Move impl.bqn to src/r.bqn

2 files changed, 456 insertions, 1 deletions

diff --git a/src/pr.bqn b/src/pr.bqn
index d68b3453..f695e4cb 100755
--- a/src/pr.bqn
+++ b/src/pr.bqn
@@ -2,7 +2,7 @@
 
 # Process BQN runtime
 
-impl ← •LNS •path∾"../impl.bqn"
+impl ← •LNS •path∾"r.bqn"
 
 chrs←⟨
   "+-×÷⋆√⌊⌈|¬∧∨<>≠=≤≥≡≢⊣⊢⥊∾≍↑↓↕⌽⍉/⍋⍒⊏⊑⊐⊒∊⍷⊔!"
diff --git a/src/r.bqn b/src/r.bqn
new file mode 100644
index 00000000..7b873db7
--- /dev/null
+++ b/src/r.bqn
@@ -0,0 +1,455 @@
+◶ ← {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}     # LIMITED to number left operand result
+⊘ ← {𝕨((1{𝔽}𝕨)-0)◶𝔽‿𝔾 𝕩}
+⊢ ← {𝕩}
+⊣ ← {𝕩}⊘{𝕨}
+˜ ← {𝕩𝔽𝕨⊣𝕩}
+∘ ← {𝔽𝕨𝔾𝕩}
+○ ← {(𝔾𝕨)𝔽𝔾𝕩}
+⊸ ← {(𝔽𝕨⊣𝕩)𝔾𝕩}
+⟜ ← {(𝕨⊣𝕩)𝔽𝔾𝕩}
+⍟ ← {𝕨((𝕨𝔾𝕩)⊑⊢‿𝕗){𝔽}𝕩}   # LIMITED to boolean right operand result
+
+# LIMITED to numeric arguments for scalar cases
+< ← {⟨⟩⥊⟨𝕩⟩} ⊘ (1-≤˜)
+> ←            (1-≤)
+≢ ↩ IsArray◶⟨⟩‿≢  # LIMITED to monadic case
+≠ ← (0<=)◶⟨1⋄0⊑≢⟩
+
+_fold←{
+  ! 1==𝕩
+  l←≠v←𝕩 ⋄ F←𝔽
+  r←𝕨 (0<l)◶{𝕩⋄Identity f}‿{l↩l-1⋄l⊑𝕩}⊘⊣ 𝕩
+  {r↩(𝕩⊑v)F r}⌜(l-1)⊸-⌜↕l
+  r
+}
+´ ← _fold
+
+
+#⌜
+# LAYER 2: Pervasion
+
+ToArray ← <⍟(1-IsArray)
+Int←IsArray◶⟨⌊⊸=,0⟩
+Nat←IsArray◶⟨0⊸≤×⌊⊸=,0⟩
+
+∾ ← {k←≠𝕨⋄k⊸≤◶⟨⊑⟜𝕨⋄-⟜k⊑𝕩˜⟩⌜↕k+≠𝕩}  # LIMITED to two vector arguments
+
+_eachd←{
+  _d←{ # Equal ranks
+    p←≢𝕨
+    ! 1(⊑⟜p=⊑⟜(≢𝕩))⊸×´↕=𝕨
+    p⥊ (⊑⟜(⥊𝕨)𝔽⊑⟜(⥊𝕩))⌜↕1×´p
+  }
+  _e←{ # 𝕨 has smaller or equal rank
+    p←≢𝕨 ⋄ k←=𝕨 ⋄ q←≢𝕩
+    ! 1(⊑⟜p=⊑⟜q)⊸×´↕k
+    l←1(q⊑˜k⊸+)⊸×´↕(=𝕩)-k
+    a←⥊𝕨 ⋄ b←⥊𝕩
+    q⥊⥊(≠a) (⊑⟜a𝔽l⊸×⊸+⊑b˜)⌜○↕ l
