Add divrem and fldmod (#24)

Author: aplavin

src/functions.jl

@@ -53,3 +53,21 @@ end
 invlog1(b, x) = b^x
 
 invlog2(b, x) = x^inv(b)
+
+
+function invdivrem((q, r), divisor)
+    res = muladd(q, divisor, r)
+    if abs(r) ≤ abs(divisor) && (iszero(r) || sign(r) == sign(res))
+        res
+    else
+        throw(DomainError((q, r), "inverse for divrem(x) is not defined at this point"))
+    end
+end
+
+function invfldmod((q, r), divisor)
+    if abs(r) ≤ abs(divisor) && (iszero(r) || sign(r) == sign(divisor))
+        muladd(q, divisor, r)
+    else
+        throw(DomainError((q, r), "inverse for fldmod(x) is not defined at this point"))
+    end
+end

src/inverse.jl

@@ -143,3 +143,8 @@ inverse(f::Base.Fix1{typeof(log)}) = Base.Fix1(invlog1, f.x)
 inverse(f::Base.Fix1{typeof(invlog1)}) = Base.Fix1(log, f.x)
 inverse(f::Base.Fix2{typeof(log)}) = Base.Fix2(invlog2, f.x)
 inverse(f::Base.Fix2{typeof(invlog2)}) = Base.Fix2(log, f.x)
+
+inverse(f::Base.Fix2{typeof(divrem)}) = Base.Fix2(invdivrem, f.x)
+inverse(f::Base.Fix2{typeof(invdivrem)}) = Base.Fix2(divrem, f.x)
+inverse(f::Base.Fix2{typeof(fldmod)}) = Base.Fix2(invfldmod, f.x)
+inverse(f::Base.Fix2{typeof(invfldmod)}) = Base.Fix2(fldmod, f.x)

test/test_inverse.jl

@@ -52,6 +52,15 @@ InverseFunctions.inverse(f::Bar) = Bar(inv(f.A))
     end
     InverseFunctions.test_inverse(conj, 2 - 3im)
 
+    x = rand(0:10)
+    for f in (Base.Fix2(divrem, rand([-5:-1; 1:5])), Base.Fix2(fldmod, rand([-5:-1; 1:5])), Base.Fix2(divrem, 0.123), Base.Fix2(fldmod, 0.123))
+        compare = (a, b) -> all(isapprox.(a, b))
+        InverseFunctions.test_inverse(f, x; compare=compare)
+        InverseFunctions.test_inverse(f, -x; compare=compare)
+        InverseFunctions.test_inverse(f, x/9; compare=compare)
+        InverseFunctions.test_inverse(f, -x/9; compare=compare)
+    end
+
     # ensure that inverses have domains compatible with original functions
     @test_throws DomainError inverse(Base.Fix1(*, 0))
     @test_throws DomainError inverse(Base.Fix2(^, 0))
@@ -66,6 +75,11 @@ InverseFunctions.inverse(f::Bar) = Bar(inv(f.A))
     @test_throws DomainError inverse(Base.Fix1(^, -2))(3)
     @test_throws DomainError inverse(Base.Fix1(^, -2))(3)
 
+    @test_throws DomainError inverse(Base.Fix2(divrem, 5))((-3, 2))
+    @test_throws DomainError inverse(Base.Fix2(fldmod, 5))((-3, -2))
+    InverseFunctions.test_inverse(inverse(Base.Fix2(divrem, 5)), (-3, -2); compare=(==))
+    InverseFunctions.test_inverse(inverse(Base.Fix2(fldmod, 5)), (-3, 2); compare=(==))
+
     A = rand(5, 5)
     for f in (
             identity, inv, adjoint, transpose,