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tool_server/.venv/lib/python3.12/site-packages/vllm/vllm_flash_attn/layers/rotary.py

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+# Adapted from https://github.com/vllm-project/flash-attention/blob/main/flash_attn/layers/rotary.py
+# Modified lines are marked with `# modified from original` comment
+# Copyright (c) 2023, Tri Dao.
+
+import math
+from typing import Optional, Tuple, Union
+
+import torch
+from einops import rearrange, repeat
+from ..ops.triton.rotary import apply_rotary   # modified from original
+
+
+def rotate_half(x, interleaved=False):
+    if not interleaved:
+        x1, x2 = x.chunk(2, dim=-1)
+        return torch.cat((-x2, x1), dim=-1)
+    else:
+        x1, x2 = x[..., ::2], x[..., 1::2]
+        return rearrange(torch.stack((-x2, x1), dim=-1), "... d two -> ... (d two)", two=2)
+
+
+def apply_rotary_emb_torch(x, cos, sin, interleaved=False):
+    """
+    x: (batch_size, seqlen, nheads, headdim)
+    cos, sin: (seqlen, rotary_dim / 2) or (batch_size, seqlen, rotary_dim / 2)
+    """
+    ro_dim = cos.shape[-1] * 2
+    assert ro_dim <= x.shape[-1]
+    cos = repeat(cos, "... d -> ... 1 (2 d)" if not interleaved else "... d -> ... 1 (d 2)")
+    sin = repeat(sin, "... d -> ... 1 (2 d)" if not interleaved else "... d -> ... 1 (d 2)")
+    return torch.cat(
+        [x[..., :ro_dim] * cos + rotate_half(x[..., :ro_dim], interleaved) * sin, x[..., ro_dim:]],
+        dim=-1,
+    )
+
+
+class ApplyRotaryEmb(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx,
+        x,
+        cos,
+        sin,
+        interleaved=False,
+        inplace=False,
+        seqlen_offsets: Union[int, torch.Tensor] = 0,
+        cu_seqlens: Optional[torch.Tensor] = None,
+        max_seqlen: Optional[int] = None,
+    ):
+        out = apply_rotary(
+            x,
+            cos,
+            sin,
+            seqlen_offsets=seqlen_offsets,
+            cu_seqlens=cu_seqlens,
+            max_seqlen=max_seqlen,
+            interleaved=interleaved,
+            inplace=inplace,
+        )
+        if isinstance(seqlen_offsets, int):
+            ctx.save_for_backward(cos, sin, cu_seqlens)  # Can't save int with save_for_backward
+            ctx.seqlen_offsets = seqlen_offsets
+        else:
+            ctx.save_for_backward(cos, sin, cu_seqlens, seqlen_offsets)
+            ctx.seqlen_offsets = None
+        ctx.interleaved = interleaved
+        ctx.inplace = inplace
+        ctx.max_seqlen = max_seqlen
+        return out if not inplace else x
+
+    @staticmethod
+    def backward(ctx, do):
+        seqlen_offsets = ctx.seqlen_offsets
+        if seqlen_offsets is None:
+            cos, sin, cu_seqlens, seqlen_offsets = ctx.saved_tensors
+        else:
+            cos, sin, cu_seqlens = ctx.saved_tensors
+        # TD [2023-09-02]: For some reason Triton (2.0.0.post1) errors with
+        # "[CUDA]: invalid device context", and cloning makes it work. Idk why. Triton 2.1.0 works.
+        if not ctx.interleaved and not ctx.inplace:
+            do = do.clone()
+        dx = apply_rotary(
+            do,
+            cos,
+            sin,
+            seqlen_offsets=seqlen_offsets,
+            cu_seqlens=cu_seqlens,
+            max_seqlen=ctx.max_seqlen,
+            interleaved=ctx.interleaved,
+            inplace=ctx.inplace,
+            conjugate=True,
+        )
+        return dx, None, None, None, None, None, None, None
+
+
+def apply_rotary_emb(
+    x,
+    cos,
+    sin,
+    interleaved=False,
+    inplace=False,
+    seqlen_offsets: Union[int, torch.Tensor] = 0,
+    cu_seqlens: Optional[torch.Tensor] = None,
+    max_seqlen: Optional[int] = None,
+):
+    """
+    Arguments:
+        x: (batch_size, seqlen, nheads, headdim) if cu_seqlens is None
+            else (total_seqlen, nheads, headdim)
+        cos, sin: (seqlen_rotary, rotary_dim / 2)
+        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead
+            of 1st half and 2nd half (GPT-NeoX style).
