec(None))
        return dx_sharding, dgamma_sharding

    @staticmethod
    def partition(epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormBwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        g_spec = get_padded_spec(arg_infos[3])
        if g_spec[-1] is not None:
            warnings.warn(
                f"{RmsNormBwdPrimitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        dx_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        dgamma_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_shardings = dx_sharding, dgamma_sharding
        x_shardings = (dx_sharding,) * 2    # dz and x should have the same sharding.
        rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        arg_shardings = (*x_shardings, rsigma_sharding, NamedSharding(mesh, PartitionSpec(None)))

        def sharded_impl(dz, x, rsigma, gamma):
            local_dx, local_dgamma = \
                RmsNormBwdPrimitive.impl(dz, x, rsigma, gamma, epsilon=epsilon)
            global_dgamma = all_reduce_sum_along_dp_fsdp(local_dgamma)
            return local_dx, global_dgamma

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(RmsNormBwdPrimitive)


def rmsnorm_bwd(dz: jnp.ndarray, x: jnp.ndarray, rsigma: jnp.ndarray, gamma: jnp.ndarray,
                epsilon: float):
    """
    Wrapper for TE layernorm bwd
    """
    return RmsNormBwdPrimitive.outer_primitive.bind(dz, x, rsigma, gamma, epsilon=epsilon)


class SoftmaxPrimitive(BasePrimitive):
    """
    Softmax Primitive
    """
    max_k_seqlen_supported = 4096
    name = "te_softmax_internal_placeholder"

    @staticmethod
    @abstractmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        raise NotImplementedError

    @staticmethod
    def get_batch_per_block(k_seqlen: int) -> int:
        """Get batch per CTA in Softmax kernels"""
        threads_per_warp = 32
        threads_per_block = 128    # Depends on the kernel implmentation

        pow2 = 1 << (k_seqlen - 1).bit_length()
        warp_size = pow2 if pow2 < threads_per_warp else threads_per_warp
        batches_per_warp = 2 if pow2 <= 128 else 1
        warps_per_block = threads_per_block // warp_size
        batches_per_block = warps_per_block * batches_per_warp
        return batches_per_block

    @staticmethod
    def forward_abstract(logits_aval, scale_factor):
        """
        softmax_forward abstract
        """
        del scale_factor
        i_dtype = dtypes.canonicalize_dtype(logits_aval.dtype)
        assert i_dtype in [jnp.float16, jnp.bfloat16]
        i_shape = logits_aval.shape
        # Assume [...Batch, Head, Q_Seqlen, K_Seqlen]
        q_seqlen = i_shape[-2]
        k_seqlen = i_shape[-1]
        assert k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported
        assert q_seqlen > 1

        out_aval = core.raise_to_shaped(logits_aval)
        return out_aval

    @staticmethod
    def forward_lowering(name, ctx, logits, *, scale_factor):
        """
        softmax_forward lowering rules
        """
        i_aval, = ctx.avals_in
        i_type = ir.RankedTensorType(logits.type)
        i_shape = i_type.shape
        # Assume [...Batch, Head, Q_Seqlen, K_Seqlen]
        batch = reduce(operator.mul, i_shape[:-3])
        pad_batch = batch
        heads = i_shape[-3]
        q_seqlen = i_shape[-2]
        k_seqlen = i_shape[-1]

        out_types = [ir.RankedTensorType.get(i_shape, i_type.element_type)]
        operands = [logits]
        operand_shapes = [i_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_softmax_descriptor(batch, pad_batch, heads, q_seqlen,
                                                                k_seqlen,
                                                                jax_dtype_to_te_dtype(i_aval.dtype),
                                                                scale_factor)

        out = custom_caller(name, args, opaque, False)

        return [out]

    @staticmethod
    def forward_impl(primitive, logits, scale_factor):
        """
        softmax_forward implementation
        """
        assert primitive is not None
        output = primitive.bind(logits, scale_factor=scale_factor)
        return output

    @staticmethod
    def forward_batcher(primitive, batched_args, batch_dims, *, scale_factor):
        """
        softmax_forward batcher
        """
        assert primitive is not None
        logits, = batched_args
        logits_bdim, = batch_dims

        out_bdims = logits_bdim
        return primitive.bind(logits, scale_factor=scale_factor), out_bdims

    @classmethod
    def forward_infer_sharding_from_operands(cls, scale_factor, mesh, arg_infos, result_infos):
        """
        softmax_forward infer_sharding_from_operands
        """
        del scale_factor, result_infos    # Unused.
        logits_spec = get_padded_spec(arg_infos[0])
        if logits_spec[-1] is not None:
            warnings.warn(
                f"Sharding the hidden dimension is not supported in {cls.name}! " \
                f"Forcing XLA to not shard the hidden dim, which might introduce extra " \
                f"collective ops and hurt performance."
            )
        out_sharding = NamedSharding(mesh, PartitionSpec(*logits_spec[:-1], None))
        return out_sharding

    @classmethod
    def forward_partition(cls, impl, scale_factor, mesh, arg_infos, result_infos):
        """
        softmax_forward partitioning
        """
        del result_infos
        logits_spec = get_padded_spec(arg_infos[0])
        if logits_spec[-1] is not None:
            warnings.warn(
                f"Sharding the hidden dimension is not supported in {cls.name}! " \
                f"Forcing XLA to not shard the hidden dim, which might introduce extra " \
                f"collective ops and hurt performance."
            )
        out_shardings = NamedSharding(mesh, PartitionSpec(*logits_spec[:-1], None))
        arg_shardings = (out_shardings,)
        impl = partial(impl, scale_factor=scale_factor)
        return mesh, impl, out_shardings, arg_shardings

    @staticmethod
    def backward_abstract(dz_aval, softmax_out_aval, scale_factor=None):    # pylint: disable=unused-argument
        """
        softmax_backward abstract
        """
        dz_dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        softmax_out_dtype = dtypes.canonicalize_dtype(softmax_out_aval.dtype)
        assert dz_dtype == softmax_out_dtype
        assert dz_dtype in [jnp.float16, jnp.bfloat16]
        assert softmax_out_dtype in [jnp.float16, jnp.bfloat16]

        assert dz_aval.shape == softmax_out_aval.shape

        dx_aval = core.raise_to_shaped(dz_aval)
        return dx_aval

    @staticmethod
    def backward_lowering(name, ctx, dz, softmax_out, *, scale_factor):
        """
        softmax_backward lowering rules
        """
        dz_aval, _ = ctx.avals_in

        dz_type = ir.RankedTensorType(dz.type)
        dz_shape = dz_type.shape

        # Assume [...Batch, Head, Q_Seqlen, K_Seqlen]
        batch = reduce(operator.mul, dz_shape[:-3])
        pad_batch = batch    # unused
        heads = dz_shape[-3]
        q_seqlen = dz_shape[-2]
        k_seqlen = dz_shape[-1]

        softmax_out_type = ir.RankedTensorType(softmax_out.type)
        softmax_out_shape = softmax_out_type.shape

        out_types = [ir.RankedTensorType.get(dz_shape, dz_type.element_type)]
        operands = [dz, softmax_out]
        operand_shapes = [dz_shape, softmax_out_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_softmax_descriptor(
            batch, pad_batch, heads, q_seqlen, k_seqlen, jax_dtype_to_te_dtype(dz_aval.dtype),
            scale_factor)

        out = custom_caller(name, args, opaque, False)

        return [out]

    @staticmethod
    def backward_impl(primitive, dz, softmax_out, scale_factor):
        """
        softmax_backward implementation
        """
        assert primitive is not None
        dx = primitive.bind(dz, softmax_out, scale_factor=scale_factor)
        return dx

    @staticmethod
    def backward_batcher(primitive, batched_args, batch_dims, *, scale_factor):
        """
        softmax_backward batcher
        """
        assert primitive is not None
        dz, softmax_out = batched_args
        _, softmax_out_bdim = batch_dims

        out_bdims = softmax_out_bdim
        return primitive.bind(dz, softmax_out, scale_factor=scale_factor), out_bdims

    @classmethod
    def backward_infer_sharding_from_operands(cls, scale_factor, mesh, arg_infos, result_infos):
        """
        softmax_backward infer_sharding_from_operands
        """
        del scale_factor, result_infos    # Unused.
        dz_spec = get_padded_spec(arg_infos[0])
        if dz_spec[-1] is not None:
            warnings.warn(
                f"Sharding the hidden dimension is not supported in {cls.name}! " \
                f"Forcing XLA to not shard the hidden dim, which might introduce extra " \
                f"collective ops and hurt performance."
            )
        dx_sharding = NamedSharding(mesh, PartitionSpec(*dz_spec[:-1], None))
        return dx_sharding

    @classmethod
    def backward_partition(cls, impl, scale_factor, mesh, arg_infos, result_infos):
        """
        softmax_backward partition
        """
        del result_infos

        dz_spec = get_padded_spec(arg_infos[0])
        softmax_out_spec = get_padded_spec(arg_infos[1])
        if dz_spec[-1] is not None or softmax_out_spec[-1] is not None:
            warnings.warn(
                f"Sharding the hidden dimension is not supported in {cls.name}! " \
                f"Forcing XLA to not shard the hidden dim, which might introduce extra " \
                f"collective ops and hurt performance."
            )

        dz_sharding = NamedSharding(mesh, PartitionSpec(*dz_spec[:-1], None))
        softmax_out_sharding = NamedSharding(mesh, PartitionSpec(*softmax_out_spec[:-1], None))
        dx_sharding = dz_sharding
        arg_shardings = (dz_sharding, softmax_out_sharding)
        out_shardings = dx_sharding

        impl = partial(impl, scale_factor=scale_factor)
        return mesh, impl, out_shardings, arg_shardings


class ScaledSoftmaxFwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Softmax Fwd Primitive
    """
    name = "te_scaled_softmax_forward"
    multiple_results = False
    impl_static_args = (1,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        attn_batches = batch * heads

        dtype = dtypes.canonicalize_dtype(dtype)
        if (dtype in [jnp.float16, jnp.bfloat16]
                and 16 < k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported
        # k_seqlen must be 16 ~ 4096
                and q_seqlen % 4 == 0    # q_seqlen must be divisor of 4
                and attn_batches % 4 == 0    # batch * heads must be divisor of 4
           ):
            if 0 <= k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported:
                batch_per_block = SoftmaxPrimitive.get_batch_per_block(k_seqlen)
                return q_seqlen % batch_per_block == 0
        return False

    @staticmethod
    def abstract(logits_aval, scale_factor):    # pylint: disable=unused-argument
        """
        te_scaled_softmax_forward abstract
        """
        return SoftmaxPrimitive.forward_abstract(logits_aval, scale_factor)

    @staticmethod
    def lowering(ctx, logits, *, scale_factor):
        """
        te_scaled_softmax_forward lowering rules
        """
        return SoftmaxPrimitive.forward_lowering(ScaledSoftmaxFwdPrimitive.name,
                                                 ctx,
                                                 logits,
                                                 scale_factor=scale_factor)

    @staticmethod
    def impl(logits, scale_factor):
        return SoftmaxPrimitive.forward_impl(ScaledSoftmaxFwdPrimitive.inner_primitive, logits,
                                             scale_factor)

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        return SoftmaxPrimitive.forward_batcher(ScaledSoftmaxFwdPrimitive.outer_primitive,
                                                batched_args,
                                                batch_dims,
                                                scale_factor=scale_factor)

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledSoftmaxFwdPrimitive.forward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledSoftmaxFwdPrimitive.forward_partition(ScaledSoftmaxFwdPrimitive.impl,
                                                           scale_factor, mesh, arg_infos,
                                                           result_infos)


register_primitive(ScaledSoftmaxFwdPrimitive)


def scaled_softmax_fwd(logits: jnp.ndarray, scale_factor: float) -> jnp.ndarray:
    """
    scaled_softmax_forward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledSoftmaxFwdPrimitive.outer_primitive.bind(logits, scale_factor=scale_factor)


class ScaledSoftmaxBwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Softmax Bwd Primitive
    """
    name = "te_scaled_softmax_backward"
    multiple_results = False
    impl_static_args = (2,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        return ScaledSoftmaxFwdPrimitive.is_kernel_available(batch, heads, q_seqlen, k_seqlen,
                                                             dtype)

    @staticmethod
    def abstract(dz_aval, softmax_out_aval, scale_factor):
        """
        te_scaled_softmax_backward abstract
        """
        return SoftmaxPrimitive.backward_abstract(dz_aval, softmax_out_aval, scale_factor)

    @staticmethod
    def lowering(ctx, dz, softmax_out, *, scale_factor):
        """
        te_scaled_softmax_backward lowering rules
        """
        out = SoftmaxPrimitive.backward_lowering(ScaledSoftmaxBwdPrimitive.name,
                                                 ctx,
                                                 dz,
                                                 softmax_out,
                                                 scale_factor=scale_factor)

        return out

    @staticmethod
    def impl(dz, softmax_out, scale_factor):
        return SoftmaxPrimitive.backward_impl(ScaledSoftmaxBwdPrimitive.inner_primitive,
                                              dz,
                                              softmax_out,
                                              scale_factor=scale_factor)

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        return SoftmaxPrimitive.backward_batcher(ScaledSoftmaxBwdPrimitive.outer_primitive,
                                                 batched_args,
                                                 batch_dims,
                                                 scale_factor=scale_factor)

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledSoftmaxBwdPrimitive.backward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledSoftmaxBwdPrimitive.backward_partition(ScaledSoftmaxBwdPrimitive.impl,
                                                            scale_factor, mesh, arg_infos,
                                                            result_infos)


register_primitive(ScaledSoftmaxBwdPrimitive)


def scaled_softmax_bwd(dz: jnp.ndarray, softmax_out: jnp.ndarray,
                       scale_factor: float) -> jnp.ndarray:
    """
    scaled_backward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledSoftmaxBwdPrimitive.outer_primitive.bind(dz,
                                                          softmax_out,
                                                          scale_factor=scale_factor)


class ScaledMaskedSoftmaxFwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Masked Softmax Fwd Primitive
    """
    name = "te_scaled_masked_softmax_forward"
    multiple_results = False
    impl_static_args = (2,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        attn_batches = batch * heads

        dtype = dtypes.canonicalize_dtype(dtype)
        if (dtype in [jnp.float16, jnp.bfloat16]
                and 16 < k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported
        # k_seqlen must be 16 ~ 4096
                and q_seqlen % 4 == 0    # q_seqlen must be divisor of 4
                and attn_batches % 4 == 0    # batch * heads must be divisor of 4
           ):
            if 0 <= k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported:
                batch_per_block = SoftmaxPrimitive.get_batch_per_block(k_seqlen)
                return q_seqlen % batch_per_block == 0
        return False

    @staticmethod
    def abstract(logits_aval, mask_aval, scale_factor):    # pylint: disable=unused-argument
        """
        te_scaled_masked_softmax_forward abstract
        """

        i_dtype = dtypes.canonicalize_dtype(logits_aval.dtype)
        assert i_dtype in [jnp.float16, jnp.bfloat16]
        i_shape = logits_aval.shape

        # Assume [...Batch, Head, Q_Seqlen, K_Seqlen]
        batch = reduce(operator.mul, i_shape[:-3])
        q_seqlen = i_shape[-2]
        k_seqlen = i_shape[-1]
        assert k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported
        assert q_seqlen > 1

        mask_dtype = dtypes.canonicalize_dtype(mask_aval.dtype)
        assert mask_dtype in [
            jnp.uint8,
        ]
        mask_shape = mask_aval.shape
        pad_batch = batch = reduce(operator.mul, mask_shape[:-3])
        assert pad_batch in (1, batch)    # 1 means broadcast
        assert mask_shape[-3] == 1    # 1 means broadcast
        assert mask_shape[-2] == q_seqlen
        assert mask_shape[-1] == k_seqlen

        out_aval = core.raise_to_shaped(logits_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, logits, mask, *, scale_factor):
        """
        te_scaled_masked_softmax_forward lowering rules
        """

        logits_aval, _ = ctx.avals_in
        i_type = ir.RankedTensorType(logits.type)
        i_shape = i_type.shape
        # Assume [...Batch, Head, Q_Seqlen, K_Seqlen]
        batch = reduce(operator.mul, i_shape[:-3])
        heads = i_shape[-3]
        q_seqlen = i_shape[-2]
        k_seqlen = i_shape[-1]

        mask_type = ir.RankedTensorType(mask.type)
        mask_shape = mask_type.shape
        pad_batch = reduce(operator.mul, mask_shape[:-3])

        out_types = [ir.RankedTensorType.get(i_shape, i_type.element_type)]
        operands = [logits, mask]
        operand_shapes = [i_shape, mask_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_softmax_descriptor(
            batch, pad_batch, heads, q_seqlen, k_seqlen, jax_dtype_to_te_dtype(logits_aval.dtype),
            scale_factor)

        out = custom_caller(ScaledMaskedSoftmaxFwdPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(logits, mask, scale_factor):
        assert ScaledMaskedSoftmaxFwdPrimitive.inner_primitive is not None
        output = ScaledMaskedSoftmaxFwdPrimitive.inner_primitive.bind(logits,
                                                                      mask,
                                                                      scale_factor=scale_factor)
        return output

