README and benchmarks

benchmark/benchmarks.jl

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+# some random benchmarks; for j=50000 you need more than 8GB of memory
+using WignerSymbols
+
+@time wigner3j(BigFloat, 15, 30, 40, 2, 2, -4)
+@time wigner3j(BigFloat, 200, 200, 200, -10, 60, -50)
+@time wigner3j(BigFloat, 50000, 50000, 50000, 1000, -6000, 5000)
+
+j = 8
+@time wigner6j(BigFloat, j, j, j, j, j, j)
+j = 200
+@time wigner6j(BigFloat, j, j, j, j, j, j)
+j = 600
+@time wigner6j(BigFloat, j, j, j, j, j, j)
+j = 10000
+@time wigner6j(BigFloat, j, j, j, j, j, j)
+j = 50000
+@time wigner6j(BigFloat, j, j, j, j, j, j)
+
+function compute3jmax(jmax)
+    for j₁ = 0:1//2:jmax
+        for j₂ = 0:1//2:j₁
+            for j₃ = abs(j₁-j₂):j₂
+                if isinteger(j₁)
+                    m₁ = 0
+                    M₂ = min(j₂, j₃-m₁)
+                    for m₂ = M₂:(-1):0
+                        wigner3j(j₁,j₂,j₃,0, m₂)
+                    end
+                    for m₁ = 1:j₁
+                        M₂ = min(j₂, j₃-m₁)
+                        for m₂ = -M₂:M₂
+                            wigner3j(j₁, j₂, j₃, m₁, m₂)
+                        end
+                    end
+                else
+                    for m₁ = 1//2:j₁
+                        M₂ = min(j₂, j₃-m₁)
+                        for m₂ = -M₂:M₂
+                            wigner3j(j₁, j₂, j₃, m₁, m₂)
+                        end
+                    end
+                end
+            end
+        end
+    end
+    return nothing
+end
+
+@time compute3jmax(10)
+
+function computeinteger3jmax(jmax)
+    for j₁ = 0:jmax
+        for j₂ = 0:j₁
+            for j₃ = abs(j₁-j₂):j₂
+                m₁ = 0
+                M₂ = min(j₂, j₃-m₁)
+                for m₂ = M₂:(-1):0
+                    wigner3j(j₁,j₂,j₃,0, m₂)
+                end
+                for m₁ = 1:j₁
+                    M₂ = min(j₂, j₃-m₁)
+                    for m₂ = -M₂:M₂
+                        wigner3j(j₁, j₂, j₃, m₁, m₂)
+                    end
+                end
+            end
+        end
+    end
+    return nothing
+end
+
+function compute6jmax(jmax)
+    for j₁ = 0:1//2:jmax
+        for j₂ = 0:1//2:j₁
+            for j₃ = abs(j₁-j₂):j₂
+                for j₄ = 0:1//2:jmax
+                    for j₅ = abs(j₃-j₄):min(jmax,j₃+j₄)
+                        for j₆ = min(abs(j₂-j₄),abs(j₁-j₅)):min(j₂+j₄,j₁+j₅,jmax)
+                            wigner6j(j₁, j₂, j₃, j₄, j₅, j₆)
+                        end
+                    end
+                end
+            end
+        end
+    end
+    return nothing
+end
+@time compute6jmax(10)
+
+
+function computeinteger6jmax(jmax)
+    for j₁ = 0:jmax
+        for j₂ = 0:j₁
+            for j₃ = abs(j₁-j₂):j₂
+                for j₄ = 0:jmax
+                    for j₅ = abs(j₃-j₄):min(jmax,j₃+j₄)
+                        for j₆ = min(abs(j₂-j₄),abs(j₁-j₅)):min(j₂+j₄,j₁+j₅,jmax)
+                            wigner6j(j₁, j₂, j₃, j₄, j₅, j₆)
+                        end
+                    end
+                end
+            end
+        end
+    end
+    return nothing
+end