+        inplace: if True, apply rotary embedding in-place.
+        seqlen_offsets: (batch_size,) or int. Each sequence in x is shifted by this amount.
+            Most commonly used in inference when we have KV cache.
+        cu_seqlens: (batch + 1,) or None
+        max_seqlen: int
+    Return:
+        out: (batch_size, seqlen, nheads, headdim) if cu_seqlens is None
+            else (total_seqlen, nheads, headdim)
+    rotary_dim must be <= headdim
+    Apply rotary embedding to the first rotary_dim of x.
+    """
+    return ApplyRotaryEmb.apply(
+        x, cos, sin, interleaved, inplace, seqlen_offsets, cu_seqlens, max_seqlen
+    )
+
+
+# For backward compatibility
+apply_rotary_emb_func = apply_rotary_emb
+
+
+class ApplyRotaryEmbQKV_(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx,
+        qkv,
+        cos,
+        sin,
+        cos_k=None,
+        sin_k=None,
+        interleaved=False,
+        seqlen_offsets: Union[int, torch.Tensor] = 0,
+        num_heads_q: Union[int] = None,
+    ):
+        if cos_k is None and sin_k is None and qkv.is_contiguous():
+            # Call 1 kernel instead of 2 kernels
+            # We need qkv to be contiguous so that when we reshape to combine (3, nheads)
+            # dimensions, we get the same tensor
+            if qkv.dim() == 5:
+                batch, seqlen, three, nheads, headdim = qkv.shape
+                assert three == 3
+                # qk = rearrange(qkv[:, :, :2], "b s t h d -> b s (t h) d")
+                qk = qkv[:, :, :2].reshape(batch, seqlen, -1, headdim)
+            else:
+                assert qkv.dim() == 4
+                assert num_heads_q is not None
+                num_heads_k = (qkv.shape[2] - num_heads_q) // 2
+                assert qkv.shape[2] == num_heads_q + 2 * num_heads_k
+                qk = qkv[:, :, :num_heads_q + num_heads_k]
+            apply_rotary(
+                qk, cos, sin, seqlen_offsets=seqlen_offsets, interleaved=interleaved, inplace=True
+            )
+        else:
+            cos_k = cos if cos_k is None else cos_k
+            sin_k = sin if sin_k is None else sin_k
+            if qkv.dim() == 5:
+                q, k = qkv[:, :, 0], qkv[:, :, 1]
+            else:
+                assert qkv.dim() == 4
+                assert num_heads_q is not None
+                num_heads_k = (qkv.shape[2] - num_heads_q) // 2
+                assert qkv.shape[2] == num_heads_q + 2 * num_heads_k
+                q, k = qkv[:, :, :num_heads_q], qkv[:, :, num_heads_q : num_heads_q + num_heads_k]
+            apply_rotary(q, cos, sin, seqlen_offsets, interleaved=interleaved, inplace=True)
+            apply_rotary(k, cos_k, sin_k, seqlen_offsets, interleaved=interleaved, inplace=True)
+            ctx.save_for_backward(cos, sin, cos_k, sin_k)
+        if isinstance(seqlen_offsets, int):
+            ctx.save_for_backward(cos, sin, cos_k, sin_k)
+            ctx.seqlen_offsets = seqlen_offsets
+        else:
+            ctx.save_for_backward(cos, sin, cos_k, sin_k, seqlen_offsets)
+            ctx.seqlen_offsets = None
+        ctx.interleaved = interleaved
+        ctx.num_heads_q = num_heads_q
+        return qkv
+
+    @staticmethod
+    def backward(ctx, dqkv):
+        seqlen_offsets = ctx.seqlen_offsets
+        if seqlen_offsets is None:
+            cos, sin, cos_k, sin_k, seqlen_offsets = ctx.saved_tensors
