Apache TVM 是一个端到端的深度学习编译框架，适用于 CPU、GPU 和各种机器学习加速芯片。更多 TVM 中文文档可访问 → https://tvm.hyper.ai/
作者：Tianqi Chen
下面介绍如何在 TVM 中进行递归计算（神经网络中的典型模式）。
from __future__ import absolute_import, print_functionimport tvmimport tvm.testingfrom tvm import teimport numpy as npTVM 用线性算子来描述符号循环。以下线性算子计算 X 列上的累积和。
线性在张量的最高维度上进行。s_state 是描述线性转换状态的占位符。s_init 描述如何初始化前 k 个时间步长，其第一个维度为 1，描述了如何初始化第一个时间步长的状态。
s_update 描述了如何更新时间步长 t 处的值，更新的值可通过状态占位符引用上一个时间步长的值。注意在当前或之后的时间步长引用 s_state 是无效的。
线性包含状态占位符、初始值和更新描述。推荐列出线性单元的输入，线性的结果是一个张量—— s_state 在时域更新后的结果。
m = te.var("m")n = te.var("n")X = te.placeholder((m, n), name="X")s_state = te.placeholder((m, n))s_init = te.compute((1, n), lambda _, i: X[0, i])s_update = te.compute((m, n), lambda t, i: s_state[t - 1, i] + X[t, i])s_scan = tvm.te.scan(s_init, s_update, s_state, inputs=[X])通过分别调度 update 和 init 部分来调度线性体。注意，调度更新部分的第一个迭代维度是无效的。要在时间迭代上拆分，用户可以在 scan_op.scan_axis 上进行调度。
s = te.create_schedule(s_scan.op)num_thread = 256block_x = te.thread_axis("blockIdx.x")thread_x = te.thread_axis("threadIdx.x")xo, xi = s[s_init].split(s_init.op.axis[1], factor=num_thread)s[s_init].bind(xo, block_x)s[s_init].bind(xi, thread_x)xo, xi = s[s_update].split(s_update.op.axis[1], factor=num_thread)s[s_update].bind(xo, block_x)s[s_update].bind(xi, thread_x)print(tvm.lower(s, [X, s_scan], simple_mode=True))输出结果：
@main = primfn(X_1: handle, scan_1: handle) -> () attr = {"from_legacy_te_schedule": True, "global_symbol": "main", "tir.noalias": True} buffers = {X: Buffer(X_2: Pointer(float32), float32, [(stride: int32*m: int32)], [], type="auto"), scan: Buffer(scan_2: Pointer(float32), float32, [(stride_1: int32*m)], [], type="auto")} buffer_map = {X_1: X, scan_1: scan} preflattened_buffer_map = {X_1: X_3: Buffer(X_2, float32, [m, n: int32], [stride, stride_2: int32], type="auto"), scan_1: scan_3: Buffer(scan_2, float32, [m, n], [stride_1, stride_3: int32], type="auto")} { attr [IterVar(blockIdx.x: int32, (nullptr), "ThreadIndex", "blockIdx.x")] "thread_extent" = floordiv((n + 255), 256); attr [IterVar(threadIdx.x: int32, (nullptr), "ThreadIndex", "threadIdx.x")] "thread_extent" = 256; if @tir.likely((((blockIdx.x*256) + threadIdx.x) 可以像其他 TVM 内核一样构建线性内核，这里用 numpy 来验证结果的正确性。
fscan = tvm.build(s, [X, s_scan], "cuda", name="myscan")dev = tvm.cuda(0)n = 1024m = 10a_np = np.random.uniform(size=(m, n)).astype(s_scan.dtype)a = tvm.nd.array(a_np, dev)b = tvm.nd.array(np.zeros((m, n), dtype=s_scan.dtype), dev)fscan(a, b)tvm.testing.assert_allclose(b.numpy(), np.cumsum(a_np, axis=0))以上示例用 s_update 中的一个张量计算阶段描述了线性单元，可以在线性单元中使用多个张量级。
以下代码演示了有两个阶段操作的线性单元中的线性过程：
m = te.var("m")n = te.var("n")X = te.placeholder((m, n), name="X")s_state = te.placeholder((m, n))s_init = te.compute((1, n), lambda _, i: X[0, i])s_update_s1 = te.compute((m, n), lambda t, i: s_state[t - 1, i] * 2, name="s1")s_update_s2 = te.compute((m, n), lambda t, i: s_update_s1[t, i] + X[t, i], name="s2")s_scan = tvm.te.scan(s_init, s_update_s2, s_state, inputs=[X])这些中间张量可以正常调度。为了确保正确性，TVM 创建了一个组约束——禁用线性循环之外的 compute_at 位置的线性体。
