Add tests for numerical error

README.md

@@ -116,6 +116,17 @@ T4 GPUs are commonly used for inference, so we also measure speedup on the forwa
 
 We see speedups between 2.5x-4.5x on the forward pass.
 
+## Tests
+We test that FlashAttention produces the same output and gradient as a reference
+implementation, up to some numerical tolerance. In particular, we check that the
+maximum numerical error of FlashAttention is at most twice the numerical error
+of a baseline implementation in Pytorch (for different head dimensions, input
+dtype, sequence length, causal / non-causal).
+
+To run the tests:
+```
+pytest -q -s tests/test_flash_attn.py
+```
 ## When you encounter issues
 
 This alpha release of FlashAttention contains code written for a research

tests/test_flash_attn.py

+import math
+
+import torch
+import torch.nn.functional as F
+
+import pytest
+
+from einops import rearrange, repeat
+
+from flash_attn.flash_attn_interface import flash_attn_func, flash_attn_unpadded_qkvpacked_func, _get_block_size, flash_attn_unpadded_kvpacked_func, flash_attn_unpadded_func
+from flash_attn.bert_padding import unpad_input, pad_input, index_first_axis
+
+
+is_sm75 = torch.cuda.get_device_capability('cuda') == (7, 5)
+
+
+def generate_random_padding_mask(max_seqlen, batch_size, device, mode='random'):
+    assert mode in ['full', 'random', 'third']
+    if mode == 'full':
+        lengths = torch.full((batch_size, 1), max_seqlen, device=device, dtype=torch.int32)
+    elif mode == 'random':
+        lengths = torch.randint(max(1, max_seqlen - 20), max_seqlen, (batch_size, 1), device=device)
+    elif mode == 'third':
+        lengths = torch.randint(max_seqlen // 3, max_seqlen, (batch_size, 1), device=device)
+    padding_mask = repeat(torch.arange(max_seqlen, device=device), 's -> b s', b=batch_size) < lengths
+    return padding_mask
+
+
+def generate_qkv(x, Wqkv, nheads, query_padding_mask=None, key_padding_mask=None,
+                 kvpacked=False, qkvpacked=False):
+    """
+    Arguments:
+        x: (batch_size, seqlen, nheads * d)
+        Wqkv: nn.Linear(nheads * d, 3 * nheads * d)
+        query_padding_mask: (batch_size, seqlen), bool
+        key_padding_mask: (batch_size, seqlen), bool
+    """
+    assert not (kvpacked and qkvpacked)
+    batch_size, seqlen, dim = x.shape
+    q, k, v = Wqkv(x).chunk(3, dim=-1)
+
+    if query_padding_mask is not None:
+        q_unpad, indices_q, cu_seqlens_q, max_seqlen_q = unpad_input(q, query_padding_mask)
+        q_unpad = rearrange(q_unpad, 'nnz (h d) -> nnz h d', h=nheads)
+        output_pad_fn = lambda output_unpad: rearrange(
+            pad_input(rearrange(output_unpad, 'nnz h d -> nnz (h d)'), indices_q, batch_size, seqlen),
+            'b s (h d) -> b s h d', h=nheads
+        )
+    else:
+        q_unpad = rearrange(q, 'b s (h d) -> (b s) h d', h=nheads)
+        cu_seqlens_q = torch.arange(0, (batch_size + 1) * seqlen, step=seqlen, dtype=torch.int32,
+                                    device=q_unpad.device)
+        max_seqlen_q = seqlen
+        output_pad_fn = lambda output_unpad: rearrange(output_unpad, '(b s) h d -> b s h d', b=batch_size)
+
+    if key_padding_mask is not None:
+        k_unpad, indices_k, cu_seqlens_k, max_seqlen_k = unpad_input(k, key_padding_mask)
+        k_unpad = rearrange(k_unpad, 'nnz (h d) -> nnz h d', h=nheads)
+        v_unpad, _, _, _ = unpad_input(v, key_padding_mask)
+        v_unpad = rearrange(v_unpad, 'nnz (h d) -> nnz h d', h=nheads)
+    else:
+        k_unpad = rearrange(k, 'b s (h d) -> (b s) h d', h=nheads)
+        v_unpad = rearrange(v, 'b s (h d) -> (b s) h d', h=nheads)
+        cu_seqlens_k = torch.arange(0, (batch_size + 1) * seqlen, step=seqlen, dtype=torch.int32,
+                                    device=q_unpad.device)
+        max_seqlen_k = seqlen
+
+    if qkvpacked:
+        assert (query_padding_mask == key_padding_mask).all()
+        qkv_unpad = torch.stack([q_unpad, k_unpad, v_unpad], dim=1)
+        qkv = rearrange(torch.stack([q, k, v], dim=2), 'b s t (h d) -> b s t h d', h=nheads)
+        if query_padding_mask is not None:
+            dqkv_pad_fn = lambda dqkv_unpad: rearrange(
+                pad_input(rearrange(dqkv_unpad, 'nnz t h d -> nnz (t h d)'), indices_q, batch_size, seqlen),
+                'b s (t h d) -> b s t h d', t=3, h=nheads
+            )
