From c9bf7595e624279f929068f20969c9bfa1e4f79a Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Fri, 5 Apr 2024 22:27:28 +0100
Subject: [PATCH 01/20] Remove / comment out explicit Glicko2 stuff

---
 src/lib/glicko2.hoon   | 62 -------------------------------------
 src/lib/telos.hoon     | 54 ++++++++++++++++-----------------
 src/sur/glicko2.hoon   | 52 -------------------------------
 src/sur/telos.hoon     |  4 +--
 src/tests/glicko2.hoon | 69 ------------------------------------------
 5 files changed, 29 insertions(+), 212 deletions(-)
 delete mode 100644 src/lib/glicko2.hoon
 delete mode 100644 src/sur/glicko2.hoon
 delete mode 100644 src/tests/glicko2.hoon

diff --git a/src/lib/glicko2.hoon b/src/lib/glicko2.hoon
deleted file mode 100644
index 74025b5..0000000
--- a/src/lib/glicko2.hoon
+++ /dev/null
@@ -1,62 +0,0 @@
-/-  *glicko2
-|%
-++  delta
-  |=  [[(list r) (list rd) (list outcome)] @rs]
-  ::  XX where possible, these `@rs`s should be /sur types
-  ^-  @rs
-  .20211718190.033577
-::
-++  eee
-  |=  [@ @]
-  ^-  @rs
-  .0.0004206362164754052
-::
-++  gee
-  |=  rd
-  ^-  @rs
-  .0.0051822143113334366
-::
-++  get-rating
-  |=  =player-data
-  ^+  r.player-data
-  .~1.500
-::
-++  get-rd
-  |=  =player-data
-  ^+  rd.player-data
-  .~350.0
-::
-++  new-vol
-  |=  [[(list r) (list rd) (list outcome)] @rs]
-  ^-  @rd
-  .~0.06000004916805347
-::
-++  pre-rating-rd
-  |=  =rd
-  ^+  rd
-  .~2.015655080250959
-::
-++  scale-rat
-  |=  =r
-  ^+  r
-  .~0
-::
-++  scale-rd
-  |=  =rd
-  ^+  rd
-  .~2.014761872416068
-::
-++  update-player
-  |=  [=player-data matches=(list (pair player-data outcome))]
-  ^+  player-data
-  :*  .~1300  :: dummy r
-      .~300   :: dummy rd
-      .~0.03  :: dummy vol
-  ==
-::
-++  vee
-  |=  [(list r) (list rd)]
-  ^-  @rs
-  .795778282.6043352
-::
---
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 7ef0ef7..955fd06 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -1,5 +1,4 @@
 /-  *telos
-/+  glicko2
 |%
 ::
 +|  %poke-helpers
@@ -195,30 +194,31 @@
 ++  update-ratings
   |=  [players=(map player player-data) =winner =loser draw=?]
   ^+  players
-  ::
-  ::  add default player-data for new players
-  =/  winner-data
-    %+  fall
-      (~(get by players) winner)
-    *player-data
-  =/  loser-data
-    %+  fall
-      (~(get by players) loser)
-    *player-data
-  ::
-  ::  get new data for both players
-  =+
-    ^=  [new-winner-data new-loser-data]
-    ?.  draw
-      :-  (update-player:glicko2 winner-data [[loser-data %win] ~])
-      (update-player:glicko2 loser-data [[winner-data %loss] ~])
-    :-  (update-player:glicko2 winner-data [[loser-data %draw] ~])
-    (update-player:glicko2 loser-data [[winner-data %draw] ~])
-  ::
-  ::  add new data to players
-  %+  %~  put
-        by
-      (~(put by players) winner new-winner-data)
-    loser
-  new-loser-data
+  (my [[winner [.~1500 .~250 .~0.05]] [loser [.~1500 .~250 .~0.05]] ~])
+  ::  ::
+  ::  ::  add default player-data for new players
+  ::  =/  winner-data
+  ::    %+  fall
+  ::      (~(get by players) winner)
+  ::    *player-data
+  ::  =/  loser-data
+  ::    %+  fall
+  ::      (~(get by players) loser)
+  ::    *player-data
+  ::  ::
+  ::  ::  get new data for both players
+  ::  =+
+  ::    ^=  [new-winner-data new-loser-data]
+  ::    ?.  draw
+  ::      :-  (update-player:glicko2 winner-data [[loser-data %win] ~])
+  ::      (update-player:glicko2 loser-data [[winner-data %loss] ~])
+  ::    :-  (update-player:glicko2 winner-data [[loser-data %draw] ~])
+  ::    (update-player:glicko2 loser-data [[winner-data %draw] ~])
+  ::  ::
+  ::  ::  add new data to players
+  ::  %+  %~  put
+  ::        by
+  ::      (~(put by players) winner new-winner-data)
+  ::    loser
+  ::  new-loser-data
 --
diff --git a/src/sur/glicko2.hoon b/src/sur/glicko2.hoon
deleted file mode 100644
index d713537..0000000
--- a/src/sur/glicko2.hoon
+++ /dev/null
@@ -1,52 +0,0 @@
-|%
-::
-::  define constants as in step 1 of the glicko-2 system
-::
-::  τ, the change in player's volatility over time
-::  XX settle on a strategy behind the default value of tau and rd
-::       ideally, a player's rating should jump around a
-::       lot in their first ~10 matches so they hit
-::       an accurate estimate of their skill quickly.
