From 232907da58277c3669776f2f729a49b09e0ece34 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Sun, 2 Jun 2024 01:06:51 -0400
Subject: [PATCH 01/16] add ForwardDiff and ChainRules extension

---
 Project.toml                 | 10 ++++++++-
 ext/PolyLogChainRulesExt.jl  | 10 +++++++++
 ext/PolyLogForwardDiffExt.jl | 41 ++++++++++++++++++++++++++++++++++++
 test/Li.jl                   |  3 +++
 test/Li1.jl                  |  3 +++
 test/Li2.jl                  |  3 +++
 test/Li3.jl                  |  3 +++
 test/Li4.jl                  |  3 +++
 test/runtests.jl             |  1 +
 9 files changed, 76 insertions(+), 1 deletion(-)
 create mode 100644 ext/PolyLogChainRulesExt.jl
 create mode 100644 ext/PolyLogForwardDiffExt.jl

diff --git a/Project.toml b/Project.toml
index 8f4fd2c0..9cae4038 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,5 +10,13 @@ julia = "1.0"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[weakdeps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+
+[extensions]
+PolyLogForwardDiffExt = "ForwardDiff"
+PolyLogChainRulesExt = "ChainRulesCore"
+
 [targets]
-test = ["Test", "DelimitedFiles"]
+test = ["Test", "DelimitedFiles", "ForwardDiff"]
diff --git a/ext/PolyLogChainRulesExt.jl b/ext/PolyLogChainRulesExt.jl
new file mode 100644
index 00000000..e16bba9a
--- /dev/null
+++ b/ext/PolyLogChainRulesExt.jl
@@ -0,0 +1,10 @@
+module PolyLogChainRulesExt
+
+using PolyLog
+using ChainRulesCore
+@scalar_rule reli4(x) reli3(x)/x
+@scalar_rule reli3(x) reli2(x)/x
+@scalar_rule reli2(x) reli1(x)/x
+@scalar_rule reli1(x) one(x)/(one(x)-x)
+@scalar_rule reli(n,x) reli(n-1,x)/x
+end #module
\ No newline at end of file
diff --git a/ext/PolyLogForwardDiffExt.jl b/ext/PolyLogForwardDiffExt.jl
new file mode 100644
index 00000000..32188c5d
--- /dev/null
+++ b/ext/PolyLogForwardDiffExt.jl
@@ -0,0 +1,41 @@
+module PolyLogForwardDiffExt
+
+using PolyLog
+using ForwardDiff
+using ForwardDiff: Dual, partials
+function PolyLog.reli4(d::Dual{T}) where T
+    val = ForwardDiff.value(d)
+    x = reli4(val)
+    dx = reli3(val)/val
+    return Dual{T}(x, dx * partials(d))
+end
+
+function PolyLog.reli3(d::Dual{T}) where T
+    val = ForwardDiff.value(d)
+    x = reli3(val)
+    dx = reli2(val)/val
+    return Dual{T}(x, dx * partials(d))
+end
+
+function PolyLog.reli2(d::Dual{T}) where T
+    val = ForwardDiff.value(d)
+    x = reli2(val)
+    dx = reli1(val)/val
+    return Dual{T}(x, dx * partials(d))
+end
+
+function PolyLog.reli1(d::Dual{T}) where T
+    val = ForwardDiff.value(d)
+    x = reli1(val)
+    dx = one(val) / (one(val) - val)
+    return Dual{T}(x, dx*partials(d))
+end
+
+function PolyLog.reli(n::Integer,d::Dual{T}) where T
+    val = ForwardDiff.value(d)
+    x = reli(val)
+    dx = PolyLog.reli(n-1,val)/val
+    return Dual{T}(x, dx*partials(d))
+end
+
+end #module
\ No newline at end of file
diff --git a/test/Li.jl b/test/Li.jl
index 4b93d5e4..870a567b 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -128,4 +128,7 @@ end
             end
         end
     end
+
+    #ForwardDiff Test
+    @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,6),float(pi)) == PolyLog.reli(5,float(pi))
 end
diff --git a/test/Li1.jl b/test/Li1.jl
index d3dc8fde..cbf1a76d 100644
--- a/test/Li1.jl
+++ b/test/Li1.jl
@@ -59,4 +59,7 @@
     # test value that causes overflow if squared
     @test PolyLog.li1(1e300 + 1im) ≈ -690.77552789821371 + 3.14159265358979im rtol=eps(Float64)
     @test PolyLog.li1(1.0 + 1e300im) ≈ -690.77552789821371 + 1.5707963267948966im rtol=eps(Float64)
+
+    #ForwardDiff Test
+    @test ForwardDiff.derivative(PolyLog.reli1,float(pi)) == 1/(1 - pi)
 end
diff --git a/test/Li2.jl b/test/Li2.jl
index 580d9378..e937b22b 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -66,4 +66,7 @@
     # test value that causes overflow if squared
     @test PolyLog.li2(1e300 + 1im) ≈ -238582.12510339421 + 2170.13532372464im rtol=eps(Float64)
     @test PolyLog.li2(1.0 + 1e300im) ≈ -238585.82620504462 + 1085.06766186232im rtol=eps(Float64)
+
+    #ForwardDiff Test
+    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == reli1(float(pi))
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index dc0dddb6..c37bcc9c 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -60,4 +60,7 @@
     # test value that causes overflow if squared
     @test PolyLog.li3(1e300 + 1im) ≈ -5.4934049431527088e7 + 749538.186928224im rtol=eps(Float64)
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
+
+    #ForwardDiff Test
+    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == reli2(float(pi))
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 70e6aaf2..620e2ddb 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -52,4 +52,7 @@
     # test value that causes overflow if squared
     @test PolyLog.li4(1e300 + 1im) ≈ -9.4863817894708364e9 + 1.725875455850714e8im rtol=eps(Float64)
     @test PolyLog.li4(1.0 + 1e300im) ≈ -9.4872648206269765e9 + 8.62951114411071e7im rtol=eps(Float64)
+
+    #ForwardDiff Test
+    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == reli3(float(pi))
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 5a8a7fc9..52a3bac9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,5 +1,6 @@
 using Test
 import PolyLog
+import ForwardDiff
 