+        else:
+            dqkv_pad_fn = lambda dqkv_unpad: rearrange(dqkv_unpad, '(b s) t h d -> b s t h d', b=batch_size)
+        return (qkv_unpad.detach().requires_grad_(), cu_seqlens_q, max_seqlen_q,
+                qkv.detach().requires_grad_(), output_pad_fn, dqkv_pad_fn)
+    elif kvpacked:
+        kv_unpad = torch.stack([k_unpad, v_unpad], dim=1)
+        q = rearrange(q, 'b s (h d) -> b s h d', h=nheads)
+        kv = rearrange(torch.stack([k, v], dim=2), 'b s t (h d) -> b s t h d', h=nheads)
+        dq_pad_fn = output_pad_fn
+        if key_padding_mask is not None:
+            dkv_pad_fn = lambda dkv_unpad: rearrange(
+                pad_input(rearrange(dkv_unpad, 'nnz t h d -> nnz (t h d)'), indices_k, batch_size, seqlen),
+                'b s (t h d) -> b s t h d', t=2, h=nheads
+            )
+        else:
+            dkv_pad_fn = lambda dkv_unpad: rearrange(dkv_unpad, '(b s) t h d -> b s t h d', b=batch_size)
+        return (q_unpad.detach().requires_grad_(), kv_unpad.detach().requires_grad_(),
+                cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+                q.detach().requires_grad_(), kv.detach().requires_grad_(),
+                output_pad_fn, dq_pad_fn, dkv_pad_fn)
+    else:
+        q, k, v = [rearrange(z, 'b s (h d) -> b s h d', h=nheads).detach().requires_grad_()
+                   for z in [q, k, v]]
+        dq_pad_fn = output_pad_fn
+        if key_padding_mask is not None:
+            dk_pad_fn = lambda dk_unpad: rearrange(
+                pad_input(rearrange(dk_unpad, 'nnz h d -> nnz (h d)'), indices_k, batch_size, seqlen),
+                'b s (h d) -> b s h d', h=nheads
+            )
+        else:
+            dk_pad_fn = lambda dk_unpad: rearrange(dk_unpad, '(b s) h d -> b s h d', b=batch_size)
+        return (q_unpad.detach().requires_grad_(), k_unpad.detach().requires_grad_(),
+                v_unpad.detach().requires_grad_(),
+                cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+                q, k, v,
+                output_pad_fn, dq_pad_fn, dk_pad_fn)
+
+
+def attention_ref(q, k, v, query_padding_mask=None, key_padding_mask=None, dropout_p=0.0,
+                  dropout_mask=None, causal=False, upcast=True, reorder_ops=False):
+    """
+    Arguments:
+        q: (batch_size, seqlen_q, nheads, head_dim)
+        k: (batch_size, seqlen_k, nheads, head_dim)
+        v: (batch_size, seqlen_k, nheads, head_dim)
+        query_padding_mask: (batch_size, seqlen_q)
+        key_padding_mask: (batch_size, seqlen_k)
+        dropout_p: float
+        dropout_mask: (batch_size, nheads, seqlen_q, seqlen_k)
+        upcast: whether to cast all inputs to fp32, do all computation in fp32, then cast
+            output back to fp16/bf16.
+        reorder_ops: whether to change the order of operations (scaling k instead of scaling k, etc.)
+            without changing the math. This is to estimate the numerical error from operation
+            reordering.
+    Output:
+        output: (batch_size, seqlen_q, nheads, head_dim)
+        attention: (batch_size, nheads, seqlen_q, seqlen_k), softmax after dropout
+    """
+    dtype_og = q.dtype
+    if upcast:
+        q, k, v = q.float(), k.float(), v.float()
+    seqlen_q, seqlen_k = q.shape[1], k.shape[1]
+    d = q.shape[-1]
+    if not reorder_ops:
+        scores = torch.einsum('bthd,bshd->bhts', q / math.sqrt(d), k)
+    else:
+        scores = torch.einsum('bthd,bshd->bhts', q, k / math.sqrt(d))
+    if key_padding_mask is not None:
+        scores.masked_fill_(rearrange(~key_padding_mask, 'b s -> b 1 1 s'), float('-inf'))
+    if causal:
+        causal_mask = torch.triu(torch.ones(seqlen_q, seqlen_k, dtype=torch.bool, device=q.device), 1)
+        scores.masked_fill_(causal_mask, float('-inf'))
+    attention = torch.softmax(scores, dim=-1)
+    dropout_scaling = 1.0 / (1 - dropout_p)
+    # attention_drop = attention.masked_fill(~dropout_mask, 0.0) * dropout_scaling
+    # output = torch.einsum('bhts,bshd->bthd', attention_drop , v)
+    if dropout_mask is not None:
+        attention_drop = attention.masked_fill(~dropout_mask, 0.0)
+    output = torch.einsum('bhts,bshd->bthd', attention_drop, v * dropout_scaling)
+    if query_padding_mask is not None:
+        output.masked_fill_(rearrange(~query_padding_mask, 'b s -> b s 1 1'), 0.0)