-::       this might require a %server-action poke
-::       to adjust tau manually
-+$  tau
-  $~  .~0.5
-  @rd
-::
-::  other constants
-::
-::  epsilon
-+$  eps
-  $~  .~0.0000001
-  @rd
-::
-::  player's rating
-+$  r
-  $~  .~1500
-  @rd
-::
-::  player's rating deviation
-+$  rd
-  $~  .~250
-  @rd
-::
-::  player's rating volatility
-+$  vol
-  $~  .~0.05
-  @rd
-::
-::  structures
-+$  player-data
-  $:  =r
-      =rd
-      =vol
-  ==
-::
-::  outcome
-+$  outcome
-  $?  %win
-      %loss
-      %draw
-  ==
-::
---
diff --git a/src/sur/telos.hoon b/src/sur/telos.hoon
index 780d50f..c7b5fcc 100644
--- a/src/sur/telos.hoon
+++ b/src/sur/telos.hoon
@@ -1,4 +1,3 @@
-/-  *glicko2
 |%
 +$  payload  *     ::  arbitrary data on any match
 +$  source   @p    ::  our source for a match record
@@ -8,9 +7,10 @@
 +$  id       @uvF  ::  unique id for a match and its payload
 +$  loser    player
 +$  winner   player
++$  player-data  [r=@rd rd=@rd vol=@rd]  :: placeholder
 ::
 +$  match
-  ::       
+  ::
   $:  =id
       =date
       =winner
diff --git a/src/tests/glicko2.hoon b/src/tests/glicko2.hoon
deleted file mode 100644
index e427bb3..0000000
--- a/src/tests/glicko2.hoon
+++ /dev/null
@@ -1,69 +0,0 @@
-/+  *test, *glicko2
-|%
-++  test-delta
-  %+  expect-eq
-    !>  .20211718190.033577
-    !>  %-  delta
-      :-  :-  ~[1.400 1.500 1.700]
-          :-  ~[.30.0 .100.0 .300.0]
-            ~[[%win .1.00] [%loss .0.00] [%loss .0.00]]
-      .795778282.6043352
-::
-++  test-eee
-  %+  expect-eq
-    !>  .0.0004206362164754052
-    !>  %-  eee
-      :-  1.500
-        .350.0
-::
-++  test-gee
-  %+  expect-eq
-    !>  .0.0051822143113334366
-    !>  %-  gee  .350.0
-::
-++  test-get-rating
-  %+  expect-eq
-    !>  1.500
-    !>  %-  get-rating  [1.500 .350.0 .0.06]
-::
-++  test-get-dev
-  %+  expect-eq
-    !>  .350.0
-    !>  %-  get-dev  [1.500 .350.0 .0.06]
-::
-++  test-new-vol
-  %+  expect-eq
-    !>  .0.06000004916805347
-    !>  %-  new-vol
-      :-  :-  ~[1.400 1.500 1.700]
-          :-  ~[.30.0 .100.0 .300.0]
-            ~[[%win .1.00] [%loss .0.00] [%loss .0.00]]
-      .795778282.6043352
-::
-++  test-pre-rating-dev
-  %+  expect-eq
-    !>  .2.015655080250959
-    !>  %-  pre-rating-dev  .350.0
-::
-++  test-scale-rat
-  %+  expect-eq
-    !>  0
-    !>  %-  scale-rat  1.500
-::
-++  test-scale-dev
-  %+  expect-eq
-    !>  .2.014761872416068
-    !>  %-  scale-dev  .350.0
-::
-++  test-update-player
-  %+  expect-eq
-    !>  [1.441 .193.0 .0.06]
-    !>  %-  update-player
-      :-  [1.500 .350.0 .0.06]
-    ~[[%win .1.00] [%loss .0.00] [%loss .0.00]]
-::
-++  test-vee
-  %+  expect-eq
-    !>  .795778282.6043352
-    !>  %+  vee  ~[1.400 1.500 1.700]  ~[.30.0 .100.0 .300.0]
---

From 9594cf8c9ba33bbaf20bec618720916e9b772d54 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Fri, 5 Apr 2024 22:27:43 +0100
Subject: [PATCH 02/20] Update for 411k

---
 src/lib/telos.hoon | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 955fd06..318ebe9 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -40,7 +40,7 @@
 ++  delete-player-from-ratings
   |=  [=game =player =ratings]
   ^+  ratings
-  %-  ~(rut by ratings)
+  %-  ~(urn by ratings)
   |=  [=^game players=(map ^player player-data)]
   ^+  players
   ?.  =(game ^game)
@@ -140,7 +140,7 @@
   %-  zing
   %+  turn
     %~  tap  by
-      %-  ~(rut by ratings)
+      %-  ~(urn by ratings)
     |=  [=game players=(map player player-data)]
     ^-  (list player)
     %+  skim

From 9eb886d06048c460c55eb6c93f875425c3732e07 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Fri, 5 Apr 2024 22:31:39 +0100