+  }
+  =○=◶⟨>○=◶⟨𝔽_e⋄𝔽˜_e˜⟩⋄𝔽_d⟩
+}
+
+_perv←{ # Pervasion
+  R←𝔽{𝕨𝔽_perv𝕩}
+  +○IsArray◶⟨𝔽⋄R⌜⊘(>○IsArray◶{𝕨{𝕗R𝕩}⌜𝕩}‿{𝕩{𝕩R𝕗}⌜𝕨})⋄R _eachd⟩
+}
+
+⌜ ↩ {𝔽⌜○ToArray}
+¨ ↩ {(𝔽⌜)⊘(𝔽_eachd○ToArray)}
+
+match←{(0⊑𝕨)◶(1⊑𝕨)‿𝕩}´⟨
+  ⟨=○IsArray, 0⟩
+  ⟨IsArray∘⊢, =⟩
+  ⟨=○=      , 0⟩
+  ⟨1×´=¨○≢  , 0⟩
+  {1×´⥊𝕨Match¨𝕩}
+⟩
+
+Cmp0 ← ≤˜-≤
+Cmp1 ← (0<1×´≢∘⊢)◶⟨1, IsArray∘⊢◶(1-2×≤)‿{𝕨Cmp1𝕩}⟜(0⊑⥊)⟩
+Cmp ← +○IsArray◶⟨
+  Cmp0
+  IsArray∘⊣◶⟨Cmp1,-Cmp1˜⟩
+  {
+    lc←𝕨CmpLen○≢𝕩
+    cc ← (⊑⟜(⥊𝕨))⊸Cmp⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
+    Cc˜0
+  }
+⟩
+_grade←{
+  ! 1≤=𝕩
+  m←1×´1 Cell 𝕩
+  cc←m 𝔽○(⊑⟜(⥊𝕩)) _getCellCmp 0
+  GT←Cc>0˜
+  l←≠𝕩
+  B←l⊸≤◶⊢‿l
+  (↕l){
+    i←-d←𝕨 ⋄ j←ei←ej←0
+    e←3 ⋄ G←GT○(⊑⟜(m⊸ר⍟(1-m=1)𝕩)) ⋄ c←⟨G,0,1,2⟩
+    s←(8≤d)⊑⟨+,{(𝕩-1){𝕩⋄e↩2⋄j↩i⋄i↩𝕩}⍟(1-G)⍟(1-e)𝕩}⟩
+    N←{i↩d+𝕨⋄ej↩B d+ei↩B j↩d+𝕩⋄e↩l≤j⋄S ei⋄i R j}
+    R←{𝕨e◶c𝕩}◶{e+↩2×ei=i↩1+𝕨⋄𝕨}‿{e+↩ej=j↩1+𝕩⋄𝕩}‿N
+    {(i R j)⊑𝕩}⟜𝕩¨𝕩
+  }´(2⋆ni-1+⊢)¨↕ni←-⌊-2 Log l+l=0
+}
+
+Indices←{
+  ! 1==𝕩
+  l←≠𝕩
+  {
+    ! 1×´Nat¨𝕩
+    k←l-1
+    N ← ((⊢+-×0=𝕩⊑˜⊢)`k⊸-⌜↕l)⊑˜k-⊢  # Next nonzero
+    E ← ⊑⟜(+`𝕩)
+    ei←E i←N 0
+    {{ei↩E i↩N𝕩+1⋄i}⍟(𝕩=ei)i}¨↕E k
+  }⍟(0<l)𝕩
+}
+
+_under_←{
+  i←↕l←1×´s←≢𝕩
+  v←⥊𝕨𝔽○𝔾𝕩
+  g←Cmp0 _grade gi←⥊𝔾s⥊i
+  P←(≠g)⊸≤◶⟨(⊑⟜g)⊑gi˜,l⟩
+  e←P j←0
+  s⥊{e=𝕩}◶⟨⊑⟜(⥊𝕩),{𝕩⋄r←(j⊑g)⊑v⋄e↩P j↩1+j⋄r}⟩¨i
+}
+⌾ ← _under_
+
++ ↩ + _perv
+- ↩ - _perv
+× ↩ (0⊸(<->) ⊘ ×) _perv
+÷ ↩ ÷ _perv
+⋆ ↩ ⋆ _perv
+√ ← ⋆⟜(÷2)   ⊘ (⋆⟜÷˜)
+| ← (×⟜×     ⊘ {𝕩-𝕨×⌊𝕩÷𝕨}) _perv