+        attention = attention.masked_fill(rearrange(~query_padding_mask, 'b s -> b 1 s 1'), 0.0)
+    return output.to(dtype=dtype_og), attention.to(dtype=dtype_og)
+
+
+def attention_kvpacked_ref(q, kv, query_padding_mask=None, key_padding_mask=None, dropout_p=0.0,
+                           dropout_mask=None, causal=False, upcast=True, reorder_ops=False):
+    return attention_ref(q, kv[:, :, 0], kv[:, :, 1], query_padding_mask,
+                         key_padding_mask, dropout_p, dropout_mask, upcast=upcast, causal=causal,
+                         reorder_ops=reorder_ops)
+
+
+def attention_qkvpacked_ref(qkv, key_padding_mask=None, dropout_p=0.0,
+                            dropout_mask=None, causal=False, upcast=True, reorder_ops=False):
+    return attention_ref(qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], key_padding_mask,
+                         key_padding_mask, dropout_p, dropout_mask, upcast=upcast, causal=causal,
+                         reorder_ops=reorder_ops)
+
+
+def generate_sparsity_mask(seqlen, sparsity=0.3):
+    repeats = seqlen // 16 // 2
+    # mask = torch.stack([torch.tensor([1, 0] * repeats, dtype=torch.bool, device='cuda'),
+    #                     torch.tensor([0, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
+    # mask = torch.stack([torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda'),
+    #                     torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
+    # mask = torch.stack([torch.tensor([1, 1] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
+    # mask = torch.stack([torch.tensor([1, 0] * repeats, dtype=torch.bool, device='cuda')], dim=-1)
+    nrow, ncol = seqlen // 16, seqlen // 256
+    mask = torch.rand(nrow, ncol, device='cuda') < sparsity
+    return mask
+
+
+def attention_blocksparse_ref(qkv, blockmask, attn_mask, dropout_p, dropout_mask):
+    """
+    Arguments:
+        qkv: (batch_size, seqlen, 3, nheads, head_dim)
+        blockmask: (seqlen / 16, seqlen / 256)
+        attn_mask: (batch_size, seqlen)
+        dropout_p: float
+        dropout_mask: (batch_size, nheads, seqlen, seqlen)
+    Output:
+        output: (batch_size, seqlen, nheads, head_dim)
+        attention: softmax after dropout
+    """
+    q, k, v = qkv.float().unbind(dim=2)
+    d = qkv.shape[-1]
+    seqlen = qkv.shape[1]
+    scores = torch.einsum('bthd,bshd->bhts', q / math.sqrt(d), k)
+    scores.masked_fill_(rearrange(~attn_mask, 'b s -> b 1 1 s'), float('-inf'))
+    blockmask = repeat(blockmask, 's_16 s_256 -> (s_16 16) (s_256 256)')
+    blockmask = blockmask[:seqlen, :seqlen]
+    scores.masked_fill_(rearrange(~blockmask, 't s -> 1 1 t s'), float('-inf'))
+    attention = torch.softmax(scores, dim=-1)
+    attention = attention.masked_fill(rearrange(~attn_mask, 'b s -> b 1 s 1'), 0.0)
+    attention = attention.masked_fill_(rearrange(~blockmask, 't s -> 1 1 t s'), 0.0)
+    attention_drop = attention.masked_fill(~dropout_mask, 0.0) / (1 - dropout_p)
+    output = torch.einsum('bhts,bshd->bthd', attention_drop , v)
+    output.masked_fill_(rearrange(~attn_mask, 'b s -> b s 1 1'), 0)
+    return output.to(dtype=qkv.dtype), attention.to(dtype=qkv.dtype)
+
+
+def convert_flash_attn_S_to_softmax(S, query_padding_mask, key_padding_mask, head_dim, is_dropout,
+                                    causal=False):
+    """FlashAttention stores the S matrix in a different way.
+    Arguments:
+        S: (batch_size, nheads, seqlen_q, seqlen_k)
+        query_padding_mask: (batch_size, seqlen_q)
+        key_padding_mask: (batch_size, seqlen_k)
+    """
+    S_flat = rearrange(S, 'b h t s -> b h (t s)')
+    seqlen_q, seqlen_k = S.shape[-2:]
+    block_size = _get_block_size(S.device, head_dim, is_dropout)
+    loop_steps = (seqlen_k + block_size - 1) // block_size
+    warps_n = 4
+    mmas_n = (seqlen_k // warps_n // 16) if seqlen_k <= block_size else (block_size // warps_n // 16)
+    S_converted = rearrange(S_flat, 'b h (loop nsteps mmas_n warps_n eight t r c0 c1) -> b h (nsteps r eight) (loop mmas_n warps_n c0 t c1)',
+                            loop=loop_steps, nsteps=seqlen_q // 16, mmas_n=mmas_n, warps_n=warps_n, eight=8, t=4,
+                            r=2, c0=2, c1=2)
+
+    # Need to zero out things not in attention_mask in case S was initialized with random values
+    # and some of those values aren't overwritten.