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        assert ScaledMaskedSoftmaxFwdPrimitive.outer_primitive is not None
        logits, mask = batched_args
        logits_bdim, _ = batch_dims

        out_bdims = logits_bdim
        return ScaledMaskedSoftmaxFwdPrimitive.outer_primitive.bind(
            logits, mask, scale_factor=scale_factor), out_bdims

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledMaskedSoftmaxFwdPrimitive.forward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledMaskedSoftmaxFwdPrimitive.backward_partition(
            ScaledMaskedSoftmaxFwdPrimitive.impl, scale_factor, mesh, arg_infos, result_infos)


register_primitive(ScaledMaskedSoftmaxFwdPrimitive)


def scaled_masked_softmax_fwd(logits: jnp.ndarray, mask: jnp.ndarray,
                              scale_factor: float) -> jnp.ndarray:
    """
    scaled_masked_softmax_forward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledMaskedSoftmaxFwdPrimitive.outer_primitive.bind(logits,
                                                                mask,
                                                                scale_factor=scale_factor)


class ScaledMaskedSoftmaxBwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Masked Softmax Bwd Primitive
    """
    name = "te_scaled_masked_softmax_backward"
    multiple_results = False
    impl_static_args = (2,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        return ScaledSoftmaxFwdPrimitive.is_kernel_available(batch, heads, q_seqlen, k_seqlen,
                                                             dtype)

    @staticmethod
    def abstract(dz_aval, softmax_out_aval, *, scale_factor):
        """
        te_scaled_upper_triang_masked_backward abstract
        """
        return SoftmaxPrimitive.backward_abstract(dz_aval, softmax_out_aval, scale_factor)

    @staticmethod
    def lowering(ctx, dz, softmax_out, *, scale_factor):
        """
        te_scaled_upper_triang_masked_backward lowering rules
        """
        out = SoftmaxPrimitive.backward_lowering(ScaledMaskedSoftmaxBwdPrimitive.name,
                                                 ctx,
                                                 dz,
                                                 softmax_out,
                                                 scale_factor=scale_factor)

        return out

    @staticmethod
    def impl(dz, softmax_out, scale_factor):
        return SoftmaxPrimitive.backward_impl(ScaledMaskedSoftmaxBwdPrimitive.inner_primitive,
                                              dz,
                                              softmax_out,
                                              scale_factor=scale_factor)

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        return SoftmaxPrimitive.backward_batcher(ScaledMaskedSoftmaxBwdPrimitive.outer_primitive,
                                                 batched_args,
                                                 batch_dims,
                                                 scale_factor=scale_factor)

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledMaskedSoftmaxBwdPrimitive.backward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledMaskedSoftmaxBwdPrimitive.backward_partition(
            ScaledMaskedSoftmaxBwdPrimitive.impl, scale_factor, mesh, arg_infos, result_infos)


register_primitive(ScaledMaskedSoftmaxBwdPrimitive)


def scaled_masked_softmax_bwd(dz: jnp.ndarray, softmax_out: jnp.ndarray,
                              scale_factor: float) -> jnp.ndarray:
    """
    scaled_masked_backward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledMaskedSoftmaxBwdPrimitive.outer_primitive.bind(dz,
                                                                softmax_out,
                                                                scale_factor=scale_factor)


class ScaledUpperTriangMaskedSoftmaxFwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Upper Triang Masked Softmax Fwd Primitive
    """
    name = "te_scaled_upper_triang_masked_softmax_forward"
    multiple_results = False
    impl_static_args = (1,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        attn_batches = batch * heads

        dtype = dtypes.canonicalize_dtype(dtype)
        if (dtype in [jnp.float16, jnp.bfloat16]
                and 16 < k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported
        # k_seqlen must be 16 ~ 4096
                and q_seqlen % 4 == 0    # q_seqlen must be divisor of 4
                and attn_batches % 4 == 0    # batch * heads must be divisor of 4
           ):
            if 0 <= k_seqlen <= SoftmaxPrimitive.max_k_seqlen_supported:
                batch_per_block = SoftmaxPrimitive.get_batch_per_block(k_seqlen)
                return attn_batches % batch_per_block == 0
        return False

    @staticmethod
    def abstract(logits_aval, scale_factor):    # pylint: disable=unused-argument
        """
        te_scaled_upper_triang_masked_softmax_forward abstract
        """
        q_seqlen = logits_aval.shape[-2]
        k_seqlen = logits_aval.shape[-1]
        assert q_seqlen == k_seqlen
        return SoftmaxPrimitive.forward_abstract(logits_aval, scale_factor)

    @staticmethod
    def lowering(ctx, logits, *, scale_factor):
        """
        te_scaled_upper_triang_masked_softmax_forward lowering rules
        """
        return SoftmaxPrimitive.forward_lowering(ScaledUpperTriangMaskedSoftmaxFwdPrimitive.name,
                                                 ctx,
                                                 logits,
                                                 scale_factor=scale_factor)

    @staticmethod
    def impl(logits, scale_factor):
        return SoftmaxPrimitive.forward_impl(
            ScaledUpperTriangMaskedSoftmaxFwdPrimitive.inner_primitive, logits, scale_factor)

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        return SoftmaxPrimitive.forward_batcher(
            ScaledUpperTriangMaskedSoftmaxFwdPrimitive.outer_primitive,
            batched_args,
            batch_dims,
            scale_factor=scale_factor)

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledUpperTriangMaskedSoftmaxFwdPrimitive.forward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledUpperTriangMaskedSoftmaxFwdPrimitive.forward_partition(
            ScaledUpperTriangMaskedSoftmaxFwdPrimitive.impl, scale_factor, mesh, arg_infos,
            result_infos)


register_primitive(ScaledUpperTriangMaskedSoftmaxFwdPrimitive)


def scaled_upper_triang_masked_softmax_fwd(logits: jnp.ndarray, scale_factor: float) -> jnp.ndarray:
    """
    scaled_upper_triang_masked_softmax_forward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledUpperTriangMaskedSoftmaxFwdPrimitive.outer_primitive.bind(
        logits, scale_factor=scale_factor)


class ScaledUpperTriangMaskedSoftmaxBwdPrimitive(SoftmaxPrimitive):
    """
    Scaled Upper Triang Masked Softmax Bwd Primitive
    """
    name = "te_scaled_upper_triang_masked_softmax_backward"
    multiple_results = False
    impl_static_args = (2,)    # scale_factor
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def is_kernel_available(batch: int, heads: int, q_seqlen: int, k_seqlen: int,
                            dtype: jnp.dtype) -> bool:
        """Check Softmax kernel availability based on size"""
        return ScaledUpperTriangMaskedSoftmaxFwdPrimitive.is_kernel_available(
            batch, heads, q_seqlen, k_seqlen, dtype)

    @staticmethod
    def abstract(dz_aval, softmax_out_aval, *, scale_factor):
        """
        te_scaled_upper_triang_masked_backward abstract
        """
        return SoftmaxPrimitive.backward_abstract(dz_aval, softmax_out_aval, scale_factor)

    @staticmethod
    def lowering(ctx, dz, softmax_out, *, scale_factor):
        """
        te_scaled_upper_triang_masked_backward lowering rules
        """
        out = SoftmaxPrimitive.backward_lowering(ScaledUpperTriangMaskedSoftmaxBwdPrimitive.name,
                                                 ctx,
                                                 dz,
                                                 softmax_out,
                                                 scale_factor=scale_factor)

        return out

    @staticmethod
    def impl(dz, softmax_out, scale_factor):
        return SoftmaxPrimitive.backward_impl(
            ScaledUpperTriangMaskedSoftmaxBwdPrimitive.inner_primitive,
            dz,
            softmax_out,
            scale_factor=scale_factor)

    @staticmethod
    def batcher(batched_args, batch_dims, *, scale_factor):
        _check_valid_batch_dims(batch_dims)
        return SoftmaxPrimitive.backward_batcher(
            ScaledUpperTriangMaskedSoftmaxBwdPrimitive.outer_primitive,
            batched_args,
            batch_dims,
            scale_factor=scale_factor)

    @staticmethod
    def infer_sharding_from_operands(scale_factor, mesh, arg_infos, result_infos):
        return ScaledUpperTriangMaskedSoftmaxBwdPrimitive.backward_infer_sharding_from_operands(
            scale_factor, mesh, arg_infos, result_infos)

    @staticmethod
    def partition(scale_factor, mesh, arg_infos, result_infos):
        return ScaledUpperTriangMaskedSoftmaxBwdPrimitive.backward_partition(
            ScaledUpperTriangMaskedSoftmaxBwdPrimitive.impl, scale_factor, mesh, arg_infos,
            result_infos)


register_primitive(ScaledUpperTriangMaskedSoftmaxBwdPrimitive)


def scaled_upper_triang_masked_softmax_bwd(dz: jnp.ndarray, softmax_out: jnp.ndarray,
                                           scale_factor: float) -> jnp.ndarray:
    """
    scaled_upper_triang_masked_backward wrapper
    Return FP16/BF16 tensor
    """
    return ScaledUpperTriangMaskedSoftmaxBwdPrimitive.outer_primitive.bind(
        dz, softmax_out, scale_factor=scale_factor)


@dataclass(frozen=True)
class FusedAttnHelper:
    """
    Helper for the fused attention backend
    """

    q_dtype: jnp.dtype
    kv_dtype: jnp.dtype
    qkv_layout: NVTE_QKV_Layout
    attn_bias_type: NVTE_Bias_Type
    attn_mask_type: NVTE_Mask_Type
    dropout_probability: float
    q_num_heads: int
    kv_num_heads: int
    q_max_seqlen: int
    kv_max_seqlen: int
    head_dim: int

    def is_fused_attn_kernel_available(self):
        """Check if there is available fused attention kernel"""
        return self.get_fused_attn_backend() != NVTE_Fused_Attn_Backend.NVTE_No_Backend

    def get_fused_attn_backend(self):
        """Get the fused attention kernel backend"""
        return transformer_engine_jax.get_fused_attn_backend(
            jax_dtype_to_te_dtype(self.q_dtype), jax_dtype_to_te_dtype(self.kv_dtype),
            self.qkv_layout, self.attn_bias_type, self.attn_mask_type, self.dropout_probability,
            self.q_num_heads, self.kv_num_heads, self.q_max_seqlen, self.kv_max_seqlen,
            self.head_dim)

    @staticmethod
    def parse_qkv_aval(q_aval, k_aval, v_aval, qkv_layout):
        """Parse qkv aval"""
        match qkv_layout:
            case NVTE_QKV_Layout.NVTE_BS3HD:
                *q_batch_shape, q_max_seqlen, nqkv, attn_heads, q_head_dim = q_aval.shape
                kv_batch_shape = q_batch_shape
                kv_max_seqlen = q_max_seqlen
                num_gqa_groups = attn_heads
                kv_head_dim = q_head_dim
                assert nqkv == 3
            case NVTE_QKV_Layout.NVTE_BSHD_BS2HD:
                *q_batch_shape, q_max_seqlen, attn_heads, q_head_dim = q_aval.shape
                *kv_batch_shape, kv_max_seqlen, nkv, num_gqa_groups, kv_head_dim = k_aval.shape
                assert nkv == 2
            case NVTE_QKV_Layout.NVTE_BSHD_BSHD_BSHD:
                *q_batch_shape, q_max_seqlen, attn_heads, q_head_dim = q_aval.shape
                *kv_batch_shape, kv_max_seqlen, num_gqa_groups, kv_head_dim = k_aval.shape
                assert k_aval.shape == v_aval.shape
            case _:
                raise ValueError(f"Unexpected {qkv_layout=}")
        assert q_batch_shape == kv_batch_shape
        assert q_head_dim == kv_head_dim
        assert q_aval.dtype == k_aval.dtype == v_aval.dtype

        return (q_batch_shape, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups, q_head_dim)


@dataclass(frozen=True)
class _FusedAttnRNGStateChecker:
    """
    Checker for guarding the fused attention rng state.
    The fused attention backend requires a 64 bits seed and a 64 bits offset.
    However, JAX doesn't enable 64 bits by default,
    so we have to emulate seed as two 32 bits array.
    The offset calculation is maintained in the backend.
    """
    rng_state_dtype: jnp.dtype = jnp.uint32
    # (seed,) with internal dtype int64
    seed_size: int = 2
    # (seed, offset) with internal dtype int64
    rng_state_size: int = 2 * 2

    def check_seed(self, seed, dropout_probability, is_training):
        """
        Check the seed and convert the data type of seed if possible.
        """
        # Jax can't bind None, create a dummy tensor for None
        if seed is None:
            dropout_enabled = dropout_probability > 0 and is_training
            assert not dropout_enabled, "seed is not allowed to be None when dropout is enabled."
            seed = jnp.zeros(2, dtype=self.rng_state_dtype)
            seed = jnp.repeat(seed, num_of_devices())

        if seed.dtype != self.rng_state_dtype:
            warnings.warn(
                f"Requested {seed.dtype=} is not available, and will be "
                f"casted to dtype {self.rng_state_dtype}. "
                f"Please use threefry/rbg/unsafe_rbg PRNG implementations to remove this warning.")
            seed = seed.astype(self.rng_state_dtype)

        assert seed.dtype == self.rng_state_dtype
        # Backend takes an int64_t seed, so only the first two u32 elements are taken
        assert seed.size >= self.seed_size

        return seed


def generate_cu_seqlen(actual_seqlen):
    """
    Generating cumsum seqlen for a batch
    """
    cu_seqlen = jnp.cumsum(actual_seqlen)
    cu_seqlen = jnp.hstack((0, cu_seqlen))
    return cu_seqlen


class FusedAttnFwdPrimitive(BasePrimitive):
    """
    Fused Attention Forward Primitive
    """
    name = "te_fused_attn_forward"
    multiple_results = True
    impl_static_args = (7, 8, 9, 10, 11, 12)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(q_aval, k_aval, v_aval, bias_aval, q_seqlen_or_cu_seqlen_aval,
                 kv_seqlen_or_cu_seqlen_aval, seed_aval, *, attn_bias_type, attn_mask_type,
                 qkv_layout, scaling_factor, dropout_probability, is_training):
        """
        Fused attention fwd abstract
        """
        q_dtype = dtypes.canonicalize_dtype(q_aval.dtype)
        k_dtype = dtypes.canonicalize_dtype(k_aval.dtype)
        v_dtype = dtypes.canonicalize_dtype(v_aval.dtype)
        bias_dtype = dtypes.canonicalize_dtype(bias_aval.dtype)
        assert q_dtype == k_dtype == v_dtype == bias_dtype
        assert q_seqlen_or_cu_seqlen_aval.dtype == kv_seqlen_or_cu_seqlen_aval.dtype

        batch_shape, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups, head_dim = \
            FusedAttnHelper.parse_qkv_aval(q_aval, k_aval, v_aval, qkv_layout)

        output_shape = (*batch_shape, q_max_seqlen, attn_heads, head_dim)
        out_aval = q_aval.update(shape=output_shape, dtype=q_dtype)

        # backend determines the softmax buffer shape/dtype
        backend = FusedAttnHelper(q_dtype, k_dtype, qkv_layout, attn_bias_type, attn_mask_type,
                                  dropout_probability, attn_heads, num_gqa_groups, q_max_seqlen,
                                  kv_max_seqlen, head_dim).get_fused_attn_backend()

        if backend == NVTE_Fused_Attn_Backend.NVTE_F16_max512_seqlen:
            softmax_shape = (*batch_shape, attn_heads, q_max_seqlen, kv_max_seqlen)
            softmax_dtype = q_dtype
        elif backend == NVTE_Fused_Attn_Backend.NVTE_F16_arbitrary_seqlen:
            softmax_shape = (*batch_shape, attn_heads, q_max_seqlen, 1)
            softmax_dtype = dtypes.canonicalize_dtype(jnp.float32)
        else:
            raise ValueError(f'Unsupported {backend=}')
        softmax_aux_aval = q_aval.update(shape=softmax_shape, dtype=softmax_dtype)

        # JAX does not enable 64-bit int by default so we get XLA to allocate x8 memory with
        # 32-bit unsigned int to get the buffer size we need in the C++ kernel
        checker = _FusedAttnRNGStateChecker()
        seed_dtype = dtypes.canonicalize_dtype(seed_aval.dtype)
        assert seed_dtype == checker.rng_state_dtype
        rng_state_shape = (seed_aval.shape[0], checker.rng_state_size)
        rng_state_aval = seed_aval.update(shape=rng_state_shape, dtype=checker.rng_state_dtype)

        if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
            bias_batch = bias_heads = 0
        else:
            *bias_batch_shape, bias_heads, _, _ = bias_aval.shape
            bias_batch = reduce(operator.mul, bias_batch_shape)