+⌊ ↩ (⌊       ⊘ {(𝕨>𝕩)⊑𝕨‿𝕩}) _perv
+⌈ ← (-∘⌊∘-   ⊘ {(𝕨<𝕩)⊑𝕨‿𝕩}) _perv
+¬ ← 1+-
+∧ ←            ×
+∨ ←            (+-×)
+< ↩ {⟨⟩⥊⟨𝕩⟩} ⊘ ((1-≤˜) _perv)
+> ↩             (1-≤) _perv
+≠ ↩ ≠        ⊘ ((1-=) _perv)
+= ↩ =        ⊘ (= _perv)
+≥ ← !∘0      ⊘ (≤˜_perv)
+≤ ↩ !∘0      ⊘ (≤ _perv)
+identity ← (0⊑⟨!∘0⟩) {(0⊑𝕨){𝕗=𝕩}◶𝕩‿(1⊑𝕨)}´ ⟨+‿0,-‿0,×‿1,÷‿1,⋆‿1,√‿1,∧‿1,∨‿0,|‿0,⌊‿∞,⌈‿¯∞,<‿0,≤‿1,=‿1,≥‿1,>‿0,≠‿0⟩
+
+SelSub←{
+  ! IsArray 𝕨
+  ! 1×´⥊Int¨ 𝕨
+  l←≠𝕩
+  ! 1×´⥊ ((-l)⊸≤×l⊸>)¨ 𝕨
+  ((⊢+l×0>⊢)¨𝕨)(1==𝕩)◶{
+    c←1×´s←1 Cell 𝕩
+    𝕨((⥊𝕩)⊑˜c⊸×⊸+)⌜s⥊↕c
+  }‿{
+    ⊑⟜𝕩¨𝕨
+  }𝕩
+}
+
+
+#⌜
+# LAYER 3: Remove other limits
+# Now all implementations are full except ∾ and ⊑; ↕ is monadic only
+
+Deshape←IsArray◶{⟨𝕩⟩}‿⥊
+Reshape←{
+  ! 1≥=𝕨
+  𝕨↩Deshape 𝕨
+  ! ∧´Nat¨𝕨
+  l←×´𝕨
+  n←×´≢𝕩
+  𝕨⥊{
+    𝕩(0<n)◶⟨Type⊸(⊣⌜)⋄⥊⊸{⊑⟜𝕨¨n|𝕩}⟩↕l
+  }⍟(l≠n)𝕩
+}⟜ToArray
+⥊ ↩ Deshape        ⊘ Reshape
+
+Range←{
+  I←{!Nat𝕩⋄↕𝕩}
+  M←{!1==𝕩⋄(<⟨⟩)⥊⊸∾⌜´I¨𝕩}
+  IsArray◶I‿M 𝕩
+}
+
+Depth←IsArray◶0‿{1+0⌈´Depth¨⥊𝕩}
+
+≡ ← Depth          ⊘ Match
+≢ ↩ ≢              ⊘ (¬Match)
+
+
+#⌜
+# LAYER 4: Operators
+
+
+DropV← {⊑⟜𝕩¨𝕨+↕𝕨-˜≠𝕩}
+Cell ← DropV⟜≢
+Pair ← {⟨𝕩⟩} ⊘ {⟨𝕨,𝕩⟩}
+
+Merge←{
+  c←≢0⊑⥊𝕩
+  ! ∧´⥊(c≡≢)¨𝕩
+  𝕩⊑⟜⥊˜⌜c⥊↕×´c
+}⍟(0<≠∘⥊)
+> ↩ Merge          ⊘ >
+≍ ← >∘Pair
+_ranks ← {⟨2⟩⊘⟨1,0⟩((⊣-1+|)˜⟜≠⊑¨<∘⊢)⥊∘𝔽}
+_depthOp_←{
+  neg←0>n←𝕨𝔾_ranks𝕩 ⋄ F←𝔽
+  _d←{
+    R←(𝕗+neg)_d
+    𝕨(×⟜2⊸+´2⥊(neg∧𝕗≥0)∨(0⌈𝕗)≥Pair○≡)◶(⟨R¨⋄R⟜𝕩¨∘⊣⋄(𝕨R⊢)¨∘⊢⋄F⟩)𝕩
+  }
+  𝕨 n _d 𝕩
+}
+⚇ ← _depthOp_
+_rankOp_←{