+    seqlen_q_og = query_padding_mask.shape[-1]
+    if seqlen_q_og < seqlen_q:
+        query_padding_mask = F.pad(query_padding_mask, (0, seqlen_q - seqlen_q_og))
+    else:
+        query_padding_mask = query_padding_mask[:, :seqlen_q]
+    S_converted = S_converted.masked_fill(rearrange(~query_padding_mask, 'b s -> b 1 s 1'), 0.0)
+    seqlen_k_og = key_padding_mask.shape[-1]
+    if seqlen_k_og < seqlen_k:
+        key_padding_mask = F.pad(key_padding_mask, (0, seqlen_k - seqlen_k_og))
+    else:
+        key_padding_mask = key_padding_mask[:, :seqlen_k]
+    S_converted = S_converted.masked_fill(rearrange(~key_padding_mask, 'b s -> b 1 1 s'), 0.0)
+    if causal:
+        causal_mask = torch.triu(torch.ones(seqlen_q, seqlen_k, dtype=torch.bool, device=S.device), 1)
+        S_converted.masked_fill_(causal_mask, 0.0)
+    if seqlen_q_og < seqlen_q:
+        S_converted = S_converted[:, :, :seqlen_q_og, :]
+    else:
+        S_converted = F.pad(S_converted, (0, 0, 0, seqlen_q_og - seqlen_q))
+    if seqlen_k_og < seqlen_k:
+        S_converted = S_converted[:, :, :, :seqlen_k_og]
+    else:
+        S_converted = F.pad(S_converted, (0, seqlen_k_og - seqlen_k))
+    return S_converted
+
+
+def normalize_flash_attn_S(attn_unnorm, q, k, v, query_padding_mask=None, key_padding_mask=None,
+                           is_dropout=False, causal=False):
+    """
+    Arguments:
+        q: (batch_size, seqlen_q, nheads, head_dim)
+        k, v: (batch_size, seqlen_k, nheads, head_dim)
+        key_padding_mask: (batch_size, seqlen_q)
+    Output:
+        softmax_lse: (batch_size, nheads, seqlen_q)
+        softmax_max: (batch_size, nheads, seqlen_q)
+    """
+    q, k, v = q.float(), k.float(), v.float()
+    _, seqlen_q, _, head_dim = q.shape
+    seqlen_k = k.shape[1]
+    scores = torch.einsum('bthd,bshd->bhts', q / math.sqrt(head_dim), k)
+    if key_padding_mask is not None:
+        scores.masked_fill_(rearrange(~key_padding_mask, 'b s -> b 1 1 s'), float('-inf'))
+    if causal:
+        causal_mask = torch.triu(torch.ones(seqlen_q, seqlen_k, dtype=torch.bool, device=q.device), 1)
+        scores.masked_fill_(causal_mask, float('-inf'))
+    block_size = _get_block_size(scores.device, head_dim, is_dropout)
+    scores_block = scores.split(block_size, dim=-1)
+    lse_block = torch.stack([torch.logsumexp(s, dim=-1) for s in scores_block], dim=-1)
+    lcse_block = torch.logcumsumexp(lse_block, dim=-1).unbind(dim=-1)
+    scores_max_block = ([torch.amax(scores_block[0], dim=-1)]
+                        + [torch.maximum(torch.amax(s, dim=-1), lcse)
+                           for s, lcse in zip(scores_block[1:], lcse_block[:-1])])
+    attn_unnorm_block = attn_unnorm.split(block_size, dim=-1)
+    attn_norm = torch.cat([a / rearrange(torch.exp(lcse_block[-1] - m), 'b h s -> b h s 1')
+                           for a, m in zip(attn_unnorm_block, scores_max_block)], dim=-1)
+    if query_padding_mask is not None:
+        attn_norm.masked_fill_(rearrange(~query_padding_mask, 'b s -> b 1 s 1'), 0.0)
+    return attn_norm.to(dtype=attn_unnorm.dtype)
+
+
+def get_dropout_fraction(dropout_mask, query_padding_mask=None, key_padding_mask=None, causal=False):
+    """
+    dropout_mask: (batch_size, nheads, seqlen_q, seqlen_k), bool. True means keep, False means drop.
+    query_padding_mask: (batch_size, seqlen_q)
+    key_padding_mask: (batch_size, seqlen_k)
+    """
+    batch_size, nheads, seqlen_q, seqlen_k = dropout_mask.shape
+    dropped = ~dropout_mask
+    if query_padding_mask is not None:
+        dropped.masked_fill_(rearrange(~query_padding_mask, 'b s -> b 1 s 1'), False)
+    if key_padding_mask is not None:
+        dropped.masked_fill_(rearrange(~key_padding_mask, 'b s -> b 1 1 s'), False)
+    if causal:
+        causal_mask = torch.triu(torch.ones(seqlen_q, seqlen_k, dtype=torch.bool,
+                                            device=dropout_mask.device), 1)
+        dropped.masked_fill_(causal_mask, False)
+    dropped_total = dropped.sum()
+    query_lengths = (query_padding_mask.sum(dim=-1) if query_padding_mask is not None
+                     else torch.full((batch_size,), seqlen_q, device=dropout_mask.device))
+    key_lengths = (key_padding_mask.sum(dim=-1) if key_padding_mask is not None
+                   else torch.full((batch_size,), seqlen_k, device=dropout_mask.device))
+    if not causal:
+        numel_per_batch = query_lengths * key_lengths
+    else:
+        numel_per_batch = torch.where(
+            query_lengths <= key_lengths,
+            query_lengths * (query_lengths + 1) / 2,
