from typing import Optional, Tuple, Union import torch from einops import rearrange import torch.nn.functional as F import triton import triton.language as tl @triton.jit def rotary_kernel( OUT, X, COS, SIN, CU_SEQLENS, SEQLEN_OFFSETS, seqlen, nheads, rotary_dim, seqlen_ro, CACHE_KEY_SEQLEN, # strides stride_out_batch, stride_out_nheads, stride_out_seqlen, stride_out_headdim, stride_x_batch, stride_x_nheads, stride_x_seqlen, stride_x_headdim, 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_batch = tl.program_id(axis=1) pid_head = 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 COS = COS + pid_batch * seqlen_ro * rotary_dim_half SIN = SIN + pid_batch * seqlen_ro * rotary_dim_half 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 ) sin = tl.load( SIN, mask=(rm_cs[:, None] < seqlen_ro) & (rk_half[None, :] < rotary_dim_half), other=0.0 ) x0 = tl.load( X, mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half), other=0.0 ) x1 = tl.load( X + rotary_dim_half * stride_x_headdim, mask=(rm[:, None] < seqlen) & (rk_half[None, :] < rotary_dim_half), other=0.0, ) 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) """ batch, nheads, seqlen, headdim = x.shape batch_ro, seqlen_ro, rotary_dim = cos.shape assert batch == batch_ro 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"]), batch, nheads) # noqa BLOCK_M = 4 if interleaved else (8 if rotary_dim <= 64 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 nheads, rotary_dim, seqlen_ro, seqlen // 128, # key for triton cache (limit number of compilations) output.stride(0), # batch_strides output.stride(-3), # nheads_stride output.stride(-2), # seqlen_stride output.stride(-1), # headdim_stride x.stride(0), # batch_strides x.stride(-3), # nheads stride x.stride(-2), # seqlen stride x.stride(-1), # headdim stride BLOCK_K, isinstance(seqlen_offsets, torch.Tensor), False, interleaved, conjugate, BLOCK_M, ) return output 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 FastRotaryEmbedding(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, 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 = 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) 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 self.cos = None self.sin = None def _compute_inv_freq(self, device=None): return 1.0 / ( self.base ** (torch.arange(0, self.dim, 2, device=device) / self.dim) # ** (torch.arange(0, self.dim, 2, device=device).float() / self.dim) ) def _update_cos_sin_cache(self, seqlen, position_id, device=None, dtype=None): if ( seqlen > self._seq_len_cached ): 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 freqs = torch.einsum("i,j->ij", 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, q: torch.Tensor, k: torch.Tensor, position_ids: torch.Tensor, max_seqlen, ) -> Tuple[torch.Tensor, torch.Tensor]: """ q: (batch, nheads, seqlen, headdim) k: (batch, nheads, seqlen, headdim) position_id: (batch, seqlen) max_seqlen: int layer_id: int only if layer_id == 0, then update cons and sin Apply rotary embedding *inplace* to q k. """ self._update_cos_sin_cache(max_seqlen, position_ids, device=q.device, dtype=q.dtype) cos, sin = F.embedding(position_ids, self._cos_cached), F.embedding(position_ids, self._sin_cached) q = apply_rotary_emb_func( q, cos, sin, interleaved=self.interleaved, inplace=True ) k = apply_rotary_emb_func( k, cos, sin, interleaved=self.interleaved, inplace=True ) return q, k