Data update

Task/Calkin-Wilf-sequence/Uiua/calkin-wilf-sequence.uiua

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+# Generate Calkin-Wilf sequence, then use continued fractions
+# to discover position in the sequence of any given a/b.
+
+Gcd ← ⊙◌⍢(⟜◿:|±,)°⊟
+Reduce ← ÷⊸Gcd             # Reduce a rational [a b] to its normal form.
+Add ← Reduce ⊟⊓/+(⊢⇌)∩×⇌,, # Add pair of rationals [a b] [c d]
+Subtract ← Add ⊙⍜⊢¯        # Difference of pair of rationals [a b] [c d]
+Multiply ← Reduce ×        # Multiply pair of rationals [a b] [c d]
+Divide ← Multiply ⊙⇌
+Floor ← Reduce ⊟:1⌊/÷⇌
+
+CwNext ← ⇌Subtract:⟜(Add1_1Multiply2_1Floor)
+&p"First twenty terms of Calkin-Wilf sequence:"
+&p/◇⊂≡(□$"_/_ "°⊟)⇌[⍥(CwNext.)20 [1 1]]
+
+Cf ← ⇌Subtract⟜(.⊟:1⌊÷:°⊟)
+
+ContFracRat ← ⇌≡⊢↘1[⍢(Cf|≠0⊡1)]               # Continued Fraction for rational [a b].
+OddContFrac ← ⍥(⊂:1⍜(↙¯1|-1))¬◿2⧻.ContFracRat # Force length to be odd.
+CwPos ← °⋯⇌∧(⊂↯°⊟)⍉⊟⟜(¬◿2⇡⧻):[] OddContFrac   # Calculate pos as described.
+&p""
+{[9 4] [83116 51639]}
+≡◇(&p $"_/_ is at position _ in the sequence"°⊟⟜CwPos)
+&p""
+# And show that the relation works in reverse
+ContFracInt ← ⍥(⊂0)=0⊢⟜(⊜⧻.+1)⋯
+CwAt ← /(Add⇌)≡(⇌⊟1)⇌ContFracInt
+&p$"The number at position _ is _/_"⟜(°⊟CwAt)123456789