feat: add benchmark for flash_infer vs flash_mla

benchmark/bench_flash_mla.py

+# MLA Triton kernel is from: https://github.com/monellz/vllm/commit/feebaa7c063be6bfb590a876741aeef1c5f58cf8#diff-7b2e1c9032522f7266051b9887246a65753871dfb3625a258fee40109fe6e87a
+import math
+import random
+
+import torch
+import triton
+import triton.language as tl
+import argparse
+
+# pip install flashinfer-python
+from flash_mla import get_mla_metadata, flash_mla_with_kvcache
+import flashinfer
+
+def scaled_dot_product_attention(query, key, value, h_q, h_kv, is_causal=False):
+    query = query.float()
+    key = key.float()
+    value = value.float()
+    key = key.repeat_interleave(h_q // h_kv, dim=0)
+    value = value.repeat_interleave(h_q // h_kv, dim=0)
+    attn_weight = query @ key.transpose(-2, -1) / math.sqrt(query.size(-1))
+    if is_causal:
+        s_q = query.shape[-2]
+        s_k = key.shape[-2]
+        attn_bias = torch.zeros(s_q, s_k, dtype=query.dtype)
+        temp_mask = torch.ones(s_q, s_k, dtype=torch.bool).tril(diagonal=s_k - s_q)
+        attn_bias.masked_fill_(temp_mask.logical_not(), float("-inf"))
+        attn_bias.to(query.dtype)
+        attn_weight += attn_bias
+    lse = attn_weight.logsumexp(dim=-1)
+    attn_weight = torch.softmax(attn_weight, dim=-1, dtype=torch.float32)
+    return attn_weight @ value, lse
+
+
+@torch.inference_mode()
+def run_torch_mla(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    for i in range(b):
+        blocked_k.view(b, max_seqlen_pad, h_kv, d)[i, cache_seqlens[i].item():] = float("nan")
+    blocked_v = blocked_k[..., :dv]
+
+    def ref_mla():
+        out = torch.empty(b, s_q, h_q, dv, dtype=torch.float32)
+        lse = torch.empty(b, h_q, s_q, dtype=torch.float32)
+        for i in range(b):
+            begin = i * max_seqlen_pad
+            end = begin + cache_seqlens[i]
+            O, LSE = scaled_dot_product_attention(
+                q[i].transpose(0, 1),
+                blocked_k.view(-1, h_kv, d)[begin:end].transpose(0, 1),
+                blocked_v.view(-1, h_kv, dv)[begin:end].transpose(0, 1),
+                h_q, h_kv,
+                is_causal=causal,
+            )
+            out[i] = O.transpose(0, 1)
+            lse[i] = LSE
+        return out, lse
+
+    out_torch, lse_torch = ref_mla()
+    t = triton.testing.do_bench(ref_mla)
+    return out_torch, lse_torch, t
+
+@torch.inference_mode()
+def run_flash_mla(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    for i in range(b):
+        blocked_k.view(b, max_seqlen_pad, h_kv, d)[i, cache_seqlens[i].item():] = float("nan")
+    blocked_v = blocked_k[..., :dv]
+
+    tile_scheduler_metadata, num_splits = get_mla_metadata(cache_seqlens, s_q * h_q // h_kv, h_kv)
+
+    def flash_mla():
+        return flash_mla_with_kvcache(
+            q, blocked_k, block_table, cache_seqlens, dv,
+            tile_scheduler_metadata, num_splits, causal=causal,
+        )
+
+    out_flash, lse_flash = flash_mla()
+    t = triton.testing.do_bench(flash_mla)
+    return out_flash, lse_flash, t
+
+
+@torch.inference_mode()
+def run_flash_infer(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    
