Add more info about where autodiff can be applied

Author: ZuseZ4

library/core/src/autodiff.md

@@ -0,0 +1,153 @@
+This module provides support for automatic differentiation. For precise information on
+differences between the `autodiff_forward` and `autodiff_reverse` macros and how to
+use them, see their respective documentation.
+
+## General usage
+
+Autodiff macros can be applied to almost all function definitions, see below for examples.
+They can be applied to functions accepting structs, arrays, slices, vectors, tuples, and more.
+
+It is possible to apply multiple autodiff macros to the same function. As an example, this can
+be helpful to compute the partial derivatives with respect to `x` and `y` independently:
+```rust,ignore (optional component)
+#[autodiff_forward(dsquare1, Dual, Const, Dual)]
+#[autodiff_forward(dsquare2, Const, Dual, Dual)]
+#[autodiff_forward(dsquare3, Active, Active, Active)]
+fn square(x: f64, y: f64) -> f64 {
+  x * x + 2.0 * y
+}
+```
+
+We also support autodiff on functions with generic parameters:
+```rust,ignore (optional component)
+#[autodiff_forward(generic_derivative, Duplicated, Active)]
+fn generic_f<T: std::ops::Mul<Output = T> + Copy>(x: &T) -> T {
+ x * x
+}
+```
+
+or applying autodiff to nested functions:
+```rust,ignore (optional component)
+fn outer(x: f64) -> f64 {
+  #[autodiff_forward(inner_derivative, Dual, Const)]
+  fn inner(y: f64) -> f64 {
+    y * y
+  }
+  inner_derivative(x, 1.0)
+}
+
+fn main() {
+    assert_eq!(outer(3.14), 6.28);
+}
+```
+The generated function will be available in the same scope as the function differentiated, and
+have the same private/pub usability.
+
+## Traits and impls
+Autodiff macros can be used in multiple ways in combination with traits:
+```rust,ignore (optional component)
+struct Foo {
+    a: f64,
+}
+
+trait MyTrait {
+    #[autodiff_reverse(df, Const, Active, Active)]
+    fn f(&self, x: f64) -> f64;
+}
+
+impl MyTrait for Foo {
+    fn f(&self, x: f64) -> f64 {
+        x.sin()
+    }
+}
+
+fn main() {
+    let foo = Foo { a: 3.0f64 };
+    assert_eq!(foo.f(2.0), 2.0_f64.sin());
+    assert_eq!(foo.df(2.0, 1.0).1, 2.0_f64.cos());
+}
+```
+In this case `df` will be the default implementation provided by the library who provided the
+trait. A user implementing `MyTrait` could then decide to use the default implementation of
+`df`, or overwrite it with a custom implementation as a form of "custom derivatives".
+
+On the other hand, a function generated by either autodiff macro can also be used to implement a
+trait:
+```rust,ignore (optional component)
+struct Foo {
+    a: f64,
+}
+
+trait MyTrait {
+    fn f(&self, x: f64) -> f64;
+    fn df(&self, x: f64, seed: f64) -> (f64, f64);
+}
+
+impl MyTrait for Foo {
+    #[autodiff_reverse(df, Const, Active, Active)]
+    fn f(&self, x: f64) -> f64 {
+        self.a * 0.25 * (x * x - 1.0 - 2.0 * x.ln())
+    }
+}
+```
+
+Simple `impl` blocks without traits are also supported. Differentiating with respect to the
+implemented struct will then require the use of a "shadow struct" to hold the derivatives of the
+struct fields:
+
+```rust,ignore (optional component)
+struct OptProblem {
+    a: f64,
+    b: f64,
+}
+
+impl OptProblem {
+    #[autodiff_reverse(d_objective, Duplicated, Duplicated, Duplicated)]
+    fn objective(&self, x: &[f64], out: &mut f64) {
+        *out = self.a + x[0].sqrt() * self.b
+    }
+}
+fn main() {
+    let p = OptProblem { a: 1., b: 2. };
+    let mut p_shadow = OptProblem { a: 0., b: 0. };
+    let mut dx = [0.0];
+    let mut out = 0.0;
+    let mut dout = 1.0;
+
+    p.d_objective(&mut p_shadow, &x, &mut dx, &mut out, &mut dout);
+}
+```
+
+## Higher-order derivatives
+Finally, it is possible to generate higher-order derivatives (e.g. Hessian) by applying an
+autodiff macro to a function that is already generated by an autodiff macro, via a thin wrapper.
+The following example uses Forward mode over Reverse mode
+
+```rust,ignore (optional component)
+#[autodiff_reverse(df, Duplicated, Duplicated)]
+fn f(x: &[f64;2], y: &mut f64) {
+  *y = x[0] * x[0] + x[1] * x[0]
+}
+
+#[autodiff_forward(h, Dual, Dual, Dual, Dual)]
+fn wrapper(x: &[f64;2], dx: &mut [f64;2], y: &mut f64, dy: &mut f64) {
+  df(x, dx, y, dy);
+}
+
+fn main() {
+    let mut y = 0.0;
+    let x = [2.0, 2.0];
+
+    let mut dy = 0.0;
+    let mut dx = [1.0, 0.0];
+
+    let mut bx = [0.0, 0.0];
+    let mut by = 1.0;
+    let mut dbx = [0.0, 0.0];
+    let mut dby = 0.0;
+    h(&x, &mut dx, &mut bx, &mut dbx, &mut y, &mut dy, &mut by, &mut dby);
+    assert_eq!(&dbx, [2.0, 1.0]);
+}
+```
+
+

library/core/src/lib.rs

@@ -218,7 +218,7 @@ pub mod from {
 
 // We don't export this through #[macro_export] for now, to avoid breakage.
 #[unstable(feature = "autodiff", issue = "124509")]
-/// Unstable module containing the unstable `autodiff` macro.
+#[doc = include_str!("../../core/src/autodiff.md")]
 pub mod autodiff {
     #[unstable(feature = "autodiff", issue = "124509")]
     pub use crate::macros::builtin::{autodiff_forward, autodiff_reverse};

library/std/src/lib.rs

@@ -634,7 +634,7 @@ pub mod simd {
 }
 
 #[unstable(feature = "autodiff", issue = "124509")]
-/// This module provides support for automatic differentiation.
+#[doc = include_str!("../../core/src/autodiff.md")]
 pub mod autodiff {
     /// This macro handles automatic differentiation.
     pub use core::autodiff::{autodiff_forward, autodiff_reverse};