docs: improve API documentation for library consumers (#5)

* docs: improve API documentation for library consumers

- Enable compile-testing on Differentiable doc examples (was `ignore`)
- Document Send+Sync requirement on ReverseRule and ForwardRule traits
- Add Wirtinger/CR-calculus convention section for complex scalars
- Document rrule first-argument convention (result vs input x)
- Clarify result vs x parameter on individual rrule functions
- Add Getting Started section to README with dependency and usage examples

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* chore: trigger CI

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: shinaoka

README.md

@@ -16,6 +16,52 @@ It intentionally does **not** ship a tape, traced value type, or any other AD
 engine runtime. Those live in separate engine crates such as
 [`tidu-rs`](https://github.com/tensor4all/tidu-rs).
 
+## Getting Started
+
+Add `chainrules` (or `chainrules-core` alone if you only need the traits) as a
+git dependency:
+
+```toml
+[dependencies]
+chainrules = { git = "https://github.com/tensor4all/chainrules-rs" }
+
+# For complex scalar support, also add:
+num-complex = "0.4"
+```
+
+### Using scalar rules
+
+```rust
+use chainrules::{exp_frule, sin_rrule, powf_frule};
+
+// Forward rule: returns (primal, tangent)
+let (y, dy) = exp_frule(1.0_f64, 1.0);
+assert!((y - 1.0_f64.exp()).abs() < 1e-12);
+
+// Reverse rule: returns input cotangent
+let dx = sin_rrule(0.5_f64, 1.0);
+assert!((dx - 0.5_f64.cos()).abs() < 1e-12);
+```
+
+### Implementing custom AD types
+
+```rust
+use chainrules::{Differentiable, ReverseRule, AdResult, NodeId};
+
+#[derive(Clone)]
+struct MyVec(Vec<f64>);
+
+impl Differentiable for MyVec {
+    type Tangent = MyVec;
+    fn zero_tangent(&self) -> MyVec { MyVec(vec![0.0; self.0.len()]) }
+    fn accumulate_tangent(a: MyVec, b: &MyVec) -> MyVec {
+        MyVec(a.0.iter().zip(&b.0).map(|(x, y)| x + y).collect())
+    }
+    fn num_elements(&self) -> usize { self.0.len() }
+    fn seed_cotangent(&self) -> MyVec { MyVec(vec![1.0; self.0.len()]) }
+}
+```
+
 ## Design Goals
 
 - Keep differentiation rules reusable across projects and AD engines

crates/chainrules-core/src/lib.rs

@@ -21,7 +21,7 @@
 //!
 //! Implementing `Differentiable` for a custom type:
 //!
-//! ```ignore
+//! ```
 //! use chainrules_core::Differentiable;
 //!
 //! #[derive(Clone)]
@@ -61,11 +61,9 @@
 ///
 /// # Examples
 ///
-/// ```ignore
+/// ```
 /// use chainrules_core::Differentiable;
 ///
-/// // Tensor<f64> implements Differentiable with Tangent = Tensor<f64>
-/// // (defined in tenferro-tensor crate)
 /// fn example<V: Differentiable>(x: &V) {
 ///     let zero = x.zero_tangent();
 ///     let _acc = V::accumulate_tangent(zero.clone(), &x.zero_tangent());
@@ -257,6 +255,9 @@ pub enum SavePolicy {
 ///
 /// The type parameter `V` is the differentiable value type (e.g., `Tensor<f64>`).
 ///
+/// Implementors must be `Send + Sync` because rule objects may be stored on an
+/// AD tape that is shared across threads.
+///
 /// # Examples
 ///
 /// Custom reverse rule for scalar multiplication `output = a * b`:
@@ -334,6 +335,9 @@ pub trait ReverseRule<V: Differentiable>: Send + Sync {
 ///
 /// The type parameter `V` is the differentiable value type (e.g., `Tensor<f64>`).
 ///
+/// Implementors must be `Send + Sync` because rule objects may be stored on an
+/// AD tape that is shared across threads.
+///
 /// # Examples
 ///
 /// Custom forward rule for scalar multiplication `output = a * b`:

crates/chainrules/README.md

@@ -61,6 +61,32 @@ repository-local tests:
   in repository-local formula tests such as `tests/smooth_basis_tests.rs`
 - complex reverse-mode checks remain conjugate-Wirtinger for real-valued losses
 