 include("TestPrecision.jl")
 include("DataReader.jl")

From 4213578233117a25dcb59e752c75ddaf4dae434f Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Sun, 2 Jun 2024 01:15:50 -0400
Subject: [PATCH 02/16] forgot to divide by x in test

---
 test/Li.jl  | 2 +-
 test/Li2.jl | 2 +-
 test/Li3.jl | 2 +-
 test/Li4.jl | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/test/Li.jl b/test/Li.jl
index 870a567b..c07eb9d5 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -130,5 +130,5 @@ end
     end
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,6),float(pi)) == PolyLog.reli(5,float(pi))
+    @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,6),float(pi)) == PolyLog.reli(5,float(pi))/float(pi)
 end
diff --git a/test/Li2.jl b/test/Li2.jl
index e937b22b..a23a4dbc 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -68,5 +68,5 @@
     @test PolyLog.li2(1.0 + 1e300im) ≈ -238585.82620504462 + 1085.06766186232im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == reli1(float(pi))
+    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == reli1(float(pi))/float(pi)
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index c37bcc9c..3a855798 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -62,5 +62,5 @@
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == reli2(float(pi))
+    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == reli2(float(pi))/float(pi)
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 620e2ddb..f3e14eb8 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -54,5 +54,5 @@
     @test PolyLog.li4(1.0 + 1e300im) ≈ -9.4872648206269765e9 + 8.62951114411071e7im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == reli3(float(pi))
+    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == reli3(float(pi))/float(pi)
 end

From feb22c76d72cc2a9a2f793c7507ef1d445b9d16a Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Sun, 2 Jun 2024 13:12:05 -0400
Subject: [PATCH 03/16] add missing module prefixes and spaces