+        else:
+            cos, sin, cos_k, sin_k = ctx.saved_tensors
+        if cos_k is None and sin_k is None and dqkv.is_contiguous():
+            # Call 1 kernel instead of 2 kernels
+            # We need dqkv to be contiguous so that when we reshape to combine (3, nheads)
+            # dimensions, we get the same tensor
+            if dqkv.dim() == 5:
+                dqk = rearrange(dqkv[:, :, :2], "b s t h d -> b s (t h) d")
+            else:
+                assert dqkv.dim() == 4
+                assert ctx.num_heads_q is not None
+                num_heads_k = (dqkv.shape[2] - ctx.num_heads_q) // 2
+                assert dqkv.shape[2] == ctx.num_heads_q + 2 * num_heads_k
+                dqk = dqkv[:, :, : ctx.num_heads_q + num_heads_k]
+            apply_rotary(
+                dqk,
+                cos,
+                sin,
+                seqlen_offsets=seqlen_offsets,
+                interleaved=ctx.interleaved,
+                inplace=True,
+                conjugate=True,
+            )
+        else:
+            cos_k = cos if cos_k is None else cos_k
+            sin_k = sin if sin_k is None else sin_k
+            if dqkv.dim() == 5:
+                dq, dk = dqkv[:, :, 0], dqkv[:, :, 1]
+            else:
+                assert dqkv.dim() == 4
+                assert ctx.num_heads_q is not None
+                num_heads_k = (dqkv.shape[2] - ctx.num_heads_q) // 2
+                assert dqkv.shape[2] == ctx.num_heads_q + 2 * num_heads_k
+                dq = dqkv[:, :, : ctx.num_heads_q]
+                dk = dqkv[:, :, ctx.num_heads_q : ctx.num_heads_q + num_heads_k]
+            apply_rotary(
+                dq,
+                cos,
+                sin,
+                seqlen_offsets,
+                interleaved=ctx.interleaved,
+                inplace=True,
+                conjugate=True,
+            )
+            apply_rotary(
+                dk,
+                cos_k,
+                sin_k,
+                seqlen_offsets,
+                interleaved=ctx.interleaved,
+                inplace=True,
+                conjugate=True,
+            )
+        return dqkv, None, None, None, None, None, None, None
+
+
+def apply_rotary_emb_qkv_(
+    qkv,
+    cos,
+    sin,
+    cos_k=None,
+    sin_k=None,
+    interleaved=False,
+    seqlen_offsets: Union[int, torch.Tensor] = 0,
+    num_heads_q: Optional[int] = None,
+):
+    """
+    Arguments:
+        qkv: (batch_size, seqlen, 3, nheads, headdim) or (batch_size, seqlen, num_heads_q + 2 * num_heads_k, headdim).
+            If qkv has shape (batch_size, seqlen, num_heads_q + 2 * num_heads_k, headdim) (e.g. MQA / GQA),
+            then num_heads_q must be provided.
+        cos, sin: (seqlen, rotary_dim / 2)
+        cos_k, sin_k: (seqlen, rotary_dim / 2), optional
+        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead of
+            1st half and 2nd half (GPT-NeoX style).
+        seqlen_offsets: (batch_size,) or int. Each sequence in Q and K is shifted by this amount.
+            Most commonly used in inference when we have KV cache.
+    Return:
+        qkv: (batch_size, seqlen, 3, nheads, headdim) or (batch_size, seqlen, num_heads_q + 2 * num_heads_k, headdim)
+    rotary_dim must be <= headdim
+    Apply rotary embedding *inplace* to the first rotary_dim of Q and K.