        # do a dummy kernel call here to get workspace buffer shapes/dtypes that XLA needs to
        # prepare for the active fused-attn backend
        input_batch = reduce(operator.mul, batch_shape)
        wkspace_info = transformer_engine_jax.get_fused_attn_fwd_workspace_sizes(
            input_batch, bias_batch, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups,
            bias_heads, head_dim, scaling_factor, dropout_probability, attn_bias_type,
            attn_mask_type, qkv_layout, jax_dtype_to_te_dtype(q_aval.dtype), is_training)
        wkspace_aval = q_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))

        return out_aval, softmax_aux_aval, rng_state_aval, wkspace_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        Fused attention fwd outer primitive abstract
        """
        out_aval, softmax_aux_aval, rng_state_aval, _ = \
            FusedAttnFwdPrimitive.abstract(*args, **kwargs)
        return out_aval, softmax_aux_aval, rng_state_aval

    @staticmethod
    def lowering(ctx, q, k, v, bias, q_cu_seqlen, kv_cu_seqlen, seed, *, attn_bias_type,
                 attn_mask_type, qkv_layout, scaling_factor, dropout_probability, is_training):
        """
        Fused attention fwd lowering rules
        """
        operands = [q, k, v, bias, q_cu_seqlen, kv_cu_seqlen, seed]
        operand_shapes = map(lambda x: x.type.shape, operands)
        out_types = [
            ir.RankedTensorType.get(output.shape, mlir.dtype_to_ir_type(output.dtype))
            for output in ctx.avals_out
        ]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        q_aval, k_aval, v_aval, bias_aval, *_ = ctx.avals_in

        batch_shape, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups, head_dim = \
            FusedAttnHelper.parse_qkv_aval(q_aval, k_aval, v_aval, qkv_layout)

        input_batch = reduce(operator.mul, batch_shape)

        if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
            bias_batch = bias_heads = 0
        else:
            *bias_batch_shape, bias_heads, _, _ = bias_aval.shape
            bias_batch = reduce(operator.mul, bias_batch_shape)

        wkspace_aval = ctx.avals_out[-1]

        opaque = transformer_engine_jax.pack_fused_attn_descriptor(
            input_batch, bias_batch, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups,
            bias_heads, head_dim, wkspace_aval.size, scaling_factor, dropout_probability,
            attn_bias_type, attn_mask_type, qkv_layout, jax_dtype_to_te_dtype(q_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype), is_training)

        out = custom_caller(FusedAttnFwdPrimitive.name, args, opaque, has_side_effect=False)

        return out

    @staticmethod
    def impl(q, k, v, bias, q_seqlen, kv_seqlen, seed, attn_bias_type, attn_mask_type, qkv_layout,
             scaling_factor, dropout_probability, is_training):
        assert FusedAttnFwdPrimitive.inner_primitive is not None

        q_cu_seqlen = generate_cu_seqlen(q_seqlen)
        kv_cu_seqlen = generate_cu_seqlen(kv_seqlen)

        output, softmax_aux, rng_state, _ = FusedAttnFwdPrimitive.inner_primitive.bind(
            q,
            k,
            v,
            bias,
            q_cu_seqlen,
            kv_cu_seqlen,
            seed,
            attn_bias_type=attn_bias_type,
            attn_mask_type=attn_mask_type,
            qkv_layout=qkv_layout,
            scaling_factor=scaling_factor,
            dropout_probability=dropout_probability,
            is_training=is_training)
        return output, softmax_aux, rng_state

    @staticmethod
    def batcher(batched_args, batch_dims, *, attn_bias_type, attn_mask_type, qkv_layout,
                scaling_factor, dropout_probability, is_training):
        _check_valid_batch_dims(batch_dims)
        assert FusedAttnFwdPrimitive.outer_primitive is not None
        q_bdim, *_, seed_bdim = batch_dims

        out_bdims = q_bdim, q_bdim, seed_bdim
        return FusedAttnFwdPrimitive.outer_primitive.bind(*batched_args,
                                                          attn_bias_type=attn_bias_type,
                                                          attn_mask_type=attn_mask_type,
                                                          qkv_layout=qkv_layout,
                                                          scaling_factor=scaling_factor,
                                                          dropout_probability=dropout_probability,
                                                          is_training=is_training), out_bdims

    @staticmethod
    def infer_sharding_from_operands(attn_bias_type, attn_mask_type, qkv_layout, scaling_factor,
                                     dropout_probability, is_training, mesh, arg_infos,
                                     result_infos):
        del attn_bias_type, attn_mask_type, scaling_factor
        del dropout_probability, is_training, result_infos
        q_spec = get_padded_spec(arg_infos[0])
        k_spec = get_padded_spec(arg_infos[1])
        match qkv_layout:
            case NVTE_QKV_Layout.NVTE_BS3HD:
                # q_spec = (...batch, q_seqlen, head, hidden)
                out_sharding = NamedSharding(mesh, PartitionSpec(*q_spec[:-3], *q_spec[-2:]))
                softmax_aux_sharding = NamedSharding(
                    mesh, PartitionSpec(*q_spec[:-4], q_spec[-2], q_spec[-4], None))
            case NVTE_QKV_Layout.NVTE_BSHD_BS2HD:
                # q_spec = (...batch, q_seqlen, head, hidden)
                # k_spec = (...batch, kv_seqlen, 2, num_gqa_groups, hidden)
                out_sharding = NamedSharding(mesh, PartitionSpec(*q_spec))
                softmax_aux_sharding = NamedSharding(
                    mesh, PartitionSpec(*q_spec[:-3], q_spec[-2], q_spec[-3], k_spec[-4]))
            case NVTE_QKV_Layout.NVTE_BSHD_BSHD_BSHD:
                # q_spec = (...batch, q_seqlen, head, hidden)
                # k_spec = (...batch, kv_seqlen, num_gqa_groups, hidden)
                out_sharding = NamedSharding(mesh, PartitionSpec(*q_spec))
                softmax_aux_sharding = NamedSharding(
                    mesh, PartitionSpec(*q_spec[:-3], q_spec[-2], q_spec[-3], k_spec[-3]))
            case _:
                raise ValueError(f"Unsupported {qkv_layout=}")
        rng_state_sharding = NamedSharding(mesh, PartitionSpec(get_all_mesh_axes(), None))
        return (out_sharding, softmax_aux_sharding, rng_state_sharding)

    @staticmethod
    def partition(attn_bias_type, attn_mask_type, qkv_layout, scaling_factor, dropout_probability,
                  is_training, mesh, arg_infos, result_infos):
        out_sharding = result_infos[0].sharding
        softmax_aux_sharding = result_infos[1].sharding
        rng_state_sharding = seed_sharding = NamedSharding(mesh,
                                                           PartitionSpec(get_all_mesh_axes(), None))
        arg_shardings = tuple([arg_i.sharding for arg_i in arg_infos[:-1]] + [seed_sharding])
        out_shardings = (out_sharding, softmax_aux_sharding, rng_state_sharding)
        impl = partial(FusedAttnFwdPrimitive.impl,
                       attn_bias_type=attn_bias_type,
                       attn_mask_type=attn_mask_type,
                       qkv_layout=qkv_layout,
                       scaling_factor=scaling_factor,
                       dropout_probability=dropout_probability,
                       is_training=is_training)
        return mesh, impl, out_shardings, arg_shardings


register_primitive(FusedAttnFwdPrimitive)


class FusedAttnBwdPrimitive(BasePrimitive):
    """
    Fused Attention Backward Primitive
    """
    name = "te_fused_attn_backward"
    multiple_results = True
    impl_static_args = (10, 11, 12, 13, 14, 15)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(q_aval, k_aval, v_aval, bias_aval, softmax_aux_aval, rng_state_aval, output_aval,
                 doutput_aval, q_cu_seqlen_aval, kv_cu_seqlen_aval, *, attn_bias_type,
                 attn_mask_type, qkv_layout, scaling_factor, dropout_probability, is_training):
        """
        Fused attention bwd abstract
        """
        del softmax_aux_aval, rng_state_aval, output_aval

        q_dtype = dtypes.canonicalize_dtype(q_aval.dtype)
        k_dtype = dtypes.canonicalize_dtype(k_aval.dtype)
        v_dtype = dtypes.canonicalize_dtype(v_aval.dtype)
        bias_dtype = dtypes.canonicalize_dtype(bias_aval.dtype)
        doutput_dtype = dtypes.canonicalize_dtype(doutput_aval.dtype)
        assert q_dtype == k_dtype == v_dtype == bias_dtype == doutput_dtype
        assert q_cu_seqlen_aval.dtype == kv_cu_seqlen_aval.dtype

        batch_shape, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups, head_dim = \
            FusedAttnHelper.parse_qkv_aval(q_aval, k_aval, v_aval, qkv_layout)

        if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
            bias_batch = bias_heads = 0
        else:
            *bias_batch_shape, bias_heads, _, _ = bias_aval.shape
            bias_batch = reduce(operator.mul, bias_batch_shape)

        input_batch = reduce(operator.mul, batch_shape)
        wkspace_shape, wkspace_dtype = \
            transformer_engine_jax.get_fused_attn_bwd_workspace_sizes(
                input_batch, bias_batch, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups,
                bias_heads, head_dim, scaling_factor, dropout_probability, attn_bias_type,
                attn_mask_type, qkv_layout, jax_dtype_to_te_dtype(q_aval.dtype), is_training)

        dq_aval = q_aval.update(shape=q_aval.shape, dtype=q_dtype)
        dk_aval = k_aval.update(shape=k_aval.shape, dtype=k_dtype)
        dv_aval = v_aval.update(shape=v_aval.shape, dtype=v_dtype)
        dbias_aval = bias_aval.update(shape=bias_aval.shape, dtype=bias_dtype)
        wkspace_aval = q_aval.update(shape=wkspace_shape,
                                     dtype=te_dtype_to_jax_dtype(wkspace_dtype))

        return dq_aval, dk_aval, dv_aval, dbias_aval, wkspace_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        Fused attention fwd outer primitive abstract
        """
        dq_aval, dk_aval, dv_aval, dbias_aval, _ = \
            FusedAttnBwdPrimitive.abstract(*args, **kwargs)
        return dq_aval, dk_aval, dv_aval, dbias_aval

    @staticmethod
    def lowering(ctx, q, k, v, bias, softmax_aux, rng_state, output, doutput, q_cu_seqlen,
                 kv_cu_seqlen, *, attn_bias_type, attn_mask_type, qkv_layout, scaling_factor,
                 dropout_probability, is_training):
        """
        Fused attention bwd lowering rules
        """
        operands = [
            q, k, v, bias, softmax_aux, rng_state, output, doutput, q_cu_seqlen, kv_cu_seqlen
        ]
        operand_shapes = map(lambda x: x.type.shape, operands)
        out_types = [
            ir.RankedTensorType.get(output.shape, mlir.dtype_to_ir_type(output.dtype))
            for output in ctx.avals_out
        ]

        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        q_aval, k_aval, v_aval, bias_aval, *_ = ctx.avals_in

        batch_shape, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups, head_dim = \
            FusedAttnHelper.parse_qkv_aval(q_aval, k_aval, v_aval, qkv_layout)

        input_batch = reduce(operator.mul, batch_shape)

        if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
            bias_batch = bias_heads = 0
        else:
            *bias_batch_shape, bias_heads, _, _ = bias_aval.shape
            bias_batch = reduce(operator.mul, bias_batch_shape)

        wkspace_aval = ctx.avals_out[-1]

        opaque = transformer_engine_jax.pack_fused_attn_descriptor(
            input_batch, bias_batch, q_max_seqlen, kv_max_seqlen, attn_heads, num_gqa_groups,
            bias_heads, head_dim, wkspace_aval.size, scaling_factor, dropout_probability,
            attn_bias_type, attn_mask_type, qkv_layout, jax_dtype_to_te_dtype(q_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype), is_training)

        out = custom_caller(FusedAttnBwdPrimitive.name, args, opaque, has_side_effect=False)

        return out

    @staticmethod
    def impl(q, k, v, bias, softmax_aux, rng_state, output, doutput, q_seqlen, kv_seqlen,
             attn_bias_type, attn_mask_type, qkv_layout, scaling_factor, dropout_probability,
             is_training):
        assert FusedAttnBwdPrimitive.inner_primitive is not None

        q_cu_seqlen = generate_cu_seqlen(q_seqlen)
        kv_cu_seqlen = generate_cu_seqlen(kv_seqlen)

        dq, dk, dv, dbias, _ = FusedAttnBwdPrimitive.inner_primitive.bind(
            q,
            k,
            v,
            bias,
            softmax_aux,
            rng_state,
            output,
            doutput,
            q_cu_seqlen,
            kv_cu_seqlen,
            attn_bias_type=attn_bias_type,
            attn_mask_type=attn_mask_type,
            qkv_layout=qkv_layout,
            scaling_factor=scaling_factor,
            dropout_probability=dropout_probability,
            is_training=is_training)
        return dq, dk, dv, dbias

    @staticmethod
    def batcher(batched_args, batch_dims, *, attn_bias_type, attn_mask_type, qkv_layout,
                scaling_factor, dropout_probability, is_training):
        _check_valid_batch_dims(batch_dims)
        assert FusedAttnBwdPrimitive.outer_primitive is not None
        q_bdim, k_bdim, v_bdim, *_ = batch_dims

        out_bdims = q_bdim, k_bdim, v_bdim, q_bdim
        return FusedAttnBwdPrimitive.outer_primitive.bind(*batched_args,
                                                          attn_bias_type=attn_bias_type,
                                                          attn_mask_type=attn_mask_type,
                                                          qkv_layout=qkv_layout,
                                                          scaling_factor=scaling_factor,
                                                          dropout_probability=dropout_probability,
                                                          is_training=is_training), out_bdims

    @staticmethod
    def infer_sharding_from_operands(attn_bias_type, attn_mask_type, qkv_layout, scaling_factor,
                                     dropout_probability, is_training, mesh, arg_infos,
                                     result_infos):
        del attn_bias_type, attn_mask_type, qkv_layout, scaling_factor
        del dropout_probability, is_training, result_infos
        q_spec = get_padded_spec(arg_infos[0])
        k_spec = get_padded_spec(arg_infos[1])
        v_spec = get_padded_spec(arg_infos[2])
        bias_spec = get_padded_spec(arg_infos[3])
        dq_sharding = NamedSharding(mesh, PartitionSpec(*q_spec))
        dk_sharding = NamedSharding(mesh, PartitionSpec(*k_spec))
        dv_sharding = NamedSharding(mesh, PartitionSpec(*v_spec))
        dbias_sharding = NamedSharding(mesh, PartitionSpec(*bias_spec))
        return (dq_sharding, dk_sharding, dv_sharding, dbias_sharding)

    @staticmethod
    def partition(attn_bias_type, attn_mask_type, qkv_layout, scaling_factor, dropout_probability,
                  is_training, mesh, arg_infos, result_infos):
        del result_infos
        q_spec = get_padded_spec(arg_infos[0])
        k_spec = get_padded_spec(arg_infos[1])
        v_spec = get_padded_spec(arg_infos[2])
        bias_spec = get_padded_spec(arg_infos[3])
        dq_sharding = NamedSharding(mesh, PartitionSpec(*q_spec))
        dk_sharding = NamedSharding(mesh, PartitionSpec(*k_spec))
        dv_sharding = NamedSharding(mesh, PartitionSpec(*v_spec))
        dbias_sharding = NamedSharding(mesh, PartitionSpec(*bias_spec))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (dq_sharding, dk_sharding, dv_sharding, dbias_sharding)

        def sharded_impl(q, k, v, bias, softmax_aux, rng_state, output, doutput, q_cu_seqlen,
                         kv_cu_seqlen):
            local_dq, local_dk, local_dv, local_dbias = FusedAttnBwdPrimitive.impl(
                q,
                k,
                v,
                bias,
                softmax_aux,
                rng_state,
                output,
                doutput,
                q_cu_seqlen,
                kv_cu_seqlen,
                attn_bias_type=attn_bias_type,
                attn_mask_type=attn_mask_type,
                qkv_layout=qkv_layout,
                scaling_factor=scaling_factor,
                dropout_probability=dropout_probability,
                is_training=is_training)
            global_dbias = local_dbias
            if attn_bias_type is not NVTE_Bias_Type.NVTE_NO_BIAS:
                global_dbias = all_reduce_sum_along_dp_fsdp(local_dbias)
            return local_dq, local_dk, local_dv, global_dbias

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(FusedAttnBwdPrimitive)


def fused_attn_fwd_qkvpacked(qkv: jnp.ndarray, bias: jnp.ndarray, seqlen: jnp.ndarray,
                             seed: jnp.ndarray, attn_bias_type: NVTE_Bias_Type,
                             attn_mask_type: NVTE_Mask_Type, scaling_factor: float,
                             dropout_probability: float, is_training: bool):
    """
    Wrapper for TE self fused attention fwd
    Return BMM1 -> (PreBias) -> ScaleMaskSoftmax -> (PostBias) -> (Dropout) -> BMM2
    """
    checker = _FusedAttnRNGStateChecker()
    seed = checker.check_seed(seed, dropout_probability, is_training)