---
 ext/PolyLogChainRulesExt.jl | 13 +++++++------
 test/Li2.jl                 |  2 +-
 test/Li3.jl                 |  2 +-
 test/Li4.jl                 |  2 +-
 4 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/ext/PolyLogChainRulesExt.jl b/ext/PolyLogChainRulesExt.jl
index e16bba9a..caad9137 100644
--- a/ext/PolyLogChainRulesExt.jl
+++ b/ext/PolyLogChainRulesExt.jl
@@ -2,9 +2,10 @@ module PolyLogChainRulesExt
 
 using PolyLog
 using ChainRulesCore
-@scalar_rule reli4(x) reli3(x)/x
-@scalar_rule reli3(x) reli2(x)/x
-@scalar_rule reli2(x) reli1(x)/x
-@scalar_rule reli1(x) one(x)/(one(x)-x)
-@scalar_rule reli(n,x) reli(n-1,x)/x
-end #module
\ No newline at end of file
+@scalar_rule PolyLog.reli4(x) PolyLog.reli3(x)/x
+@scalar_rule PolyLog.reli3(x) PolyLog.reli2(x)/x
+@scalar_rule PolyLog.reli2(x) PolyLog.reli1(x)/x
+@scalar_rule PolyLog.reli1(x) one(x)/(one(x)-x)
+@scalar_rule PolyLog.reli(n,x) PolyLog.reli(n-1,x)/x
+end #module
+
diff --git a/test/Li2.jl b/test/Li2.jl
index a23a4dbc..688db0c5 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -68,5 +68,5 @@
     @test PolyLog.li2(1.0 + 1e300im) ≈ -238585.82620504462 + 1085.06766186232im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == reli1(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == ForwardDiff.reli1(float(pi))/float(pi)
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index 3a855798..9dc2d7e7 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -62,5 +62,5 @@
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == reli2(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == ForwardDiff.reli2(float(pi))/float(pi)
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index f3e14eb8..9458b2a1 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -54,5 +54,5 @@
     @test PolyLog.li4(1.0 + 1e300im) ≈ -9.4872648206269765e9 + 8.62951114411071e7im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == reli3(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == ForwardDiff.reli3(float(pi))/float(pi)
 end

From f8c996e57f05fad9a4a2fe0d4af7f46c037d5087 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Sun, 2 Jun 2024 23:34:48 -0400
Subject: [PATCH 04/16] enbarrasing typo

---
 test/Li2.jl | 2 +-
 test/Li3.jl | 2 +-
 test/Li4.jl | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/Li2.jl b/test/Li2.jl
index 688db0c5..2c22fcfc 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -68,5 +68,5 @@
     @test PolyLog.li2(1.0 + 1e300im) ≈ -238585.82620504462 + 1085.06766186232im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == ForwardDiff.reli1(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == PolyLog.reli1(float(pi))/float(pi)
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index 9dc2d7e7..d923b630 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -62,5 +62,5 @@
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == ForwardDiff.reli2(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 9458b2a1..7b63e47a 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -54,5 +54,5 @@
     @test PolyLog.li4(1.0 + 1e300im) ≈ -9.4872648206269765e9 + 8.62951114411071e7im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == ForwardDiff.reli3(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == PolyLog.reli3(float(pi))/float(pi)
 end

From 8390cc0c446086fb7c4acd563e9e4f936daa9169 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Sun, 2 Jun 2024 23:55:59 -0400
Subject: [PATCH 05/16] move test of FD + reli to ni loop, fix error in
 derivative

---
 ext/PolyLogForwardDiffExt.jl | 2 +-
 test/Li.jl                   | 4 +++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/ext/PolyLogForwardDiffExt.jl b/ext/PolyLogForwardDiffExt.jl
index 32188c5d..0c3869dd 100644
--- a/ext/PolyLogForwardDiffExt.jl
+++ b/ext/PolyLogForwardDiffExt.jl
@@ -33,7 +33,7 @@ end
 
 function PolyLog.reli(n::Integer,d::Dual{T}) where T
     val = ForwardDiff.value(d)
-    x = reli(val)
+    x = reli(n,val)
     dx = PolyLog.reli(n-1,val)/val
     return Dual{T}(x, dx*partials(d))
 end
diff --git a/test/Li.jl b/test/Li.jl
index c07eb9d5..96e737e7 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -93,6 +93,8 @@ end
         @test PolyLog.li(n, 1//1 + 0//1im) ≈ zeta
         @test PolyLog.li(n, 1 + 0im) ≈ zeta
         @test PolyLog.li(n, BigFloat("1.0") + 0im) == PolyLog.zeta(n, BigFloat)
+
+        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n,float(pi))/float(pi)
     end
 
