docs: typetree in autodiff

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 +1,163 @@
+# TypeTrees for Autodiff
+
+## What are TypeTrees?
+Memory layout descriptors for Enzyme. Tell Enzyme exactly how types are structured in memory so it can compute derivatives efficiently.
+
+## Structure
+```rust
+TypeTree(Vec<Type>)
+
+Type {
+    offset: isize,  // byte offset (-1 = everywhere)
+    size: usize,    // size in bytes
+    kind: Kind,     // Float, Integer, Pointer, etc.
+    child: TypeTree // nested structure
+}
+```
+
+## Example: `fn compute(x: &f32, data: &[f32]) -> f32`
+
+**Input 0: `x: &f32`**
+```rust
+TypeTree(vec![Type {
+    offset: -1, size: 8, kind: Pointer,
+    child: TypeTree(vec![Type {
+        offset: -1, size: 4, kind: Float,
+        child: TypeTree::new()
+    }])
+}])
+```
+
+**Input 1: `data: &[f32]`**
+```rust
+TypeTree(vec![Type {
+    offset: -1, size: 8, kind: Pointer,
+    child: TypeTree(vec![Type {
+        offset: -1, size: 4, kind: Float,  // -1 = all elements
+        child: TypeTree::new()
+    }])
+}])
+```
+
+**Output: `f32`**
+```rust
+TypeTree(vec![Type {
+    offset: -1, size: 4, kind: Float,
+    child: TypeTree::new()
+}])
+```
+
+## Why Needed?
+- Enzyme can't deduce complex type layouts from LLVM IR
+- Prevents slow memory pattern analysis
+- Enables correct derivative computation for nested structures
+- Tells Enzyme which bytes are differentiable vs metadata
+
+## What Enzyme Does With This Information:
+
+Without TypeTrees:
+```llvm
+; Enzyme sees generic LLVM IR:
+define float @distance(i8* %p1, i8* %p2) {
+; Has to guess what these pointers point to
+; Slow analysis of all memory operations
+; May miss optimization opportunities
+}
+```
+
+With TypeTrees:
+```llvm
+define "enzyme_type"="{[]:Float@float}" float @distance(
+    ptr "enzyme_type"="{[]:Pointer}" %p1, 
+    ptr "enzyme_type"="{[]:Pointer}" %p2
+) {
+; Enzyme knows exact type layout
+; Can generate efficient derivative code directly
+}
+```
+
+# TypeTrees - Offset and -1 Explained
+
+## Type Structure
+
+```rust
+Type {
+    offset: isize, // WHERE this type starts
+    size: usize,   // HOW BIG this type is
+    kind: Kind,    // WHAT KIND of data (Float, Int, Pointer)
+    child: TypeTree // WHAT'S INSIDE (for pointers/containers)
+}
+```
+
+## Offset Values
+
+### Regular Offset (0, 4, 8, etc.)
+**Specific byte position within a structure**
+
+```rust
+struct Point {
+    x: f32, // offset 0, size 4
+    y: f32, // offset 4, size 4
+    id: i32, // offset 8, size 4
+}
+```
+
+TypeTree for `&Point` (internal representation):
+```rust
+TypeTree(vec![
+    Type { offset: 0, size: 4, kind: Float },   // x at byte 0
+    Type { offset: 4, size: 4, kind: Float },   // y at byte 4
+    Type { offset: 8, size: 4, kind: Integer }  // id at byte 8
+])
+```
+
+Generates LLVM:
+```llvm
+"enzyme_type"="{[]:Float@float}"
+```
+
+### Offset -1 (Special: "Everywhere")
+**Means "this pattern repeats for ALL elements"**
+
+#### Example 1: Array `[f32; 100]`
+```rust
+TypeTree(vec![Type {
+    offset: -1, // ALL positions
+    size: 4,    // each f32 is 4 bytes
+    kind: Float, // every element is float
+}])
+```
+
+Instead of listing 100 separate Types with offsets `0,4,8,12...396`
+
+#### Example 2: Slice `&[i32]`
+```rust
+// Pointer to slice data
+TypeTree(vec![Type {
+    offset: -1, size: 8, kind: Pointer,
+    child: TypeTree(vec![Type {
+        offset: -1, // ALL slice elements
+        size: 4,    // each i32 is 4 bytes
+        kind: Integer
+    }])
+}])
+```
+
+#### Example 3: Mixed Structure
+```rust
+struct Container {
+    header: i64,        // offset 0
+    data: [f32; 1000],  // offset 8, but elements use -1
+}
+```
+
+```rust
+TypeTree(vec![
+    Type { offset: 0, size: 8, kind: Integer }, // header
+    Type { offset: 8, size: 4000, kind: Pointer,
+        child: TypeTree(vec![Type {
+            offset: -1, size: 4, kind: Float // ALL array elements
+        }])
+    }
+])
+```