+    """
+    return ApplyRotaryEmbQKV_.apply(
+        qkv, cos, sin, cos_k, sin_k, interleaved, seqlen_offsets, num_heads_q
+    )
+
+
+class ApplyRotaryEmbKV_(torch.autograd.Function):
+    @staticmethod
+    def forward(ctx, kv, cos, sin, interleaved=False, seqlen_offsets: Union[int, torch.Tensor] = 0):
+        batch, seqlen, two, nheads, headdim = kv.shape
+        assert two == 2
+        k = kv[:, :, 0]
+        apply_rotary(
+            k, cos, sin, seqlen_offsets=seqlen_offsets, interleaved=interleaved, inplace=True
+        )
+        if isinstance(seqlen_offsets, int):
+            ctx.save_for_backward(cos, sin)  # Can't save int with save_for_backward
+            ctx.seqlen_offsets = seqlen_offsets
+        else:
+            ctx.save_for_backward(cos, sin, seqlen_offsets)
+            ctx.seqlen_offsets = None
+        ctx.interleaved = interleaved
+        return kv
+
+    @staticmethod
+    def backward(ctx, dkv):
+        seqlen_offsets = ctx.seqlen_offsets
+        if seqlen_offsets is None:
+            cos, sin, seqlen_offsets = ctx.saved_tensors
+        else:
+            cos, sin = ctx.saved_tensors
+        apply_rotary(
+            dkv[:, :, 0],
+            cos,
+            sin,
+            seqlen_offsets=seqlen_offsets,
+            interleaved=ctx.interleaved,
+            inplace=True,
+            conjugate=True,
+        )
+        return dkv, None, None, None, None
+
+
+apply_rotary_emb_kv_ = ApplyRotaryEmbKV_.apply
+
+
+def apply_rotary_emb_kv_(
+    kv,
+    cos,
+    sin,
+    interleaved=False,
+    seqlen_offsets: Union[int, torch.Tensor] = 0,
+):
+    """
+    Arguments:
+        kv: (batch_size, seqlen, 2, nheads, headdim)
+        cos, sin: (seqlen, rotary_dim / 2)
+        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead of
+            1st half and 2nd half (GPT-NeoX style).
+        seqlen_offsets: (batch_size,) or int. Each sequence in Q and K is shifted by this amount.
+            Most commonly used in inference when we have KV cache.
+    Return:
+        kv: (batch_size, seqlen, 2, nheads, headdim)
+    rotary_dim must be <= headdim
+    Apply rotary embedding *inplace* to the first rotary_dim of K.
+    """
+    return ApplyRotaryEmbKV_.apply(kv, cos, sin, interleaved, seqlen_offsets)
+
+
+class RotaryEmbedding(torch.nn.Module):
+    """
+    The rotary position embeddings from RoFormer_ (Su et. al).
+    A crucial insight from the method is that the query and keys are
+    transformed by rotation matrices which depend on the relative positions.
+
+    Other implementations are available in the Rotary Transformer repo_ and in
+    GPT-NeoX_, GPT-NeoX was an inspiration
+
+    .. _RoFormer: https://arxiv.org/abs/2104.09864
+    .. _repo: https://github.com/ZhuiyiTechnology/roformer
+    .. _GPT-NeoX: https://github.com/EleutherAI/gpt-neox
+
+    If scale_base is not None, this implements XPos (Sun et al., https://arxiv.org/abs/2212.10554).
+    A recommended value for scale_base is 512: https://github.com/HazyResearch/flash-attention/issues/96
+    Reference: https://github.com/sunyt32/torchscale/blob/main/torchscale/component/xpos_relative_position.py
+    """
+
+    def __init__(
+        self,
+        dim: int,
+        base=10000.0,
+        interleaved=False,
+        scale_base=None,
+        pos_idx_in_fp32=True,
+        device=None,
+    ):
+        """
+        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead
+            of 1st half and 2nd half (GPT-NeoX style).
+        pos_idx_in_fp32: if True, the position indices [0.0, ..., seqlen - 1] are in fp32,
+            otherwise they might be in lower precision.
+            This option was added because previously (before 2023-07-02), when we construct
+            the position indices, we use the dtype of self.inv_freq. In most cases this would
+            be fp32, but if the model is trained in pure bf16 (not mixed precision), then
+            self.inv_freq would be bf16, and the position indices are also in bf16.
+            Because of the limited precision of bf16 (e.g. 1995.0 is rounded to 2000.0), the
+            embeddings for some positions will coincide.
+            To maintain compatibility with models previously trained in pure bf16,
+            we add this option.
