Use irrational constants

Author: devmotion

src/chainrules.jl

@@ -33,14 +33,17 @@ ChainRulesCore.@scalar_rule(
 )
 ChainRulesCore.@scalar_rule(dawson(x), 1 - (2 * x * Ω))
 ChainRulesCore.@scalar_rule(digamma(x), trigamma(x))
-ChainRulesCore.@scalar_rule(erf(x), (2 / sqrt(π)) * exp(-x^2))
-ChainRulesCore.@scalar_rule(erfc(x), -(2 / sqrt(π)) * exp(-x^2))
-ChainRulesCore.@scalar_rule(logerfc(x), -(2 / sqrt(π)) * exp(-x^2 - Ω))
-ChainRulesCore.@scalar_rule(erfcinv(x), -(sqrt(π) / 2) * exp(Ω^2))
-ChainRulesCore.@scalar_rule(erfcx(x), (2 * x * Ω) - (2 / sqrt(π)))
-ChainRulesCore.@scalar_rule(logerfcx(x), 2 * x - (2 / sqrt(π)) * exp(-Ω))
-ChainRulesCore.@scalar_rule(erfi(x), (2 / sqrt(π)) * exp(x^2))
-ChainRulesCore.@scalar_rule(erfinv(x), (sqrt(π) / 2) * exp(Ω^2))
+
+# TODO: use `invsqrtπ` if it is added to IrrationalConstants
+ChainRulesCore.@scalar_rule(erf(x), (2 * exp(-x^2)) / sqrtπ)
+ChainRulesCore.@scalar_rule(erf(x, y), (- (2 * exp(-x^2)) / sqrtπ, (2 * exp(-y^2)) / sqrtπ))
+ChainRulesCore.@scalar_rule(erfc(x), - (2 * exp(-x^2)) / sqrtπ)
+ChainRulesCore.@scalar_rule(logerfc(x), - (2 * exp(-x^2 - Ω)) / sqrtπ)
+ChainRulesCore.@scalar_rule(erfcinv(x), - (sqrtπ * (exp(Ω^2) / 2)))
+ChainRulesCore.@scalar_rule(erfcx(x), 2 * x * Ω - 2 / sqrtπ)
+ChainRulesCore.@scalar_rule(logerfcx(x), 2 * (x - exp(-Ω) / sqrtπ))
+ChainRulesCore.@scalar_rule(erfi(x), (2 * exp(x^2)) / sqrtπ)
+ChainRulesCore.@scalar_rule(erfinv(x), sqrtπ * (exp(Ω^2) / 2))
 
 ChainRulesCore.@scalar_rule(gamma(x), Ω * digamma(x))
 ChainRulesCore.@scalar_rule(
@@ -70,8 +73,7 @@ ChainRulesCore.@scalar_rule(
 )
 ChainRulesCore.@scalar_rule(trigamma(x), polygamma(2, x))
 
-# binary
-ChainRulesCore.@scalar_rule(erf(x, y), (-(2 / sqrt(π)) * exp(-x^2), (2 / sqrt(π)) * exp(-y^2)))
+# Bessel functions
 ChainRulesCore.@scalar_rule(
     besselj(ν, x),
     (
@@ -135,6 +137,7 @@ ChainRulesCore.@scalar_rule(
         (hankelh2x(ν - 1, x) - hankelh2x(ν + 1, x)) / 2 + im * Ω,
     ),
 )
+
 ChainRulesCore.@scalar_rule(
     polygamma(m, x),
     (
@@ -188,5 +191,5 @@ ChainRulesCore.@scalar_rule(
     )
 )
 ChainRulesCore.@scalar_rule(expinti(x), exp(x) / x)
-ChainRulesCore.@scalar_rule(sinint(x), sinc(x / π))
+ChainRulesCore.@scalar_rule(sinint(x), sinc(invπ * x))
 ChainRulesCore.@scalar_rule(cosint(x), cos(x) / x)

test/chainrules.jl

@@ -143,4 +143,31 @@
             test_scalar(cosint, x)
         end
     end
+
+    # https://github.com/JuliaMath/SpecialFunctions.jl/issues/307
+    @testset "promotions" begin
+        # one argument
+        for f in (erf, erfc, logerfc, erfcinv, logerfcx, erfi, erfinv, sinint)
+            _, ẏ = frule((NoTangent(), 1f0), f, 1f0)
+            @test ẏ isa Float32
+            _, back = rrule(f, 1f0)
+            _, x̄ = back(1f0)
+            @test x̄ isa Float32
+        end
+
+        # two arguments
+        _, ẏ = frule((NoTangent(), 1f0, 1f0), erf, 1f0, 1f0)
+        @test ẏ isa Float32
+        _, back = rrule(erf, 1f0, 1f0)
+        _, x̄ = back(1f0)
+        @test x̄ isa Float32
+
+        # currently broken, can be fixed if `invsqrtπ` is available:
+        # https://github.com/JuliaMath/IrrationalConstants.jl/pull/8#issuecomment-925828753
+        _, ẏ = frule((NoTangent(), 1f0), erfcx, 1f0)
+        @test_broken ẏ isa Float32
+        _, back = rrule(erfcx, 1f0)
+        _, x̄ = back(1f0)
+        @test x̄ isa Float32
+    end
 end