    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=qkv.dtype)

    _not_used = jnp.zeros(0, qkv.dtype)
    return FusedAttnFwdPrimitive.outer_primitive.bind(qkv,
                                                      _not_used,
                                                      _not_used,
                                                      bias,
                                                      seqlen,
                                                      seqlen,
                                                      seed,
                                                      attn_bias_type=attn_bias_type,
                                                      attn_mask_type=attn_mask_type,
                                                      qkv_layout=NVTE_QKV_Layout.NVTE_BS3HD,
                                                      scaling_factor=scaling_factor,
                                                      dropout_probability=dropout_probability,
                                                      is_training=is_training)


def fused_attn_bwd_qkvpacked(qkv: jnp.ndarray, bias: jnp.ndarray, softmax_aux: jnp.ndarray,
                             rng_state: jnp.ndarray, output: jnp.ndarray, doutput: jnp.ndarray,
                             seqlen: jnp.ndarray, attn_bias_type: NVTE_Bias_Type,
                             attn_mask_type: NVTE_Mask_Type, scaling_factor: float,
                             dropout_probability: float, is_training: bool):
    """
    Wrapper for TE self fused attention bwd
    Return the gradients of self fused attention with packed qkv input
    """
    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=qkv.dtype)
    dummy_input = jnp.zeros(0, dtype=qkv.dtype)
    dqkv, *_, dbias = FusedAttnBwdPrimitive.outer_primitive.bind(
        qkv,
        dummy_input,
        dummy_input,
        bias,
        softmax_aux,
        rng_state,
        output,
        doutput,
        seqlen,
        seqlen,
        attn_bias_type=attn_bias_type,
        attn_mask_type=attn_mask_type,
        qkv_layout=NVTE_QKV_Layout.NVTE_BS3HD,
        scaling_factor=scaling_factor,
        dropout_probability=dropout_probability,
        is_training=is_training)
    return dqkv, dbias


def fused_attn_fwd_kvpacked(q: jnp.ndarray, kv: jnp.ndarray, bias: jnp.ndarray,
                            q_seqlen: jnp.ndarray, kv_seqlen: jnp.ndarray, seed: jnp.ndarray,
                            attn_bias_type: NVTE_Bias_Type, attn_mask_type: NVTE_Mask_Type,
                            scaling_factor: float, dropout_probability: float, is_training: bool):
    """
    Wrapper for TE fused attention fwd with kvpacked inputs
    Return BMM1 -> (PreBias) -> ScaleMaskSoftmax -> (PostBias) -> (Dropout) -> BMM2
    """
    checker = _FusedAttnRNGStateChecker()
    seed = checker.check_seed(seed, dropout_probability, is_training)

    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=q.dtype)

    return FusedAttnFwdPrimitive.outer_primitive.bind(q,
                                                      kv,
                                                      jnp.zeros(0, q.dtype),
                                                      bias,
                                                      q_seqlen,
                                                      kv_seqlen,
                                                      seed,
                                                      attn_bias_type=attn_bias_type,
                                                      attn_mask_type=attn_mask_type,
                                                      qkv_layout=NVTE_QKV_Layout.NVTE_BSHD_BS2HD,
                                                      scaling_factor=scaling_factor,
                                                      dropout_probability=dropout_probability,
                                                      is_training=is_training)


def fused_attn_bwd_kvpacked(q: jnp.ndarray, kv: jnp.ndarray, bias: jnp.ndarray,
                            softmax_aux: jnp.ndarray, rng_state: jnp.ndarray, output: jnp.ndarray,
                            doutput: jnp.ndarray, q_seqlen: jnp.ndarray, kv_seqlen: jnp.ndarray,
                            attn_bias_type: NVTE_Bias_Type, attn_mask_type: NVTE_Mask_Type,
                            scaling_factor: float, dropout_probability: float, is_training: bool):
    """
    Wrapper for TE fused attention bwd with kvpacked inputs
    Return the gradients of fused attention with packed kv input
    """
    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=q.dtype)
    dummy_input = jnp.zeros(0, q.dtype)
    dq, dkv, _, dbias = FusedAttnBwdPrimitive.outer_primitive.bind(
        q,
        kv,
        dummy_input,
        bias,
        softmax_aux,
        rng_state,
        output,
        doutput,
        q_seqlen,
        kv_seqlen,
        attn_bias_type=attn_bias_type,
        attn_mask_type=attn_mask_type,
        qkv_layout=NVTE_QKV_Layout.NVTE_BSHD_BS2HD,
        scaling_factor=scaling_factor,
        dropout_probability=dropout_probability,
        is_training=is_training)
    return dq, dkv, dbias


def fused_attn_fwd(q: jnp.ndarray, k: jnp.ndarray, v: jnp.ndarray, bias: jnp.ndarray,
                   q_seqlen: jnp.ndarray, kv_seqlen: jnp.ndarray, seed: jnp.ndarray,
                   attn_bias_type: NVTE_Bias_Type, attn_mask_type: NVTE_Mask_Type,
                   scaling_factor: float, dropout_probability: float, is_training: bool):
    """
    Wrapper for TE fused attention fwd, where query, key, value are seperated tensors
    Return BMM1 -> (PreBias) -> ScaleMaskSoftmax -> (PostBias) -> (Dropout) -> BMM2
    """
    checker = _FusedAttnRNGStateChecker()
    seed = checker.check_seed(seed, dropout_probability, is_training)

    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=q.dtype)

    return FusedAttnFwdPrimitive.outer_primitive.bind(
        q,
        k,
        v,
        bias,
        q_seqlen,
        kv_seqlen,
        seed,
        attn_bias_type=attn_bias_type,
        attn_mask_type=attn_mask_type,
        qkv_layout=NVTE_QKV_Layout.NVTE_BSHD_BSHD_BSHD,
        scaling_factor=scaling_factor,
        dropout_probability=dropout_probability,
        is_training=is_training)


def fused_attn_bwd(q: jnp.ndarray, k: jnp.ndarray, v: jnp.ndarray, bias: jnp.ndarray,
                   softmax_aux: jnp.ndarray, rng_state: jnp.ndarray, output: jnp.ndarray,
                   doutput: jnp.ndarray, q_seqlen: jnp.ndarray, kv_seqlen: jnp.ndarray,
                   attn_bias_type: NVTE_Bias_Type, attn_mask_type: NVTE_Mask_Type,
                   scaling_factor: float, dropout_probability: float, is_training: bool):
    """
    Wrapper for TE fused attention bwd
    Return the gradients of fused attention with seperated query, key, value tensors
    """
    if attn_bias_type == NVTE_Bias_Type.NVTE_NO_BIAS:
        assert bias is None
        bias = jnp.zeros(0, dtype=q.dtype)
    return FusedAttnBwdPrimitive.outer_primitive.bind(
        q,
        k,
        v,
        bias,
        softmax_aux,
        rng_state,
        output,
        doutput,
        q_seqlen,
        kv_seqlen,
        attn_bias_type=attn_bias_type,
        attn_mask_type=attn_mask_type,
        qkv_layout=NVTE_QKV_Layout.NVTE_BSHD_BSHD_BSHD,
        scaling_factor=scaling_factor,
        dropout_probability=dropout_probability,
        is_training=is_training)


class GeluPrimitive(BasePrimitive):
    """
    Gelu Froward Primitive
    """
    name = "te_gelu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(x_aval):
        """
        gated_gelu abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]

        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, x):
        """
        gated_gelu lowering rules
        """
        (x_aval,) = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        out_shape = ir_x_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_x_type.element_type),
        ]
        operands = [x]
        operand_shapes = [ir_x_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-1])
        in_dtype = jax_dtype_to_te_dtype(x_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size), in_dtype,
                                                               in_dtype)

        out = custom_caller(GeluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(x):
        assert GeluPrimitive.inner_primitive is not None
        out = GeluPrimitive.inner_primitive.bind(x)
        return out

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        gated_gelu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert GeluPrimitive.outer_primitive is not None
        inputs, = batched_args
        inputs_bdim, = batch_dims

        out_bdims = inputs_bdim
        return GeluPrimitive.outer_primitive.bind(inputs), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        gated_gelu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        return out_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        gated_gelu partitioning
        """
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        impl = GeluPrimitive.impl
        return mesh, impl, out_sharding, arg_shardings


register_primitive(GeluPrimitive)


def gelu(inputs: jnp.ndarray) -> jnp.ndarray:
    """
    gelu wrapper
    Return geglu(inputs)
    Assume inputs has two dimensions shape and the memory layout is (N..., H)
    """
    return GeluPrimitive.outer_primitive.bind(inputs)


class DGeluPrimitive(BasePrimitive):
    """
    Dgated Gelu Primitive
    """
    name = "te_dgelu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(dz_aval, x_aval):
        """
        dgelu abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert dz_aval.shape == x_aval.shape

        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, dz, x):
        """
        dgelu lowering rules
        """
        in_aval, gi_aval = ctx.avals_in
        assert in_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert gi_aval.dtype == in_aval.dtype
        ir_in_type = ir.RankedTensorType(dz.type)
        ir_in_shape = ir_in_type.shape
        gi_type = ir.RankedTensorType(x.type)
        gi_shape = gi_type.shape
        assert ir_in_shape == gi_shape

        ir_batch_size = reduce(operator.mul, ir_in_shape[:-1])
        i_hidden_size = ir_in_shape[-1]
        out_dtype = ir_in_type.element_type
        out_shape = gi_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, out_dtype),
        ]
        operands = [dz, x]
        operand_shapes = [ir_in_shape, gi_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        in_dtype = jax_dtype_to_te_dtype(in_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((ir_batch_size, i_hidden_size),
                                                               in_dtype, in_dtype)

        out = custom_caller(DGeluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(dz, x):
        """
        dgelu implementation
        """
        assert DGeluPrimitive.inner_primitive is not None
        dx = DGeluPrimitive.inner_primitive.bind(dz, x)
        return dx

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        dgelu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert DGeluPrimitive.outer_primitive is not None
        dz, x = batched_args
        _, x_bdim = batch_dims

        out_bdims = x_bdim
        return DGeluPrimitive.outer_primitive.bind(dz, x), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        dgelu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        gelu_out_spec = get_padded_spec(arg_infos[1])
        dx_sharding = NamedSharding(mesh, PartitionSpec(*gelu_out_spec))
        return dx_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        dgelu partition
        """
        del result_infos
        dx_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = dx_sharding
        impl = DGeluPrimitive.impl
        return mesh, impl, out_shardings, arg_shardings


register_primitive(DGeluPrimitive)


def dgelu(inputs: jnp.ndarray, gelu_inputs: jnp.ndarray) -> jnp.ndarray:
    """
    dgelu fusion wrapper
    Return dgeglu(inputs)
    """
    return DGeluPrimitive.outer_primitive.bind(inputs, gelu_inputs)


class GatedGeluPrimitive(BasePrimitive):
    """
    Gated Gelu Froward Primitive
    """
    name = "te_gated_gelu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(x_aval):
        """
        gated_gelu abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        x_shape = x_aval.shape
        assert x_shape[-2] == 2    # Assume x in (....., 2, hidden)
        hidden_size = x_shape[-1]
        batch_shapes = x_shape[:-2]
        x_shape = x_aval.shape
        out_aval = core.raise_to_shaped(x_aval)
        out_shape = (batch_shapes) + (hidden_size,)
        out_aval = out_aval.update(shape=out_shape, dtype=dtype)

        return out_aval

    @staticmethod
    def lowering(ctx, x):
        """
        gated_gelu lowering rules
        """
        (x_aval,) = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        out_shape = ir_x_shape[:-2] + [ir_x_shape[-1]]

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_x_type.element_type),
        ]
        operands = [x]
        operand_shapes = [ir_x_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-2])
        in_dtype = jax_dtype_to_te_dtype(x_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size), in_dtype,
                                                               in_dtype)

        out = custom_caller(GatedGeluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(x):
        assert GatedGeluPrimitive.inner_primitive is not None
        out = GatedGeluPrimitive.inner_primitive.bind(x)
        return out

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        gated_gelu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert GatedGeluPrimitive.outer_primitive is not None
        inputs, = batched_args
        inputs_bdim, = batch_dims

        out_bdims = inputs_bdim
        return GatedGeluPrimitive.outer_primitive.bind(inputs), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        gated_gelu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        return out_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        gated_gelu partitioning
        """
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        impl = GatedGeluPrimitive.impl
        return mesh, impl, out_sharding, arg_shardings


register_primitive(GatedGeluPrimitive)


def gated_gelu(inputs: jnp.ndarray) -> jnp.ndarray:
    """
    gated gelu wrapper
    Return FP8(geglu(inputs))
    Assume inputs has two dimensions shape and the memory layout is (N, 2, H)
    """
    return GatedGeluPrimitive.outer_primitive.bind(inputs)


class DgatedGeluPrimitive(BasePrimitive):
    """
    Dgated Gelu Primitive
    """
    name = "te_dgated_gelu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(dz_aval, x_aval):
        """
        dgated_gelu abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        for axis in range(len(dz_aval.shape) - 1):
            assert dz_aval.shape[axis] == x_aval.shape[axis]

        assert x_aval.shape[-2] == 2    # Assume x in (....., 2, hidden)

        i_hidden_size = dz_aval.shape[-1]
        g_hidden_size = x_aval.shape[-1]
        assert i_hidden_size == g_hidden_size
        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, dz, x):
        """
        dgated_gelu lowering rules
        """
        in_aval, gi_aval = ctx.avals_in
        assert in_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert gi_aval.dtype == in_aval.dtype
        ir_in_type = ir.RankedTensorType(dz.type)
        ir_in_shape = ir_in_type.shape
        gi_type = ir.RankedTensorType(x.type)
        gi_shape = gi_type.shape
        for axis in range(len(ir_in_shape) - 1):
            assert ir_in_shape[axis] == gi_shape[axis]

        ir_batch_size = reduce(operator.mul, ir_in_shape[:-1])
        i_hidden_size = ir_in_shape[-1]
        g_hidden_size = gi_shape[-1]
        assert i_hidden_size == g_hidden_size
        out_dtype = ir_in_type.element_type
        out_shape = gi_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, out_dtype),
        ]
        operands = [dz, x]
        operand_shapes = [ir_in_shape, gi_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        in_dtype = jax_dtype_to_te_dtype(in_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((ir_batch_size, i_hidden_size),
                                                               in_dtype, in_dtype)

        out = custom_caller(DgatedGeluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(dz, x):
        """
        dgated_gelu implementation
        """
        assert DgatedGeluPrimitive.inner_primitive is not None
        dx = DgatedGeluPrimitive.inner_primitive.bind(dz, x)
        return dx

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        dgated_gelu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert DgatedGeluPrimitive.outer_primitive is not None
        dz, x = batched_args
        _, x_bdim = batch_dims

        out_bdims = x_bdim
        return DgatedGeluPrimitive.outer_primitive.bind(dz, x), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        dgated_gelu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        gelu_out_spec = get_padded_spec(arg_infos[1])
        dx_sharding = NamedSharding(mesh, PartitionSpec(*gelu_out_spec))
        return dx_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        dgated_gelu partition
        """
        del result_infos
        dx_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = dx_sharding
        impl = DgatedGeluPrimitive.impl
        return mesh, impl, out_shardings, arg_shardings


register_primitive(DgatedGeluPrimitive)


def dgated_gelu(inputs: jnp.ndarray, gelu_inputs: jnp.ndarray) -> jnp.ndarray:
    """
    dgated_gelu fusion wrapper
    Return dgeglu(inputs)
    """
    return DgatedGeluPrimitive.outer_primitive.bind(inputs, gelu_inputs)


def _normalize_axis_boundary(axis, ndim):
    return axis if axis >= 0 else ndim + axis


def _multidim_transpose(shape, static_axis_boundary, transpose_axis_boundary):
    """
    te_cast_transpose_p multi-dims transpose

    static_axis_boundary: int, Indicate those axes <= static_axis_boundary would not be
        involved into transpose, -1 means all axes involve into transpose.
    transpose_axis_boundary: int, Indicate how to split multi-dimensions tensors to 2D matrix for
        transpose. Note, transpose_axis_boundary should be greater than static_axis_boundary

    examples:
        X in shape (dim0, dim1, dim2, dim3, dim4)

        static_axis_boundary == -1, transpose_axis_boundary == 2
            Xt = (dim2, dim3, dim4, dim0, dim1)

        static_axis_boundary == 0, transpose_axis_boundary == 2
            Xt = (dim0, dim2, dim3, dim4, dim1)

        static_axis_boundary == 0, transpose_axis_boundary == 3
            Xt = (dim0, dim3, dim4, dim1. dim2)
    """
    if static_axis_boundary < 0:
        static_axis_boundary = -1    # means no static axes
    assert static_axis_boundary < len(shape) - 2    # at least 2 remaining for transpose.
    transpose_start_idx = static_axis_boundary + 1
    transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, len(shape))
    assert transpose_start_idx < transpose_axis_boundary
    return (*shape[:transpose_start_idx], *shape[transpose_axis_boundary:],
            *shape[transpose_start_idx:transpose_axis_boundary])


class CastTransposePrimitive(BasePrimitive):
    """
    Cast Transpose Primitive
    """
    name = "te_cast_transpose"
    multiple_results = True
    impl_static_args = (4, 5, 6)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype, static_axis_boundary,
                 transpose_axis_boundary):
        """
        te_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        transposed_x_shape = _multidim_transpose(x_aval.shape, static_axis_boundary,
                                                 transpose_axis_boundary)

        casted_x_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        casted_xt_aval = x_aval.update(shape=transposed_x_shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return casted_x_aval, casted_xt_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype, static_axis_boundary,
                 transpose_axis_boundary):
        """
        te_cast_transpose_p lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        if static_axis_boundary >= 0:
            for i in range(static_axis_boundary + 1):
                assert ir_x_shape[i] == 1
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        transposed_x_shape = _multidim_transpose(ir_x_shape, static_axis_boundary,
                                                 transpose_axis_boundary)

        out_types = [
            ir.RankedTensorType.get(ir_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        contracted_x_shape = (reduce(operator.mul, ir_x_shape[:transpose_axis_boundary]),
                              reduce(operator.mul, ir_x_shape[transpose_axis_boundary:]))
        opaque = transformer_engine_jax.pack_common_descriptor(contracted_x_shape,
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(CastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 2})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype, static_axis_boundary, transpose_axis_boundary):
        """
        te_cast_transpose implementation
        """
        assert CastTransposePrimitive.inner_primitive is not None
        casted_x, casted_transposed_x, updated_amax = \
            CastTransposePrimitive.inner_primitive.bind(
                x, amax, scale, scale_inv, out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary,
                transpose_axis_boundary=transpose_axis_boundary)
        return casted_x, casted_transposed_x, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary,
                transpose_axis_boundary):
        _check_valid_batch_dims(batch_dims)
        assert CastTransposePrimitive.outer_primitive is not None
        assert static_axis_boundary < 0