+    for i in range(b):
+        blocked_k.view(b, max_seqlen_pad, h_kv, d)[i, cache_seqlens[i].item():] = float("nan")
+
+    assert d > dv, "mla with rope dim should be larger than no rope dim"
+    q_nope, q_pe = q[..., :dv].contiguous(), q[..., dv:].contiguous()
+    blocked_k_nope, blocked_k_pe = blocked_k[..., :dv].contiguous(), blocked_k[..., dv:].contiguous()
+    
+    
+    kv_indptr = [0]
+    kv_indices = []
+    for i in range(b):
+        seq_len = cache_seqlens[i]
+        assert seq_len > 0
+        num_blocks = (seq_len + block_size - 1) // block_size
+        kv_indices.extend(block_table[i, :num_blocks])
+        kv_indptr.append(kv_indptr[-1] + num_blocks)
+    for seq_len in cache_seqlens[1:]:
+        kv_indptr.append((seq_len + block_size - 1) // block_size + kv_indptr[-1])
+        
+    q_indptr = torch.arange(0, b + 1).int() * s_q
+    kv_indptr = torch.tensor(kv_indptr, dtype=torch.int32)
+    kv_indices = torch.tensor(kv_indices, dtype=torch.int32)
+
+    mla_wrapper = flashinfer.mla.BatchMLAPagedAttentionWrapper(
+        torch.empty(128 * 1024 * 1024, dtype=torch.int8),
+        backend="fa3"
+    )
+    mla_wrapper.plan(
+        q_indptr,
+        kv_indptr,
+        kv_indices,
+        cache_seqlens,
+        h_q,
+        dv,
+        d-dv,
+        block_size,
+        causal,
+        1 / math.sqrt(d),
+        q.dtype,
+        blocked_k.dtype,
+    )
+
+    def flash_infer():
+        output, lse = mla_wrapper.run(q_nope.view(-1, h_q, dv), q_pe.view(-1, h_q, d-dv), blocked_k_nope, blocked_k_pe, return_lse=True)
+        return output.view(b, -1, h_q, dv), lse.view(b, h_q, 1)
+
+    out_flash, lse_flash = flash_infer()
+    t = triton.testing.do_bench(flash_infer)
+    return out_flash, lse_flash, t
+
+
+@triton.jit
+def _mla_attn_kernel(
+    Q_nope,
+    Q_pe,
+    Kv_c_cache,
+    K_pe_cache,
+    Req_to_tokens,
+    B_seq_len,
+    O,
+    sm_scale,
+    stride_q_nope_bs,
+    stride_q_nope_h,
+    stride_q_pe_bs,
+    stride_q_pe_h,
+    stride_kv_c_bs,
+    stride_k_pe_bs,
+    stride_req_to_tokens_bs,
+    stride_o_b,
+    stride_o_h,
+    stride_o_s,
+    BLOCK_H: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    NUM_KV_SPLITS: tl.constexpr,
+    PAGE_SIZE: tl.constexpr,
+    HEAD_DIM_CKV: tl.constexpr,
+    HEAD_DIM_KPE: tl.constexpr,
+):
+    cur_batch = tl.program_id(1)
+    cur_head_id = tl.program_id(0)
+    split_kv_id = tl.program_id(2)
+
+    cur_batch_seq_len = tl.load(B_seq_len + cur_batch)
+
+    offs_d_ckv = tl.arange(0, HEAD_DIM_CKV)
+    cur_head = cur_head_id * BLOCK_H + tl.arange(0, BLOCK_H)
+    offs_q_nope = cur_batch * stride_q_nope_bs + cur_head[:, None] * stride_q_nope_h + offs_d_ckv[None, :]
+    q_nope = tl.load(Q_nope + offs_q_nope)
+
+    offs_d_kpe = tl.arange(0, HEAD_DIM_KPE)
+    offs_q_pe = cur_batch * stride_q_pe_bs + cur_head[:, None] * stride_q_pe_h + offs_d_kpe[None, :]
+    q_pe = tl.load(Q_pe + offs_q_pe)
+
+    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
+    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
+    acc = tl.zeros([BLOCK_H, HEAD_DIM_CKV], dtype=tl.float32)
+
+    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
