Data commit

Task/Miller-Rabin-primality-test/BQN/miller-rabin-primality-test-1.bqn

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+_modMul ← { n _𝕣: n|× }
+MillerRabin ← {  𝕊n: 10𝕊n ; iter 𝕊 n: !2|n
+  # n = 1 + d×2⋆s
+  s ← 0 {𝕨 2⊸|◶⟨+⟜1𝕊2⌊∘÷˜⊢,⊣⟩ 𝕩} n-1
+  d ← (n-1) ÷ 2⋆s
+
+  # Arithmetic mod n
+  Mul ← n _modMul
+  Pow ← Mul{𝔽´𝔽˜⍟(/2|⌊∘÷⟜2⍟(↕1+·⌊2⋆⁼⊢)𝕩)𝕨}
+
+  # Miller-Rabin test
+  MR ← {
+       1 =𝕩 ? 𝕨≠s ;
+    (n-1)=𝕩 ? 0   ;
+        𝕨≤1 ? 1   ;
+    (𝕨-1) 𝕊 Mul˜𝕩
+  }
+  C ← { 𝕊a: s MR a Pow d }  # Is composite
+  {0:1; C •rand.Range⌾(-⟜2) n ? 0; 𝕊𝕩-1} iter
+}

Task/Miller-Rabin-primality-test/BQN/miller-rabin-primality-test-2.bqn

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+# Compute n|𝕨×𝕩 in high precision
+_modMul ← { n _𝕣:
+  # Split each argument into two 26-bit numbers, with the remaining
+  # mantissa bit encoded in the sign of the lower-order part.
+  q←1+2⋆27
+  Split ← { h←(q×𝕩)(⊣--)𝕩 ⋄ ⟨𝕩-h,h⟩ }
+  # The product, and an error relative to precise split multiplication.
+  Mul ← × (⊣ ⋈ -⊸(+´)) ·⥊×⌜○Split
+  ((n×<⟜0)⊸+ -⟜n+⊢)´ n | Mul
+}

Task/Miller-Rabin-primality-test/BQN/miller-rabin-primality-test-3.bqn

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+   MillerRabin 15485867
+1
+   MillerRabin¨⊸/ 101+2×↕10
+⟨ 101 103 107 109 113 ⟩