Update README based on new docs

README.md

@@ -4,26 +4,68 @@
 
 [![](https://img.shields.io/badge/docs-dev-blue.svg)](https://juliacomputing.github.io/AllocCheck.jl/dev/)
 
-AllocCheck.jl is a Julia package that statically checks if a function call may allocate, analyzing the generated LLVM IR of it and it's callees using LLVM.jl and GPUCompiler.jl
+[AllocCheck.jl](https://github.com/JuliaComputing/AllocCheck.jl) is a Julia package that statically checks if a function call may allocate, analyzing the generated LLVM IR of it and it's callees using LLVM.jl and GPUCompiler.jl
 
-#### Examples
+AllocCheck operates on _functions_, trying to statically determine wether or not a function _may_ allocate memory, and if so, _where_ that allocation appears. This is different from measuring allocations using, e.g., `@time` or `@allocated`, which measures the allocations that _did_ happen during the execution of a function.
 
+## Getting started
+
+The primary entry point to check allocations is the macro [`@check_allocs`](@ref) which is used to annotate a function definition that you'd like to enforce allocation checks for:
 ```julia
-julia> mymod(x) = mod(x, 2.5)
+julia> using AllocCheck
+
+julia> @check_allocs multiply(x,y) = x * y
+multiply (generic function with 1 method)
+
+julia> multiply(1.5, 2.5) # call automatically checked for allocations
+3.75
+
+julia> multiply(rand(3,3), rand(3,3)) # result matrix requires an allocation
+ERROR: @check_alloc function contains 1 allocations.
+```
+
+The `multiply(::Float64, ::Float64)` call happened without error, indicating that the function was proven not to allocate. On the other hand, the `multiply(::Matrix{Float64}, ::Matrix{Float64})` call raised an `AllocCheckFailure` due to one internal allocation.
 
-julia> length(check_allocs(mymod, (Float64,)))
-0
+The `allocs` field can be used to inspect the individual errors:
+```julia
+julia> try multiply(rand(3,3), rand(3,3)) catch err err.allocs[1] end
+Allocation of Matrix{Float64} in ./boot.jl:477
+  | Array{T,2}(::UndefInitializer, m::Int, n::Int) where {T} =
 
-julia> linsolve(a, b) = a \ b
+Stacktrace:
+ [1] Array
+   @ ./boot.jl:477 [inlined]
+ [2] Array
+   @ ./boot.jl:485 [inlined]
+ [3] similar
+   @ ./array.jl:418 [inlined]
+ [4] *(A::Matrix{Float64}, B::Matrix{Float64})
+   @ LinearAlgebra ~/.julia/juliaup/julia-1.10.0-rc1+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jl:113
+ [5] var"##multiply#235"(x::Matrix{Float64}, y::Matrix{Float64})
+   @ Main ./REPL[13]:1
+```
+
+### Functions that throw exceptions
+
+Some functions that we do not expect may allocate memory, like `sin`, actually may:
+```julia
+julia> @allocated try sin(Inf) catch end
+48
+```
+
+The reason for this is that `sin` needs to allocate if it **throws an error**.
+
+By default, `@check_allocs` ignores all such allocations and assumes that no exceptions are thrown. If you care about detecting these allocations anyway, you can use `ignore_throw=false`:
+```julia
+julia> @check_allocs mysin1(x) = sin(x)
 
-julia> length(check_allocs(linsolve, (Matrix{Float64}, Vector{Float64})))
-175
+julia> @check_allocs ignore_throw=false mysin2(x) = sin(x)
 
-julia> length(check_allocs(sin, (Float64,)))
-2
+julia> mysin1(1.5)
+0.9974949866040544
 
-julia> length(check_allocs(sin, (Float64,); ignore_throw=true)) # ignore allocations that only happen when throwing errors
-0
+julia> mysin2(1.5)
+ERROR: @check_alloc function contains 2 allocations.
 ```
 
 #### Limitations