        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, *_ = batch_dims

        # Minus batch dim.
        transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, x.ndim - 1)
        transpose_axis_boundary += 1    # Plus batch dim

        out_bdims = x_bdim, x_bdim, amax_bdim
        return CastTransposePrimitive.outer_primitive.bind(
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=x_bdim,
            transpose_axis_boundary=transpose_axis_boundary), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh,
                                     arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (casted_x_sharding, casted_transposed_x_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh, arg_infos,
                  result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_cx, local_cxt, local_updated_amax = \
                CastTransposePrimitive.impl(x, amax, scale, scale_inv,
                     out_dtype=out_dtype,
                       static_axis_boundary=static_axis_boundary,
                       transpose_axis_boundary=transpose_axis_boundary)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_updated_amax)

            return local_cx, local_cxt, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(CastTransposePrimitive)


def cast_transpose(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
                   out_dtype: jnp.dtype, static_axis_boundary: int,
                   transpose_axis_boundary: int) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose wrapper
    Return two tensors, FP8(inputs) and FP8(inputs.T), which are scaled by `scale`
    """
    return CastTransposePrimitive.outer_primitive.bind(
        x,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary,
        transpose_axis_boundary=transpose_axis_boundary)


class CastFP8Primitive(BasePrimitive):
    """
    Cast Primitive
    """
    name = "te_quantize"
    multiple_results = True
    impl_static_args = (4,)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype):
        """
        te_cast abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        casted_x_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return casted_x_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype):
        """
        te_cast lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        out_types = [
            ir.RankedTensorType.get(ir_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_common_descriptor(ir_x_shape,
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(CastFP8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 1})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype):
        """
        te_cast implementation
        """
        assert CastFP8Primitive.inner_primitive is not None
        casted_x, updated_amax = \
            CastFP8Primitive.inner_primitive.bind(
                x, amax, scale, scale_inv, out_dtype=out_dtype)
        return casted_x, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype):
        _check_valid_batch_dims(batch_dims)
        assert CastFP8Primitive.outer_primitive is not None

        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, *_ = batch_dims

        out_bdims = x_bdim, amax_bdim
        return CastFP8Primitive.outer_primitive.bind(x, amax, scale, scale_inv,
                                                     out_dtype=out_dtype), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, mesh, arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (casted_x_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_cx, local_updated_amax = \
                CastFP8Primitive.impl(x, amax, scale, scale_inv, out_dtype=out_dtype)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_updated_amax)

            return local_cx, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(CastFP8Primitive)


def cast_fp8(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
             out_dtype: TEDType) -> Tuple[jnp.ndarray, jnp.ndarray]:
    """
    Cast wrapper
    Return FP8 tensor
    """
    return CastFP8Primitive.outer_primitive.bind(x, amax, scale, scale_inv, out_dtype=out_dtype)


class TransposePrimitive(BasePrimitive):
    """
    Transpose Primitive
    """
    name = "te_transpose"
    multiple_results = False
    impl_static_args = (1, 2)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, *, static_axis_boundary, transpose_axis_boundary):
        """
        _transpose abstract
        """
        transposed_x_shape = _multidim_transpose(x_aval.shape, static_axis_boundary,
                                                 transpose_axis_boundary)
        xt_aval = x_aval.update(shape=transposed_x_shape, dtype=x_aval.dtype)

        return xt_aval

    @staticmethod
    def lowering(ctx, x, *, static_axis_boundary, transpose_axis_boundary):
        """
        _transpose cuda lowering
        """

        x_aval = ctx.avals_in[0]
        assert x_aval.dtype in [
            jnp.float32, jnp.float16, jnp.bfloat16, jnp.float8_e4m3fn, jnp.float8_e5m2
        ]

        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(x_aval.dtype)
        if static_axis_boundary >= 0:
            for i in range(static_axis_boundary + 1):
                assert ir_x_shape[i] == 1

        transposed_x_shape = _multidim_transpose(ir_x_shape, static_axis_boundary,
                                                 transpose_axis_boundary)

        out_types = [ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype)]
        operands = [x]
        operand_shapes = [ir_x_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        te_dtype = jax_dtype_to_te_dtype(x_aval.dtype)
        contracted_x_shape = (reduce(operator.mul, ir_x_shape[:transpose_axis_boundary]),
                              reduce(operator.mul, ir_x_shape[transpose_axis_boundary:]))
        opaque = transformer_engine_jax.pack_common_descriptor(contracted_x_shape, te_dtype,
                                                               te_dtype)

        out = custom_caller(TransposePrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(x, static_axis_boundary, transpose_axis_boundary):
        """
        tcast_transpose implementation
        """
        assert TransposePrimitive.inner_primitive is not None
        transposed_x = \
            TransposePrimitive.inner_primitive.bind(x,
                                                    static_axis_boundary=static_axis_boundary,
                                                    transpose_axis_boundary=transpose_axis_boundary)
        return transposed_x

    @staticmethod
    def batcher(batched_args, batch_dims, *, static_axis_boundary, transpose_axis_boundary):
        _check_valid_batch_dims(batch_dims)
        assert TransposePrimitive.outer_primitive is not None
        assert static_axis_boundary < 0

        x, = batched_args
        x_bdim, = batch_dims

        # Minus batch dim.
        transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, x.ndim - 1)
        transpose_axis_boundary += 1    # Plus batch dim

        out_bdims = x_bdim
        return TransposePrimitive.outer_primitive.bind(
            x, static_axis_boundary=x_bdim,
            transpose_axis_boundary=transpose_axis_boundary), out_bdims

    @staticmethod
    def infer_sharding_from_operands(static_axis_boundary, transpose_axis_boundary, mesh, arg_infos,
                                     result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        return transposed_x_sharding

    @staticmethod
    def partition(static_axis_boundary, transpose_axis_boundary, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = transposed_x_sharding

        impl = partial(TransposePrimitive.impl,
                       static_axis_boundary=static_axis_boundary,
                       transpose_axis_boundary=transpose_axis_boundary)

        return mesh, impl, out_shardings, arg_shardings


register_primitive(TransposePrimitive)


def transpose(x: jnp.ndarray, static_axis_boundary: int,
              transpose_axis_boundary: int) -> jnp.ndarray:
    """
    transpose wrapper
    """
    return TransposePrimitive.outer_primitive.bind(x,
                                                   static_axis_boundary=static_axis_boundary,
                                                   transpose_axis_boundary=transpose_axis_boundary)


class LayerNormFwdFp8Primitive(BasePrimitive):
    """
    Layer Normalization Forward FP8 Primitive
    """
    name = "te_layernorm_forward_fp8"
    multiple_results = True
    impl_static_args = (6, 7, 8)    # out_type, zero_centered_gamma, epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, gamma_aval, beta_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 zero_centered_gamma, epsilon):
        """
        LayerNorm fwd (fp8 out) inner primitive abstract
        """
        x_dtype = dtypes.canonicalize_dtype(x_aval.dtype)

        assert x_dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        mu_rsigama_dtype = jnp.float32

        assert gamma_aval.size == beta_aval.size

        wkspace_info, barrier_info = transformer_engine_jax.get_layernorm_fwd_workspace_sizes(
            x_aval.size // gamma_aval.size,    # batch size
            gamma_aval.size,    # hidden size
            jax_dtype_to_te_dtype(x_aval.dtype),    # in type
            jax_dtype_to_te_dtype(gamma_aval.dtype),    # weight type
            jax_dtype_to_te_dtype(out_dtype),
            True,
            zero_centered_gamma,
            epsilon)

        out_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        mu_aval = rsigma_aval = out_aval.update(shape=out_aval.shape[:-1], dtype=mu_rsigama_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)
        wkspace_aval = x_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = x_aval.update(shape=barrier_info[0],
                                     dtype=te_dtype_to_jax_dtype(barrier_info[1]))

        return out_aval, mu_aval, rsigma_aval, updated_amax_aval, wkspace_aval, barrier_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        LayerNorm fwd (fp8 out) outer primitive abstract
        """
        out_aval, mu_aval, rsigma_aval, updated_amax_aval, _, _ = \
            LayerNormFwdFp8Primitive.abstract(*args, **kwargs)
        return out_aval, mu_aval, rsigma_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, gamma, beta, amax, scale, scale_inv, *, out_dtype, zero_centered_gamma,
                 epsilon):
        """
        LayerNorm fwd (fp8 out) lowering rules
        """
        x_aval, gamma_aval, beta_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in

        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn

        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert gamma_aval.dtype == beta_aval.dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape
        b_type = ir.RankedTensorType(beta.type)
        b_shape = b_type.shape

        assert g_type == b_type
        assert g_shape == b_shape

        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_mu_dtype = ir.F32Type.get()
        ir_rsigma_dtype = ir.F32Type.get()
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        out_shape = x_shape
        hidden_size = reduce(operator.mul, g_shape)
        batch_shape = out_shape[:-1]
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        wkspace_aval, barrier_aval = ctx.avals_out[-2:]

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(batch_shape, ir_mu_dtype),
            ir.RankedTensorType.get(batch_shape, ir_rsigma_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
            ir.RankedTensorType.get(barrier_aval.shape, jax_dtype_to_ir_dtype(barrier_aval.dtype))
        ]
        operands = [x, gamma, beta, amax, scale, scale_inv]
        operand_shapes = [
            x_shape, g_shape, b_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape
        ]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_FWD_LAYERNORM_SM_MARGIN", "0"))

        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            (0,),    # no dgamma_part in FWD pass
            (0,),    # no dbeta_part in BWD pass
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            TEDType.kByte,    # dummy dgamma_part te_dtype
            TEDType.kByte,    # dummy dbeta_part te_dtype
            zero_centered_gamma,
            epsilon,
            sm_margin,
        )

        out = custom_caller(LayerNormFwdFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={3: 3})

        return out

    @staticmethod
    def impl(x, gamma, beta, amax, scale, scale_inv, out_dtype, zero_centered_gamma, epsilon):
        """
        to describe implementation
        """
        assert LayerNormFwdFp8Primitive.inner_primitive is not None
        out, mu, rsigma, updated_amax, _, _ = LayerNormFwdFp8Primitive.inner_primitive.bind(
            x,
            gamma,
            beta,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            zero_centered_gamma=zero_centered_gamma,
            epsilon=epsilon)
        return out, mu, rsigma, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, zero_centered_gamma, epsilon):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert LayerNormFwdFp8Primitive.outer_primitive is not None
        x, gamma, beta, amax, scale, scale_inv = batched_args
        x_bdim, _, _, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, x_bdim, x_bdim, amax_bdim
        return LayerNormFwdFp8Primitive.outer_primitive.bind(
            x,
            gamma,
            beta,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            zero_centered_gamma=zero_centered_gamma,
            epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, zero_centered_gamma, epsilon, mesh, arg_infos,
                                     result_infos):
        del out_dtype, zero_centered_gamma, epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormFwdPrimitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance.")

        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        mu_sharding = rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[3])))
        return (out_sharding, mu_sharding, rsigma_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, zero_centered_gamma, epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        g_spec = get_padded_spec(arg_infos[1])
        b_spec = get_padded_spec(arg_infos[2])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {LayerNormFwdFp8Primitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        if g_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormFwdFp8Primitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        if b_spec[-1] is not None:
            warnings.warn(
                f"{LayerNormFwdFp8Primitive.name} does not support sharding of parameter beta " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        g_sharding = NamedSharding(mesh, PartitionSpec(None))
        b_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_sharding = x_sharding
        mu_sharding = rsigma_sharding = NamedSharding(
            mesh, PartitionSpec(*get_padded_spec(arg_infos[0])[:-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[3])))
        fp8_meta_sharding = amax_sharding
        arg_shardings = (x_sharding, g_sharding, b_sharding) + (fp8_meta_sharding,) * 3
        out_shardings = (out_sharding, mu_sharding, rsigma_sharding, amax_sharding)

        def sharded_impl(x, gamma, beta, amax, scale, scale_inv):
            local_x, local_mu, local_rsigma, local_amax = \
                LayerNormFwdFp8Primitive.impl(x, gamma, beta, amax, scale, scale_inv,
                                            out_dtype=out_dtype,
                                            zero_centered_gamma=zero_centered_gamma,
                                            epsilon=epsilon)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, local_mu, local_rsigma, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(LayerNormFwdFp8Primitive)


def layernorm_fwd_fp8(x: jnp.ndarray, gamma: jnp.ndarray, beta: jnp.ndarray, amax: jnp.ndarray,
                      scale: jnp.ndarray, scale_inv: jnp.ndarray, out_dtype: jnp.dtype,
                      zero_centered_gamma: bool, epsilon: float):
    """
    Wrapper for TE layernorm fwd (fp8 out)
    """
    return LayerNormFwdFp8Primitive.outer_primitive.bind(x,
                                                         gamma,
                                                         beta,
                                                         amax,
                                                         scale,
                                                         scale_inv,
                                                         out_dtype=out_dtype,
                                                         zero_centered_gamma=zero_centered_gamma,
                                                         epsilon=epsilon)


class RmsNormFwdFp8Primitive(BasePrimitive):
    """
    RMS Normalization Forward FP8 Primitive
    """
    name = "te_rmsnorm_forward_fp8"
    multiple_results = True
    impl_static_args = (5, 6)    # out_dtype, epsilon
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, gamma_aval, amax_aval, scale_aval, scale_inv_aval, out_dtype, epsilon):
        """
        RMSNorm fwd (fp8 out) inner primitive abstract
        """
        x_dtype = dtypes.canonicalize_dtype(x_aval.dtype)

        assert x_dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        hidden_size = gamma_aval.size
        assert x_aval.size % hidden_size == 0

        rsigama_dtype = jnp.float32

        wkspace_info, barrier_info = transformer_engine_jax.get_layernorm_fwd_workspace_sizes(
            x_aval.size // hidden_size,    # batch_size
            hidden_size,
            jax_dtype_to_te_dtype(x_aval.dtype),    # in te_dtype
            jax_dtype_to_te_dtype(gamma_aval.dtype),    # weight te_dtype
            jax_dtype_to_te_dtype(out_dtype),    # out te_dtype
            False,
            False,
            epsilon)

        out_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        rsigma_aval = out_aval.update(shape=out_aval.shape[:-1], dtype=rsigama_dtype)
        amax_aval = out_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)
        wkspace_aval = x_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))
        barrier_aval = x_aval.update(shape=barrier_info[0],
                                     dtype=te_dtype_to_jax_dtype(barrier_info[1]))

        return out_aval, rsigma_aval, amax_aval, wkspace_aval, barrier_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        RMSNorm fwd (fp8 out) outer primitive abstract
        """
        out_aval, rsigma_aval, amax_aval, _, _ = RmsNormFwdFp8Primitive.abstract(*args, **kwargs)
        return out_aval, rsigma_aval, amax_aval