+            query_lengths * key_lengths - (key_lengths * (key_lengths - 1) / 2)
+        )
+    return dropped_total / (numel_per_batch.sum() * nheads)
+
+
+@pytest.mark.parametrize('dtype', ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
+# @pytest.mark.parametrize('dtype', [torch.float16])
+@pytest.mark.parametrize('causal', [False, True])
+@pytest.mark.parametrize('d', [128, 64, 32, 16])
+# @pytest.mark.parametrize('d', [64])
+@pytest.mark.parametrize('seqlen', [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+# @pytest.mark.parametrize('seqlen', [128])
+@pytest.mark.parametrize('dropout_p', [0.0, 0.17])
+# @pytest.mark.parametrize('dropout_p', [0.0])
+def test_flash_attn_unpadded_qkvpacked(seqlen, d, dropout_p, causal, dtype):
+    if seqlen >= 2048 and torch.cuda.get_device_properties('cuda').total_memory <= 16 * 2**30:
+        pytest.skip()  # Reference implementation OOM
+    device = 'cuda'
+    # if dtype == torch.float16:
+    #     rtol, atol = (1e-3, 3e-4) if not causal else (1e-3, 1e-3)
+    # else:  # torch.bfloat16
+    #     rtol, atol = (3e-3, 3e-3) if not causal else (1e-3, 1e-3)
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 32
+    nheads = 4
+    x = torch.randn(batch_size, seqlen, nheads * d, device=device, dtype=dtype, requires_grad=True)
+    Wqkv = torch.nn.Linear(nheads * d, 3 * nheads * d, device=device, dtype=dtype)
+
+    key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+    # key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='full')
+
+    qkv_unpad, cu_seqlens, max_seqlen, qkv, output_pad_fn, dqkv_pad_fn = generate_qkv(
+        x, Wqkv, nheads, key_padding_mask, key_padding_mask, qkvpacked=True
+    )
+
+    output_unpad, sm_lse, S_dmask = flash_attn_unpadded_qkvpacked_func(
+        qkv_unpad, cu_seqlens, max_seqlen, dropout_p, return_attn_probs=True, causal=causal
+    )
+    output = output_pad_fn(output_unpad)
+    S_dmask_converted = convert_flash_attn_S_to_softmax(
+        S_dmask, key_padding_mask, key_padding_mask, d, dropout_p > 0.0, causal=causal
+    )
+    dropout_mask = S_dmask_converted >= 0
+    attn_unnorm = S_dmask_converted.abs()
+    attn = normalize_flash_attn_S(attn_unnorm, qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2],
+                                  key_padding_mask, key_padding_mask, dropout_p > 0.0, causal=causal)
+    dropout_fraction = get_dropout_fraction(dropout_mask, key_padding_mask, key_padding_mask,
+                                            causal=causal).item()
+
+    output_ref, attn_ref = attention_qkvpacked_ref(qkv, key_padding_mask, dropout_p, dropout_mask,
+                                                   causal=causal)
+    output_pt, attn_pt = attention_qkvpacked_ref(qkv, key_padding_mask, dropout_p, dropout_mask,
+                                                 causal=causal, upcast=False, reorder_ops=True)
+    print(f'Actual dropout fraction: {dropout_fraction}')
+    print(f'Output max diff: {(output - output_ref).abs().max().item()}')
+    print(f'Output mean diff: {(output - output_ref).abs().mean().item()}')
+    print(f'Pytorch max diff: {(output_pt - output_ref).abs().max().item()}')
+    print(f'Pytorch mean diff: {(output_pt - output_ref).abs().mean().item()}')
+    print(f'Attention max diff: {(attn - attn_ref).abs().max().item()}')
+    print(f'Attention Pytorch max diff: {(attn_pt - attn_ref).abs().max().item()}')
+
+    if not (is_sm75 and d == 128):
+        g = torch.randn_like(output)
+        dqkv_unpad, = torch.autograd.grad(output, qkv_unpad, g)
+        dqkv = dqkv_pad_fn(dqkv_unpad)
+        dqkv_ref, = torch.autograd.grad(output_ref, qkv, g)
+        dqkv_pt, = torch.autograd.grad(output_pt, qkv, g)
+        print(f'dQ max diff: {(dqkv[:, :, 0] - dqkv_ref[:, :, 0]).abs().max().item()}')
+        print(f'dK max diff: {(dqkv[:, :, 1] - dqkv_ref[:, :, 1]).abs().max().item()}')
+        print(f'dV max diff: {(dqkv[:, :, 2] - dqkv_ref[:, :, 2]).abs().max().item()}')
+        print(f'dQKV mean diff: {(dqkv - dqkv_ref).abs().mean().item()}')
+        print(f'dQ Pytorch max diff: {(dqkv_pt[:, :, 0] - dqkv_ref[:, :, 0]).abs().max().item()}')
+        print(f'dK Pytorch max diff: {(dqkv_pt[:, :, 1] - dqkv_ref[:, :, 1]).abs().max().item()}')
+        print(f'dV Pytorch max diff: {(dqkv_pt[:, :, 2] - dqkv_ref[:, :, 2]).abs().max().item()}')
+        print(f'dQKV Pytorch mean diff: {(dqkv_pt - dqkv_ref).abs().mean().item()}')
+
+    # Check that FlashAttention's numerical error is at most twice the numerical error
+    # of a Pytorch implementation.
