solve 58 in uiua (attempt sieve)

58/main.ua

@@ -1,66 +1,12 @@
-# rotate 90 deg
-r ← ⍉≡⇌
+# project euler 58
 
-# create spiral numbers with n rows and cols
-# spiral ? n
-s ← (
-  +1⇡ⁿ2 # create n^2 numbers
-  ⊸(
-    ⊸(-1×2√/↥) # t*2 - 1, where t = sqrt(max(range(n^2))) = n
-    ⌈÷2↙       # create [1 1 2 2 3 ...] until sum is n^2
-  )
-  ⊜□˜▽+1°⊏     # successively take 1, 1, 2, 2, 3, ... until all n^2 numbers taken
-  ⇌/◇(˜⊂r)⍜⊢⍚¤ # combine all taken with rotating array to form spiral
-)
+p     ← =1⧻°/×
+Sieve ← ▽⊸≡p+2⇡
 
-# memoized recursive version of s
-σ ← |1 memo(
-  ⨬(⊂⊸(++1⇡∩/↥⊃△(⊢⊢)) r σ-1
-  | ⋅(¤[1]) # base-case
-  )⊸=1
-)
-
-# generates each diagonal of spiral array
-Σ ← +1\+ +¤[2 4 6]×8 ⇡⌊÷2
-
-# get numbers on diagonal
-d ← ⊜°¤ ↥⊸r⊞=. °⊏
+Primes ← Sieve 37417
 
 # is_prime(n) ? n
-p ← =1⧻°/×
-
-┌─╴test
-  p ↚ ⊜(⊜⋕⊸≠@\s)⊸≠@\n
-  ⍤⤙≍ s 7 p $ 37 36 35 34 33 32 31
-            $ 38 17 16 15 14 13 30
-            $ 39 18  5  4  3 12 29
-            $ 40 19  6  1  2 11 28
-            $ 41 20  7  8  9 10 27
-            $ 42 21 22 23 24 25 26
-            $ 43 44 45 46 47 48 49
-└─╴
-
-Sol! ← +1×2⧻⍢(+2⟜(÷⊃⧻/+≡p ^0)|⋅(>0.1)) ⊙1
-
-# Sol!(d s) 3 # too slow
-# (σ -1×2) == s
-# Sol!(d σ -1×2) 3 # too slow (too much memory usage)
-# Sol!(⊂˜↯1÷2-1⟜(♭ Σ)) 3 # still too slow
-
-# okay... let's do it mathematically from scratch:
-
-# primes on diagonals/number of elements on diagonals
-# Chance ← ÷-1×2⟜(
-#   ⊃((+5+∩×₄⊃×₂ⁿ₂)⇡
-#   | (+3+⊃×₆(×4ⁿ2))⇡
-#   | (+7+⊃×₁₀(×4ⁿ2))⇡
-#   ) ⌊÷2
-#   /+≡p⊂⊂
-# )
-#
-# ⍢(+2|>0.1 Chance) 3
-
-# that solved it in 4 minutes (with p memoized)... too slow!
+# p ← ⨬(=|1)⊸=¯1⊸(⍣⊢¯1▽⤚(=0≡◿) Primes ¤)
 
 NewP ← (
   # get the next three prime candidates (lower right is odd square)
@@ -71,18 +17,18 @@ NewP ← (
   ++∩₃p # count how many are prime (0-3)
 )
 
-# initial values are:
-# - 5: the amount of numbers so far; 1, 3, 5, 7, 9 (counter for diagonal)
-# - NewP.: = 3, since 3, 5, 7 are prime (counter for primes on diagonal)
-# - 0: current NewP generation. NewP 0 is 3 (see above)
-5 NewP. 0
-⍢(+4 ⊙+ ⊙⊙(⊸NewP+1) # add 4 for new corners, generate NewP(n+1)
-| >0.1 ÷            # check prime ratio
+Sol ← (
+  # initial values are:
+  # - 5: the amount of numbers so far; 1, 3, 5, 7, 9 (counter for diagonal)
+  # - NewP.: = 3, since 3, 5, 7 are prime (counter for primes on diagonal)
+  # - 0: current NewP generation. NewP 0 is 3 (see above)
+  5 NewP. 0
+  ⍢(+4 ⊙+ ⊙⊙(⊸NewP+1) # add 4 for new corners, generate NewP(n+1)
+  | >0.1 ÷            # check prime ratio
+  )
+  # discard number of primes and diagonal values,
+  # scale generation up to side length
+  # newp gen 0 -> 0*2 + 3 = side length 3
+  # newp gen 1 -> 1*2 + 3 = side length 5, ...
+  ⋅⋅(+3×2)
 )
-# discard number of primes and diagonal values,
-# scale generation up to side length
-# newp gen 0 -> 0*2 + 3 = side length 3
-# newp gen 1 -> 1*2 + 3 = side length 5, ...
-⋅⋅(+3×2)
-
-# that's a 240x speedup, from 4 minutes to 1 second. we can go faster...