     # value close to boundary between series 1 and 2 in arXiv:2010.09860
@@ -130,5 +132,5 @@ end
     end
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,6),float(pi)) == PolyLog.reli(5,float(pi))/float(pi)
+    
 end

From cc3ed0885e83415354f0713163491f5915296c74 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 01:10:35 -0400
Subject: [PATCH 06/16] add branch to catch x == 0 case

---
 ext/PolyLogForwardDiffExt.jl | 12 ++++++++++++
 test/Li.jl                   |  7 +++----
 test/Li1.jl                  |  1 +
 test/Li2.jl                  |  1 +
 test/Li3.jl                  |  1 +
 test/Li4.jl                  |  1 +
 6 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/ext/PolyLogForwardDiffExt.jl b/ext/PolyLogForwardDiffExt.jl
index 0c3869dd..6dfe1dbf 100644
--- a/ext/PolyLogForwardDiffExt.jl
+++ b/ext/PolyLogForwardDiffExt.jl
@@ -5,6 +5,9 @@ using ForwardDiff
 using ForwardDiff: Dual, partials
 function PolyLog.reli4(d::Dual{T}) where T
     val = ForwardDiff.value(d)
+    if iszero(val)
+        return Dual{T}(one(val), partials(d))
+    end
     x = reli4(val)
     dx = reli3(val)/val
     return Dual{T}(x, dx * partials(d))
@@ -12,6 +15,9 @@ end
 
 function PolyLog.reli3(d::Dual{T}) where T
     val = ForwardDiff.value(d)
+    if iszero(val)
+        return Dual{T}(one(val), partials(d))
+    end
     x = reli3(val)
     dx = reli2(val)/val
     return Dual{T}(x, dx * partials(d))
@@ -19,6 +25,9 @@ end
 
 function PolyLog.reli2(d::Dual{T}) where T
     val = ForwardDiff.value(d)
+    if iszero(val)
+        return Dual{T}(one(val), partials(d))
+    end
     x = reli2(val)
     dx = reli1(val)/val
     return Dual{T}(x, dx * partials(d))
@@ -33,6 +42,9 @@ end
 
 function PolyLog.reli(n::Integer,d::Dual{T}) where T
     val = ForwardDiff.value(d)
+    if iszero(val)
+        return Dual{T}(one(val), partials(d))
+    end
     x = reli(n,val)
     dx = PolyLog.reli(n-1,val)/val
     return Dual{T}(x, dx*partials(d))
diff --git a/test/Li.jl b/test/Li.jl
index 96e737e7..1900f524 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -94,7 +94,9 @@ end
         @test PolyLog.li(n, 1 + 0im) ≈ zeta
         @test PolyLog.li(n, BigFloat("1.0") + 0im) == PolyLog.zeta(n, BigFloat)
 
+        #ForwardDiff Test
         @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n,float(pi))/float(pi)
+        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),0.0) == 1.0
     end
 
     # value close to boundary between series 1 and 2 in arXiv:2010.09860
@@ -129,8 +131,5 @@ end
                 @test typeof(PolyLog.reli(n, convert(T, x))) == T
             end
         end
-    end
-
-    #ForwardDiff Test
-    
+    end    
 end
diff --git a/test/Li1.jl b/test/Li1.jl
index cbf1a76d..67c7f1d6 100644
--- a/test/Li1.jl
+++ b/test/Li1.jl
@@ -62,4 +62,5 @@
 
     #ForwardDiff Test
     @test ForwardDiff.derivative(PolyLog.reli1,float(pi)) == 1/(1 - pi)
+    @test ForwardDiff.derivative(PolyLog.reli1,0.0) == 1.0
 end
diff --git a/test/Li2.jl b/test/Li2.jl
index 2c22fcfc..cd0f0319 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -69,4 +69,5 @@
 
