Support half precision sigmoid activation (#378)

* Support half precision sigmoid activation

* introduce a vectorized variant using fast_tanh

* move the math to fast_math.h

* fixed compile

* .raw() -> .to_half()

Co-authored-by: Haicheng Wu <haichengw@nvidia.com>

include/cutlass/epilogue/thread/activation.h

@@ -98,15 +98,7 @@ template <typename T>
 struct Sigmoid {
   CUTLASS_HOST_DEVICE
   T operator()(T const &scalar) const {
-    return T(1) / (T(1) + exp(-scalar));
+    return T(1) / (T(1) + fast_exp(-scalar));
-  }
-};
-
-template <>
-struct Sigmoid<float> {
-  CUTLASS_HOST_DEVICE
-  float operator()(float const &scalar) const {
-    return 1.0f / (1.0f + expf(-scalar));
   }
 };
 
@@ -126,6 +118,30 @@ struct Sigmoid<Array<T, N> > {
   }
 };
 
+template <int N>
+struct Sigmoid<Array<half_t, N>> {
+  using T = half_t;
+
+  CUTLASS_HOST_DEVICE
+  Array<T, N> operator()(Array<T, N> const& z) const {
+    plus<Array<T, N>> add;
+
+#if defined(CUTLASS_USE_TANH_FOR_SIGMOID)
+    multiplies<Array<T, N>> mul;
+    fast_tanh_op<Array<T, N>> tanh;
+    return mul(add(tanh(mul(z, cutlass::constants::half<T>())), cutlass::constants::one<T>()),
+               cutlass::constants::half<T>());
+#else
+    divides<Array<T, N>> div;
+    negate<Array<T, N>> neg;
+    fast_exp_op<Array<T, N>> fast_exp;
+    return div(cutlass::constants::one<T>(),
+               add(cutlass::constants::one<T>(),
+                   fast_exp(neg(z))));
+#endif
+  }
+};
+
 // SiLu (swish) operator introduced by Elfwing et al. in the following paper
 // "Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning" (2017)
 // https://arxiv.org/pdf/1702.03118.pdf

include/cutlass/fast_math.h

@@ -705,12 +705,21 @@ float fast_exp(float x) {
 CUTLASS_HOST_DEVICE
 double fast_exp(double x) {
   #if defined(__CUDA_ARCH__)
-  return ::exp(x);
+  return ::expf(x);
   #else
   return std::exp(x);
   #endif
 }
 
+CUTLASS_HOST_DEVICE
+float fast_exp(half_t x) {
+  #if defined(__CUDA_ARCH__) && (__CUDACC_VER_MAJOR__ >= 10) && (__CUDA_ARCH__ >= 750)
+      return ::hexp(x.to_half());
+  #else
+      return fast_exp(float(x));
+  #endif
+}
+
 CUTLASS_HOST_DEVICE
 float fast_log(float x) {
   #if defined(__CUDA_ARCH__)
@@ -767,6 +776,61 @@ half_t fast_tanh(half_t x) {
 
 /////////////////////////////////////////////////////////////////////////////////////////////////
 
+template <typename T>
+struct fast_exp_op {
+  CUTLASS_HOST_DEVICE
+  T operator()(T const &rhs) const {
+    return fast_exp(rhs);
+  }
+};
+
+#if defined(__CUDA_ARCH__) && (__CUDACC_VER_MAJOR__ >= 10) && (__CUDA_ARCH__ >= 750)
+template <int N>
+struct fast_exp_op<Array<half_t, N>> {
+  CUTLASS_DEVICE
+  Array<half_t, N> operator()(Array<half_t, N> const &rhs) const {
+
+    Array<half_t, N> result;
+
+    // use x2 specialization
+    __half2 const *in  = reinterpret_cast<__half2 const *>(&rhs);
+    __half2 *out = reinterpret_cast<__half2 *>(&result);
+
+    CUTLASS_PRAGMA_UNROLL
+    for (int i = 0; i < N / 2; ++i) {
+      out[i] = ::h2exp(in[i]);
+    }
+
+    // residual
+    if (N % 2) {
+      half_t last = rhs[N - 1];
+      result[N - 1] = half_t(::hexp(last.to_half()));
+    }
+
+    return result;
+  }
+};
+#endif // #if defined(__CUDA_ARCH__)
+
+template <typename T, int N>
+struct fast_exp_op<Array<T, N>> {
+  CUTLASS_HOST_DEVICE
+  Array<T, N> operator()(Array<T, N> const &rhs) const {
+
+    fast_exp_op<T> fast_op;
+    Array<T, N> y;
+
+    CUTLASS_PRAGMA_UNROLL
+    for (int i = 0; i < N; ++i) {
+      y[i] = fast_op(rhs[i]);
+    }
+
+    return y;
+  }
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////////////
+
 template <typename T>
 struct fast_tanh_op {
   CUTLASS_HOST_DEVICE