add SiLU activation

Author: jalvesz

doc/specs/stdlib_specialfunctions_activations.md

@@ -354,6 +354,60 @@ Elemental function
 
 The function returns a value with the same type and kind as input argument.
 
+## `SiLU` - Sigmoid Linear Unit function
+
+### Status
+
+Experimental
+
+### Description
+
+Computes the Sigmoid Linear Unit function:
+$$f(x) = \frac{x}{1+\exp(-x)} $$
+
+### Syntax
+
+`result = ` [[stdlib_specialfunctions(module):silu(interface)]] ` (x)`
+
+### Class
+
+Elemental function
+
+### Arguments
+
+`x`: Shall be a scalar or array of any `real` kind. 
+
+### Return value
+
+The function returns a value with the same type and kind as input argument.
+
+## `Silu_grad` - Gradient of the Sigmoid Linear Unit function
+
+### Status
+
+Experimental
+
+### Description
+
+Computes the gradient of the Sigmoid function:
+$$f(x) = \frac{\exp(x)*(x+(1+\exp(x))^2)}{(1+\exp(x))^2} $$
+
+### Syntax
+
+`result = ` [[stdlib_specialfunctions(module):silu_grad(interface)]] ` (x)`
+
+### Class
+
+Elemental function
+
+### Arguments
+
+`x`: Shall be a scalar or array of any `real` kind.
+
+### Return value
+
+The function returns a value with the same type and kind as input argument.
+
 ## `Step` - Step function
 
 ### Status
@@ -442,7 +496,7 @@ Pure function for ranks 1 to 4.
 
 The function returns an array with the same rank and kind as the input argument `x`.
 
-## `Softplus_grad` - Gradient of the Softplus function
+## `Softmax_grad` - Gradient of the Softmax function
 
 ### Status
 

src/stdlib_specialfunctions.fypp

@@ -187,6 +187,32 @@ module stdlib_specialfunctions
         #:endfor
     end interface
     public :: sigmoid_grad
+    
+    interface silu
+        !! Version: experimental
+        !!
+        !! Sigmoid Linear Unit function
+        #:for rk, rt in REAL_KINDS_TYPES
+        elemental module function silu_${rk}$( x ) result( y )
+            ${rt}$, intent(in) :: x
+            ${rt}$ :: y
+        end function
+        #:endfor
+    end interface
+    public :: silu
+
+    interface silu_grad
+        !! Version: experimental
+        !!
+        !! Gradient of the Sigmoid Linear Unit function
+        #:for rk, rt in REAL_KINDS_TYPES
+        elemental module function silu_grad_${rk}$( x ) result( y )
+            ${rt}$, intent(in) :: x
+            ${rt}$ :: y
+        end function
+        #:endfor
+    end interface
+    public :: silu_grad
 
     interface step
         !! Version: experimental

src/stdlib_specialfunctions_activations.fypp

@@ -129,6 +129,25 @@ end function
 
 #:endfor
 
+!==================================================
+! SiLU: Sigmoid Linear Unit
+!==================================================
+#:for rk, rt in REAL_KINDS_TYPES
+elemental module function silu_${rk}$( x ) result( y )
+    ${rt}$, intent(in) :: x
+    ${rt}$ :: y
+    y = x / (1._${rk}$ + exp(-x))
+end function
+
+elemental module function silu_grad_${rk}$( x ) result( y )
+    ${rt}$, intent(in) :: x
+    ${rt}$ :: y
+    y = (1._${rk}$ + exp(x))**2
+    y = exp(x) * ( x + y ) / y
+end function
+
+#:endfor
+
 !==================================================
 ! Step
 !==================================================