Quantized fast hadamard transform (#5284)

Summary:
Pull Request resolved: #5284

Demonstrate that we can calculate a quantized fast hadamard transform with integer math only, except for adjusting the scale of the result. (Not sure if there is a reason to actually commit this -- do we have a use case for quantized FHT on CPU?)

Reviewed By: kimishpatel

Differential Revision: D60866280

fbshipit-source-id: ba114f10c544b5d04c19f7d94a32043c237a2c65

Author: swolchok

extension/llm/custom_ops/spinquant/fast_hadamard_transform.cpp

@@ -0,0 +1,68 @@
+/*
+ * Copyright (c) Meta Platforms, Inc. and affiliates.
+ * All rights reserved.
+ *
+ * This source code is licensed under the BSD-style license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#include "fast_hadamard_transform.h"
+
+#include <algorithm>
+
+namespace executorch {
+void fast_hadamard_transform_symmetric_quantized_s16(
+    int16_t* vec,
+    int log2_vec_size) {
+  if (log2_vec_size == 0) {
+    return;
+  }
+
+  const int vec_size = 1 << log2_vec_size;
+  // We perform log2_vec_size rounds where each round's maximum output
+  // is at most double the maximum input, so we can at most multiply
+  // the maximum input by vec_size. Performing intermediate arithmetic
+  // in 32-bit precision should prevent overflow, since 16 +
+  // log2_vec_size should be much less than 32.
+  auto tmp = std::make_unique<int32_t[]>(vec_size);
+  std::copy(vec, vec + vec_size, tmp.get());
+
+  // Per the function-level comment in the header, we can ignore the
+  // quantization scale, so we just delegate to the usual unnormalized
+  // implementation.
+  // NOTE: if we need this to be fast on CPU, we can use FFHT to
+  // generate fht_uint32 similar to fht_float.
+  internal::fast_hadamard_transform_unnormalized_simple_impl(
+      tmp.get(), log2_vec_size);
+
+  // Normalization step: divide by sqrt(1 << log2_vec_size). Similar
+  // to fast_sqrt, if N is even, then the maximum-precision way
+  // to do this is right-shift by log2_vec_size / 2. If N is odd, we
+  // still do the right-shift, and then we have an extra division by
+  // sqrt(2) that we perform by making use of a sufficiently accurate
+  // rational approximation. (Our initial idea was to divide by sqrt(2)
+  // by adjusting the quantization scale, but that would cause this
+  // function to tend to increase the magnitude of the elements of
+  // vec, which would resulting in clipping and therefore accuracy
+  // loss, especially compounded over 30+ transformer layers.)
+  const int log2_sqrt_vec_size = log2_vec_size / 2;
+  constexpr int32_t qmin = -(1 << 15) + 1;
+  constexpr int32_t qmax = -qmin;
+  if (log2_vec_size % 2 != 0) {
+    // 408 / 577 - 1.0 / sqrt(2) ~= 1.062e-0.6, which should be close enough.
+    static const int32_t inv_sqrt_2_numerator = 408;
+    static const int32_t inv_sqrt_2_denominator = 577;
+    for (int ii = 0; ii < vec_size; ++ii) {
+      const auto val_over_sqrt_vec_size =
+          (tmp[ii] * inv_sqrt_2_numerator / inv_sqrt_2_denominator) >>
+          log2_sqrt_vec_size;
+      vec[ii] = std::clamp(val_over_sqrt_vec_size, qmin, qmax);
+    }
+  } else {
+    for (int ii = 0; ii < vec_size; ++ii) {
+      vec[ii] = std::clamp(tmp[ii] >> log2_sqrt_vec_size, qmin, qmax);
+    }
+  }
+  return;
+}
+} // namespace executorch

extension/llm/custom_ops/spinquant/fast_hadamard_transform.h

@@ -12,6 +12,7 @@
 #include <cassert>
 #include <cmath>
 #include <cstdint>
+#include <memory>
 
 #include "fast_hadamard_transform_special.h"
 
@@ -41,7 +42,9 @@ void normalize_after_fht(T* out, int log2_vec_size) {
 }
 
 template <typename T>
-void fast_hadamard_transform_simple_impl(T* vec, int log2_vec_size) {
+void fast_hadamard_transform_unnormalized_simple_impl(
+    T* vec,
+    int log2_vec_size) {
   if (log2_vec_size == 0) {
     return;
   }
@@ -59,7 +62,11 @@ void fast_hadamard_transform_simple_impl(T* vec, int log2_vec_size) {
     }
     step *= 2;
   }
+}
 
+template <typename T>
+void fast_hadamard_transform_simple_impl(T* vec, int log2_vec_size) {
+  fast_hadamard_transform_unnormalized_simple_impl(vec, log2_vec_size);
   normalize_after_fht(vec, log2_vec_size);
 }
 
@@ -73,6 +80,21 @@ void fast_hadamard_transform(T* vec, int log2_vec_size) {
   internal::fast_hadamard_transform_simple_impl(vec, log2_vec_size);
 }
 
+// Compute a quantized fast Walsh-Hadamard transform of vec, which
+// must be of length (1 << log2_vec_size) and symmetrically quantized.
+//
+// Note that we do not need to know the quantization scale, because
+// the Fast Hadamard transform is a series of additions and
+// subtractions with a final multiplication step, and we have the
+// following trivial identities:
+//
+// scale * a + scale * b = scale * (a + b)  (addition doesn't need the scale)
+// alpha * (scale * a) = scale * (alpha * a) (multiplication doesn't need the
+// scale)
+void fast_hadamard_transform_symmetric_quantized_s16(
+    int16_t* vec,
+    int log2_vec_size);
+
 // Like fast_hadamard_transform, but vec must be of length 28 * (1 <<
 // log2_vec_size) and the transform is computed by interpreting vec as
 // a (28, 1 << log2_vec_size) matrix and performing 28 FHTs, followed

extension/llm/custom_ops/spinquant/targets.bzl

@@ -12,5 +12,8 @@ def define_common_targets():
             "fast_hadamard_transform.h",
             "fast_hadamard_transform_special.h",
         ],
+        srcs = [
+            "fast_hadamard_transform.cpp",
+        ],
         visibility = ["@EXECUTORCH_CLIENTS"],
     )