Expand shared scalar basis and align complex JVP rules

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+Copyright 2026 Hiroshi Shinaoka, GiggleLiu, and contributors
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LICENSE-MIT

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+MIT License
+
+Copyright (c) 2026 Hiroshi Shinaoka, GiggleLiu, and contributors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
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+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
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+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

@@ -9,8 +9,8 @@ specific AD engine.
 
 It contains:
 
-- `chainrules-core`: core AD traits and error types
-- `chainrules`: reusable scalar `frule`/`rrule` helpers and related utilities
+- `chainrules-core`: engine-independent AD protocol
+- `chainrules`: shared scalar rule basis
 
 It intentionally does **not** ship a tape, traced value type, or any other AD
 engine runtime. Those live in separate engine crates such as
@@ -25,9 +25,9 @@ engine runtime. Those live in separate engine crates such as
 
 ## Repository Layout
 
-- [`crates/chainrules-core`](crates/chainrules-core): `Differentiable`,
-  `ReverseRule`, `ForwardRule`, `AutodiffError`, and related core types
-- [`crates/chainrules`](crates/chainrules): scalar rule implementations such as
+- [`crates/chainrules-core`](crates/chainrules-core): protocol-only crate for
+  `Differentiable`, `ReverseRule`, `ForwardRule`, and `AutodiffError`
+- [`crates/chainrules`](crates/chainrules): shared scalar rules such as
   `exp`, `log1p`, `sin`, `atanh`, `powf`, and `atan2`
 - [`third_party/tensor-ad-oracles`](third_party/tensor-ad-oracles): vendored
   oracle data used to validate scalar rules against published references
@@ -48,8 +48,33 @@ engine that executes those rules over a tape. The boundary is deliberate:
 - `tidu-rs` can evolve independently as an engine
 - downstream tensor libraries can swap engines without rewriting scalar rules
 
+## Crate Roles
+
+`chainrules-core` does not provide function rules.
+`chainrules` provides stateless scalar `foo`, `foo_frule`, and `foo_rrule`
+helpers.
+
+`chainrules` is a landing zone for scalar rules ported or adapted from Julia's
+`ChainRules.jl` where they fit this repository boundary, but `chainrules-rs` is
+not a full port of `ChainRules.jl`.
+
+See the crate READMEs for the supported scalar function inventory and examples.
+
 ## Testing
 