+    split_kv_start = kv_len_per_split * split_kv_id
+    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
+
+    for start_n in range(split_kv_start, split_kv_end, BLOCK_N):
+        offs_n = start_n + tl.arange(0, BLOCK_N)
+        kv_page_number = tl.load(
+            Req_to_tokens + stride_req_to_tokens_bs * cur_batch + offs_n // PAGE_SIZE,
+            mask=offs_n < split_kv_end,
+            other=0,
+        )
+        kv_loc = kv_page_number * PAGE_SIZE + offs_n % PAGE_SIZE
+        offs_k_c = kv_loc[None, :] * stride_kv_c_bs + offs_d_ckv[:, None]
+        k_c = tl.load(Kv_c_cache + offs_k_c, mask=offs_n[None, :] < split_kv_end, other=0.0)
+
+        qk = tl.dot(q_nope, k_c.to(q_nope.dtype))
+
+        offs_k_pe = kv_loc[None, :] * stride_k_pe_bs + offs_d_kpe[:, None]
+        k_pe = tl.load(K_pe_cache + offs_k_pe, mask=offs_n[None, :] < split_kv_end, other=0.0)
+
+        qk += tl.dot(q_pe, k_pe.to(q_pe.dtype))
+        qk *= sm_scale
+
+        qk = tl.where(offs_n[None, :] < split_kv_end, qk, float("-inf"))
+
+        v_c = tl.trans(k_c)
+
+        n_e_max = tl.maximum(tl.max(qk, 1), e_max)
+        re_scale = tl.exp(e_max - n_e_max)
+        p = tl.exp(qk - n_e_max[:, None])
+        acc *= re_scale[:, None]
+        acc += tl.dot(p.to(v_c.dtype), v_c)
+
+        e_sum = e_sum * re_scale + tl.sum(p, 1)
+        e_max = n_e_max
+    offs_o = cur_batch * stride_o_b + cur_head[:, None] * stride_o_h + split_kv_id * stride_o_s + offs_d_ckv[None, :]
+    tl.store(O + offs_o, acc / e_sum[:, None])
+    offs_o_1 = cur_batch * stride_o_b + cur_head * stride_o_h + split_kv_id * stride_o_s + HEAD_DIM_CKV
+    tl.store(O + offs_o_1, e_max + tl.log(e_sum))
+
+
+def _mla_attn(
+    q_nope,
+    q_pe,
+    kv_c_cache,
+    k_pe_cache,
+    attn_logits,
+    req_to_tokens,
+    b_seq_len,
+    num_kv_splits,
+    sm_scale,
+    page_size,
+):
+    batch_size, head_num = q_nope.shape[0], q_nope.shape[1]
+    head_dim_ckv = q_nope.shape[-1]
+    head_dim_kpe = q_pe.shape[-1]
+
+    BLOCK_H = 16
+    BLOCK_N = 64
+    grid = (
+        triton.cdiv(head_num, BLOCK_H),
+        batch_size,
+        num_kv_splits,
+    )
+    _mla_attn_kernel[grid](
+        q_nope,
+        q_pe,
+        kv_c_cache,
+        k_pe_cache,
+        req_to_tokens,
+        b_seq_len,
+        attn_logits,
+        sm_scale,
+        # stride
+        q_nope.stride(0),
+        q_nope.stride(1),
+        q_pe.stride(0),
+        q_pe.stride(1),
+        kv_c_cache.stride(-2),
+        k_pe_cache.stride(-2),
+        req_to_tokens.stride(0),
+        attn_logits.stride(0),
+        attn_logits.stride(1),
+        attn_logits.stride(2),
+        BLOCK_H=BLOCK_H,
+        BLOCK_N=BLOCK_N, 
+        NUM_KV_SPLITS=num_kv_splits,
+        PAGE_SIZE=page_size,
+        HEAD_DIM_CKV=head_dim_ckv,
+        HEAD_DIM_KPE=head_dim_kpe,
+    )
+
+@triton.jit
+def _mla_softmax_reducev_kernel(
+    Logits,
+    B_seq_len,
+    O,
+    stride_l_b,
+    stride_l_h,
+    stride_l_s,
+    stride_o_b,
+    stride_o_h,
+    NUM_KV_SPLITS: tl.constexpr,
+    HEAD_DIM_CKV: tl.constexpr,
+):
+    cur_batch = tl.program_id(0)
+    cur_head = tl.program_id(1)