Subject: [PATCH 03/20] Remove rd and vol

---
 src/lib/telos.hoon | 2 +-
 src/sur/telos.hoon | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 318ebe9..c06983d 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -194,7 +194,7 @@
 ++  update-ratings
   |=  [players=(map player player-data) =winner =loser draw=?]
   ^+  players
-  (my [[winner [.~1500 .~250 .~0.05]] [loser [.~1500 .~250 .~0.05]] ~])
+  (my [[winner .~1500] [loser .~1500] ~])
   ::  ::
   ::  ::  add default player-data for new players
   ::  =/  winner-data
diff --git a/src/sur/telos.hoon b/src/sur/telos.hoon
index c7b5fcc..8e9ae6b 100644
--- a/src/sur/telos.hoon
+++ b/src/sur/telos.hoon
@@ -7,7 +7,7 @@
 +$  id       @uvF  ::  unique id for a match and its payload
 +$  loser    player
 +$  winner   player
-+$  player-data  [r=@rd rd=@rd vol=@rd]  :: placeholder
++$  player-data  r=@rd  :: placeholder
 ::
 +$  match
   ::

From 13b584532062f5f85718c94d9d596cc9a51ecd86 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Fri, 5 Apr 2024 22:37:59 +0100
Subject: [PATCH 04/20] CTRL+F player-data into a @rd rating

---
 src/app/telos.hoon                  | 80 ++++++++++++++---------------
 src/lib/telos.hoon                  | 26 +++++-----
 src/mar/telos/data/game.hoon        |  4 +-
 src/mar/telos/data/player-game.hoon |  4 +-
 src/mar/telos/data/player.hoon      |  4 +-
 src/sur/telos.hoon                  |  5 +-
 testing/pyglicko2/glicko2.py        | 58 ++++++++++-----------
 7 files changed, 91 insertions(+), 90 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index aef500b..169f651 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -247,7 +247,7 @@
                     ~(tap by ratings)
                   has-player-in-ratings
                 player.action
-              |=  [=game (map player player-data)]
+              |=  [=game (map player rating)]
               ^-  card
               :*  %pass  ~  %agent  [our.bowl dap.bowl]
                   %poke  %delete-player-from-game  !>([game player.action])
@@ -337,34 +337,34 @@
               ::  update subscribers to this game
               %+  turn
                 new-ratings-list
-              |=  [=player =player-data]
+              |=  [=player =rating]
               ^-  card
               :*  %give  %fact  ~[/ratings/(scot %tas game.action)]
-                  %telos-player-rating  !>([player r.player-data])
+                  %telos-player-rating  !>([player rating])
               ==
               ::
               ::  update subscribers to one player in any game
               %+  turn
                 new-ratings-list
-              |=  [=player =player-data]
+              |=  [=player =rating]
               ^-  card
               :*  %give  %fact  ~[/ratings/(scot %p player)]
-                  %telos-game-rating  !>([game.action r.player-data])
+                  %telos-game-rating  !>([game.action rating])
               ==
               ::
               ::  update subscibers to one player in this game
               %+  turn
                 new-ratings-list
-              |=  [=player =player-data]
+              |=  [=player =rating]
               ^-  card
               :*  %give  %fact  ~[/ratings/game/(scot %p player)]
-                  %telos-rating  !>(r.player-data)
+                  %telos-rating  !>(rating)
               ==
           ==  ::  end of list of lists of cards
       ==  ::  end of server actions
   ==  ::  end of mark branches
 ::
-++  on-watch  
+++  on-watch
   |=  =path
   ^-  (quip card _this)
   ?+  path  (on-watch:def path)
@@ -379,13 +379,13 @@
         %+  fall
           %+  bind
             (~(get by ratings) game)