+Scalar rules are checked in complementary ways:
+
+- formula and behavior tests in `crates/chainrules/tests/scalarops_tests.rs`
+- compatibility and edge-case tests such as
+  `crates/chainrules/tests/julia_compat_trig_tests.rs` and
+  `crates/chainrules/tests/complex_helper_tests.rs`
+- oracle replay tests in `crates/chainrules/tests/oracle_scalar_rules.rs`
+  against vendored published cases from `third_party/tensor-ad-oracles`,
+  including direct float64 replay and selected direct Complex64 replay for
+  `tan`, `exp2`, and `log2`; complex
+  forward-mode checks use the standard JVP convention on `C ~= R^2`, while
+  complex reverse-mode checks remain conjugate-Wirtinger for real-valued losses
+
 ```bash
 cargo test --workspace --release
 cargo llvm-cov --workspace --json --output-path coverage.json

crates/chainrules-core/README.md

@@ -0,0 +1,31 @@
+# chainrules-core
+
+`chainrules-core` defines the engine-independent AD protocol used by
+`chainrules-rs`.
+
+It is intentionally small and does not provide function rules. The crate exists
+to define the traits and error types that downstream AD engines and rule
+libraries build on.
+
+## What It Provides
+
+- `Differentiable`
+- `ReverseRule`
+- `ForwardRule`
+- `AutodiffError`
+- `NodeId`
+- `SavePolicy`
+
+## Example
+
+```rust
+use chainrules_core::NodeId;
+
+let id = NodeId::new(7);
+assert_eq!(id.index(), 7);
+```
+
+## Notes
+
+This crate is protocol-only. Shared scalar `frule` and `rrule` helpers live in
+[`chainrules`](../chainrules).

crates/chainrules-core/src/lib.rs

@@ -1,3 +1,5 @@
+#![doc = include_str!("../README.md")]
+
 //! Core AD trait definitions (like Julia's ChainRulesCore.jl).
 //!
 //! This crate defines the interface for automatic differentiation without

crates/chainrules/README.md

@@ -0,0 +1,86 @@
+# chainrules
+
+`chainrules` provides a shared scalar rule basis for Rust automatic
+differentiation crates.
+
+It is designed for reusable scalar calculus, not for tapes, traced values, or
+tensor-specific execution engines. The crate focuses on stateless helpers that
+can be called from downstream AD runtimes and tensor libraries.
+
+## What It Provides
+
+- stateless scalar primal helpers
+- stateless scalar `foo_frule` helpers
+- stateless scalar `foo_rrule` helpers
+- real/complex projection helpers for common scalar formulas
+
+Supported scalar domains:
+
+- `f32`
+- `f64`
+- `Complex32`
+- `Complex64`
+
+## Supported Functions
+
+Current shipped scalar families:
+
+- arithmetic: `add`, `sub`, `mul`, `div`
+- powers and roots: `powf`, `powi`, `sqrt`
+- exponentials and logs: `exp`, `expm1`, `log`, `log1p`
+- trigonometric: `sin`, `cos`, `asin`, `acos`, `atan`
+- hyperbolic: `sinh`, `cosh`, `tanh`, `asinh`, `acosh`, `atanh`
+- Julia-compatible trigonometric helpers: `sec`, `csc`, `cot`, `sinpi`, `cospi`, `sincospi`, `sind`, `cosd`, `tand`
+- Julia-compatible hyperbolic helpers: `sech`, `csch`, `coth`
+- non-smooth real helpers: `round`, `floor`, `ceil`, `sign`, `min`, `max`
+- smooth helpers: `cbrt`, `inv`, `exp2`, `exp10`, `log2`, `log10`, `hypot`, `pow`, `sincos`, `tan`
+- complex and projection helpers: `conj`, `abs`, `abs2`, `angle`, `real`, `imag`, `complex`
+- real-valued binary helpers: `atan2`
+
+This crate is a landing zone for scalar rules ported or adapted from Julia's
+`ChainRules.jl` where they fit this crate boundary, but it is not a full port
+of `ChainRules.jl`.
+
+## Validation
+
+Rules in this crate are not accepted on provenance alone. They are checked with
+repository-local tests:
+
+- `tests/scalarops_tests.rs` covers direct formulas, edge cases, and smooth
+  real/complex behavior
+- `tests/julia_compat_trig_tests.rs` covers Julia migration helpers, including
+  landmark real inputs and representative Complex64 behavior
+- `tests/nonsmooth_scalar_tests.rs` covers the documented zero-gradient and
+  tie-routing policies for non-smooth helpers
+- `tests/complex_helper_tests.rs` covers the projection helpers and complex
+  constructor surface
+- `tests/oracle_scalar_rules.rs` replays vendored published oracle cases from
+  `../../third_party/tensor-ad-oracles`, with direct float64 replay and
+  selected direct Complex64 replay for `tan`, `exp2`, and `log2`
+- complex forward-mode checks use the standard JVP convention on `C ~= R^2`
+  in repository-local formula tests such as `tests/smooth_basis_tests.rs`
+- complex reverse-mode checks remain conjugate-Wirtinger for real-valued losses
+
+## Examples
+
+```rust
+use chainrules::{powf, powf_frule, powf_rrule};
+
+let y = powf(2.0_f64, 3.0_f64);
+assert_eq!(y, 8.0_f64);
+
+let (y, dy) = powf_frule(2.0_f64, 3.0_f64, 1.0_f64);
+assert_eq!(y, 8.0_f64);
+assert_eq!(dy, 12.0_f64);
+
+let dx = powf_rrule(2.0_f64, 3.0_f64, 1.0_f64);
+assert_eq!(dx, 12.0_f64);
+```
+
+## Notes
+
+This crate is the landing zone for shared scalar rule logic, including
+Julia-style convenience functions when they help migration.
+
+It does not define tensor, array, broadcast, reduction, or engine-specific
+rules.