    @staticmethod
    def lowering(ctx, x, gamma, amax, scale, scale_inv, *, out_dtype, epsilon):
        """
        RMSNorm fwd (fp8 out) lowering rules
        """

        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn

        x_aval, gamma_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in

        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        g_type = ir.RankedTensorType(gamma.type)
        g_shape = g_type.shape

        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_rsigma_dtype = ir.F32Type.get()
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        out_shape = x_shape
        hidden_size = reduce(operator.mul, g_shape)
        batch_shape = out_shape[:-1]
        batch_size = reduce(operator.mul, x_shape) // hidden_size

        wkspace_aval, barrier_aval = ctx.avals_out[-2:]

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(batch_shape, ir_rsigma_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
            ir.RankedTensorType.get(barrier_aval.shape, jax_dtype_to_ir_dtype(barrier_aval.dtype))
        ]
        operands = [x, gamma, amax, scale, scale_inv]
        operand_shapes = [x_shape, g_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        sm_margin = int(os.getenv("NVTE_FWD_LAYERNORM_SM_MARGIN", "0"))

        opaque = transformer_engine_jax.pack_norm_descriptor(
            batch_size,
            hidden_size,
            wkspace_aval.size,
            barrier_aval.size,
            (0,),    # no dgamma_part in FWD pass
            (0,),    # no dbeta_part in BWD pass
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(gamma_aval.dtype),
            jax_dtype_to_te_dtype(wkspace_aval.dtype),
            jax_dtype_to_te_dtype(barrier_aval.dtype),
            TEDType.kByte,    # dummy dgamma_part te_dtype
            TEDType.kByte,    # dummy dbeta_part te_dtype
            False,    # RMSNorm doesn't support zero_centered_gamma
            epsilon,
            sm_margin,
        )

        out = custom_caller(RmsNormFwdFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={2: 2})

        return out

    @staticmethod
    def impl(x, gamma, amax, scale, scale_inv, out_dtype, epsilon):
        """
        to describe implementation
        """
        assert RmsNormFwdFp8Primitive.inner_primitive is not None
        out, rsigma, amax, _, _ = RmsNormFwdFp8Primitive.inner_primitive.bind(x,
                                                                              gamma,
                                                                              amax,
                                                                              scale,
                                                                              scale_inv,
                                                                              out_dtype=out_dtype,
                                                                              epsilon=epsilon)
        return out, rsigma, amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, epsilon):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert RmsNormFwdFp8Primitive.outer_primitive is not None
        x, gamma, amax, scale, scale_inv = batched_args
        x_bdim, _, amax_bdim, _, _ = batch_dims
        out_bdims = x_bdim, x_bdim, amax_bdim
        return RmsNormFwdFp8Primitive.outer_primitive.bind(x,
                                                           gamma,
                                                           amax,
                                                           scale,
                                                           scale_inv,
                                                           out_dtype=out_dtype,
                                                           epsilon=epsilon), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, epsilon, mesh, arg_infos, result_infos):
        del out_dtype, epsilon, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormFwdFp8Primitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        rsigma_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, rsigma_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, epsilon, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        g_spec = get_padded_spec(arg_infos[1])
        if x_spec[-1] is not None:
            warnings.warn(
                f"Does not support to shard hidden dim in {RmsNormFwdFp8Primitive.name}! " \
                f"Force to not shard the hidden dim, which might introduce extra collective ops, " \
                f"and hurt performance."
            )
        if g_spec[-1] is not None:
            warnings.warn(
                f"{RmsNormFwdFp8Primitive.name} does not support sharding of parameter gamma " \
                f"Enforcing no sharding of parameters hidden dim! " \
            )
        x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-1], None))
        g_sharding = NamedSharding(mesh, PartitionSpec(None))
        out_sharding = x_sharding
        rsigma_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[0])[:-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        fp8_meta_sharding = amax_sharding
        arg_shardings = (x_sharding, g_sharding) + (fp8_meta_sharding,) * 3
        out_shardings = (out_sharding, rsigma_sharding, amax_sharding)

        def sharded_impl(x, gamma, amax, scale, scale_inv):
            local_x, local_rsigma, local_amax= \
                RmsNormFwdFp8Primitive.impl(x, gamma, amax, scale, scale_inv,
                                            out_dtype=out_dtype, epsilon=epsilon)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, local_rsigma, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(RmsNormFwdFp8Primitive)


def rmsnorm_fwd_fp8(x: jnp.ndarray, gamma: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray,
                    scale_inv: jnp.ndarray, out_dtype: jnp.dtype, epsilon: float):
    """
    Wrapper for TE rmsnorm fwd (fp8 out)
    """
    return RmsNormFwdFp8Primitive.outer_primitive.bind(x,
                                                       gamma,
                                                       amax,
                                                       scale,
                                                       scale_inv,
                                                       out_dtype=out_dtype,
                                                       epsilon=epsilon)


class GeluFp8Primitive(BasePrimitive):
    """
    Gelu FP8 Primitive
    """
    name = "te_gelu_fp8"
    multiple_results = True
    impl_static_args = (4,)    #out_dtype
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype):
        """
        te_gelu_p abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        out_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return out_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype):
        """
        te_gated_gelu_p lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-1])
        out_shape = ir_x_shape
        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size),
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(GeluFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 1})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype):
        """
        to describe implementation
        """
        assert GeluFp8Primitive.inner_primitive is not None
        out, updated_amax = GeluFp8Primitive.inner_primitive.bind(x,
                                                                  amax,
                                                                  scale,
                                                                  scale_inv,
                                                                  out_dtype=out_dtype)
        return out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert GeluFp8Primitive.outer_primitive is not None
        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, amax_bdim
        return GeluFp8Primitive.outer_primitive.bind(x, amax, scale, scale_inv,
                                                     out_dtype=out_dtype), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, mesh, arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (out_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_x, local_amax = GeluFp8Primitive.impl(x,
                                                        amax,
                                                        scale,
                                                        scale_inv,
                                                        out_dtype=out_dtype)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(GeluFp8Primitive)


def gelu_fp8(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
             out_dtype: jnp.dtype) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    gated gelu wrapper
    Return FP8(geglu(x))
    """
    return GeluFp8Primitive.outer_primitive.bind(x, amax, scale, scale_inv, out_dtype=out_dtype)


class DGeluDBiasCastTransposePrimitive(BasePrimitive):
    """
    DGelu DBias Cast Transpose Primitive
    """
    name = "te_dgelu_dbias_cast_transpose"
    multiple_results = True
    # out_dtype, static_axis_boundary, transpose_axis_boundary
    impl_static_args = (5, 6, 7)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 static_axis_boundary, transpose_axis_boundary):
        """
        te_dgelu_dbais_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_hidden_szie = dz_aval.shape[-1]
        gi_hidden_size = x_aval.shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        t_shape = _multidim_transpose(x_aval.shape, static_axis_boundary, transpose_axis_boundary)
        out = dz_aval.update(shape=x_aval.shape, dtype=out_dtype)
        t_out = dz_aval.update(shape=t_shape, dtype=out_dtype)

        dbias_shape = (*x_aval.shape[:static_axis_boundary + 1], gi_hidden_size)
        dbias = dz_aval.update(shape=dbias_shape, dtype=dtype)

        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        wkspace_info, = transformer_engine_jax.get_dact_dbias_ct_workspace_sizes(
            x_aval.size // gi_hidden_size,
            gi_hidden_size,
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype),
        )
        wkspace_aval = x_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))

        return out, t_out, dbias, updated_amax_aval, wkspace_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        te_dgelu_dbais_cast_transpose_p outer abstract
        """

        out, t_out, dbias, updated_amax_aval, _ = \
            DGeluDBiasCastTransposePrimitive.abstract(*args, **kwargs)
        return out, t_out, dbias, updated_amax_aval

    @staticmethod
    def lowering(ctx, dz, x, amax, scale, scale_inv, *, out_dtype, static_axis_boundary,
                 transpose_axis_boundary):
        """
        te_dgated_gelu_cast_transpose_p lowering rules
        """
        dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert dz_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dz_aval.dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_dz_type = ir.RankedTensorType(dz.type)
        ir_dz_shape = ir_dz_type.shape
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        assert ir_dz_shape == x_shape

        batch_szie = reduce(operator.mul, ir_dz_shape[:-1])
        ir_hidden_szie = ir_dz_shape[-1]
        contracted_x_shape = (batch_szie, ir_hidden_szie)

        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape
        transposed_x_shape = _multidim_transpose(x_shape, static_axis_boundary,
                                                 transpose_axis_boundary)
        dbias_shape = (*x_shape[:static_axis_boundary + 1], ir_hidden_szie)

        wkspace_aval = ctx.avals_out[-1]

        out_types = [
            ir.RankedTensorType.get(x_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(dbias_shape, ir_dz_type.element_type),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
        ]
        operands = [dz, x, amax, scale, scale_inv]
        operand_shapes = [ir_dz_shape, x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)
        opaque = transformer_engine_jax.pack_common_wk_descriptor(
            contracted_x_shape, wkspace_aval.shape, jax_dtype_to_te_dtype(dz_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype), jax_dtype_to_te_dtype(wkspace_aval.dtype))

        out = custom_caller(DGeluDBiasCastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={2: 3})

        return out

    @staticmethod
    def impl(dz, x, amax, scale, scale_inv, out_dtype, static_axis_boundary,
             transpose_axis_boundary):
        """
        to describe implementation
        """
        assert DGeluDBiasCastTransposePrimitive.inner_primitive is not None
        out, t_out, dbias, updated_amax, _ = DGeluDBiasCastTransposePrimitive.inner_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=static_axis_boundary,
            transpose_axis_boundary=transpose_axis_boundary)
        return out, t_out, dbias, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary,
                transpose_axis_boundary):
        """
        to describe batch rules for vmap
        """
        del static_axis_boundary
        _check_valid_batch_dims(batch_dims)
        assert DGeluDBiasCastTransposePrimitive.outer_primitive is not None
        dz, x, amax, scale, scale_inv = batched_args
        x_bdim, _, amax_bdim, _, _ = batch_dims

        # Minus batch dim.
        transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, x.ndim - 1)
        transpose_axis_boundary += 1    # Plus batch dim

        out_bdims = x_bdim, x_bdim, x_bdim, amax_bdim
        return DGeluDBiasCastTransposePrimitive.outer_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=x_bdim,
            transpose_axis_boundary=transpose_axis_boundary), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh,
                                     arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        tranposed_out_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, tranposed_out_sharding, dbias_shaprding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh, arg_infos,
                  result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))

        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))

        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, dbias_shaprding,
                         amax_sharding)

        def sharded_impl(dz, x, amax, scale, scale_inv):
            local_out, local_t_out, local_dbias, local_amax = DGeluDBiasCastTransposePrimitive.impl(
                dz,
                x,
                amax,
                scale,
                scale_inv,
                out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary,
                transpose_axis_boundary=transpose_axis_boundary)
            global_dbias = all_reduce_sum_along_dp_fsdp(local_dbias)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)
            return local_out, local_t_out, global_dbias, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(DGeluDBiasCastTransposePrimitive)


def dgelu_dbias_cast_transpose(
        dz: jnp.ndarray,
        x: jnp.ndarray,
        amax: jnp.ndarray,
        scale: jnp.ndarray,
        scale_inv: jnp.ndarray,
        out_dtype: TEDType,
        static_axis_boundary: int,
        transpose_axis_boundary: int = -1) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose dgelu and dbias fusion wrapper
    Return FP8(dgeglu(inputs)), dbias
    """
    if static_axis_boundary < 0:
        static_axis_boundary = -1    # means no static axes

    return DGeluDBiasCastTransposePrimitive.outer_primitive.bind(
        dz,
        x,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary,
        transpose_axis_boundary=transpose_axis_boundary)


class DBiasCastTransposePrimitive(BasePrimitive):
    """
    DBias Cast Transpose Primitive
    """
    name = "te_dbias_cast_transpose"
    multiple_results = True
    # out_dtype, static_axis_boundary, transpose_axis_boundary
    impl_static_args = (4, 5, 6)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 static_axis_boundary, transpose_axis_boundary):
        """
        te_dbias_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        gi_hidden_size = dz_aval.shape[-1]
        t_shape = _multidim_transpose(dz_aval.shape, static_axis_boundary, transpose_axis_boundary)
        out = dz_aval.update(shape=dz_aval.shape, dtype=out_dtype)
        t_out = dz_aval.update(shape=t_shape, dtype=out_dtype)

        if dz_aval.shape[-2] == 2:
            gi_hidden_size *= 2
        dbias_shape = (*dz_aval.shape[:static_axis_boundary + 1], gi_hidden_size)
        dbias = dz_aval.update(shape=dbias_shape, dtype=dtype)

        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)
        wkspace_info, = transformer_engine_jax.get_dbias_ct_workspace_sizes(
            dz_aval.size // gi_hidden_size,
            gi_hidden_size,
            jax_dtype_to_te_dtype(dz_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype)
        )
        wkspace_aval = dz_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))

        return out, t_out, dbias, updated_amax_aval, wkspace_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        te_dbias_cast_transpose_p outer abstract
        """

        out, t_out, dbias, updated_amax_aval, _ = \
        DBiasCastTransposePrimitive.abstract(*args, **kwargs)
        return out, t_out, dbias, updated_amax_aval

    @staticmethod
    def lowering(ctx, dz, amax, scale, scale_inv, *, out_dtype, static_axis_boundary,
                 transpose_axis_boundary):
        """
        te_dbias_cast_transpose_p lowering rules
        """
        dz_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert dz_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_dz_type = ir.RankedTensorType(dz.type)
        ir_dz_shape = ir_dz_type.shape
        ir_hidden_szie = ir_dz_shape[-1]
        if dz_aval.shape[-2] == 2:
            batch_szie = reduce(operator.mul, ir_dz_shape[:-2])
            ir_hidden_szie *= 2
        else:
            batch_szie = reduce(operator.mul, ir_dz_shape[:-1])
        contracted_dz_shape = (batch_szie, ir_hidden_szie)
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape
        transposed_dz_shape = _multidim_transpose(ir_dz_shape, static_axis_boundary,
                                                 transpose_axis_boundary)
        dbias_shape = (*ir_dz_shape[:static_axis_boundary + 1], ir_hidden_szie)

        wkspace_aval = ctx.avals_out[-1]

        out_types = [
            ir.RankedTensorType.get(ir_dz_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_dz_shape, ir_out_dtype),
            ir.RankedTensorType.get(dbias_shape, ir_dz_type.element_type),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
        ]
        operands = [dz, amax, scale, scale_inv]
        operand_shapes = [ir_dz_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)
        opaque = transformer_engine_jax.pack_common_wk_descriptor(
            contracted_dz_shape, wkspace_aval.shape, jax_dtype_to_te_dtype(dz_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype), jax_dtype_to_te_dtype(wkspace_aval.dtype))

        out = custom_caller(DBiasCastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 3})

        return out

    @staticmethod
    def impl(dz, amax, scale, scale_inv, out_dtype, static_axis_boundary,
             transpose_axis_boundary):
        """
        to describe implementation
        """
        assert DBiasCastTransposePrimitive.inner_primitive is not None
        out, t_out, dbias, updated_amax, _ = DBiasCastTransposePrimitive.inner_primitive.bind(
            dz,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=static_axis_boundary,
            transpose_axis_boundary=transpose_axis_boundary)
        return out, t_out, dbias, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary,
                transpose_axis_boundary):
        """
        to describe batch rules for vmap
        """
        del static_axis_boundary
        _check_valid_batch_dims(batch_dims)
        assert DBiasCastTransposePrimitive.outer_primitive is not None
        dz, amax, scale, scale_inv = batched_args
        dz_bdim, _, amax_bdim, _, _ = batch_dims

        # Minus batch dim.
        transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, dz.ndim - 1)
        transpose_axis_boundary += 1    # Plus batch dim

        out_bdims = dz_bdim, dz_bdim, dz_bdim, amax_bdim
        return DBiasCastTransposePrimitive.outer_primitive.bind(
            dz,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=dz_bdim,
            transpose_axis_boundary=transpose_axis_boundary), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh,
                                     arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        tranposed_out_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, tranposed_out_sharding, dbias_shaprding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh, arg_infos,
                  result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))

        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))

