[fp8] add fp8 linear (#5967)

* [fp8] add fp8 linear

* [test] fix fp8 linear test condition

* [test] fix fp8 linear test condition

* [test] fix fp8 linear test condition

colossalai/quantization/fp8.py

@@ -1,4 +1,4 @@
-from typing import Any
+from typing import Any, Optional
 
 import numpy as np
 import torch
@@ -415,3 +415,62 @@ def gather_fp8(output_list, input_, group=None, fp8_format="e5m2"):
         output = tensor_list[i].view(fp8_type)
         scale = scale_list[i]
         output_list[i].copy_(cast_from_fp8(output, scale, input_type))
+
+
+class _LinearFp8(torch.autograd.Function):
+    @staticmethod
+    def forward(
+        ctx: Any,
+        x: torch.Tensor,
+        w: torch.Tensor,
+        bias: Optional[torch.Tensor],
+    ) -> Any:
+        assert (
+            x.dtype in (torch.bfloat16, torch.float16) and x.dtype == w.dtype
+        ), "Only float16 and bfloat16 are allowed."
+        if bias is not None:
+            assert bias.dtype == x.dtype, "Bias should have the same dtype as input."
+        # ensure x and w are row-major
+        assert x.is_contiguous() and w.is_contiguous(), "Input and weight should be contiguous."
+        ctx.x_shape = x.shape
+        ctx.has_bias = bias is not None
+        ctx.out_dtype = x.dtype
+        x = x.reshape(-1, x.shape[-1])
+
+        x_fp8, inv_scale_x = cast_to_fp8(x, fp8_format="e4m3")
+        w_fp8, inv_scale_w = cast_to_fp8(w, fp8_format="e4m3")
+        ctx.x_fp8 = x_fp8
+        ctx.w_fp8_t = w_fp8.t()
+        ctx.inv_scale_x = inv_scale_x
+        ctx.inv_scale_w = inv_scale_w
+        out = torch._scaled_mm(
+            x_fp8, ctx.w_fp8_t, bias=bias, out_dtype=ctx.out_dtype, scale_a=inv_scale_x, scale_b=inv_scale_w
+        )[0]
+        return out.reshape(*ctx.x_shape[:-1], w.shape[0])
+
+    @staticmethod
+    def backward(ctx: Any, out_grad) -> Any:
+        out_grad = out_grad.reshape(-1, out_grad.shape[-1])
+        out_grad_fp8, out_grad_scale = cast_to_fp8(out_grad, fp8_format="e5m2")
+        x_grad = torch._scaled_mm(
+            out_grad_fp8,
+            ctx.w_fp8_t.contiguous().t(),
+            out_dtype=ctx.out_dtype,
+            scale_a=out_grad_scale,
+            scale_b=ctx.inv_scale_w,
+        )[0]
+        w_grad = torch._scaled_mm(
+            out_grad_fp8.t().contiguous(),
+            ctx.x_fp8.t().contiguous().t(),
+            out_dtype=ctx.out_dtype,
+            scale_a=out_grad_scale,
+            scale_b=ctx.inv_scale_x,
+        )[0]
+        bias_grad = None
+        if ctx.has_bias:
+            bias_grad = out_grad.sum(0)
+        return x_grad.reshape(ctx.x_shape), w_grad, bias_grad
+
+
+def linear_fp8(x: torch.Tensor, w: torch.Tensor, bias: Optional[torch.Tensor] = None) -> torch.Tensor:
+    return _LinearFp8.apply(x, w, bias)