+        """
+        super().__init__()
+        self.dim = dim
+        self.base = float(base)
+        self.pos_idx_in_fp32 = pos_idx_in_fp32
+        # Generate and save the inverse frequency buffer (non trainable)
+        inv_freq = self._compute_inv_freq(device)
+        self.register_buffer("inv_freq", inv_freq, persistent=False)
+        self.interleaved = interleaved
+        self.scale_base = scale_base
+        scale = (
+            (torch.arange(0, dim, 2, device=device, dtype=torch.float32) + 0.4 * dim) / (1.4 * dim)
+            if scale_base is not None
+            else None
+        )
+        self.register_buffer("scale", scale, persistent=False)
+
+        self._seq_len_cached = 0
+        self._cos_cached = None
+        self._sin_cached = None
+        self._cos_k_cached = None
+        self._sin_k_cached = None
+
+    def _compute_inv_freq(self, device=None):
+        return 1.0 / (
+            self.base
+            ** (torch.arange(0, self.dim, 2, device=device, dtype=torch.float32) / self.dim)
+        )
+
+    def _update_cos_sin_cache(self, seqlen, device=None, dtype=None):
+        # Reset the tables if the sequence length has changed,
+        # if we're on a new device (possibly due to tracing for instance),
+        # or if we're switching from inference mode to training
+        if (
+            seqlen > self._seq_len_cached
+            or self._cos_cached is None
+            or self._cos_cached.device != device
+            or self._cos_cached.dtype != dtype
+            or (self.training and self._cos_cached.is_inference())
+        ):
+            self._seq_len_cached = seqlen
+            # We want fp32 here, not self.inv_freq.dtype, since the model could be loaded in bf16
+            # And the output of arange can be quite large, so bf16 would lose a lot of precision.
+            # However, for compatibility reason, we add an option to use the dtype of self.inv_freq.
+            if self.pos_idx_in_fp32:
+                t = torch.arange(seqlen, device=device, dtype=torch.float32)
+                # We want fp32 here as well since inv_freq will be multiplied with t, and the output
+                # will be large. Having it in bf16 will lose a lot of precision and cause the
+                # cos & sin output to change significantly.
+                # We want to recompute self.inv_freq if it was not loaded in fp32
+                if self.inv_freq.dtype != torch.float32:
+                    inv_freq = self._compute_inv_freq(device=device)
+                else:
+                    inv_freq = self.inv_freq
+            else:
+                t = torch.arange(seqlen, device=device, dtype=self.inv_freq.dtype)
+                inv_freq = self.inv_freq
+            # Don't do einsum, it converts fp32 to fp16 under AMP
+            # freqs = torch.einsum("i,j->ij", t, self.inv_freq)
+            freqs = torch.outer(t, inv_freq)
+            if self.scale is None:
+                self._cos_cached = torch.cos(freqs).to(dtype)
+                self._sin_cached = torch.sin(freqs).to(dtype)
+            else:
+                power = (
+                    torch.arange(seqlen, dtype=self.scale.dtype, device=self.scale.device)
+                    - seqlen // 2
+                ) / self.scale_base
+                scale = self.scale.to(device=power.device) ** rearrange(power, "s -> s 1")
+                # We want the multiplication by scale to happen in fp32
+                self._cos_cached = (torch.cos(freqs) * scale).to(dtype)
+                self._sin_cached = (torch.sin(freqs) * scale).to(dtype)
+                self._cos_k_cached = (torch.cos(freqs) / scale).to(dtype)
+                self._sin_k_cached = (torch.sin(freqs) / scale).to(dtype)
+
+    def forward(
+        self,
+        qkv: torch.Tensor,
+        kv: Optional[torch.Tensor] = None,
+        seqlen_offset: Union[int, torch.Tensor] = 0,
+        max_seqlen: Optional[int] = None,
+        num_heads_q: Optional[int] = None,
+    ) -> Union[torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]:
+        """
+        qkv: (batch, seqlen, 3, nheads, headdim) or (batch, seqlen, num_heads_q + 2 * num_heads_k, headdim)
+            if kv is none, else it's just q of shape (batch, seqlen, nheads, headdim).
+            If qkv has shape (batch, seqlen, num_heads_q + 2 * num_heads_k, headdim) (e.g. MQA / GQA),
+            then num_heads_q must be provided.
+        kv: (batch, seqlen, 2, nheads, headdim)
+        seqlen_offset: (batch_size,) or int. Each sequence in x is shifted by this amount.
+            Most commonly used in inference when we have KV cache.
+            If it's a tensor of shape (batch_size,), then to update the cos / sin cache, one
+            should pass in max_seqlen, which will update the cos / sin cache up to that length.
+        Apply rotary embedding *inplace* to qkv and / or kv.