-          |=  ratings=(map player player-data)
+          |=  ratings=(map player rating)
           ~(tap by ratings)
         ~
-      |=  [=player =player-data]
+      |=  [=player =rating]
       ^-  card
       :*  %give  %fact  ~
-          %telos-player-rating  !>([player r.player-data])
+          %telos-player-rating  !>([player rating])
       ==
     ::
     ::  ratings updates for a player
@@ -397,10 +397,10 @@
             ~(tap by ratings)
           has-player-in-ratings
         player
-      |=  [=game players=(map ^player player-data)]
+      |=  [=game players=(map ^player rating)]
       ^-  card
       :*  %give  %fact  ~
-          %telos-game-rating  !>([game r:(~(got by players) player)])
+          %telos-game-rating  !>([game (~(got by players) player)])
       ==
     ::
     ::  ratings updates for a player in one game
@@ -411,11 +411,11 @@
       ?>  (~(has by ratings) game)
       :_  this
       %+  turn
-        ^-  (list player-data)
+        ^-  (list rating)
         (drop (~(get by (~(got by ratings) game)) player))
-      |=  =player-data
+      |=  =rating
       :*  %give  %fact  ~
-          %telos-rating  !>(r.player-data)
+          %telos-rating  !>(rating)
       ==
   ==  ::  end of path branches
 ::
@@ -456,8 +456,8 @@
           ~(tap by ratings)
         has-player-in-ratings
       player
-    |=  [=game players=(map ^player player-data)]
-    ^-  [^game (pair player-data (list match))]
+    |=  [=game players=(map ^player rating)]
+    ^-  [^game (pair rating (list match))]
     :-  game
     :-  (~(got by players) player)
     (skim (~(got by archive) game) (curr has-player-in-match player))
@@ -476,8 +476,8 @@
       ~
     %+  bind
       (~(get by (~(got by ratings) game)) player)
-    |=  =player-data
-    :-  r.player-data
+    |=  =rating
+    :-  rating
     %+  skim
       (~(got by archive) game)
     (curr has-player-in-match player)
@@ -513,8 +513,8 @@
     ?~  players=(~(get by ratings) game)
       ~
     %-  ~(run by u.players)
-    |=  =player-data
-    r.player-data
+    |=  =rating
+    rating
   ::
   ::  return all ratings for a player
   ::  .^(noun %gx /=telos=/ratings/~sampel-palnet/noun)
@@ -530,9 +530,9 @@
           ~(tap by ratings)
         has-player-in-ratings
       player
-    |=  [=game ratings=(map ^player player-data)]
+    |=  [=game ratings=(map ^player rating)]
     ^-  [^game @rd]
-    [game r:(~(got by ratings) player)]
+    [game (~(got by ratings) player)]
   ::
   ::  return rating for one player in one game
   ::  .^(noun %gx /=telos=/ratings/chess/~sampel-palnet/noun)
@@ -547,8 +547,8 @@
       ~
     %+  bind
       (~(get by (~(got by ratings) game)) player)
-    |=  =player-data
-    r.player-data
+    |=  =rating
+    rating
   ::
   ::  return ratings within a range for one game
   ::  .^(noun %gx /=telos=/ratings/chess/.~1250/.~1750/25/0/noun)
@@ -571,12 +571,12 @@
       %+  skim
         %+  skim
           ~(tap by (~(got by ratings) game))
-        |=  [player =player-data]
-        (lth r.player-data hi)
-      |=  [player =player-data]
-      (gth r.player-data lo)
-    |=  [=player =player-data]
-    [player r.player-data]
+        |=  [player =rating]
+        (lth rating hi)
+      |=  [player =rating]
+      (gth rating lo)
+    |=  [=player =rating]
+    [player rating]
   ==  ::  end of scries
 ::
 ++  on-agent
@@ -617,29 +617,29 @@
             ::  confirm results
             :-  :~  ::  update players with their new ratings
                     :*  %pass  ~  %agent  [winner game]
-                        %poke  %win  !>([id loser r.winner-new-data])