     #ForwardDiff Test
     @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == PolyLog.reli1(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli2,0.0) == 1.0
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index d923b630..f3a1f6e9 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -63,4 +63,5 @@
 
     #ForwardDiff Test
     @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli3,0.0) == 1.0
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 7b63e47a..8e3cf680 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -55,4 +55,5 @@
 
     #ForwardDiff Test
     @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == PolyLog.reli3(float(pi))/float(pi)
+    @test ForwardDiff.derivative(PolyLog.reli4,0.0) == 1.0
 end

From adefae572eab4bf3cb3aafacb64b0cc5a67e3a38 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 01:15:08 -0400
Subject: [PATCH 07/16] add ifelse in CRC too

---
 ext/PolyLogChainRulesExt.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/ext/PolyLogChainRulesExt.jl b/ext/PolyLogChainRulesExt.jl
index caad9137..dd6d567a 100644
--- a/ext/PolyLogChainRulesExt.jl
+++ b/ext/PolyLogChainRulesExt.jl
@@ -2,10 +2,10 @@ module PolyLogChainRulesExt
 
 using PolyLog
 using ChainRulesCore
-@scalar_rule PolyLog.reli4(x) PolyLog.reli3(x)/x
-@scalar_rule PolyLog.reli3(x) PolyLog.reli2(x)/x
-@scalar_rule PolyLog.reli2(x) PolyLog.reli1(x)/x
+@scalar_rule PolyLog.reli4(x) ifelse(iszero(x), one(x), PolyLog.reli3(x)/x)
+@scalar_rule PolyLog.reli3(x) ifelse(iszero(x), one(x), PolyLog.reli2(x)/x)
+@scalar_rule PolyLog.reli2(x) ifelse(iszero(x), one(x), PolyLog.reli1(x)/x)
 @scalar_rule PolyLog.reli1(x) one(x)/(one(x)-x)
-@scalar_rule PolyLog.reli(n,x) PolyLog.reli(n-1,x)/x
+@scalar_rule PolyLog.reli(n,x) ifelse(iszero(x), one(x), PolyLog.reli(n-1,x)/x)
 end #module
 

From e455404c805bc9d955d50b5f1b362d9a6b60432f Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 13:44:34 -0400
Subject: [PATCH 08/16] typo in ForwardDiff reli test

---
 test/Li.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Li.jl b/test/Li.jl
index 1900f524..2abbac71 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -95,7 +95,7 @@ end
         @test PolyLog.li(n, BigFloat("1.0") + 0im) == PolyLog.zeta(n, BigFloat)
 
         #ForwardDiff Test
-        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n,float(pi))/float(pi)
+        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n-1,float(pi))/float(pi)
         @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),0.0) == 1.0
     end
 

From fd6c684874a93a155bccd655b4fdbb155d82d004 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 14:03:22 -0400
Subject: [PATCH 09/16] only test derivatives on 1.9 onwards

---
 test/Li.jl       | 6 ++++--
 test/Li1.jl      | 6 ++++--
 test/Li2.jl      | 6 ++++--
 test/Li3.jl      | 6 ++++--
 test/Li4.jl      | 6 ++++--
 test/runtests.jl | 4 +++-
 6 files changed, 23 insertions(+), 11 deletions(-)

diff --git a/test/Li.jl b/test/Li.jl
index 2abbac71..d2329324 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -95,8 +95,10 @@ end
         @test PolyLog.li(n, BigFloat("1.0") + 0im) == PolyLog.zeta(n, BigFloat)
 
         #ForwardDiff Test
-        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n-1,float(pi))/float(pi)
-        @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),0.0) == 1.0
+        if isdefined(Base,:get_extension)
+            @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n-1,float(pi))/float(pi)
+            @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),0.0) == 1.0
+        end
     end
 