+    cur_batch_seq_len = tl.load(B_seq_len + cur_batch)
+
+    offs_d_ckv = tl.arange(0, HEAD_DIM_CKV)
+
+    e_sum = 0.0
+    e_max = -float("inf")
+    acc = tl.zeros([HEAD_DIM_CKV], dtype=tl.float32)
+
+    offs_l = cur_batch * stride_l_b + cur_head * stride_l_h + offs_d_ckv
+    offs_l_1 = cur_batch * stride_l_b + cur_head * stride_l_h + HEAD_DIM_CKV
+
+    for split_kv_id in range(0, NUM_KV_SPLITS):
+        kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
+        split_kv_start = kv_len_per_split * split_kv_id
+        split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
+
+        if split_kv_end > split_kv_start:
+            logits = tl.load(Logits + offs_l + split_kv_id * stride_l_s)
+            logits_1 = tl.load(Logits + offs_l_1 + split_kv_id * stride_l_s)
+
+            n_e_max = tl.maximum(logits_1, e_max)
+            old_scale = tl.exp(e_max - n_e_max)
+            acc *= old_scale
+            exp_logic = tl.exp(logits_1 - n_e_max)
+            acc += exp_logic * logits
+
+            e_sum = e_sum * old_scale + exp_logic
+            e_max = n_e_max
+    
+    tl.store(
+        O + cur_batch * stride_o_b + cur_head * stride_o_h + offs_d_ckv,
+        acc / e_sum,
+    )
+
+
+def _mla_softmax_reducev(
+    logits,
+    o,
+    b_seq_len,
+    num_kv_splits,
+):
+    batch_size, head_num, head_dim_ckv = o.shape[0], o.shape[1], o.shape[2]
+    grid = (batch_size, head_num)
+    _mla_softmax_reducev_kernel[grid](
+        logits,
+        b_seq_len,
+        o,
+        logits.stride(0),
+        logits.stride(1),
+        logits.stride(2),
+        o.stride(0),
+        o.stride(1),
+        NUM_KV_SPLITS=num_kv_splits,
+        HEAD_DIM_CKV=head_dim_ckv,
+        num_warps=4,
+        num_stages=2,
+    )
+
+def mla_decode_triton(
+    q_nope,
+    q_pe,
+    kv_c_cache,
+    k_pe_cache,
+    o,
+    req_to_tokens,
+    b_seq_len,
+    attn_logits,
+    num_kv_splits,
+    sm_scale,
+    page_size,
+):
+    assert num_kv_splits == attn_logits.shape[2]
+    _mla_attn(
+        q_nope,
+        q_pe,
+        kv_c_cache,
+        k_pe_cache,
+        attn_logits,
+        req_to_tokens,
+        b_seq_len,
+        num_kv_splits,
+        sm_scale,
+        page_size,
+    )
+    _mla_softmax_reducev(
+        attn_logits,
+        o,
+        b_seq_len,
+        num_kv_splits,
+    )
+    
+
+@torch.inference_mode()
+def run_flash_mla_triton(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    
+    for i in range(b):
+        blocked_k.view(b, max_seqlen_pad, h_kv, d)[i, cache_seqlens[i].item():] = float("nan")
+    blocked_v = blocked_k[..., :dv]
+    
+    assert d > dv, "mla with rope dim should be larger than no rope dim"
+    q_nope, q_pe = q[..., :dv].contiguous(), q[..., dv:].contiguous()
+    blocked_k_nope, blocked_k_pe = blocked_k[..., :dv].contiguous(), blocked_k[..., dv:].contiguous()
+
+    def flash_mla_triton():
+        num_kv_splits = 32
+        o = torch.empty([b * s_q, h_q, dv])
+        attn_logits = torch.empty([b * s_q, h_q, num_kv_splits, dv + 1])
+        mla_decode_triton(q_nope.view(-1, h_q, dv), q_pe.view(-1, h_q, d-dv), blocked_k_nope.view(-1, dv), blocked_k_pe.view(-1, d-dv), o, block_table, cache_seqlens, attn_logits, num_kv_splits, 1 / math.sqrt(d), block_size)
