[TOPI][Testing] Enable conv2d NHWC fp16 topi testing for arm_cpu

This commit adds fp16 test cases to the conv2d NHWC TOPI schedules for `arm_cpu`.
Following the example of apache#8529, the numpy reference conv2d output is computed in fp32 instead of fp16, while the absolute tolerance varies for each test case according to the size of the summed axis and the output's largest element.

Author: Anndrey24

tests/python/topi/test_topi_conv2d_nhwc.py

@@ -53,7 +53,7 @@
         topi.arm_cpu.schedule_conv2d_nhwc_spatial_pack,
     ),
     (
-        "llvm --device arm_cpu --mtriple aarch64-linux-gnu -mattr=+v8.2a",
+        "llvm --device arm_cpu --mtriple aarch64-linux-gnu -mattr=+v8.2a,+fullfp16",
         topi.arm_cpu.compute_conv2d_NHWC_hybrid,
         topi.arm_cpu.schedule_conv2d_NHWC_hybrid,
     ),
@@ -64,7 +64,7 @@
     ),
 )
 
-dtype = tvm.testing.parameter("float32")
+dtype = tvm.testing.parameter("float16", "float32")
 
 batch, in_channel, in_size, num_filter, kernel, stride, padding, dilation = tvm.testing.parameters(
     # Pad M, N, K
@@ -104,14 +104,36 @@ def ref_data(dtype, batch, in_channel, in_size, num_filter, kernel, stride, padd
     a_shape = (batch, in_height, in_width, in_channel)
     w_shape = (kernel, kernel, in_channel, num_filter)
 
+    np.random.seed(0)
     a_np = np.random.uniform(size=a_shape).astype(dtype)
     w_np = np.random.uniform(size=w_shape).astype(dtype)
     dw_np = tvm.topi.testing.dilate_python(w_np, (dilation, dilation, 1, 1))
-    b_np = tvm.topi.testing.conv2d_nhwc_python(a_np, dw_np, stride, padding)
+
+    # scipy.signal.convolve2d does not support float16 data types,
+    # and the python fallback would be too slow for general use.
+    conv_dtype = "float32" if dtype == "float16" else dtype
+    b_np = tvm.topi.testing.conv2d_nhwc_python(
+        a_np.astype(conv_dtype), dw_np.astype(conv_dtype), stride, padding
+    ).astype(dtype)
     return a_np, w_np, b_np
 
 
-def test_conv2d_nhwc_gemm_fp32(device, ref_data, dtype, stride, padding, dilation):
+def get_tolerance(dtype, w_np, b_np):
+    if dtype == "float16":
+        # A summation in float16 with a single accumulator very
+        # quickly runs into large rounding errors.
+        # This tolerance is necessary to ensure no false negatives,
+        # but it may introduce false positives, depending on schedule behaviour.
+        num_values_summed = w_np.shape[0] * w_np.shape[1] * w_np.shape[2]
+        next_float_gap_size = np.nextafter(b_np.max(), np.inf, dtype=b_np.dtype) - b_np.max()
+        tol = {"rtol": 1e-5, "atol": num_values_summed * next_float_gap_size / 2}
+    else:
+        tol = {"rtol": 1e-5, "atol": 1e-7}
+
+    return tol
+
+
+def test_conv2d_nhwc_gemm(device, ref_data, dtype, stride, padding, dilation):
     a_np, w_np, b_np = ref_data
 
     A = te.placeholder(a_np.shape, name="A", dtype=dtype)
@@ -137,7 +159,8 @@ def test_conv2d_nhwc_gemm_fp32(device, ref_data, dtype, stride, padding, dilatio
             return
 
         func(a, w, b)
-    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=1e-5)
+    tol = get_tolerance(dtype, w_np, b_np)
+    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=tol["rtol"], atol=tol["atol"])
 
 
 def test_conv2d_nhwc_hwio(target, dev, ref_data, dtype, stride, padding, dilation):
@@ -155,7 +178,8 @@ def test_conv2d_nhwc_hwio(target, dev, ref_data, dtype, stride, padding, dilatio
     b = tvm.nd.array(np.zeros(get_const_tuple(B.shape), dtype=B.dtype), dev)
     func = tvm.build(s, [A, W, B], target)
     func(a, w, b)
-    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=1e-5)
+    tol = get_tolerance(dtype, w_np, b_np)
+    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=tol["rtol"], atol=tol["atol"])
 
 
 def test_conv2d_nhwc_ohwi(ref_data, dtype, stride, padding, dilation):
@@ -184,7 +208,8 @@ def test_conv2d_nhwc_ohwi(ref_data, dtype, stride, padding, dilation):
     b = tvm.nd.array(np.zeros(get_const_tuple(B.shape), dtype=B.dtype), dev)
     func = tvm.build(s, [A, W, B], target)
     func(a, w, b)
-    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=1e-5)
+    tol = get_tolerance(dtype, w_np_hwio, b_np)
+    tvm.testing.assert_allclose(b.numpy(), b_np, rtol=tol["rtol"], atol=tol["atol"])
 
 
 if __name__ == "__main__":