     # value close to boundary between series 1 and 2 in arXiv:2010.09860
diff --git a/test/Li1.jl b/test/Li1.jl
index 67c7f1d6..7cf3b738 100644
--- a/test/Li1.jl
+++ b/test/Li1.jl
@@ -61,6 +61,8 @@
     @test PolyLog.li1(1.0 + 1e300im) ≈ -690.77552789821371 + 1.5707963267948966im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli1,float(pi)) == 1/(1 - pi)
-    @test ForwardDiff.derivative(PolyLog.reli1,0.0) == 1.0
+    if isdefined(Base,:get_extension)
+        @test ForwardDiff.derivative(PolyLog.reli1,float(pi)) == 1/(1 - pi)
+        @test ForwardDiff.derivative(PolyLog.reli1,0.0) == 1.0
+    end
 end
diff --git a/test/Li2.jl b/test/Li2.jl
index cd0f0319..c843e392 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -68,6 +68,8 @@
     @test PolyLog.li2(1.0 + 1e300im) ≈ -238585.82620504462 + 1085.06766186232im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == PolyLog.reli1(float(pi))/float(pi)
-    @test ForwardDiff.derivative(PolyLog.reli2,0.0) == 1.0
+    if isdefined(Base,:get_extension)
+        @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == PolyLog.reli1(float(pi))/float(pi)
+        @test ForwardDiff.derivative(PolyLog.reli2,0.0) == 1.0
+    end
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index f3a1f6e9..5a2b65ea 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -62,6 +62,8 @@
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
-    @test ForwardDiff.derivative(PolyLog.reli3,0.0) == 1.0
+    if isdefined(Base, :ForwardDiff)
+        @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
+        @test ForwardDiff.derivative(PolyLog.reli3,0.0) == 1.0
+    end
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 8e3cf680..9afe1390 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -54,6 +54,8 @@
     @test PolyLog.li4(1.0 + 1e300im) ≈ -9.4872648206269765e9 + 8.62951114411071e7im rtol=eps(Float64)
 
     #ForwardDiff Test
-    @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == PolyLog.reli3(float(pi))/float(pi)
-    @test ForwardDiff.derivative(PolyLog.reli4,0.0) == 1.0
+    if isdefined(Base,:get_extension)
+        @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == PolyLog.reli3(float(pi))/float(pi)
+        @test ForwardDiff.derivative(PolyLog.reli4,0.0) == 1.0
+    end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 52a3bac9..00798420 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,8 @@
 using Test
 import PolyLog
-import ForwardDiff
+if isdefined(Base,:get_extension)
+    import ForwardDiff
+end
 
 include("TestPrecision.jl")
 include("DataReader.jl")

From 57237f42ce416540904ec63b7ca7dc310ecc981a Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 14:58:07 -0400
Subject: [PATCH 10/16] support 1.0: add ForwardDiff to extras

---
 Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Project.toml b/Project.toml
index 9cae4038..3e68f55f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,6 +9,7 @@ julia = "1.0"
 [extras]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"

From 475646a2b45d50e351e89ebf410cc5061f162362 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Mon, 3 Jun 2024 22:40:28 -0400
Subject: [PATCH 11/16] typo in conditional

---
 test/Li3.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Li3.jl b/test/Li3.jl
index 5a2b65ea..109b46bb 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -62,7 +62,7 @@
     @test PolyLog.li3(1.0 + 1e300im) ≈ -5.4936606061973454e7 + 374771.031356405im rtol=eps(Float64)
 
     #ForwardDiff Test
-    if isdefined(Base, :ForwardDiff)
+    if isdefined(Base, :get_extension)
         @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
         @test ForwardDiff.derivative(PolyLog.reli3,0.0) == 1.0
     end

From 7a22a963a675fbe51b8721f596d89200db5c067f Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Tue, 4 Jun 2024 18:59:09 -0400
Subject: [PATCH 12/16] add ChainRules tests