+        return o.view([b, s_q, h_q, dv])
+
+    out_flash = flash_mla_triton()
+    t = triton.testing.do_bench(flash_mla_triton)
+    return out_flash, None, t
+
+
+FUNC_TABLE = {
+    "torch": run_torch_mla,
+    "flash_mla": run_flash_mla,
+    "flash_infer": run_flash_infer,
+    "flash_mla_triton": run_flash_mla_triton,
+}
+    
+def compare_ab(baseline, target, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    print(f"comparing {baseline} vs {target}: {b=}, {s_q=}, mean_seqlens={cache_seqlens.float().mean()}, {h_q=}, {h_kv=}, {d=}, {dv=}, {causal=}, {dtype=}")
+    device = torch.device("cuda:0")
+    torch.set_default_dtype(dtype)
+    torch.set_default_device(device)
+    torch.cuda.set_device(device)
+    torch.manual_seed(0)
+    random.seed(0)
+    assert baseline in FUNC_TABLE
+    assert target in FUNC_TABLE
+    baseline_func = FUNC_TABLE[baseline]
+    target_func = FUNC_TABLE[target]
+    
+    total_seqlens = cache_seqlens.sum().item()
+    mean_seqlens = cache_seqlens.float().mean().int().item()
+    max_seqlen = cache_seqlens.max().item()
+    max_seqlen_pad = triton.cdiv(max_seqlen, 256) * 256
+    # print(f"{total_seqlens=}, {mean_seqlens=}, {max_seqlen=}")
+
+    q = torch.randn(b, s_q, h_q, d)
+    block_size = 64
+    block_table = torch.arange(b * max_seqlen_pad // block_size, dtype=torch.int32).view(b, max_seqlen_pad // block_size)
+    blocked_k = torch.randn(block_table.numel(), block_size, h_kv, d)
+    
+    out_a, lse_a, perf_a = baseline_func(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype)
+    out_b, lse_b, perf_b = target_func(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype)
+    
+    torch.testing.assert_close(out_b.float(), out_a.float(), atol=1e-2, rtol=1e-2), "out"
+    if target not in ["flash_infer", "flash_mla_triton"]:
+        # flash_infer has a different lse return value
+        # flash_mla_triton doesn't return lse
+        torch.testing.assert_close(lse_b.float(), lse_a.float(), atol=1e-2, rtol=1e-2), "lse"
+
+    FLOPS = s_q * total_seqlens * h_q * (d + dv) * 2
+    bytes = (total_seqlens * h_kv * d + b * s_q * h_q * d + b * s_q * h_q * dv) * (torch.finfo(dtype).bits // 8)
+    print(f"perf {baseline}: {perf_a:.3f} ms, {FLOPS / 10 ** 9 / perf_a:.0f} TFLOPS, {bytes / 10 ** 6 / perf_a:.0f} GB/s")
+    print(f"perf {target}: {perf_b:.3f} ms, {FLOPS / 10 ** 9 / perf_b:.0f} TFLOPS, {bytes / 10 ** 6 / perf_b:.0f} GB/s")
+
+
+def compare_a(target, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype):
+    print(f"{target}: {b=}, {s_q=}, mean_seqlens={cache_seqlens.float().mean()}, {h_q=}, {h_kv=}, {d=}, {dv=}, {causal=}, {dtype=}")
+    torch.set_default_dtype(dtype)
+    device = torch.device("cuda:0")
+    torch.set_default_device(device)
+    torch.cuda.set_device(device)
+    torch.manual_seed(0)
+    random.seed(0)
+    assert target in FUNC_TABLE
+    target_func = FUNC_TABLE[target]
+    
+    total_seqlens = cache_seqlens.sum().item()
+    mean_seqlens = cache_seqlens.float().mean().int().item()
+    max_seqlen = cache_seqlens.max().item()
