allow printing using at-printf (#511)

* allow printing using at-printf

I implemented specializations of `Printf.tofloat` to allow printing (the `value` of) dual numbers.
This is useful when differentiating functions that print some information during the computation, cf.
https://discourse.julialang.org/t/forwarddiff-jl-and-printf/57694.

Author: ranocha

Project.toml

@@ -8,6 +8,7 @@ DiffResults = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
 DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

src/ForwardDiff.jl

@@ -6,6 +6,7 @@ using StaticArrays
 using Random
 using LinearAlgebra
 
+import Printf
 import NaNMath
 import SpecialFunctions
 import CommonSubexpressions

src/dual.jl

@@ -690,3 +690,7 @@ end
 function Base.typemax(::Type{ForwardDiff.Dual{T,V,N}}) where {T,V,N}
     ForwardDiff.Dual{T,V,N}(typemax(V))
 end
+
+if VERSION >= v"1.6.0-rc1"
+    Printf.tofloat(d::Dual) = Printf.tofloat(value(d))
+end

test/DualTest.jl

@@ -1,6 +1,7 @@
 module DualTest
 
 using Test
+using Printf
 using Random
 using ForwardDiff
 using ForwardDiff: Partials, Dual, value, partials
@@ -504,4 +505,14 @@ end
     @test !isfinite(dinf)
 end
 
+if VERSION >= v"1.6.0-rc1"
+    @testset "@printf" begin
+        for T in (Float16, Float32, Float64, BigFloat)
+            d1 = Dual(one(T))
+            @test_nowarn @printf("Testing @printf: %.2e\n", d1)
+            @test @sprintf("Testing @sprintf: %.2e\n", d1) == "Testing @sprintf: 1.00e+00\n"
+        end
+    end
+end
+
 end # module