---
 Project.toml                |  3 ++-
 ext/PolyLogChainRulesExt.jl | 12 ++++++------
 test/Li.jl                  |  2 ++
 test/Li1.jl                 |  2 ++
 test/Li2.jl                 |  2 ++
 test/Li3.jl                 |  2 ++
 test/Li4.jl                 |  2 ++
 test/runtests.jl            |  1 +
 8 files changed, 19 insertions(+), 7 deletions(-)

diff --git a/Project.toml b/Project.toml
index 3e68f55f..6e732f2e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,6 +10,7 @@ julia = "1.0"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -20,4 +21,4 @@ PolyLogForwardDiffExt = "ForwardDiff"
 PolyLogChainRulesExt = "ChainRulesCore"
 
 [targets]
-test = ["Test", "DelimitedFiles", "ForwardDiff"]
+test = ["Test", "DelimitedFiles", "ForwardDiff", "ChainRulesTestUtils"]
diff --git a/ext/PolyLogChainRulesExt.jl b/ext/PolyLogChainRulesExt.jl
index dd6d567a..bb58fecf 100644
--- a/ext/PolyLogChainRulesExt.jl
+++ b/ext/PolyLogChainRulesExt.jl
@@ -2,10 +2,10 @@ module PolyLogChainRulesExt
 
 using PolyLog
 using ChainRulesCore
-@scalar_rule PolyLog.reli4(x) ifelse(iszero(x), one(x), PolyLog.reli3(x)/x)
-@scalar_rule PolyLog.reli3(x) ifelse(iszero(x), one(x), PolyLog.reli2(x)/x)
-@scalar_rule PolyLog.reli2(x) ifelse(iszero(x), one(x), PolyLog.reli1(x)/x)
-@scalar_rule PolyLog.reli1(x) one(x)/(one(x)-x)
-@scalar_rule PolyLog.reli(n,x) ifelse(iszero(x), one(x), PolyLog.reli(n-1,x)/x)
-end #module
+ChainRulesCore.@scalar_rule PolyLog.reli4(x) ifelse(iszero(x), one(x), PolyLog.reli3(x)/x)
+ChainRulesCore.@scalar_rule PolyLog.reli3(x) ifelse(iszero(x), one(x), PolyLog.reli2(x)/x)
+ChainRulesCore.@scalar_rule PolyLog.reli2(x) ifelse(iszero(x), one(x), PolyLog.reli1(x)/x)
+ChainRulesCore.@scalar_rule PolyLog.reli1(x) one(x)/(one(x)-x)
+ChainRulesCore.@scalar_rule(PolyLog.reli(n, x),(ChainRulesCore.NoTangent(),ifelse(iszero(x), one(x), PolyLog.reli(n-1,x)/x)))
 
+end #module
diff --git a/test/Li.jl b/test/Li.jl
index d2329324..7045f8fb 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -98,6 +98,8 @@ end
         if isdefined(Base,:get_extension)
             @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),float(pi)) == PolyLog.reli(n-1,float(pi))/float(pi)
             @test ForwardDiff.derivative(Base.Fix1(PolyLog.reli,n),0.0) == 1.0
+            ChainRulesTestUtils.test_frule(PolyLog.reli, n, 0.0)
+            ChainRulesTestUtils.test_rrule(PolyLog.reli, n, float(pi))
         end
     end
 