+    assert (output - output_ref).abs().max().item() <= 2 * (output_pt - output_ref).abs().max().item()
+    # assert torch.allclose(output, output_ref, rtol=rtol, atol=atol)
+    assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+    # assert torch.allclose(attn, attn_ref, rtol=rtol, atol=atol)
+    if dropout_p == 0.0:
+        assert dropout_mask.all()
+    else:
+        assert 0.99 <= dropout_fraction / dropout_p <= 1.01
+
+    if not (is_sm75 and d == 128):
+        assert (dqkv - dqkv_ref).abs().max().item() <= 2 * (dqkv_pt - dqkv_ref).abs().max().item()
+        # assert torch.allclose(dqkv, dqkv_ref, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize('dtype', ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
+# @pytest.mark.parametrize('dtype', [torch.float16])
+@pytest.mark.parametrize('causal', [False, True])
+@pytest.mark.parametrize('d', [128, 64, 32, 16])
+# @pytest.mark.parametrize('d', [64])
+@pytest.mark.parametrize('seqlen', [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+# @pytest.mark.parametrize('seqlen', [128])
+@pytest.mark.parametrize('dropout_p', [0.0, 0.17])
+# @pytest.mark.parametrize('dropout_p', [0.0])
+def test_flash_attn_unpadded_kvpacked(seqlen, d, dropout_p, causal, dtype):
+    if seqlen >= 2048 and torch.cuda.get_device_properties('cuda').total_memory <= 16 * 2**30:
+        pytest.skip()  # Reference implementation OOM
+    device = 'cuda'
+    # if dtype == torch.float16:
+    #     rtol, atol = (1e-3, 3e-4) if not causal else (1e-3, 1e-3)
+    # else:  # torch.bfloat16
+    #     rtol, atol = (3e-3, 3e-3) if not causal else (1e-3, 1e-3)
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 32
+    nheads = 4
+    x = torch.randn(batch_size, seqlen, nheads * d, device=device, dtype=dtype, requires_grad=True)
+    Wqkv = torch.nn.Linear(nheads * d, 3 * nheads * d, device=device, dtype=dtype)
+
+    query_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+    key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+
+    (q_unpad, kv_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k, q, kv,
+     output_pad_fn, dq_pad_fn, dkv_pad_fn) = generate_qkv(
+         x, Wqkv, nheads, query_padding_mask, key_padding_mask, kvpacked=True
+     )
+
+    output_unpad, sm_lse, S_dmask = flash_attn_unpadded_kvpacked_func(
+        q_unpad, kv_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+        dropout_p, return_attn_probs=True, causal=causal
+    )
+    output = output_pad_fn(output_unpad)
+    S_dmask_converted = convert_flash_attn_S_to_softmax(
+        S_dmask, query_padding_mask, key_padding_mask, d, dropout_p > 0.0, causal=causal
+    )
+    dropout_mask = S_dmask_converted >= 0
+    attn_unnorm = S_dmask_converted.abs()
+    attn = normalize_flash_attn_S(attn_unnorm, q, kv[:, :, 0], kv[:, :, 1],
+                                  query_padding_mask, key_padding_mask, dropout_p > 0.0, causal=causal)
+    dropout_fraction = get_dropout_fraction(dropout_mask, query_padding_mask, key_padding_mask,
+                                            causal=causal)
+
+    output_ref, attn_ref = attention_kvpacked_ref(q, kv, query_padding_mask, key_padding_mask,
+                                                  dropout_p, dropout_mask, causal=causal)
+    output_pt, attn_pt = attention_kvpacked_ref(q, kv, query_padding_mask, key_padding_mask,
+                                                dropout_p, dropout_mask, causal=causal,
+                                                upcast=False, reorder_ops=True)
+    print(f'Actual dropout fraction: {dropout_fraction}')
+    print(f'Output max diff: {(output - output_ref).abs().max().item()}')
+    print(f'Output mean diff: {(output - output_ref).abs().mean().item()}')
+    print(f'Pytorch max diff: {(output_pt - output_ref).abs().max().item()}')
+    print(f'Pytorch mean diff: {(output_pt - output_ref).abs().mean().item()}')
+    print(f'Attention max diff: {(attn - attn_ref).abs().max().item()}')
+    print(f'Attention Pytorch max diff: {(attn_pt - attn_ref).abs().max().item()}')
+
+    if not (is_sm75 and d == 128):
+        g = torch.randn_like(output)
+        dq_unpad, dkv_unpad, = torch.autograd.grad(output, (q_unpad, kv_unpad), g)
+        dq = dq_pad_fn(dq_unpad)
+        dkv = dkv_pad_fn(dkv_unpad)
+        dq_ref, dkv_ref, = torch.autograd.grad(output_ref, (q, kv), g)
+        dq_pt, dkv_pt = torch.autograd.grad(output_pt, (q, kv), g)
+        print(f'dQ max diff: {(dq - dq_ref).abs().max().item()}')
+        print(f'dK max diff: {(dkv[:, :, 0] - dkv_ref[:, :, 0]).abs().max().item()}')
+        print(f'dV max diff: {(dkv[:, :, 1] - dkv_ref[:, :, 1]).abs().max().item()}')
+        print(f'dQ Pytorch max diff: {(dq_pt - dq_ref).abs().max().item()}')
+        print(f'dK Pytorch max diff: {(dkv_pt[:, :, 0] - dkv_ref[:, :, 0]).abs().max().item()}')
+        print(f'dV Pytorch max diff: {(dkv_pt[:, :, 1] - dkv_ref[:, :, 1]).abs().max().item()}')
+
+    # Check that FlashAttention's numerical error is at most twice the numerical error
+    # of a Pytorch implementation.
