docs: update benchmarks with in-place FK/Jacobian results (3x faster than Pinocchio)

Author: ferrolho

docs/src/man/benchmarks.md

@@ -4,20 +4,20 @@ This page compares the performance of ModernRoboticsBook.jl against [Pinocchio](
 
 ## Results
 
-| Function | ModernRoboticsBook.jl | Pinocchio 3.9 (C++) | Ratio |
-|----------|----------------------:|--------------------:|------:|
-| Forward kinematics | 0.40 μs | 0.86 μs | **0.5x (faster)** |
-| Jacobian | 0.45 μs | 1.0 μs | **0.5x (faster)** |
-| Inverse dynamics | 3.64 μs | 0.64 μs | ~6x |
-| Mass matrix | 22.0 μs | 0.65 μs | ~34x |
-| Gravity forces | 3.68 μs | 0.48 μs | ~8x |
-| Forward dynamics | 34.0 μs | 2.82 μs | ~12x |
+| Function | ModernRoboticsBook.jl | In-place (`!`) | Pinocchio 3.9 (C++) | Ratio (in-place) |
+|----------|----------------------:|---------------:|--------------------:|------------------:|
+| Forward kinematics | 0.31 μs | **0.30 μs** | 0.86 μs | **0.35x (faster)** |
+| Jacobian | 0.39 μs | **0.36 μs** | 1.0 μs | **0.36x (faster)** |
+| Inverse dynamics | 3.68 μs | — | 0.64 μs | ~6x |
+| Mass matrix | 22.2 μs | — | 0.65 μs | ~34x |
+| Gravity forces | 3.73 μs | — | 0.48 μs | ~8x |
+| Forward dynamics | 34.2 μs | — | 2.82 μs | ~12x |
 
 *Measured on Apple M2 (16 GB), Julia 1.12, Python 3.13. Julia timings are median values from BenchmarkTools.jl.*
 
 ## Analysis
 
-Forward kinematics and Jacobian computation are **faster than Pinocchio** thanks to Julia's StaticArrays, which eliminate heap allocations for small fixed-size matrices (4×4, 6×6).
+Forward kinematics and Jacobian computation are **~3x faster than Pinocchio** thanks to Julia's StaticArrays, which eliminate heap allocations for small fixed-size matrices (4×4, 6×6). The in-place variants (`forward_kinematics_space!`, `jacobian_space!`, etc.) achieve **zero allocations**.
 
 The remaining gap in dynamics functions comes from algorithmic differences:
 
@@ -28,15 +28,13 @@ The remaining gap in dynamics functions comes from algorithmic differences:
 
 ### Allocations
 
-With StaticArrays, allocations are dramatically reduced compared to the initial implementation:
-
-| Function | Allocations | Memory |
-|----------|------------:|-------:|
-| Forward kinematics | 2 | 208 B |
-| Jacobian | 2 | 384 B |
-| Inverse dynamics | 186 | 13.4 KiB |
-| Mass matrix | 1,114 | 80.7 KiB |
-| Forward dynamics | 1,702 | 125.6 KiB |
+| Function | Allocations | Memory | In-place |
+|----------|------------:|-------:|---------:|
+| Forward kinematics | 2 | 208 B | **0 (0 B)** |
+| Jacobian | 2 | 384 B | **0 (0 B)** |
+| Inverse dynamics | 186 | 13.4 KiB | — |
+| Mass matrix | 1,114 | 80.7 KiB | — |
+| Forward dynamics | 1,702 | 125.6 KiB | — |
 
 ### When does this matter?