basic type docs for auto diff

Author: KMJ-007

src/SUMMARY.md

@@ -108,6 +108,7 @@
     - [Installation](./autodiff/installation.md)
     - [How to debug](./autodiff/debugging.md)
     - [Autodiff flags](./autodiff/flags.md)
+    - [Type Trees](./autodiff/type-trees.md)
 
 # Source Code Representation
 

src/autodiff/type-trees.md

@@ -0,0 +1,118 @@
+# Type Trees in Enzyme
+
+This document describes type trees as used by Enzyme for automatic differentiation.
+
+## What are Type Trees?
+
+Type trees in Enzyme are a way to represent the types of variables, including their activity (e.g., whether they are active, duplicated, or contain duplicated data) for automatic differentiation. They provide a structured way for Enzyme to understand how to handle different data types during the differentiation process.
+
+## Representing Rust Types as Type Trees
+
+Enzyme needs to understand the structure and properties of Rust types to perform automatic differentiation correctly. This is where type trees come in. They provide a detailed map of a type, including pointer indirections and the underlying concrete data types.
+
+The `-enzyme-rust-type` flag in Enzyme helps in interpreting types more accurately in the context of Rust's memory layout and type system.
+
+### Primitive Types
+
+#### Floating-Point Types (`f32`, `f64`)
+
+Consider a Rust reference to a 32-bit floating-point number, `&f32`.
+
+In LLVM IR, this might be represented, for instance, as an `i8*` (a generic byte pointer) that is then `bitcast` to a `float*`. Consider the following LLVM IR function:
+
+```llvm
+define internal void @callee(i8* %x) {
+start:
+  %x.dbg.spill = bitcast i8* %x to float*
+  ; ...
+  ret void
+}
+```
+
+When Enzyme analyzes this function (with appropriate flags like `-enzyme-rust-type`), it might produce the following type information for the argument `%x` and the result of the bitcast:
+
+```llvm
+i8* %x: {[-1]:Pointer, [-1,0]:Float@float}
+%x.dbg.spill = bitcast i8* %x to float*: {[-1]:Pointer, [-1,0]:Float@float}
+```
+
+**Understanding the Type Tree: `{[-1]:Pointer, [-1,0]:Float@float}`**
+
+This string is the type tree representation. Let's break it down:
+
+*   **`{ ... }`**: This encloses the set of type information for the variable.
+*   **`[-1]:Pointer`**:
+    *   `[-1]` is an index or path. In this context, `-1` often refers to the base memory location or the immediate value pointed to.
+    *   `Pointer` indicates that the variable `%x` itself is treated as a pointer.
+*   **`[-1,0]:Float@float`**:
+    *   `[-1,0]` is a path. It means: start with the base item `[-1]` (the pointer), and then look at offset `0` from the memory location it points to.
+    *   `Float` is the `CConcreteType` (from `enzyme_ffi.rs`, corresponding to `DT_Float`). It signifies that the data at this location is a floating-point number.
+    *   `@float` is a subtype or specific variant of `Float`. In this case, it specifies a single-precision float (like Rust's `f32`).
+
+A reference to an `f64` (e.g., `&f64`) is handled very similarly. The LLVM IR might cast to `double*`:
+```llvm
+define internal void @callee(i8* %x) {
+start:
+  %x.dbg.spill = bitcast i8* %x to double*
+  ; ...
+  ret void
+}
+```
+
+And the type tree would be:
+
+```llvm
+i8* %x: {[-1]:Pointer, [-1,0]:Float@double}
+```
+The key difference is `@double`, indicating a double-precision float.
+
+This level of detail allows Enzyme to know, for example, that if `x` is an active variable in differentiation, the floating-point value it points to needs to be handled according to AD rules for its specific precision.
+
+### Compound Types
+
+#### Structs
+
+Consider a Rust struct `T` with two `f32` fields (e.g., a reference `&T`):
+
+```rust
+struct T {
+    x: f32,
+    y: f32,
+}
+
+// And a function taking a reference to it:
+// fn callee(t: &T) { /* ... */ }
+```
+
+In LLVM IR, a pointer to this struct might be initially represented as `i8*` and then cast to the specific struct type, like `{ float, float }*`:
+
+```llvm
+define internal void @callee(i8* %t) {
+start:
+  %t.dbg.spill = bitcast i8* %t to { float, float }*
+  ; ...
+  ret void
+}
+```
+
+The Enzyme type analysis output for `%t` would be:
+
+```llvm
+i8* %t: {[-1]:Pointer, [-1,0]:Float@float, [-1,4]:Float@float}
+```
+
+**Understanding the Struct Type Tree: `{[-1]:Pointer, [-1,0]:Float@float, [-1,4]:Float@float}`**
+
+*   **`[-1]:Pointer`**: As before, this indicates that `%t` is a pointer.
+*   **`[-1,0]:Float@float`**:
+    *   This describes the first field of the struct (`x`).
+    *   `[-1,0]` means: from the memory location pointed to by `%t` (`-1`), at offset `0` bytes.
+    *   `Float@float` indicates this field is an `f32`.
+*   **`[-1,4]:Float@float`**:
+    *   This describes the second field of the struct (`y`).
+    *   `[-1,4]` means: from the memory location pointed to by `%t` (`-1`), at offset `4` bytes.
+    *   `Float@float` indicates this field is also an `f32`.
+
+The offset `4` comes from the size of the first field (`f32` is 4 bytes). If the first field were, for example, an `f64` (8 bytes), the second field might be at offset `[-1,8]`. Enzyme uses these offsets to pinpoint the exact memory location of each field within the struct.
+
+This detailed mapping is crucial for Enzyme to correctly track the activity of individual struct fields during automatic differentiation.