+        """
+        seqlen = qkv.shape[1]
+        if max_seqlen is not None:
+            self._update_cos_sin_cache(max_seqlen, device=qkv.device, dtype=qkv.dtype)
+        elif isinstance(seqlen_offset, int):
+            self._update_cos_sin_cache(seqlen + seqlen_offset, device=qkv.device, dtype=qkv.dtype)
+        if kv is None:
+            if self.scale is None:
+                return apply_rotary_emb_qkv_(
+                    qkv,
+                    self._cos_cached,
+                    self._sin_cached,
+                    interleaved=self.interleaved,
+                    seqlen_offsets=seqlen_offset,
+                    num_heads_q=num_heads_q,
+                )
+            else:
+                return apply_rotary_emb_qkv_(
+                    qkv,
+                    self._cos_cached,
+                    self._sin_cached,
+                    self._cos_k_cached,
+                    self._sin_k_cached,
+                    interleaved=self.interleaved,
+                    seqlen_offsets=seqlen_offset,
+                    num_heads_q=num_heads_q,
+                )
+        else:
+            q = qkv
+            q = apply_rotary_emb_func(
+                q,
+                self._cos_cached,
+                self._sin_cached,
+                interleaved=self.interleaved,
+                inplace=True,
+                seqlen_offsets=seqlen_offset,
+            )
+            if self.scale is None:
+                kv = apply_rotary_emb_kv_(
+                    kv,
+                    self._cos_cached,
+                    self._sin_cached,
+                    interleaved=self.interleaved,
+                    seqlen_offsets=seqlen_offset,
+                )
+            else:
+                kv = apply_rotary_emb_kv_(
+                    kv,
+                    self._cos_k_cached,
+                    self._sin_k_cached,
+                    interleaved=self.interleaved,
+                    seqlen_offsets=seqlen_offset,
+                )
+            return q, kv

tool_server/.venv/lib/python3.12/site-packages/vllm/vllm_flash_attn/ops/triton/__init__.py

@@ -0,0 +1 @@
+

tool_server/.venv/lib/python3.12/site-packages/vllm/vllm_flash_attn/ops/triton/rotary.py

@@ -0,0 +1,229 @@
+# Copy from https://github.com/vllm-project/flash-attention/blob/main/flash_attn/ops/triton/rotary.py
+# Copyright (c) 2023, Tri Dao.
+
+from typing import Optional, Union
+
+import torch
+
+import triton
+import triton.language as tl
+
+
+@triton.jit
+def rotary_kernel(
+    OUT,  # Pointers to matrices
+    X,
+    COS,
+    SIN,
+    CU_SEQLENS,
+    SEQLEN_OFFSETS,  # this could be int or a pointer
+    # Matrix dimensions
+    seqlen,
+    rotary_dim,
+    seqlen_ro,
+    # strides
+    stride_out_batch,
+    stride_out_seqlen,
+    stride_out_nheads,
+    stride_out_headdim,
+    stride_x_batch,
+    stride_x_seqlen,
+    stride_x_nheads,
+    stride_x_headdim,
+    # Meta-parameters
+    BLOCK_K: tl.constexpr,
+    IS_SEQLEN_OFFSETS_TENSOR: tl.constexpr,
+    IS_VARLEN: tl.constexpr,
+    INTERLEAVED: tl.constexpr,
+    CONJUGATE: tl.constexpr,
+    BLOCK_M: tl.constexpr,
+):
+    pid_m = tl.program_id(axis=0)
+    pid_head = tl.program_id(axis=1)
+    pid_batch = tl.program_id(axis=2)
+    rotary_dim_half = rotary_dim // 2
+
+    if not IS_VARLEN:
+        X = X + pid_batch * stride_x_batch + pid_head * stride_x_nheads
+        OUT = OUT + pid_batch * stride_out_batch + pid_head * stride_out_nheads
+    else:
+        start_idx = tl.load(CU_SEQLENS + pid_batch)
+        seqlen = tl.load(CU_SEQLENS + pid_batch + 1) - start_idx
+        X = X + start_idx * stride_x_seqlen + pid_head * stride_x_nheads
+        OUT = OUT + start_idx * stride_out_seqlen + pid_head * stride_out_nheads
+
+    if pid_m * BLOCK_M >= seqlen:
+        return
+    rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
+    if not IS_SEQLEN_OFFSETS_TENSOR:
+        rm_cs = rm + SEQLEN_OFFSETS
+    else:
+        rm_cs = rm + tl.load(SEQLEN_OFFSETS + pid_batch)
+    rk = tl.arange(0, BLOCK_K)
+    rk_half = tl.arange(0, BLOCK_K // 2)
+
+    if not INTERLEAVED:
+        # Load the 1st and 2nd halves of X, do calculation, then store to 1st and 2nd halves of OUT
+        X = X + (rm[:, None] * stride_x_seqlen + rk_half[None, :] * stride_x_headdim)
+        COS = COS + (rm_cs[:, None] * rotary_dim_half + rk_half[None, :])
+        SIN = SIN + (rm_cs[:, None] * rotary_dim_half + rk_half[None, :])
+        cos = tl.load(
+            COS, mask=(rm_cs[:, None] < seqlen_ro) & (rk_half[None, :] < rotary_dim_half), other=1.0
+        ).to(tl.float32)
+        sin = tl.load(
+            SIN, mask=(rm_cs[:, None] < seqlen_ro) & (rk_half[None, :] < rotary_dim_half), other=0.0
+        ).to(tl.float32)
+        x0 = tl.load(
+            X, mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half), other=0.0
+        ).to(tl.float32)
+        x1 = tl.load(
+            X + rotary_dim_half * stride_x_headdim,
+            mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half),
+            other=0.0,
+        ).to(tl.float32)
+        if CONJUGATE:
+            sin = -sin
+        o0 = x0 * cos - x1 * sin
+        o1 = x0 * sin + x1 * cos
+        # write back result
+        OUT = OUT + (rm[:, None] * stride_out_seqlen + rk_half[None, :] * stride_out_headdim)
+        tl.store(OUT, o0, mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half))
+        tl.store(
+            OUT + rotary_dim_half * stride_out_headdim,
+            o1,
+            mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half),
+        )
+    else:
+        # We don't want to load X[0, 2, 4, ...] and X[1, 3, 5, ...] separately since both are slow.
+        # Instead, we load x0 = X[0, 1, 2, 3, ...] and x1 = X[1, 0, 3, 2, ...].
+        # Loading x0 will be fast but x1 will be slow.
+        # Then we load cos = COS[0, 0, 1, 1, ...] and sin = SIN[0, 0, 1, 1, ...].
+        # Then we do the calculation and use tl.where to pick put the right outputs for the even
+        # and for the odd indices.
+        rk_swap = rk + ((rk + 1) % 2) * 2 - 1  # 1, 0, 3, 2, 5, 4, ...
+        rk_repeat = tl.arange(0, BLOCK_K) // 2
+        X0 = X + (rm[:, None] * stride_x_seqlen + rk[None, :] * stride_x_headdim)
+        X1 = X + (rm[:, None] * stride_x_seqlen + rk_swap[None, :] * stride_x_headdim)
+        COS = COS + (rm_cs[:, None] * rotary_dim_half + rk_repeat[None, :])
+        SIN = SIN + (rm_cs[:, None] * rotary_dim_half + rk_repeat[None, :])
+        cos = tl.load(
+            COS,
+            mask=(rm_cs[:, None] < seqlen_ro) & (rk_repeat[None, :] < rotary_dim_half),
+            other=1.0,
+        ).to(tl.float32)
+        sin = tl.load(
+            SIN,
+            mask=(rm_cs[:, None] < seqlen_ro) & (rk_repeat[None, :] < rotary_dim_half),
+            other=0.0,
+        ).to(tl.float32)
+        x0 = tl.load(X0, mask=(rm[:, None] < seqlen) & (rk[None, :] < rotary_dim), other=0.0).to(
+            tl.float32
+        )
+        x1 = tl.load(
+            X1, mask=(rm[:, None] < seqlen) & (rk_swap[None, :] < rotary_dim), other=0.0
+        ).to(tl.float32)
+        if CONJUGATE:
+            sin = -sin
+        x0_cos = x0 * cos
+        x1_sin = x1 * sin
+        out = tl.where(rk[None, :] % 2 == 0, x0_cos - x1_sin, x0_cos + x1_sin)
+        OUT = OUT + (rm[:, None] * stride_out_seqlen + rk[None, :] * stride_out_headdim)
+        tl.store(OUT, out, mask=(rm[:, None] < seqlen) & (rk[None, :] < rotary_dim))
+
+
+def apply_rotary(
+    x: torch.Tensor,
+    cos: torch.Tensor,
+    sin: torch.Tensor,
+    seqlen_offsets: Union[int, torch.Tensor] = 0,
+    cu_seqlens: Optional[torch.Tensor] = None,
+    max_seqlen: Optional[int] = None,
+    interleaved=False,
+    inplace=False,
+    conjugate=False,
+) -> torch.Tensor:
+    """
+    Arguments:
+        x: (batch, seqlen, nheads, headdim) if cu_seqlens is None
+            else (total_seqlen, nheads, headdim).