        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, dbias_shaprding,
                         amax_sharding)

        def sharded_impl(dz, amax, scale, scale_inv):
            local_out, local_t_out, local_dbias, local_amax = DBiasCastTransposePrimitive.impl(
                dz,
                amax,
                scale,
                scale_inv,
                out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary,
                transpose_axis_boundary=transpose_axis_boundary)
            global_dbias = all_reduce_sum_along_dp_fsdp(local_dbias)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)
            return local_out, local_t_out, global_dbias, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(DBiasCastTransposePrimitive)


def dbias_cast_transpose(
    dz: jnp.ndarray,
    amax: jnp.ndarray,
    scale: jnp.ndarray,
    scale_inv: jnp.ndarray,
    out_dtype: TEDType,
    static_axis_boundary: int,
    transpose_axis_boundary: int = -1) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose dbias partial fusion wrapper
    Return FP8(inputs), dbias
    """
    if static_axis_boundary < 0:
        static_axis_boundary = -1    # means no static axes

    return DBiasCastTransposePrimitive.outer_primitive.bind(
        dz,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary,
        transpose_axis_boundary=transpose_axis_boundary)


class GatedGeluFp8Primitive(BasePrimitive):
    """
    Gated Gelu FP8 Primitive
    """
    name = "te_gated_gelu_fp8"
    multiple_results = True
    impl_static_args = (4,)    #out_dtype
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype):
        """
        te_gated_gelu_p abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        assert x_aval.shape[-2] == 2    # Assume x in (....., 2, hidden)
        hidden_size = x_aval.shape[-1]
        batch_shape = x_aval.shape[:-2]
        out_shape = (batch_shape) + (hidden_size,)
        out_aval = x_aval.update(shape=out_shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return out_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype):
        """
        te_gated_gelu_p lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        hidden_size = ir_x_shape[-1]
        batch_shape = ir_x_shape[:-2]
        batch_size = reduce(operator.mul, batch_shape)
        out_shape = batch_shape + [hidden_size]
        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, out_shape[-1]),
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(GatedGeluFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 1})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype):
        """
        to describe implementation
        """
        assert GatedGeluFp8Primitive.inner_primitive is not None
        out, updated_amax = GatedGeluFp8Primitive.inner_primitive.bind(x,
                                                                       amax,
                                                                       scale,
                                                                       scale_inv,
                                                                       out_dtype=out_dtype)
        return out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert GatedGeluFp8Primitive.outer_primitive is not None
        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, amax_bdim
        return GatedGeluFp8Primitive.outer_primitive.bind(x,
                                                          amax,
                                                          scale,
                                                          scale_inv,
                                                          out_dtype=out_dtype), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, mesh, arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (out_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_x, local_amax = GatedGeluFp8Primitive.impl(x,
                                                             amax,
                                                             scale,
                                                             scale_inv,
                                                             out_dtype=out_dtype)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(GatedGeluFp8Primitive)


def gated_gelu_fp8(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
                   out_dtype: jnp.dtype) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    gated gelu wrapper
    Return FP8(geglu(x))
    """
    return GatedGeluFp8Primitive.outer_primitive.bind(x,
                                                      amax,
                                                      scale,
                                                      scale_inv,
                                                      out_dtype=out_dtype)


class DgatedGeluCastTransposePrimitive(BasePrimitive):
    """
    Dgated Gelu Cast Transpose Primitive
    """
    name = "te_dgated_gelu_cast_transpose"
    multiple_results = True
    impl_static_args = (5, 6)    # out_dtype, static_axis_boundary
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 static_axis_boundary):
        """
        te_dgated_gelu_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert x_aval.shape[-2] == 2    # Linear + GeLU
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_hidden_szie = dz_aval.shape[-1]
        gi_hidden_size = x_aval.shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        t_shape = _multidim_transpose(x_aval.shape, static_axis_boundary, -2)
        out = dz_aval.update(shape=x_aval.shape, dtype=out_dtype)
        t_out = dz_aval.update(shape=t_shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)
        return out, t_out, updated_amax_aval

    @staticmethod
    def lowering(ctx, dz, x, amax, scale, scale_inv, *, out_dtype, static_axis_boundary):
        """
        te_dgated_gelu_cast_transpose_p lowering rules
        """
        dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert dz_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dz_aval.dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_dz_type = ir.RankedTensorType(dz.type)
        ir_dz_shape = ir_dz_type.shape
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        dz_batch_szie = reduce(operator.mul, ir_dz_shape[:-1])
        x_batch_size = reduce(operator.mul, x_shape[:-2])
        assert dz_batch_szie == x_batch_size
        assert x_shape[-2] == 2    # Linear + GeLU
        ir_hidden_szie = ir_dz_shape[-1]
        gi_hidden_size = x_shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape
        transposed_x_shape = _multidim_transpose(x_shape, static_axis_boundary, -2)
        out_types = [
            ir.RankedTensorType.get(x_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [dz, x, amax, scale, scale_inv]
        operand_shapes = [ir_dz_shape, x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)
        contracted_x_shape = (x_batch_size, x_shape[-1])
        opaque = transformer_engine_jax.pack_common_descriptor(contracted_x_shape,
                                                               jax_dtype_to_te_dtype(dz_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(DgatedGeluCastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={2: 2})

        return out

    @staticmethod
    def impl(dz, x, amax, scale, scale_inv, out_dtype, static_axis_boundary):
        """
        to describe implementation
        """
        assert DgatedGeluCastTransposePrimitive.inner_primitive is not None
        out, t_out, updated_amax = DgatedGeluCastTransposePrimitive.inner_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=static_axis_boundary)
        return out, t_out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary):
        """
        to describe batch rules for vmap
        """
        del static_axis_boundary
        _check_valid_batch_dims(batch_dims)
        assert DgatedGeluCastTransposePrimitive.outer_primitive is not None
        dz, x, amax, scale, scale_inv = batched_args
        x_bdim, _, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, x_bdim, amax_bdim
        return DgatedGeluCastTransposePrimitive.outer_primitive.bind(
            dz, x, amax, scale, scale_inv, out_dtype=out_dtype,
            static_axis_boundary=x_bdim), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, mesh, arg_infos,
                                     result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, -2)
        tranposed_out_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, tranposed_out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, -2)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))

        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, amax_sharding)

        def sharded_impl(dz, x, amax, scale, scale_inv):
            local_out, local_t_out, local_amax = DgatedGeluCastTransposePrimitive.impl(
                dz,
                x,
                amax,
                scale,
                scale_inv,
                out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)
            return local_out, local_t_out, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(DgatedGeluCastTransposePrimitive)


def dgated_gelu_cast_transpose(
        dz: jnp.ndarray, x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray,
        scale_inv: jnp.ndarray, out_dtype: TEDType,
        static_axis_boundary: int) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose d_gated_gelu fusion wrapper
    Return FP8(dgeglu(inputs))
    """
    return DgatedGeluCastTransposePrimitive.outer_primitive.bind(
        dz,
        x,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary)

#  Primitives for SwiGLU and SiLU
class SiluPrimitive(BasePrimitive):
    """
    Silu Froward Primitive
    """
    name = "te_silu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(x_aval):
        """
        gated_silu abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]

        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, x):
        """
        gated_silu lowering rules
        """
        (x_aval,) = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        out_shape = ir_x_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_x_type.element_type),
        ]
        operands = [x]
        operand_shapes = [ir_x_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-1])
        in_dtype = jax_dtype_to_te_dtype(x_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size), in_dtype,
                                                               in_dtype)

        out = custom_caller(SiluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(x):
        assert SiluPrimitive.inner_primitive is not None
        out = SiluPrimitive.inner_primitive.bind(x)
        return out

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        gated_silu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert SiluPrimitive.outer_primitive is not None
        inputs, = batched_args
        inputs_bdim, = batch_dims

        out_bdims = inputs_bdim
        return SiluPrimitive.outer_primitive.bind(inputs), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        gated_silu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        return out_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        gated_silu partitioning
        """
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        impl = SiluPrimitive.impl
        return mesh, impl, out_sharding, arg_shardings


register_primitive(SiluPrimitive)


def silu(inputs: jnp.ndarray) -> jnp.ndarray:
    """
    silu wrapper
    Return geglu(inputs)
    Assume inputs has two dimensions shape and the memory layout is (N..., H)
    """
    return SiluPrimitive.outer_primitive.bind(inputs)


class DSiluPrimitive(BasePrimitive):
    """
    Dgated Silu Primitive
    """
    name = "te_dsilu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(dz_aval, x_aval):
        """
        dsilu abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert dz_aval.shape == x_aval.shape

        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, dz, x):
        """
        dsilu lowering rules
        """
        in_aval, gi_aval = ctx.avals_in
        assert in_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert gi_aval.dtype == in_aval.dtype
        ir_in_type = ir.RankedTensorType(dz.type)
        ir_in_shape = ir_in_type.shape
        gi_type = ir.RankedTensorType(x.type)
        gi_shape = gi_type.shape
        assert ir_in_shape == gi_shape

        ir_batch_size = reduce(operator.mul, ir_in_shape[:-1])
        i_hidden_size = ir_in_shape[-1]
        out_dtype = ir_in_type.element_type
        out_shape = gi_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, out_dtype),
        ]
        operands = [dz, x]
        operand_shapes = [ir_in_shape, gi_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        in_dtype = jax_dtype_to_te_dtype(in_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((ir_batch_size, i_hidden_size),
                                                               in_dtype, in_dtype)

        out = custom_caller(DSiluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(dz, x):
        """
        dsilu implementation
        """
        assert DSiluPrimitive.inner_primitive is not None
        dx = DSiluPrimitive.inner_primitive.bind(dz, x)
        return dx

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        dsilu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert DSiluPrimitive.outer_primitive is not None
        dz, x = batched_args
        _, x_bdim = batch_dims

        out_bdims = x_bdim
        return DSiluPrimitive.outer_primitive.bind(dz, x), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        dsilu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        silu_out_spec = get_padded_spec(arg_infos[1])
        dx_sharding = NamedSharding(mesh, PartitionSpec(*silu_out_spec))
        return dx_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        dsilu partition
        """
        del result_infos
        dx_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = dx_sharding
        impl = DSiluPrimitive.impl
        return mesh, impl, out_shardings, arg_shardings


register_primitive(DSiluPrimitive)


def dsilu(inputs: jnp.ndarray, silu_inputs: jnp.ndarray) -> jnp.ndarray:
    """
    dsilu fusion wrapper
    Return dgeglu(inputs)
    """
    return DSiluPrimitive.outer_primitive.bind(inputs, silu_inputs)


class GatedSiluPrimitive(BasePrimitive):
    """
    Gated Silu Froward Primitive
    """
    name = "te_gated_silu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(x_aval):
        """
        gated_silu abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        x_shape = x_aval.shape
        assert x_shape[-2] == 2    # Assume x in (....., 2, hidden)
        hidden_size = x_shape[-1]
        batch_shapes = x_shape[:-2]
        x_shape = x_aval.shape
        out_aval = core.raise_to_shaped(x_aval)
        out_shape = (batch_shapes) + (hidden_size,)
        out_aval = out_aval.update(shape=out_shape, dtype=dtype)

        return out_aval

    @staticmethod
    def lowering(ctx, x):
        """
        gated_silu lowering rules
        """
        (x_aval,) = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        out_shape = ir_x_shape[:-2] + [ir_x_shape[-1]]

        out_types = [
            ir.RankedTensorType.get(out_shape, ir_x_type.element_type),
        ]
        operands = [x]
        operand_shapes = [ir_x_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-2])
        in_dtype = jax_dtype_to_te_dtype(x_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size), in_dtype,
                                                               in_dtype)

        out = custom_caller(GatedSiluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(x):
        assert GatedSiluPrimitive.inner_primitive is not None
        out = GatedSiluPrimitive.inner_primitive.bind(x)
        return out

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        gated_silu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert GatedSiluPrimitive.outer_primitive is not None
        inputs, = batched_args
        inputs_bdim, = batch_dims

        out_bdims = inputs_bdim
        return GatedSiluPrimitive.outer_primitive.bind(inputs), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        gated_silu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        return out_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        gated_silu partitioning
        """
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        impl = GatedSiluPrimitive.impl
        return mesh, impl, out_sharding, arg_shardings


register_primitive(GatedSiluPrimitive)


def gated_silu(inputs: jnp.ndarray) -> jnp.ndarray:
    """
    gated silu wrapper
    Return FP8(geglu(inputs))
    Assume inputs has two dimensions shape and the memory layout is (N, 2, H)
    """
    return GatedSiluPrimitive.outer_primitive.bind(inputs)


class DgatedSiluPrimitive(BasePrimitive):
    """
    Dgated Silu Primitive
    """
    name = "te_dgated_silu"
    multiple_results = False
    inner_primitive = None
    outer_primitive = None
    impl_static_args = ()

    @staticmethod
    def abstract(dz_aval, x_aval):
        """
        dgated_silu abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        for axis in range(len(dz_aval.shape) - 1):
            assert dz_aval.shape[axis] == x_aval.shape[axis]

        assert x_aval.shape[-2] == 2    # Assume x in (....., 2, hidden)

        i_hidden_size = dz_aval.shape[-1]
        g_hidden_size = x_aval.shape[-1]
        assert i_hidden_size == g_hidden_size
        out_aval = core.raise_to_shaped(x_aval)
        return out_aval

    @staticmethod
    def lowering(ctx, dz, x):
        """
        dgated_silu lowering rules
        """
        in_aval, gi_aval = ctx.avals_in
        assert in_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert gi_aval.dtype == in_aval.dtype
        ir_in_type = ir.RankedTensorType(dz.type)
        ir_in_shape = ir_in_type.shape
        gi_type = ir.RankedTensorType(x.type)
        gi_shape = gi_type.shape
        for axis in range(len(ir_in_shape) - 1):
            assert ir_in_shape[axis] == gi_shape[axis]

        ir_batch_size = reduce(operator.mul, ir_in_shape[:-1])
        i_hidden_size = ir_in_shape[-1]
        g_hidden_size = gi_shape[-1]
        assert i_hidden_size == g_hidden_size
        out_dtype = ir_in_type.element_type
        out_shape = gi_shape

        out_types = [
            ir.RankedTensorType.get(out_shape, out_dtype),
        ]
        operands = [dz, x]
        operand_shapes = [ir_in_shape, gi_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        in_dtype = jax_dtype_to_te_dtype(in_aval.dtype)
        opaque = transformer_engine_jax.pack_common_descriptor((ir_batch_size, i_hidden_size),
                                                               in_dtype, in_dtype)

        out = custom_caller(DgatedSiluPrimitive.name, args, opaque, False)

        return [out]

    @staticmethod
    def impl(dz, x):
        """
        dgated_silu implementation
        """
        assert DgatedSiluPrimitive.inner_primitive is not None
        dx = DgatedSiluPrimitive.inner_primitive.bind(dz, x)
        return dx

    @staticmethod
    def batcher(batched_args, batch_dims):
        """
        dgated_silu batcher
        """
        _check_valid_batch_dims(batch_dims)
        assert DgatedSiluPrimitive.outer_primitive is not None
        dz, x = batched_args
        _, x_bdim = batch_dims

        out_bdims = x_bdim
        return DgatedSiluPrimitive.outer_primitive.bind(dz, x), out_bdims

    @staticmethod
    def infer_sharding_from_operands(mesh, arg_infos, result_infos):
        """
        dgated_silu infer_sharding_from_operands
        """
        del result_infos    # Unused.
        silu_out_spec = get_padded_spec(arg_infos[1])
        dx_sharding = NamedSharding(mesh, PartitionSpec(*silu_out_spec))
        return dx_sharding

    @staticmethod
    def partition(mesh, arg_infos, result_infos):
        """
        dgated_silu partition
        """
        del result_infos
        dx_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = dx_sharding
        impl = DgatedSiluPrimitive.impl
        return mesh, impl, out_shardings, arg_shardings


register_primitive(DgatedSiluPrimitive)


def dgated_silu(inputs: jnp.ndarray, silu_inputs: jnp.ndarray) -> jnp.ndarray:
    """
    dgated_silu fusion wrapper
    Return dgeglu(inputs)
    """
    return DgatedSiluPrimitive.outer_primitive.bind(inputs, silu_inputs)


class SiluFp8Primitive(BasePrimitive):
    """
    Silu FP8 Primitive
    """
    name = "te_silu_fp8"
    multiple_results = True
    impl_static_args = (4,)    #out_dtype
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype):
        """
        te_silu_p abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        out_aval = x_aval.update(shape=x_aval.shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return out_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype):
        """
        te_gated_silu_p lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        hidden_size = ir_x_shape[-1]
        batch_size = reduce(operator.mul, ir_x_shape[:-1])
        out_shape = ir_x_shape
        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, hidden_size),
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(SiluFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 1})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype):
        """
        to describe implementation
        """
        assert SiluFp8Primitive.inner_primitive is not None
        out, updated_amax = SiluFp8Primitive.inner_primitive.bind(x,
                                                                  amax,
                                                                  scale,
                                                                  scale_inv,
                                                                  out_dtype=out_dtype)
        return out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert SiluFp8Primitive.outer_primitive is not None
        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, amax_bdim
        return SiluFp8Primitive.outer_primitive.bind(x, amax, scale, scale_inv,
                                                     out_dtype=out_dtype), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, mesh, arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (out_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_x, local_amax = SiluFp8Primitive.impl(x,
                                                        amax,
                                                        scale,
                                                        scale_inv,
                                                        out_dtype=out_dtype)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(SiluFp8Primitive)


def silu_fp8(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
             out_dtype: jnp.dtype) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    gated silu wrapper
    Return FP8(geglu(x))
    """
    return SiluFp8Primitive.outer_primitive.bind(x, amax, scale, scale_inv, out_dtype=out_dtype)


class DSiluDBiasCastTransposePrimitive(BasePrimitive):
    """
    DSilu DBias Cast Transpose Primitive
    """
    name = "te_dsilu_dbias_cast_transpose"
    multiple_results = True
    # out_dtype, static_axis_boundary, transpose_axis_boundary
    impl_static_args = (5, 6, 7)
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 static_axis_boundary, transpose_axis_boundary):
        """
        te_dsilu_dbais_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_hidden_szie = dz_aval.shape[-1]
        gi_hidden_size = x_aval.shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        t_shape = _multidim_transpose(x_aval.shape, static_axis_boundary, transpose_axis_boundary)
        out = dz_aval.update(shape=x_aval.shape, dtype=out_dtype)
        t_out = dz_aval.update(shape=t_shape, dtype=out_dtype)

        dbias_shape = (*x_aval.shape[:static_axis_boundary + 1], gi_hidden_size)
        dbias = dz_aval.update(shape=dbias_shape, dtype=dtype)