+    max_seqlen_pad = triton.cdiv(max_seqlen, 256) * 256
+    # print(f"{total_seqlens=}, {mean_seqlens=}, {max_seqlen=}")
+
+    q = torch.randn(b, s_q, h_q, d)
+    block_size = 64
+    block_table = torch.arange(b * max_seqlen_pad // block_size, dtype=torch.int32).view(b, max_seqlen_pad // block_size)
+    blocked_k = torch.randn(block_table.numel(), block_size, h_kv, d)
+    
+    out_b, lse_b, perf_b = target_func(q, block_table, blocked_k, max_seqlen_pad, block_size, b, s_q, cache_seqlens, h_q, h_kv, d, dv, causal, dtype)
+
+    FLOPS = s_q * total_seqlens * h_q * (d + dv) * 2
+    bytes = (total_seqlens * h_kv * d + b * s_q * h_q * d + b * s_q * h_q * dv) * (torch.finfo(dtype).bits // 8)
+    print(f"perf {target}: {perf_b:.3f} ms, {FLOPS / 10 ** 9 / perf_b:.0f} TFLOPS, {bytes / 10 ** 6 / perf_b:.0f} GB/s")
+    return bytes / 10 ** 6 / perf_b
+
+
+available_targets = [
+    "torch",
+    "flash_mla",
+    "flash_infer",
+    "flash_mla_triton",
+]
+
+shape_configs = [
+    {"b": batch, "s_q": 1, "cache_seqlens": torch.tensor([seqlen + 2 * i for i in range(batch)], dtype=torch.int32, device="cuda"), "h_q": head, "h_kv": 1, "d": 512+64, "dv": 512, "causal": True, "dtype": torch.bfloat16}
+    for batch in [128] for seqlen in [1024, 2048, 4096, 8192, 8192*2, 8192*4] for head in [128]
+]
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--baseline", type=str, default="torch")
+    parser.add_argument("--target", type=str, default="flash_mla")
+    parser.add_argument("--all", action="store_true")
+    parser.add_argument("--one", action="store_true")
+    parser.add_argument("--compare", action="store_true")
+    args = parser.parse_args()
+    return args
+
+    
+if __name__ == "__main__":
+    args = get_args()
+    with open("all_perf.csv", "w") as fout:
+        fout.write("name,batch,seqlen,head,bw\n")
+        for shape in shape_configs:
+            if args.all:
+                for target in available_targets:
+                    perf = compare_a(target, shape["b"], shape["s_q"], shape["cache_seqlens"], shape["h_q"], shape["h_kv"], shape["d"], shape["dv"], shape["causal"], shape["dtype"])
+                    fout.write(f'{target},{shape["b"]},{shape["cache_seqlens"].float().mean().cpu().item():.0f},{shape["h_q"]},{perf:.0f}\n')
+            elif args.compare:
+                compare_ab(args.baseline, args.target, shape["b"], shape["s_q"], shape["cache_seqlens"], shape["h_q"], shape["h_kv"], shape["d"], shape["dv"], shape["causal"], shape["dtype"])
+            elif args.one:
+                compare_a(args.target, shape["b"], shape["s_q"], shape["cache_seqlens"], shape["h_q"], shape["h_kv"], shape["d"], shape["dv"], shape["causal"], shape["dtype"])
\ No newline at end of file

benchmark/visualize.py

+import matplotlib.pyplot as plt
+import pandas as pd
+
+file_path = 'all_perf.csv'
+
+df = pd.read_csv(file_path)
+
+names = df['name'].unique()
+
+for name in names:
+    subset = df[df['name'] == name]
+    plt.plot(subset['seqlen'], subset['bw'], label=name)
+
+plt.title('bandwidth')
+plt.xlabel('seqlen')
+plt.ylabel('bw (GB/s)')
+plt.legend()
+
+plt.savefig('bandwidth_vs_seqlen.png')
\ No newline at end of file