+    assert (output - output_ref).abs().max().item() <= 2 * (output_pt - output_ref).abs().max().item()
+    # assert torch.allclose(output, output_ref, rtol=rtol, atol=atol)
+    assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+    # assert torch.allclose(attn, attn_ref, rtol=rtol, atol=atol)
+    if dropout_p == 0.0:
+        assert dropout_mask.all()
+    else:
+        assert 0.99 <= dropout_fraction / dropout_p <= 1.01
+
+    if not (is_sm75 and d == 128):
+        assert (dq - dq_ref).abs().max().item() <= 2 * (dq_pt - dq_ref).abs().max().item()
+        assert (dkv - dkv_ref).abs().max().item() <= 2 * (dkv_pt - dkv_ref).abs().max().item()
+        # assert torch.allclose(dq, dq_ref, rtol=rtol, atol=atol)
+        # assert torch.allclose(dkv, dkv_ref, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize('dtype', ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
+# @pytest.mark.parametrize('dtype', [torch.float16])
+@pytest.mark.parametrize('causal', [False, True])
+@pytest.mark.parametrize('d', [128, 64, 32, 16])
+# @pytest.mark.parametrize('d', [64])
+@pytest.mark.parametrize('seqlen', [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+# @pytest.mark.parametrize('seqlen', [128])
+@pytest.mark.parametrize('dropout_p', [0.0, 0.17])
+# @pytest.mark.parametrize('dropout_p', [0.0])
+def test_flash_attn_unpadded(seqlen, d, dropout_p, causal, dtype):
+    if seqlen >= 2048 and torch.cuda.get_device_properties('cuda').total_memory <= 16 * 2**30:
+        pytest.skip()  # Reference implementation OOM
+    device = 'cuda'
+    # if dtype == torch.float16:
+    #     rtol, atol = (1e-3, 3e-4) if not causal else (1e-3, 1e-3)
+    # else:  # torch.bfloat16
+    #     rtol, atol = (3e-3, 3e-3) if not causal else (1e-3, 1e-3)
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 32
+    nheads = 4
+    x = torch.randn(batch_size, seqlen, nheads * d, device=device, dtype=dtype, requires_grad=True)
+    Wqkv = torch.nn.Linear(nheads * d, 3 * nheads * d, device=device, dtype=dtype)
+
+    query_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+    key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+
+    (q_unpad, k_unpad, v_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k, q, k, v,
+     output_pad_fn, dq_pad_fn, dk_pad_fn) = generate_qkv(
+         x, Wqkv, nheads, query_padding_mask, key_padding_mask
+     )
+
+    output_unpad, sm_lse, S_dmask = flash_attn_unpadded_func(
+        q_unpad, k_unpad, v_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+        dropout_p, return_attn_probs=True, causal=causal
+    )
+    output = output_pad_fn(output_unpad)
+    S_dmask_converted = convert_flash_attn_S_to_softmax(
+        S_dmask, query_padding_mask, key_padding_mask, d, dropout_p > 0.0, causal=causal
+    )
+    dropout_mask = S_dmask_converted >= 0
+    attn_unnorm = S_dmask_converted.abs()
+    attn = normalize_flash_attn_S(attn_unnorm, q, k, v, query_padding_mask, key_padding_mask,
+                                  dropout_p > 0.0, causal=causal)
+    dropout_fraction = get_dropout_fraction(dropout_mask, query_padding_mask, key_padding_mask,
+                                            causal=causal)
+
+    output_ref, attn_ref = attention_ref(q, k, v, query_padding_mask, key_padding_mask,
+                                         dropout_p, dropout_mask, causal=causal)
+    output_pt, attn_pt = attention_ref(q, k, v, query_padding_mask, key_padding_mask,
+                                       dropout_p, dropout_mask, causal=causal,
+                                       upcast=False, reorder_ops=True)
+    print(f'Actual dropout fraction: {dropout_fraction}')
+    print(f'Output max diff: {(output - output_ref).abs().max().item()}')
+    print(f'Output mean diff: {(output - output_ref).abs().mean().item()}')
+    print(f'Pytorch max diff: {(output_pt - output_ref).abs().max().item()}')
+    print(f'Pytorch mean diff: {(output_pt - output_ref).abs().mean().item()}')
+    print(f'Attention max diff: {(attn - attn_ref).abs().max().item()}')
+    print(f'Attention Pytorch max diff: {(attn_pt - attn_ref).abs().max().item()}')
+
+    if not (is_sm75 and d == 128):
+        g = torch.randn_like(output)
+        dq_unpad, dk_unpad, dv_unpad, = torch.autograd.grad(output, (q_unpad, k_unpad, v_unpad), g)
+        dq = dq_pad_fn(dq_unpad)
+        dk = dk_pad_fn(dk_unpad)
+        dv = dk_pad_fn(dv_unpad)
+        dq_ref, dk_ref, dv_ref, = torch.autograd.grad(output_ref, (q, k, v), g)
+        dq_pt, dk_pt, dv_pt, = torch.autograd.grad(output_pt, (q, k, v), g)
+        print(f'dQ max diff: {(dq - dq_ref).abs().max().item()}')
+        print(f'dK max diff: {(dk - dk_ref).abs().max().item()}')
+        print(f'dV max diff: {(dv - dv_ref).abs().max().item()}')
+        print(f'dQ Pytorch max diff: {(dq_pt - dq_ref).abs().max().item()}')
+        print(f'dK Pytorch max diff: {(dk_pt - dk_ref).abs().max().item()}')
+        print(f'dV Pytorch max diff: {(dv_pt - dv_ref).abs().max().item()}')
+
+    # Check that FlashAttention's numerical error is at most twice the numerical error
+    # of a Pytorch implementation.