        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        wkspace_info, = transformer_engine_jax.get_dact_dbias_ct_workspace_sizes(
            x_aval.size // gi_hidden_size,
            gi_hidden_size,
            jax_dtype_to_te_dtype(x_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype),
        )
        wkspace_aval = x_aval.update(shape=wkspace_info[0],
                                     dtype=te_dtype_to_jax_dtype(wkspace_info[1]))

        return out, t_out, dbias, updated_amax_aval, wkspace_aval

    @staticmethod
    def outer_abstract(*args, **kwargs):
        """
        te_dsilu_dbais_cast_transpose_p outer abstract
        """

        out, t_out, dbias, updated_amax_aval, _ = \
            DSiluDBiasCastTransposePrimitive.abstract(*args, **kwargs)
        return out, t_out, dbias, updated_amax_aval

    @staticmethod
    def lowering(ctx, dz, x, amax, scale, scale_inv, *, out_dtype, static_axis_boundary,
                 transpose_axis_boundary):
        """
        te_dgated_silu_cast_transpose_p lowering rules
        """
        dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert dz_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dz_aval.dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_dz_type = ir.RankedTensorType(dz.type)
        ir_dz_shape = ir_dz_type.shape
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        assert ir_dz_shape == x_shape

        batch_szie = reduce(operator.mul, ir_dz_shape[:-1])
        ir_hidden_szie = ir_dz_shape[-1]
        contracted_x_shape = (batch_szie, ir_hidden_szie)

        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape
        transposed_x_shape = _multidim_transpose(x_shape, static_axis_boundary,
                                                 transpose_axis_boundary)
        dbias_shape = (*x_shape[:static_axis_boundary + 1], ir_hidden_szie)

        wkspace_aval = ctx.avals_out[-1]

        out_types = [
            ir.RankedTensorType.get(x_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(dbias_shape, ir_dz_type.element_type),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
            ir.RankedTensorType.get(wkspace_aval.shape, jax_dtype_to_ir_dtype(wkspace_aval.dtype)),
        ]
        operands = [dz, x, amax, scale, scale_inv]
        operand_shapes = [ir_dz_shape, x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)
        opaque = transformer_engine_jax.pack_common_wk_descriptor(
            contracted_x_shape, wkspace_aval.shape, jax_dtype_to_te_dtype(dz_aval.dtype),
            jax_dtype_to_te_dtype(out_dtype), jax_dtype_to_te_dtype(wkspace_aval.dtype))

        out = custom_caller(DSiluDBiasCastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={2: 3})

        return out

    @staticmethod
    def impl(dz, x, amax, scale, scale_inv, out_dtype, static_axis_boundary,
             transpose_axis_boundary):
        """
        to describe implementation
        """
        assert DSiluDBiasCastTransposePrimitive.inner_primitive is not None
        out, t_out, dbias, updated_amax, _ = DSiluDBiasCastTransposePrimitive.inner_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=static_axis_boundary,
            transpose_axis_boundary=transpose_axis_boundary)
        return out, t_out, dbias, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary,
                transpose_axis_boundary):
        """
        to describe batch rules for vmap
        """
        del static_axis_boundary
        _check_valid_batch_dims(batch_dims)
        assert DSiluDBiasCastTransposePrimitive.outer_primitive is not None
        dz, x, amax, scale, scale_inv = batched_args
        x_bdim, _, amax_bdim, _, _ = batch_dims

        # Minus batch dim.
        transpose_axis_boundary = _normalize_axis_boundary(transpose_axis_boundary, x.ndim - 1)
        transpose_axis_boundary += 1    # Plus batch dim

        out_bdims = x_bdim, x_bdim, x_bdim, amax_bdim
        return DSiluDBiasCastTransposePrimitive.outer_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=x_bdim,
            transpose_axis_boundary=transpose_axis_boundary), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh,
                                     arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        tranposed_out_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, tranposed_out_sharding, dbias_shaprding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, transpose_axis_boundary, mesh, arg_infos,
                  result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, transpose_axis_boundary)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))

        dbias_shaprding = NamedSharding(
            mesh, PartitionSpec(*x_spec[:static_axis_boundary + 1], x_spec[-1]))

        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, dbias_shaprding,
                         amax_sharding)

        def sharded_impl(dz, x, amax, scale, scale_inv):
            local_out, local_t_out, local_dbias, local_amax = DSiluDBiasCastTransposePrimitive.impl(
                dz,
                x,
                amax,
                scale,
                scale_inv,
                out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary,
                transpose_axis_boundary=transpose_axis_boundary)
            global_dbias = all_reduce_sum_along_dp_fsdp(local_dbias)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)
            return local_out, local_t_out, global_dbias, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(DSiluDBiasCastTransposePrimitive)


def dsilu_dbias_cast_transpose(
        dz: jnp.ndarray,
        x: jnp.ndarray,
        amax: jnp.ndarray,
        scale: jnp.ndarray,
        scale_inv: jnp.ndarray,
        out_dtype: TEDType,
        static_axis_boundary: int,
        transpose_axis_boundary: int = -1) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose dsilu and dbias fusion wrapper
    Return FP8(dgeglu(inputs)), dbias
    """
    if static_axis_boundary < 0:
        static_axis_boundary = -1    # means no static axes

    return DSiluDBiasCastTransposePrimitive.outer_primitive.bind(
        dz,
        x,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary,
        transpose_axis_boundary=transpose_axis_boundary)


class GatedSiluFp8Primitive(BasePrimitive):
    """
    Gated Silu FP8 Primitive
    """
    name = "te_gated_silu_fp8"
    multiple_results = True
    impl_static_args = (4,)    #out_dtype
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype):
        """
        te_gated_silu_p abstract
        """
        dtype = dtypes.canonicalize_dtype(x_aval.dtype)
        # Currently only support casting to E4M3 only in C side.
        assert out_dtype == jnp.float8_e4m3fn
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32

        assert x_aval.shape[-2] == 2    # Assume x in (....., 2, hidden)
        hidden_size = x_aval.shape[-1]
        batch_shape = x_aval.shape[:-2]
        out_shape = (batch_shape) + (hidden_size,)
        out_aval = x_aval.update(shape=out_shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)

        return out_aval, updated_amax_aval

    @staticmethod
    def lowering(ctx, x, amax, scale, scale_inv, *, out_dtype):
        """
        te_gated_silu_p lowering rules
        """
        x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert x_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_x_type = ir.RankedTensorType(x.type)
        ir_x_shape = ir_x_type.shape
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape

        hidden_size = ir_x_shape[-1]
        batch_shape = ir_x_shape[:-2]
        batch_size = reduce(operator.mul, batch_shape)
        out_shape = batch_shape + [hidden_size]
        out_types = [
            ir.RankedTensorType.get(out_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [x, amax, scale, scale_inv]
        operand_shapes = [ir_x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)

        opaque = transformer_engine_jax.pack_common_descriptor((batch_size, out_shape[-1]),
                                                               jax_dtype_to_te_dtype(x_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(GatedSiluFp8Primitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={1: 1})

        return out

    @staticmethod
    def impl(x, amax, scale, scale_inv, out_dtype):
        """
        to describe implementation
        """
        assert GatedSiluFp8Primitive.inner_primitive is not None
        out, updated_amax = GatedSiluFp8Primitive.inner_primitive.bind(x,
                                                                       amax,
                                                                       scale,
                                                                       scale_inv,
                                                                       out_dtype=out_dtype)
        return out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype):
        """
        to describe batch rules for vmap
        """
        _check_valid_batch_dims(batch_dims)
        assert GatedSiluFp8Primitive.outer_primitive is not None
        x, amax, scale, scale_inv = batched_args
        x_bdim, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, amax_bdim
        return GatedSiluFp8Primitive.outer_primitive.bind(x,
                                                          amax,
                                                          scale,
                                                          scale_inv,
                                                          out_dtype=out_dtype), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, mesh, arg_infos, result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        return (out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[0])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec[:-2], x_spec[-1]))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[1])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (out_sharding, amax_sharding)

        def sharded_impl(x, amax, scale, scale_inv):
            local_x, local_amax = GatedSiluFp8Primitive.impl(x,
                                                             amax,
                                                             scale,
                                                             scale_inv,
                                                             out_dtype=out_dtype)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)

            return local_x, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(GatedSiluFp8Primitive)


def gated_silu_fp8(x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray, scale_inv: jnp.ndarray,
                   out_dtype: jnp.dtype) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    gated silu wrapper
    Return FP8(geglu(x))
    """
    return GatedSiluFp8Primitive.outer_primitive.bind(x,
                                                      amax,
                                                      scale,
                                                      scale_inv,
                                                      out_dtype=out_dtype)


class DgatedSiluCastTransposePrimitive(BasePrimitive):
    """
    Dgated Silu Cast Transpose Primitive
    """
    name = "te_dgated_silu_cast_transpose"
    multiple_results = True
    impl_static_args = (5, 6)    # out_dtype, static_axis_boundary
    inner_primitive = None
    outer_primitive = None

    @staticmethod
    def abstract(dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval, *, out_dtype,
                 static_axis_boundary):
        """
        te_dgated_silu_cast_transpose_p abstract
        """
        dtype = dtypes.canonicalize_dtype(dz_aval.dtype)
        assert dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dtype
        assert x_aval.shape[-2] == 2    # Linear + GeLU
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_hidden_szie = dz_aval.shape[-1]
        gi_hidden_size = x_aval.shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        t_shape = _multidim_transpose(x_aval.shape, static_axis_boundary, -2)
        out = dz_aval.update(shape=x_aval.shape, dtype=out_dtype)
        t_out = dz_aval.update(shape=t_shape, dtype=out_dtype)
        updated_amax_aval = amax_aval.update(shape=amax_aval.shape, dtype=amax_aval.dtype)
        return out, t_out, updated_amax_aval

    @staticmethod
    def lowering(ctx, dz, x, amax, scale, scale_inv, *, out_dtype, static_axis_boundary):
        """
        te_dgated_silu_cast_transpose_p lowering rules
        """
        dz_aval, x_aval, amax_aval, scale_aval, scale_inv_aval = ctx.avals_in
        assert dz_aval.dtype in [jnp.float32, jnp.float16, jnp.bfloat16]
        assert x_aval.dtype == dz_aval.dtype
        assert amax_aval.dtype == jnp.float32
        assert scale_aval.dtype == jnp.float32
        assert scale_inv_aval.dtype == jnp.float32
        ir_dz_type = ir.RankedTensorType(dz.type)
        ir_dz_shape = ir_dz_type.shape
        x_type = ir.RankedTensorType(x.type)
        x_shape = x_type.shape
        dz_batch_szie = reduce(operator.mul, ir_dz_shape[:-1])
        x_batch_size = reduce(operator.mul, x_shape[:-2])
        assert dz_batch_szie == x_batch_size
        assert x_shape[-2] == 2    # Linear + GeLU
        ir_hidden_szie = ir_dz_shape[-1]
        gi_hidden_size = x_shape[-1]
        assert ir_hidden_szie == gi_hidden_size
        ir_out_dtype = jax_dtype_to_ir_dtype(out_dtype)
        ir_amax_type = ir.RankedTensorType(amax.type)
        ir_amax_dtype = ir_amax_type.element_type
        ir_amax_shape = ir_amax_type.shape
        ir_scale_shape = ir_amax_shape
        ir_scale_inv_shape = ir_amax_shape
        transposed_x_shape = _multidim_transpose(x_shape, static_axis_boundary, -2)
        out_types = [
            ir.RankedTensorType.get(x_shape, ir_out_dtype),
            ir.RankedTensorType.get(transposed_x_shape, ir_out_dtype),
            ir.RankedTensorType.get(ir_amax_shape, ir_amax_dtype),
        ]
        operands = [dz, x, amax, scale, scale_inv]
        operand_shapes = [ir_dz_shape, x_shape, ir_amax_shape, ir_scale_shape, ir_scale_inv_shape]
        args = CustomCallArgsWrapper(out_types, operands, operand_shapes)
        contracted_x_shape = (x_batch_size, x_shape[-1])
        opaque = transformer_engine_jax.pack_common_descriptor(contracted_x_shape,
                                                               jax_dtype_to_te_dtype(dz_aval.dtype),
                                                               jax_dtype_to_te_dtype(out_dtype))

        out = custom_caller(DgatedSiluCastTransposePrimitive.name,
                            args,
                            opaque,
                            False,
                            operand_output_aliases={2: 2})

        return out

    @staticmethod
    def impl(dz, x, amax, scale, scale_inv, out_dtype, static_axis_boundary):
        """
        to describe implementation
        """
        assert DgatedSiluCastTransposePrimitive.inner_primitive is not None
        out, t_out, updated_amax = DgatedSiluCastTransposePrimitive.inner_primitive.bind(
            dz,
            x,
            amax,
            scale,
            scale_inv,
            out_dtype=out_dtype,
            static_axis_boundary=static_axis_boundary)
        return out, t_out, updated_amax

    @staticmethod
    def batcher(batched_args, batch_dims, *, out_dtype, static_axis_boundary):
        """
        to describe batch rules for vmap
        """
        del static_axis_boundary
        _check_valid_batch_dims(batch_dims)
        assert DgatedSiluCastTransposePrimitive.outer_primitive is not None
        dz, x, amax, scale, scale_inv = batched_args
        x_bdim, _, amax_bdim, _, _ = batch_dims

        out_bdims = x_bdim, x_bdim, amax_bdim
        return DgatedSiluCastTransposePrimitive.outer_primitive.bind(
            dz, x, amax, scale, scale_inv, out_dtype=out_dtype,
            static_axis_boundary=x_bdim), out_bdims

    @staticmethod
    def infer_sharding_from_operands(out_dtype, static_axis_boundary, mesh, arg_infos,
                                     result_infos):
        del out_dtype, result_infos
        x_spec = get_padded_spec(arg_infos[1])
        out_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, -2)
        tranposed_out_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))
        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        return (out_sharding, tranposed_out_sharding, amax_sharding)

    @staticmethod
    def partition(out_dtype, static_axis_boundary, mesh, arg_infos, result_infos):
        del result_infos
        x_spec = get_padded_spec(arg_infos[1])
        casted_x_sharding = NamedSharding(mesh, PartitionSpec(*x_spec))
        xt_spec = _multidim_transpose(x_spec, static_axis_boundary, -2)
        casted_transposed_x_sharding = NamedSharding(mesh, PartitionSpec(*xt_spec))

        amax_sharding = NamedSharding(mesh, PartitionSpec(*get_padded_spec(arg_infos[2])))
        arg_shardings = tuple(arg_i.sharding for arg_i in arg_infos)
        out_shardings = (casted_x_sharding, casted_transposed_x_sharding, amax_sharding)

        def sharded_impl(dz, x, amax, scale, scale_inv):
            local_out, local_t_out, local_amax = DgatedSiluCastTransposePrimitive.impl(
                dz,
                x,
                amax,
                scale,
                scale_inv,
                out_dtype=out_dtype,
                static_axis_boundary=static_axis_boundary)
            global_updated_amax = all_reduce_max_along_all_axes_except_PP(local_amax)
            return local_out, local_t_out, global_updated_amax

        return mesh, sharded_impl, out_shardings, arg_shardings


register_primitive(DgatedSiluCastTransposePrimitive)


def dgated_silu_cast_transpose(
        dz: jnp.ndarray, x: jnp.ndarray, amax: jnp.ndarray, scale: jnp.ndarray,
        scale_inv: jnp.ndarray, out_dtype: TEDType,
        static_axis_boundary: int) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """
    cast transpose d_gated_silu fusion wrapper
    Return FP8(dgeglu(inputs))
    """
    return DgatedSiluCastTransposePrimitive.outer_primitive.bind(
        dz,
        x,
        amax,
        scale,
        scale_inv,
        out_dtype=out_dtype,
        static_axis_boundary=static_axis_boundary)