add PTYQoLIrrationalConstantsExt

Author: putianyi889

ext/PTYQoLIrrationalConstantsExt.jl

@@ -0,0 +1,36 @@
+module PTYQoLIrrationalConstantsExt
+
+using IrrationalConstants
+import Base: +, -, *, /, inv, sqrt, exp, log
+
+# x+x=2x, 2x-x=x, x/2x=1/2, 2x/x=2
+for (x, halfx) in ((halfπ,quartπ), (π,halfπ), (twoπ,π), (fourπ,twoπ), (inv2π,inv4π), (invπ,inv2π), (twoinvπ,invπ), (fourinvπ,twoinvπ), (sqrt2,invsqrt2), (sqrt2π,sqrthalfπ), (sqrt4π,sqrtπ))
+    @eval +(::$(typeof(halfx)), ::$(typeof(halfx))) = $x
+    @eval -(::$(typeof(x)), ::$(typeof(halfx))) = $halfx
+    @eval /(::$(typeof(halfx)), ::$(typeof(x))) = 1/2
+    @eval /(::$(typeof(x)), ::$(typeof(halfx))) = 2
+end
+
+# x*inv(x)=1
+for (x,invx) in ((quartπ,fourinvπ), (halfπ,twoinvπ), (π,invπ), (twoπ,inv2π), (fourπ,inv4π), (sqrt2,invsqrt2), (sqrtπ,invsqrtπ), (sqrt2π,invsqrt2π))
+    @eval inv(::$(typeof(x))) = $invx
+    @eval inv(::$(typeof(invx))) = $x
+    @eval *(::$(typeof(x)), ::$(typeof(invx))) = 1
+    @eval *(::$(typeof(invx)), ::$(typeof(x))) = 1
+end
+
+# sqrt(x)*sqrt(x)=x, x/sqrt(x)=sqrt(x)
+for (x,sqrtx) in ((π,sqrtπ), (twoπ,sqrt2π), (fourπ,sqrt4π), (halfπ,sqrthalfπ), (invπ,invsqrtπ), (inv2π,invsqrt2π))
+    @eval sqrt(::$(typeof(x))) = $sqrtx
+    @eval *(::$(typeof(sqrtx)), ::$(typeof(sqrtx))) = $x
+    @eval /(::$(typeof(x)), ::$(typeof(sqrtx))) = $sqrtx
+    @eval /(::$(typeof(sqrtx)), ::$(typeof(x))) = inv($sqrtx)
+end
+
+# exp(log(x))=x
+for (x,logx) in ((π,logπ), (twoπ,log2π), (fourπ,log4π))
+    @eval log(::$(typeof(x))) = $logx
+    @eval exp(::$(typeof(logx))) = $x
+end
+
+end # module

test/runtests.jl

@@ -119,8 +119,32 @@ end
     @testset "AlgebraicNumbers" begin
         using AlgebraicNumbers
     end
-    @testset "Infinities" begin
-        using Infinities
+    @testset "IrrationalConstants" begin
+        using IrrationalConstants
+        @testset "half" begin
+            for (x, halfx) in ((halfπ,quartπ), (π,halfπ), (twoπ,π), (fourπ,twoπ), (inv2π,inv4π), (invπ,inv2π), (twoinvπ,invπ), (fourinvπ,twoinvπ), (sqrt2,invsqrt2), (sqrt2π,sqrthalfπ), (sqrt4π,sqrtπ))
+                @test halfx + halfx === x
+                @test x - halfx === halfx
+                @test halfx / x === 0.5
+                @test x / halfx === 2
+            end
+        end
+        @testset "inv" begin
+            for (x,invx) in ((quartπ,fourinvπ), (halfπ,twoinvπ), (π,invπ), (twoπ,inv2π), (fourπ,inv4π), (sqrt2,invsqrt2), (sqrtπ,invsqrtπ), (sqrt2π,invsqrt2π))
+                @test inv(x) === invx
+                @test inv(invx) === x
+                @test x*invx === 1
+                @test invx*x === 1
+            end
+        end
+        @testset "sqrt" begin
+            for (x,sqrtx) in ((π,sqrtπ), (twoπ,sqrt2π), (fourπ,sqrt4π), (halfπ,sqrthalfπ), (invπ,invsqrtπ), (inv2π,invsqrt2π))
+                @test sqrt(x) === sqrtx
+                @test sqrtx*sqrtx === x
+                @test x/sqrtx === sqrtx
+                @test sqrtx/x === inv(sqrtx)
+            end
+        end
     end
 end