+    assert (output - output_ref).abs().max().item() <= 2 * (output_pt - output_ref).abs().max().item()
+    # assert torch.allclose(output, output_ref, rtol=rtol, atol=atol)
+    assert (attn - attn_ref).abs().max().item() <= 2 * (attn_pt - attn_ref).abs().max().item()
+    # assert torch.allclose(attn, attn_ref, rtol=rtol, atol=atol)
+    if dropout_p == 0.0:
+        assert dropout_mask.all()
+    else:
+        assert 0.99 <= dropout_fraction / dropout_p <= 1.01
+
+    if not (is_sm75 and d == 128):
+        assert (dq - dq_ref).abs().max().item() <= 2 * (dq_pt - dq_ref).abs().max().item()
+        assert (dk - dk_ref).abs().max().item() <= 2 * (dk_pt - dk_ref).abs().max().item()
+        assert (dv - dv_ref).abs().max().item() <= 2 * (dv_pt - dv_ref).abs().max().item()
+        # assert torch.allclose(dq, dq_ref, rtol=rtol, atol=atol)
+        # assert torch.allclose(dk, dk_ref, rtol=rtol, atol=atol)
+        # assert torch.allclose(dv, dv_ref, rtol=rtol, atol=atol)
+
+
+@pytest.mark.parametrize('dtype', ([torch.float16] if is_sm75 else [torch.float16, torch.bfloat16]))
+# @pytest.mark.parametrize('dtype', [torch.float16])
+@pytest.mark.parametrize('causal', [False, True])
+@pytest.mark.parametrize('d', [128, 64, 32, 16])
+# @pytest.mark.parametrize('d', [64])
+@pytest.mark.parametrize('seqlen', [97, 128, 200, 256, 257, 384, 512, 768, 1024, 1025, 2048])
+# @pytest.mark.parametrize('seqlen', [128])
+@pytest.mark.parametrize('dropout_p', [0.0, 0.17])
+# @pytest.mark.parametrize('dropout_p', [0.0])
+def test_flash_attn_race_condition(seqlen, d, dropout_p, causal, dtype):
+    if seqlen >= 2048 and torch.cuda.get_device_properties('cuda').total_memory <= 16 * 2**30:
+        pytest.skip()  # Reference implementation OOM
+    device = 'cuda'
+    # set seed
+    torch.random.manual_seed(0)
+    batch_size = 32
+    nheads = 4
+    x = torch.randn(batch_size, seqlen, nheads * d, device=device, dtype=dtype, requires_grad=True)
+    Wqkv = torch.nn.Linear(nheads * d, 3 * nheads * d, device=device, dtype=dtype)
+
+    query_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+    key_padding_mask = generate_random_padding_mask(seqlen, batch_size, device, mode='random')
+
+    (q_unpad, k_unpad, v_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k, q, k, v,
+     output_pad_fn, dq_pad_fn, dk_pad_fn) = generate_qkv(
+         x, Wqkv, nheads, query_padding_mask, key_padding_mask
+     )
+
+    torch.random.manual_seed(0)
+    output_unpad_0, sm_lse_0, S_dmask_0 = flash_attn_unpadded_func(
+        q_unpad, k_unpad, v_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+        dropout_p, return_attn_probs=True, causal=causal
+    )
+    S_dmask_converted_0 = convert_flash_attn_S_to_softmax(
+        S_dmask_0, query_padding_mask, key_padding_mask, d, dropout_p > 0.0, causal=causal
+    )
+
+    if not (is_sm75 and d == 128):
+        g = torch.randn_like(output_unpad_0)
+        dq_unpad_0, dk_unpad_0, dv_unpad_0, = torch.autograd.grad(output_unpad_0,
+                                                                  (q_unpad, k_unpad, v_unpad), g)
+
+    for _ in range(10):
+        torch.random.manual_seed(0)
+        output_unpad, sm_lse, S_dmask = flash_attn_unpadded_func(
+            q_unpad, k_unpad, v_unpad, cu_seqlens_q, cu_seqlens_k, max_seqlen_q, max_seqlen_k,
+            dropout_p, return_attn_probs=True, causal=causal
+        )
+        S_dmask_converted = convert_flash_attn_S_to_softmax(
+            S_dmask, query_padding_mask, key_padding_mask, d, dropout_p > 0.0, causal=causal
+        )
+        assert torch.equal(output_unpad, output_unpad_0)
+        # sm_lse has some parts that are uninitialized from torch.empty
+        # assert torch.equal(sm_lse, sm_lse_0)
+        assert torch.equal(S_dmask_converted, S_dmask_converted_0)
+
+        if not (is_sm75 and d == 128):
+            dq_unpad, dk_unpad, dv_unpad, = torch.autograd.grad(output_unpad,
+                                                                (q_unpad, k_unpad, v_unpad), g)
+            assert torch.equal(dq_unpad, dq_unpad_0)
+            assert torch.equal(dk_unpad, dk_unpad_0)
+            assert torch.equal(dv_unpad, dv_unpad_0)