diff --git a/test/Li1.jl b/test/Li1.jl
index 7cf3b738..307d07cc 100644
--- a/test/Li1.jl
+++ b/test/Li1.jl
@@ -64,5 +64,7 @@
     if isdefined(Base,:get_extension)
         @test ForwardDiff.derivative(PolyLog.reli1,float(pi)) == 1/(1 - pi)
         @test ForwardDiff.derivative(PolyLog.reli1,0.0) == 1.0
+        ChainRulesTestUtils.test_frule(PolyLog.reli1, 0.0)
+        ChainRulesTestUtils.test_rrule(PolyLog.reli1, float(pi))
     end
 end
diff --git a/test/Li2.jl b/test/Li2.jl
index c843e392..2213df99 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -71,5 +71,7 @@
     if isdefined(Base,:get_extension)
         @test ForwardDiff.derivative(PolyLog.reli2,float(pi)) == PolyLog.reli1(float(pi))/float(pi)
         @test ForwardDiff.derivative(PolyLog.reli2,0.0) == 1.0
+        ChainRulesTestUtils.test_frule(PolyLog.reli2, 0.0)
+        ChainRulesTestUtils.test_rrule(PolyLog.reli2, float(pi))
     end
 end
diff --git a/test/Li3.jl b/test/Li3.jl
index 109b46bb..1f815c03 100644
--- a/test/Li3.jl
+++ b/test/Li3.jl
@@ -65,5 +65,7 @@
     if isdefined(Base, :get_extension)
         @test ForwardDiff.derivative(PolyLog.reli3,float(pi)) == PolyLog.reli2(float(pi))/float(pi)
         @test ForwardDiff.derivative(PolyLog.reli3,0.0) == 1.0
+        ChainRulesTestUtils.test_frule(PolyLog.reli3, 0.0)
+        ChainRulesTestUtils.test_rrule(PolyLog.reli3, float(pi))
     end
 end
diff --git a/test/Li4.jl b/test/Li4.jl
index 9afe1390..fb041120 100644
--- a/test/Li4.jl
+++ b/test/Li4.jl
@@ -57,5 +57,7 @@
     if isdefined(Base,:get_extension)
         @test ForwardDiff.derivative(PolyLog.reli4,float(pi)) == PolyLog.reli3(float(pi))/float(pi)
         @test ForwardDiff.derivative(PolyLog.reli4,0.0) == 1.0
+        ChainRulesTestUtils.test_frule(PolyLog.reli4, 0.0)
+        ChainRulesTestUtils.test_rrule(PolyLog.reli4, float(pi))
     end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 00798420..98f65563 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2,6 +2,7 @@ using Test
 import PolyLog
 if isdefined(Base,:get_extension)
     import ForwardDiff
+    import ChainRulesTestUtils
 end
 
 include("TestPrecision.jl")

From 7e29d6f8370419deec90e06b992f358df57103d9 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Tue, 4 Jun 2024 18:59:29 -0400
Subject: [PATCH 13/16] whitespace

---
 ext/PolyLogForwardDiffExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/PolyLogForwardDiffExt.jl b/ext/PolyLogForwardDiffExt.jl
index 6dfe1dbf..8831ad0a 100644
--- a/ext/PolyLogForwardDiffExt.jl
+++ b/ext/PolyLogForwardDiffExt.jl
@@ -50,4 +50,4 @@ function PolyLog.reli(n::Integer,d::Dual{T}) where T
     return Dual{T}(x, dx*partials(d))
 end
 
-end #module
\ No newline at end of file
+end #module

From d5c8d60ea8b6d9b355f01c01f6ac073a4e9b975f Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Wed, 5 Jun 2024 02:50:46 -0400
Subject: [PATCH 14/16] whitespace

---
 test/Li.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Li.jl b/test/Li.jl
index 7045f8fb..2419d41e 100644
--- a/test/Li.jl
+++ b/test/Li.jl
@@ -135,5 +135,5 @@ end
                 @test typeof(PolyLog.reli(n, convert(T, x))) == T
             end
         end
-    end    
+    end
 end

From b7810dfc072dc35b6b64803faabe7e37a117ae92 Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Fri, 7 Jun 2024 14:42:51 -0400
Subject: [PATCH 15/16] add compat

---
 Project.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Project.toml b/Project.toml
index 6e732f2e..d6f9eefc 100644
--- a/Project.toml
+++ b/Project.toml
@@ -5,6 +5,8 @@ version = "2.4.2"
 
 [compat]
 julia = "1.0"
+ChainRulesCore = "1"
+ForwardDiff = "0.11"
 
 [extras]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"

From 59bd8f8a74f97340f2971dd5ca67bfa8f7dfadef Mon Sep 17 00:00:00 2001
From: longemen3000 <longemen3000@gmail.com>
Date: Fri, 7 Jun 2024 18:05:18 -0400
Subject: [PATCH 16/16] modify ForwardDiff compat

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index d6f9eefc..3fd42516 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,7 +6,7 @@ version = "2.4.2"
 [compat]
 julia = "1.0"
 ChainRulesCore = "1"
-ForwardDiff = "0.11"
+ForwardDiff = "0.10,0.11"
 
 [extras]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"