+                        %poke  %win  !>([id loser winner-new-data])
                     ==
                     :*  %pass  ~  %agent  [loser game]
-                        %poke  %loss  !>([id winner r.loser-new-data])
+                        %poke  %loss  !>([id winner loser-new-data])
                     ==
                     ::  update other subscribers
                     :*  %give  %fact  ~[/ratings/(scot %tas game)]
-                        %telos-player-rating  !>([winner r.winner-new-data])
+                        %telos-player-rating  !>([winner winner-new-data])
                     ==
                     :*  %give  %fact  ~[/ratings/(scot %tas game)]
-                        %telos-player-rating  !>([loser r.loser-new-data])
+                        %telos-player-rating  !>([loser loser-new-data])
                     ==
                     :*  %give  %fact  ~[/ratings/(scot %p winner)]
-                        %telos-game-rating  !>([game r.winner-new-data])
+                        %telos-game-rating  !>([game winner-new-data])
                     ==
                     :*  %give  %fact  ~[/ratings/(scot %p loser)]
-                        %telos-game-rating  !>([game r.loser-new-data])
+                        %telos-game-rating  !>([game loser-new-data])
                     ==
                     :*  %give  %fact  ~[/ratings/game/(scot %p winner)]
-                        %telos-rating  !>(r.winner-new-data)
+                        %telos-rating  !>(winner-new-data)
                     ==
                     :*  %give  %fact  ~[/ratings/game/(scot %p loser)]
-                        %telos-rating  !>(r.loser-new-data)
+                        %telos-rating  !>(loser-new-data)
                     ==
                 ==
             %=  this
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index c06983d..6edda18 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -41,7 +41,7 @@
   |=  [=game =player =ratings]
   ^+  ratings
   %-  ~(urn by ratings)
-  |=  [=^game players=(map ^player player-data)]
+  |=  [=^game players=(map ^player rating)]
   ^+  players
   ?.  =(game ^game)
     players
@@ -95,19 +95,19 @@
   |=  [=rank:title =ratings]
   ^+  ratings
   %-  ~(run by ratings)
-  |=  players=(map player player-data)
+  |=  players=(map player rating)
   ^+  players
   %-  malt
   %+  skip
     ~(tap by players)
-  |=  [=player player-data]
+  |=  [=player rating]
   ^-  ?
   =(rank (clan:title player))
 ::
 ++  compute-ratings-game
   |=  matches=(list match)
-  ^-  (map player player-data)
-  =/  player-ratings  `(map player player-data)`~
+  ^-  (map player rating)
+  =/  player-ratings  `(map player rating)`~
   |-
   ?~  matches
     player-ratings
@@ -141,7 +141,7 @@
   %+  turn
     %~  tap  by
       %-  ~(urn by ratings)
-    |=  [=game players=(map player player-data)]
+    |=  [=game players=(map player rating)]
     ^-  (list player)
     %+  skim
       ~(tap in ~(key by players))
@@ -173,9 +173,9 @@
 ::
 ::  general-purpose filters
 ++  filter-ratings
-  |=  [games=(list [game (map player player-data)]) filter=$-([[game (map player player-data)] @] ?) term=@]
+  |=  [games=(list [game (map player rating)]) filter=$-([[game (map player rating)] @] ?) term=@]
   ^+  games
-  (skim games |=(x=[game (map player player-data)] (filter x term)))
+  (skim games |=(x=[game (map player rating)] (filter x term)))
 ::
 ++  has-player-in-match
   |=  [=match =player]
@@ -185,26 +185,26 @@
   ==
 ::
 ++  has-player-in-ratings
-  |=  [[game ratings=(map player player-data)] player=@]
+  |=  [[game ratings=(map player rating)] player=@]
   ^-  ?