+  k←𝕨(Pair○= (0≤⊢)◶⟨⌊⟜-,0⌈-⟩¨ 𝔾_ranks)𝕩
+  Enc←{
+    f←⊑⟜(≢𝕩)¨↕𝕨
+    c←×´s←𝕨Cell𝕩
+    f⥊⊑⟜(⥊𝕩)¨∘((s⥊↕c)+c×⊢)¨↕×´f
+  }
+  Enc↩(>⟜0+≥⟜=)◶⟨<⊢,Enc,<¨⊢⟩
+  > ((0⊑k)Enc𝕨) 𝔽¨ ((1-˜≠)⊸⊑k)Enc𝕩
+}
+⎉ ← _rankOp_
+˘ ← {𝔽⎉¯1}
+_insert←{
+  ! 1≤=𝕩
+  𝕨 𝔽´ <˘𝕩
+}
+˝ ← _insert
+
+
+#⌜
+# LAYER 5: Structural functions
+
+_onAxes_←{
+  F←𝔽
+  (𝔾<≡)∘⊣◶{ # One axis
+    ! 1≤=𝕩
+    𝕨F𝕩
+  }‿{ # Multiple axes
+    ! 1≥=𝕨
+    ! 𝕨≤○≠≢𝕩
+    l←≠𝕨 ⋄ W←⊑⟜(⥊𝕨)
+    0{(W𝕨)F(1+𝕨)⊸𝕊˘⍟(𝕨<l-1)𝕩}⍟(0<l)𝕩
+  }
+}
+
+Select←ToArray⊸(SelSub _onAxes_ 1)
+⊏ ← 0⊸Select       ⊘ Select
+
+JoinTo←∨○(1≠=)◶∾‿{
+  s←𝕨Pair○≢𝕩
+  a←1⌈´k←≠¨s
+  ! ∧´1≥a-k
+  c←(k¬a)+⟜(↕a-1)⊸⊏¨s
+  ! ≡´c
+  l←+´(a=k)⊣◶1‿(0⊑⊢)¨s
+  (⟨l⟩∾0⊑c)⥊𝕨∾○⥊𝕩
+}
+
+Take←{
+  T←{
+    ! Int 𝕨
+    l←≠𝕩 ⋄ n←𝕨<0 ⋄ e←l⌊r←|𝕨 ⋄ s←⟨r⟩
+    i ← 𝕩{s∾↩c←1 Cell 𝕨⋄𝕩(×+⌜↕∘⊢)×´c}⍟(1≠=𝕩) (l-e)+⍟n ↕e
+    s ⥊ 𝕩{(⥊𝕩)n◶⟨∾,∾˜⟩(r-e)⥊Type𝕗}⍟(l<r) ⊑⟜(⥊𝕩)¨i
+  }
+  𝕨 T _onAxes_ 0 (⟨1⟩⥊˜0⌈𝕨-○≠⊢)⊸∾∘≢⊸⥊𝕩
+}
+Prefixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Take¨<𝕩}
+↑ ← Prefixes       ⊘ Take
+Drop←{
+  s←(≠𝕨)(⊣↑⊢∾˜1⥊˜0⌈-⟜≠)≢𝕩
+  ((sׯ1⋆𝕨>0)+(-s)⌈s⌊𝕨)↑𝕩
+}
+Suffixes ← {!1≤=𝕩 ⋄ (↕1+≠𝕩)Drop¨<𝕩}
+↓ ← Suffixes       ⊘ Drop
+
+Windows←{
+  ! IsArray 𝕩
+  ! 1≥=𝕨
+  ! 𝕨≤○≠≢𝕩
+  ! ∧´Nat¨⥊𝕨
+  s←(≠𝕨)↑≢𝕩
+  ! ∧´𝕨≤1+s
+  𝕨{(∾⟜(𝕨≠⊸↓≢𝕩)∘≢⥊>)<¨⊸⊏⟜𝕩¨s(¬+⌜○Range⊢)⥊𝕨}⍟(0<≠𝕨)𝕩
+}
+
+Reverse ← {!1≤=𝕩 ⋄ (-↕⊸¬≠𝕩)⊏𝕩}
+Rotate ← {!Int𝕨 ⋄ l←≠𝕩⋄(l|𝕨+↕l)⊏𝕩} _onAxes_ 0
+
+Rep ← Indices⊸⊏
+Replicate ← {0<=𝕨}◶(⥊˜⟜≠Rep⊢)‿{!𝕨=○≠𝕩⋄𝕨Rep𝕩} _onAxes_ (1-0=≠)
+
+↕ ↩ Range          ⊘ Windows
