Use better exponent rounding in Triton MX4 quantize kernel

Summary:
As noted in [this doc](https://docs.google.com/document/d/156Du0hBRH6umG_i-OrYC574XhpQMUU5SJYG0RTS2tTg/edit#heading=h.akfcp7xpg8cr), using a ceiling round for scale calculation does a better job of not truncating some mantissa bits. This diff switches triton's floor rounding to ceil rounding.

Note that currently mx4_test doesnt pass as the cuda kernel now has different behavior than triton. Once we rebase this diff onto a similar change to the cuda kernel, we should see exact matching outputs again.

Differential Revision: D59527463

Reviewed By: jianyuh

fbgemm_gpu/fbgemm_gpu/triton/quantize.py

@@ -77,14 +77,15 @@ def _kernel_quantize_mx4(
     MAX_FP32_MANTISSA_BITS: tl.constexpr = 24  # type: ignore[Incompatible variable type]
     IMPLIED_1_BIT: tl.constexpr = 1 << 23  # type: ignore[Incompatible variable type]
     OVERFLOW_THRESHOLD: tl.constexpr = 4  # type: ignore[Incompatible variable type]
+    FP32_MIN_NORMAL: tl.constexpr = 2 ** (-126)  # type: ignore[Incompatible variable type]
 
     # First we need to compute shared exponent.
     for _k in range(0, tl.cdiv(K, BLOCK_SIZE)):
         # Load a block of values.
         a = tl.load(
             A + pid * stride_am + k_offset * stride_ak,
             mask=k_offset < K,
-            other=-float("inf"),
+            other=0,
         )
 
         # Scaling step
@@ -94,13 +95,15 @@ def _kernel_quantize_mx4(
         a_groups = tl.reshape(a, [BLOCK_SIZE // GROUP_SIZE, GROUP_SIZE])
         # Compute the shared exponent of each group.
         group_max = tl.max(tl.abs(a_groups), axis=1)
-        # Convert max to exponent via bit operations.
-        group_exp = group_max.to(tl.int32, bitcast=True) & FP32_EXP_MASK
-        group_exp = group_exp >> FP32_EXP_OFFSET
+        # Prevent infinite values in log.
+        group_max = tl.where(group_max == 0, FP32_MIN_NORMAL, group_max)
+        # Convert max to exponent via direct log computation and ceiling
+        # rounding to minimize errors.
+        group_exp = tl.ceil(tl.log2(group_max))
         # Subtract largest exponent in target datatype and remove bias.
-        group_exp = group_exp - 2 - FP32_EXP_BIAS
-        # Clamp to valid int8 range.
-        group_exp = tl.maximum(group_exp, -127)
+        group_exp = group_exp - 2
+        # Make sure exponent is in valid range.
+        group_exp = tl.clamp(group_exp, -127, 125)
 
         # Next we scale A in preparation for quantization.
         scale = tl.exp2(group_exp.to(tl.float64)).to(tl.float32)
@@ -113,10 +116,9 @@ def _kernel_quantize_mx4(
 
         # We're done with group_exp now so we can write it out.
         # We readd fp32_exp_bias for compatibility with cuda dequant.
-        group_exp = group_exp.to(tl.int8)
         tl.store(
             shared_exp + pid * stride_exp_m + stride_exp_k * group_offset,
-            group_exp + FP32_EXP_BIAS,
+            (group_exp + FP32_EXP_BIAS).to(tl.int8),
             mask=group_offset < K // GROUP_SIZE,
         )
 
@@ -228,11 +230,12 @@ def triton_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
     # We do this by finding the power of two that is closest to
     # the sqrt of the number of elements.
     num_threads = int(2 ** round(math.log2(math.sqrt(a.numel()))))
-    # Make sure that num_threads is a multiple of group_size.
-    num_threads = (num_threads // group_size) * group_size
-    if num_threads == 0:
-        num_threads = a.numel() // group_size
-    a = a.view(num_threads, -1)
+    # Make sure that the number of elements per row is a multiple of group_size.
+    K = a.numel() // num_threads
+    K = (K // group_size) * group_size
+    if K == 0:
+        K = group_size
+    a = a.view(-1, K)
     M, K = a.shape
     # If K is less than group_size, we compute a single group per row.
     if K < group_size:
@@ -382,19 +385,21 @@ def triton_dequantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor
     # View a as 2D for simplicity.
     orig_shape = a.shape
     # Unravel packed inputs from shared exponents.
-    a = a.view(-1, (group_size // 2) + 1)
+    packed_group_size = group_size // 2
+    a = a.view(-1, packed_group_size + 1)
     packed_input = a[:, :-1]
     shared_exp = a[:, -1:]
     # Find a shape that distributes work evenly over threads.
     # We do this by finding the power of two that is closest to
     # the sqrt of the number of elements.
     num_threads = int(2 ** round(math.log2(math.sqrt(packed_input.numel()))))
-    # Make sure that num_threads is a multiple of group_size.
-    num_threads = (num_threads // group_size) * group_size
-    if num_threads == 0:
-        num_threads = packed_input.numel() // group_size
-    packed_input = packed_input.reshape(num_threads, -1)
-    shared_exp = shared_exp.reshape(num_threads, -1)
+    # Make sure that the number of elements per row is a multiple of packed group_size.
+    K = packed_input.numel() // num_threads
+    K = (K // packed_group_size) * packed_group_size
+    if K == 0:
+        K = packed_group_size
+    packed_input = packed_input.reshape(-1, K)
+    shared_exp = shared_exp.reshape(-1, K // packed_group_size)
     M, K_2 = packed_input.shape
 
     # Use a lookup table to convert

fbgemm_gpu/fbgemm_gpu/triton/quantize_ref.py

@@ -46,11 +46,11 @@ def py_quantize_mx4(a: torch.Tensor, group_size: int = 32) -> torch.Tensor:
     # Convert max into an intger exponent.
     # Note this can be more efficient by just shifting and masking exp bits.
     # We can even use those directly.
-    shared_exp = torch.floor(torch.log2(shared_exp))
+    shared_exp = torch.ceil(torch.log2(shared_exp))
     # Offset exponent by largest exponent in target datatype.
     shared_exp = shared_exp - 2
     # Restrict to range expressible as int8.
-    shared_exp = torch.clamp(shared_exp, min=-127, max=127)
+    shared_exp = torch.clamp(shared_exp, min=-127, max=125)
     # Convert exponent to scale and apply to input.
     # Need to do this calculation on cpu for accuracy.
     _shared_exp = shared_exp.cpu()