+## rrule first-argument convention
+
+Some rrule helpers accept the **forward result** as their first argument
+(when the derivative can be expressed in terms of the output), while others
+accept the **input `x`** (when the derivative depends on the original
+input). The parameter name in each function signature tells you which:
+
+| First parameter | Functions |
+|-----------------|-----------|
+| `result` | `exp_rrule`, `expm1_rrule`, `exp2_rrule`, `exp10_rrule`, `sqrt_rrule`, `cbrt_rrule`, `inv_rrule`, `tanh_rrule`, `tan_rrule` |
+| `x` | `log_rrule`, `log1p_rrule`, `log2_rrule`, `log10_rrule`, `sin_rrule`, `cos_rrule`, `sinh_rrule`, `cosh_rrule`, all inverse-trig/hyperbolic rrules, `powf_rrule`, `powi_rrule`, `pow_rrule`, Julia-compat trig/hyperbolic rrules |
+| both inputs | `mul_rrule(x, y, …)`, `div_rrule(x, y, …)`, `atan2_rrule(y, x, …)`, `hypot_rrule(x, y, …)`, `min_rrule(x, y, …)`, `max_rrule(x, y, …)` |
+| cotangent only | `add_rrule`, `sub_rrule`, `conj_rrule`, `real_rrule`, `imag_rrule` |
+
+## Complex scalar convention
+
+For complex scalars (`Complex64`, `Complex32`):
+
+- **Forward-mode** (frule): uses the standard JVP convention on **C ≅ R²**
+- **Reverse-mode** (rrule): uses the **conjugate-Wirtinger** convention for
+  real-valued losses — gradients include `conj(df/dz)`
+
+For real scalars `conj` is the identity, so the convention is invisible.
+
+See the validation section below for how each convention is tested.
+
 ## Examples
 
 ```rust

crates/chainrules/src/unary/basic.rs

@@ -28,6 +28,8 @@ pub fn sqrt_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `sqrt`.
+///
+/// Takes the forward **result** `sqrt(x)`, not the input `x`.
 pub fn sqrt_rrule<S: ScalarAd>(result: S, cotangent: S) -> S {
     cotangent / (S::from_i32(2) * result.conj())
 }

crates/chainrules/src/unary/exp_log.rs

@@ -17,6 +17,8 @@ pub fn exp_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
     (y, dx * y)
 }
 /// Reverse rule for `exp`.
+///
+/// Takes the forward **result** `exp(x)`, not the input `x`.
 pub fn exp_rrule<S: ScalarAd>(result: S, cotangent: S) -> S {
     cotangent * result.conj()
 }
@@ -31,6 +33,8 @@ pub fn expm1_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
     (y, dx * scale)
 }
 /// Reverse rule for `exp(x) - 1`.
+///
+/// Takes the forward **result** `expm1(x)`, not the input `x`.
 pub fn expm1_rrule<S: ScalarAd>(result: S, cotangent: S) -> S {
     cotangent * (result + one::<S>()).conj()
 }
@@ -71,6 +75,8 @@ pub fn log_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
     (y, dy)
 }
 /// Reverse rule for `log`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn log_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * (one::<S>() / x).conj()
 }
@@ -85,6 +91,8 @@ pub fn log1p_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
     (y, dy)
 }
 /// Reverse rule for `log(1 + x)`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn log1p_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * (one::<S>() / (one::<S>() + x)).conj()
 }

crates/chainrules/src/unary/hyperbolic.rs

@@ -14,6 +14,8 @@ pub fn tanh_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `tanh`.
+///
+/// Takes the forward **result** `tanh(x)`, not the input `x`.
 pub fn tanh_rrule<S: ScalarAd>(result: S, cotangent: S) -> S {
     cotangent * (one::<S>() - result * result).conj()
 }
@@ -30,6 +32,8 @@ pub fn sinh_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `sinh`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn sinh_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * x.cosh().conj()
 }
@@ -46,6 +50,8 @@ pub fn cosh_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `cosh`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn cosh_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * x.sinh().conj()
 }

crates/chainrules/src/unary/trig.rs

@@ -13,6 +13,8 @@ pub fn sin_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `sin`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn sin_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * x.cos().conj()
 }
@@ -29,6 +31,8 @@ pub fn cos_frule<S: ScalarAd>(x: S, dx: S) -> (S, S) {
 }
 
 /// Reverse rule for `cos`.
+///
+/// Takes the original **input** `x`, not the result.
 pub fn cos_rrule<S: ScalarAd>(x: S, cotangent: S) -> S {
     cotangent * (-x.sin()).conj()
 }