+⌽ ← Reverse        ⊘ Rotate
+/ ← Indices        ⊘ Replicate
+
+
+#⌜
+# LAYER 6: Everything else
+
+Join←(1≠=)◶⟨∨´1≠=¨,1⟩◶{
+  # List of lists
+  i←j←¯1⋄e←⟨⟩⋄a←𝕩
+  {{e↩a⊑˜i↩𝕩⋄j↩¯1}⍟(i⊸≠)𝕩⋄(j↩j+1)⊑e}¨/≠¨𝕩
+}‿{
+  # Multidimensional
+  C←(<⟨⟩)⥊⊸∾⌜´⊢  # Cartesian array product
+  ! IsArray 𝕩
+  s←≢¨𝕩
+  d←≠0⊑⥊s
+  ! ∧´⥊d=≠¨s
+  ! d≥=𝕩
+  l←(≢𝕩){(𝕩⊑⟜≢a Pick1˜(j=𝕩)⊸×)¨↕𝕨}¨j←↕r←=a←𝕩
+  ! (r↑¨s)≡C l
+  i←C{p←+´¨↑𝕩⋄(↕0⊑⌽p)-𝕩/¯1↓p}¨l
+  >i<¨⊸⊏¨l/𝕩
+}⍟(0<≠∘⥊)
+
+Group←{
+  ! IsArray 𝕩
+  Chk←{!1==𝕩⋄!∧´Int¨𝕩⋄!∧´¯1≤𝕩⋄≠𝕩}
+  l←(1<≡)◶Chk‿{!1==𝕩⋄Chk¨𝕩}𝕨
+  ! l≤○≠≢𝕩
+  ! ∧´l=l≠⊸↑≢𝕩
+  (𝕨⊸=/𝕩˜)¨↕1+¯1⌈´⚇1𝕨
+}
+
+∾ ↩ Join           ⊘ JoinTo
+⊔ ← Group⟜(↕≠⚇1)   ⊘ Group
+
+Pick1←{
+  ! 1==𝕨
+  ! 𝕨=○≠s←≢𝕩
+  ! ∧´Int¨𝕨
+  ! ∧´𝕨(≥⟜-∧<)s
+  𝕨↩𝕨+s×𝕨<0
+  (⥊𝕩)⊑˜0(⊑⟜𝕨+⊑⟜s×⊢)´-↕⊸¬≠𝕨
+}
+Pickd←(∨´∘⥊IsArray¨∘⊣)◶Pick1‿{Pickd⟜𝕩¨𝕨}
+Pick←IsArray◶⥊‿⊢⊸Pickd
+
+# Searching
+IndexOf←{
+  c←1-˜=𝕨
+  ! 0≤c
+  𝕨 (0<≠𝕨)◶⟨0⎉c∘⊢,(+˝∧`)≢⌜○((0<c)◶⟨⊢,<⎉c⟩)⟩ 𝕩
+}
+UniqueMask←{
+  ! 1≤=𝕩
+  u←0↑𝕩
+  {(≠u)>0⊑⥊u IndexOf 𝕩}◶{u↩u∾𝕩⋄1}‿0˘𝕩
+}
+Find←{
+  r←=𝕨
+  ! r≤=𝕩
+  𝕨 ≡⎉r (≢𝕨) ↕⎉r 𝕩
+}
+
+⊐ ← !∘0            ⊘ IndexOf
+∊ ← UniqueMask     ⊘ (⊐˜<≠∘⊢)
+⍷ ← ∊⊸/            ⊘ Find
+
+ReorderAxes←{
+  𝕩↩<⍟(0=≡)𝕩
+  ! 1≥=𝕨
+  𝕨↩⥊𝕨
+  ! 𝕨≤○≠≢𝕩
+  ! ∧´Nat¨⥊𝕨
+  r←(=𝕩)-+´¬∊𝕨
+  ! ∧´𝕨<r
+  𝕨↩𝕨∾𝕨(¬∘∊˜/⊢)↕r
+  (𝕨⊸⊏Pick𝕩˜)¨↕⌊´¨𝕨⊔≢𝕩
+}
+Transpose←(=-1˜)⊸ReorderAxes⍟(0<=)
+⍉ ← Transpose      ⊘ ReorderAxes
+
+# Sorting
+CmpLen ← {
+  e←𝕨-˜○(∨´0⊸=)𝕩
+  𝕨(e=0)◶⟨0,e⟩‿{
+    c←×𝕨-○≠𝕩
+    r←𝕨⌊○≠𝕩
+    l←𝕨{
+      i←+´∧`𝕨=𝕩