+        cos: (seqlen_ro, rotary_dim / 2)
+        sin: (seqlen_ro, rotary_dim / 2)
+        seqlen_offsets: integer or integer tensor of size (batch,)
+        cu_seqlens: (batch + 1,) or None
+        max_seqlen: int
+    Returns:
+        y: (batch, seqlen, nheads, headdim)
+    """
+    is_varlen = cu_seqlens is not None
+    if not is_varlen:
+        batch, seqlen, nheads, headdim = x.shape
+    else:
+        assert max_seqlen is not None, "If cu_seqlens is passed in, then max_seqlen must be passed"
+        total_seqlen, nheads, headdim = x.shape
+        batch_p_1 = cu_seqlens.shape[0]
+        batch = batch_p_1 - 1
+        seqlen = max_seqlen
+    seqlen_ro, rotary_dim = cos.shape
+    assert sin.shape == cos.shape
+    rotary_dim *= 2
+    assert rotary_dim <= headdim, "rotary_dim must be <= headdim"
+    assert headdim <= 256, "Only support headdim <= 256"
+    assert seqlen_ro >= seqlen, "seqlen_ro must be >= seqlen"
+
+    assert (
+        cos.dtype == sin.dtype
+    ), f"cos and sin must have the same dtype, got {cos.dtype} and {sin.dtype}"
+    assert (
+        x.dtype == cos.dtype
+    ), f"Input and cos/sin must have the same dtype, got {x.dtype} and {cos.dtype}"
+
+    cos, sin = cos.contiguous(), sin.contiguous()
+    if isinstance(seqlen_offsets, torch.Tensor):
+        assert seqlen_offsets.shape == (batch,)
+        assert seqlen_offsets.dtype in [torch.int32, torch.int64]
+        seqlen_offsets = seqlen_offsets.contiguous()
+    else:
+        assert seqlen_offsets + seqlen <= seqlen_ro
+
+    output = torch.empty_like(x) if not inplace else x
+    if rotary_dim < headdim and not inplace:
+        output[..., rotary_dim:].copy_(x[..., rotary_dim:])
+
+    BLOCK_K = (
+        32
+        if rotary_dim <= 32
+        else (64 if rotary_dim <= 64 else (128 if rotary_dim <= 128 else 256))
+    )
+    grid = lambda META: (triton.cdiv(seqlen, META["BLOCK_M"]), nheads, batch)  # noqa
+    BLOCK_M = 4 if interleaved else (8 if rotary_dim <= 128 else 4)
+
+    # Need this, otherwise Triton tries to launch from cuda:0 and we get
+    # ValueError: Pointer argument (at 0) cannot be accessed from Triton (cpu tensor?)
+    with torch.cuda.device(x.device.index):
+        rotary_kernel[grid](
+            output,  # data ptrs
+            x,
+            cos,
+            sin,
+            cu_seqlens,
+            seqlen_offsets,
+            seqlen,  # shapes
+            rotary_dim,
+            seqlen_ro,
+            output.stride(0) if not is_varlen else 0,  # batch_strides if not varlen else 0
+            output.stride(-3),  # seqlen_stride or total_seqlen_stride
+            output.stride(-2),  # nheads_stride
+            output.stride(-1),  # headdim_stride
+            x.stride(0) if not is_varlen else 0,  # batch_strides if not varlen else 0
+            x.stride(-3),  # seqlen stride or total_seqlen_stride
+            x.stride(-2),  # nheads stride
+            x.stride(-1),  # headdim stride
+            BLOCK_K,
+            isinstance(seqlen_offsets, torch.Tensor),
+            is_varlen,
+            interleaved,
+            conjugate,
+            BLOCK_M,
+            num_warps=2 if rotary_dim <= 64 else 4,
+        )
+    return output