s = te.create_schedule(s_scan.op)xo, xi = s[s_update_s2].split(s_update_s2.op.axis[1], factor=32)s[s_update_s1].compute_at(s[s_update_s2], xo)输出结果：
print(tvm.lower(s, [X, s_scan], simple_mode=True))@main = primfn(X_1: handle, scan_1: handle) -> () attr = {"from_legacy_te_schedule": True, "global_symbol": "main", "tir.noalias": True} buffers = {X: Buffer(X_2: Pointer(float32), float32, [(stride: int32*m: int32)], [], type="auto"), scan: Buffer(scan_2: Pointer(float32), float32, [(stride_1: int32*m)], [], type="auto")} buffer_map = {X_1: X, scan_1: scan} preflattened_buffer_map = {X_1: X_3: Buffer(X_2, float32, [m, n: int32], [stride, stride_2: int32], type="auto"), scan_1: scan_3: Buffer(scan_2, float32, [m, n], [stride_1, stride_3: int32], type="auto")} { allocate(s1: Pointer(global float32), float32, [32]), storage_scope = global { for (i: int32, 0, n) { scan[(i*stride_3)] = X[(i*stride_2)] } for (scan.idx: int32, 0, (m - 1)) { for (i.outer: int32, 0, floordiv((n + 31), 32)) { for (i_1: int32, 0, 32) { if @tir.likely((((i.outer*32) + i_1) 对于像 RNN 这样的复杂应用，需要多个递归状态。线性支持多个递归状态，以下示例演示如何构建具有两种状态的递归。
m = te.var("m")n = te.var("n")l = te.var("l")X = te.placeholder((m, n), name="X")s_state1 = te.placeholder((m, n))s_state2 = te.placeholder((m, l))s_init1 = te.compute((1, n), lambda _, i: X[0, i])s_init2 = te.compute((1, l), lambda _, i: 0.0)s_update1 = te.compute((m, n), lambda t, i: s_state1[t - 1, i] + X[t, i])s_update2 = te.compute((m, l), lambda t, i: s_state2[t - 1, i] + s_state1[t - 1, 0])s_scan1, s_scan2 = tvm.te.scan( [s_init1, s_init2], [s_update1, s_update2], [s_state1, s_state2], inputs=[X])s = te.create_schedule(s_scan1.op)print(tvm.lower(s, [X, s_scan1, s_scan2], simple_mode=True))输出结果：
@main = primfn(X_1: handle, scan_2: handle, scan_3: handle) -> () attr = {"from_legacy_te_schedule": True, "global_symbol": "main", "tir.noalias": True} buffers = {X: Buffer(X_2: Pointer(float32), float32, [(stride: int32*m: int32)], [], type="auto"), scan: Buffer(scan_4: Pointer(float32), float32, [(stride_1: int32*m)], [], type="auto"), scan_1: Buffer(scan_5: Pointer(float32), float32, [(stride_2: int32*m)], [], type="auto")} buffer_map = {X_1: X, scan_2: scan, scan_3: scan_1} preflattened_buffer_map = {X_1: X_3: Buffer(X_2, float32, [m, n: int32], [stride, stride_3: int32], type="auto"), scan_2: scan_6: Buffer(scan_4, float32, [m, n], [stride_1, stride_4: int32], type="auto"), scan_3: scan_7: Buffer(scan_5, float32, [m, l: int32], [stride_2, stride_5: int32], type="auto")} { for (i: int32, 0, n) { scan[(i*stride_4)] = X[(i*stride_3)] } for (i_1: int32, 0, l) { scan_1[(i_1*stride_5)] = 0f32 } for (scan.idx: int32, 0, (m - 1)) { for (i_2: int32, 0, n) { let cse_var_1: int32 = (scan.idx + 1) scan[((cse_var_1*stride_1) + (i_2*stride_4))] = (scan[((scan.idx*stride_1) + (i_2*stride_4))] + X[((cse_var_1*stride) + (i_2*stride_3))]) } for (i_3: int32, 0, l) { scan_1[(((scan.idx + 1)*stride_2) + (i_3*stride_5))] = (scan_1[((scan.idx*stride_2) + (i_3*stride_5))] + scan[(scan.idx*stride_1)]) } }}本教程演示了如何使用线性原语。
用 init 和 update 描述线性。
将线性单元当作正常 schedule 进行调度。
对于复杂的工作负载，在线性单元中使用多个状态和步骤。