+      m←×´⊑⟜𝕨¨↕i
+      {c↩×-´𝕩⋄m↩m×⌊´𝕩}∘(⊑¨⟜𝕨‿𝕩)⍟(r⊸>)i
+      m
+    }○(((-1+↕r)+≠)⊸{⊑⟜𝕩¨𝕨})𝕩
+    ⟨l,c⟩
+  }𝕩
+}
+_getCellCmp ← {
+  Ci←𝔽⋄l←𝕨⋄c←𝕩
+  Cc←{
+    a←𝕨⋄b←𝕩
+    S←(l⊸=)◶{S∘(1+𝕩)⍟(0⊸=)a Ci○(𝕩⊸+)b}‿c
+    S 0
+  }
+  (1≠l)⊑(𝕩⍟(0⊸=)𝔽)‿Cc
+}
+
+_binSearch ← {
+  B ← 𝔽
+  {
+    R←{𝕨{a←B m←𝕩+h←⌊𝕨÷2⋄(h+a×2|𝕨)R a⊑𝕩‿m}⍟(>⟜1)𝕩}
+    1+(𝕩+1)R ¯1
+  }⍟(0⊸<)
+}
+_bins←{
+  c←1-˜=𝕨
+  ! 0≤c
+  ! c≤=𝕩
+  lw←×´sw←1 Cell 𝕨
+  cw←lw 𝔽○(⊑⟜(⥊𝕨)) _getCellCmp 0
+  ! 0⊸<◶⟨1,∧´0≤˜·cw¨⟜(lw⊸+)lw×↕∘-⟜1⟩≠𝕨
+  cx←c-˜=𝕩
+  sx←cx Cell 𝕩 ⋄ lc←sw CmpLen sx
+  cc ← (⊑⟜(⥊𝕨))⊸𝔽⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc
+  B←(×´sw)⊸×⊸Cc≤0˜
+  (≠𝕨) {B⟜𝕩 _binSearch 𝕨}¨ (×´sx) × ⥊⟜(↕×´)⊑⟜(≢𝕩)¨↕cx
+}
+
+⍋ ←   Cmp _grade   ⊘ (  Cmp _bins)
+⍒ ← -∘Cmp _grade   ⊘ (-∘Cmp _bins)
+∧ ↩ ⍋⊸⊏            ⊘ ∧
+∨ ↩ ⍒⊸⊏            ⊘ ∨
+
+OccurrenceCount ← ⊐˜(⊢-⊏)⍋∘⍋
+ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩}
+⊒ ← OccurrenceCount⊘ ProgressiveIndexOf
+
+⊑ ↩ (0⊑⥊)          ⊘ Pick
+◶ ↩ {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩}  # Same definition, new Pick
+
+inverse ← {(⊑(0⊏𝕩)⊐<) ⊑ ((1⊏𝕩)∾⟨!∘0⟩)˜} ⍉ (2∾˜2÷˜≠)⊸⥊ ⟨
+  +, +⊘(-˜)
+  -, -
+  ×, ⊢⊘(÷˜)
+  ÷, ÷
+  ⋆, Log _perv
+  √, ⋆⟜2⊘(⋆˜)
+  ∧, ⊢⊘(÷˜)
+  ∨, ⊢⊘(-˜÷1-⊢)
+  <, {!IsArray𝕩⋄!0==𝕩⋄⊑𝕩}⊘(!∘0)
+  /, {!(⍋≡↕∘≠)𝕩⋄≠¨⊔𝕩}⊘(!∘0)
+⟩
+⁼ ← {Inverse 𝕗}
+
+_repeat_←{
+  n←𝕨𝔾𝕩
+  l←u←0
+  {!Int𝕩⋄l↩l⌊𝕩⋄u↩u⌈𝕩}⚇0 n
+  a←𝕩⋄_p←{𝔽∘⊣`(1+𝕩)⥊<a}
+  pos←(𝕨𝔽 ⊢)_p u
+  neg←(𝕨𝔽⁼⊢)_p-l
+  (|⊑<⟜0⊑pos‿neg˜)⚇0 n
+}
+⍟ ↩ _repeat_