   (~(has by ratings) player)
 ::
 +|  %ratings-helper
 ::
 ++  update-ratings
-  |=  [players=(map player player-data) =winner =loser draw=?]
+  |=  [players=(map player rating) =winner =loser draw=?]
   ^+  players
   (my [[winner .~1500] [loser .~1500] ~])
   ::  ::
-  ::  ::  add default player-data for new players
+  ::  ::  add default rating for new players
   ::  =/  winner-data
   ::    %+  fall
   ::      (~(get by players) winner)
-  ::    *player-data
+  ::    *rating
   ::  =/  loser-data
   ::    %+  fall
   ::      (~(get by players) loser)
-  ::    *player-data
+  ::    *rating
   ::  ::
   ::  ::  get new data for both players
   ::  =+
diff --git a/src/mar/telos/data/game.hoon b/src/mar/telos/data/game.hoon
index 304df68..5036854 100644
--- a/src/mar/telos/data/game.hoon
+++ b/src/mar/telos/data/game.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  data=(pair (map player player-data) (list match))
+|_  data=(pair (map player rating) (list match))
 ++  grab
   |%
-  ++  noun  (pair (map player player-data) (list match))
+  ++  noun  (pair (map player rating) (list match))
   --
 ++  grow
   |%
diff --git a/src/mar/telos/data/player-game.hoon b/src/mar/telos/data/player-game.hoon
index ea0de99..2c6125a 100644
--- a/src/mar/telos/data/player-game.hoon
+++ b/src/mar/telos/data/player-game.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  data=(unit (pair player-data (list match)))
+|_  data=(unit (pair rating (list match)))
 ++  grab
   |%
-  ++  noun  (unit (pair player-data (list match)))
+  ++  noun  (unit (pair rating (list match)))
   --
 ++  grow
   |%
diff --git a/src/mar/telos/data/player.hoon b/src/mar/telos/data/player.hoon
index 0b4c6a2..d3580af 100644
--- a/src/mar/telos/data/player.hoon
+++ b/src/mar/telos/data/player.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  data=(map game (pair player-data (list match)))
+|_  data=(map game (pair rating (list match)))
 ++  grab
   |%
-  ++  noun  (map game (pair player-data (list match)))
+  ++  noun  (map game (pair rating (list match)))
   --
 ++  grow
   |%
diff --git a/src/sur/telos.hoon b/src/sur/telos.hoon
index 8e9ae6b..804d18a 100644
--- a/src/sur/telos.hoon
+++ b/src/sur/telos.hoon
@@ -3,11 +3,12 @@
 +$  source   @p    ::  our source for a match record
 +$  player   @p
 +$  date     @da
+::  XX change to @ud
++$  rating   @rd   ::  player's rating
 +$  game     @tas
 +$  id       @uvF  ::  unique id for a match and its payload
 +$  loser    player
 +$  winner   player
-+$  player-data  r=@rd  :: placeholder
 ::
 +$  match
   ::
@@ -30,7 +31,7 @@
 ::
 +$  payloads  (map id payload)
 +$  archive   (map game (list match))
-+$  ratings   (map game (map player player-data))
++$  ratings   (map game (map player rating))
 ::
 +$  client-action
   $%  [%cede-match [=game =winner =payload]]
diff --git a/testing/pyglicko2/glicko2.py b/testing/pyglicko2/glicko2.py
index a2ffd46..fa9f5b5 100644
--- a/testing/pyglicko2/glicko2.py
+++ b/testing/pyglicko2/glicko2.py
@@ -29,7 +29,7 @@ class Player:
     # Class attribute
     # The system constant, which constrains
     # the change in volatility over time.
-    # 
+    #
     # underscore = "weak internal use"; do not export
     _tau = 0.5
 
@@ -37,7 +37,7 @@ def getRating(self):
         # __double_leading_underscore
         # inside class FooBar, __boo becomes _FooBar__boo
         # "self.rating" becomes Ryan.rating in tests.py
-        # 
+        #
         # 'self' is a specific instance of parent class
         # (add (add rating.player 173.7178) 1500)
         # print(f"getRating: {(self.__rating * 173.7178) + 1500}")
@@ -64,7 +64,7 @@ def setRd(self, rd):
         self.__rd = rd / 173.7178
 
     rd = property(getRd, setRd)
-    
+
     # __double_leading_and_trailing_underscore__
     # "magic" objects or attribs that live in user-controlled namespaces
     # bascially, reserved for Python itself
@@ -74,23 +74,23 @@ def __init__(self, rating = 1500, rd = 350, vol = 0.06):
         self.setRating(rating)
         self.setRd(rd)
         self.vol = vol
-            
+
     def _preRatingRD(self):
         """ Calculates and updates the player's rating deviation for the
         beginning of a rating period.
-        
+
         preRatingRD() -> None
-        
+
         """
         # (sqrt (add (pow rd.player 2) (pow vol.player 2)))
         # print(f"preRatingRD: {math.sqrt(math.pow(self.__rd, 2) + math.pow(self.vol, 2))}")
         self.__rd = math.sqrt(math.pow(self.__rd, 2) + math.pow(self.vol, 2))
-        
+
     def update_player(self, rating_list, RD_list, outcome_list):
         """ Calculates the new rating and rating deviation of the player.
-        
+
         update_player(list[int], list[int], list[bool]) -> None
-        
+
         """
         # Convert the rating and rating deviation values for internal use.
         # (div (sub x 1500) 173.7178)
@@ -103,21 +103,21 @@ def update_player(self, rating_list, RD_list, outcome_list):
         self._preRatingRD()
         # (div 1 (sqrt (add (pow rd.player 2) (div 1 v))))
         self.__rd = 1 / math.sqrt((1 / math.pow(self.__rd, 2)) + (1 / v))
-        
+
         tempSum = 0
         for i in range(len(rating_list)):
             # (add tempSum (mul g.player (sub outcome_list[i] self._E(rating_list[i], RD_list[i])))
             tempSum += self._g(RD_list[i]) * (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
-        # (add player.rating (mul (pow rd.player 2) tempSum))
+        # (add playerating (mul (pow rd.player 2) tempSum))
         self.__rating += math.pow(self.__rd, 2) * tempSum
         # print(f"{math.pow(self.__rd, 2) * tempSum}")
-        
-        
+
+
     def _newVol(self, rating_list, RD_list, outcome_list, v):
         """ Calculating the new volatility as per the Glicko2 system.
-        
+
         _newVol(list, list, list) -> float
-        
+
         """
         # Step 5 of the Glicko-2 algorithm
         # Step 5.1
@@ -184,12 +184,12 @@ def f(x):
             / (2 * math.pow(math.pow(self.__rd, 2) + v + math.exp(x), 2)) - (x - A) / math.pow(self._tau, 2)
             # print(f"f: {math.exp(x) * (math.pow(delta, 2) - math.pow(self.__rd, 2) - v - math.exp(x)) / (2 * math.pow(math.pow(self.__rd, 2) + v + math.exp(x), 2)) - (x - A) / math.pow(self._tau, 2)}")
         return f
-        
+
     def _delta(self, rating_list, RD_list, outcome_list, v):
         """ The delta function of the Glicko2 system.
-        
+
         _delta(list, list, list) -> float
-        
+
         """
         tempSum = 0
         for i in range(len(rating_list)):
@@ -197,12 +197,12 @@ def _delta(self, rating_list, RD_list, outcome_list, v):
             tempSum += self._g(RD_list[i]) * (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
         # print(f"delta: {v * tempSum}")
         return v * tempSum
-        
+
     def _v(self, rating_list, RD_list):
         """ The v function of the Glicko2 system.
-        
+
         _v(list[int], list[int]) -> float
-        
+
         """
         tempSum = 0
         for i in range(len(rating_list)):
@@ -212,33 +212,33 @@ def _v(self, rating_list, RD_list):
         # (div 1 tempSum)
         # print(f"v: {1 / tempSum}")
         return 1 / tempSum
-        
+
     def _E(self, p2rating, p2RD):
         """ The Glicko E function.
-        
+
         _E(int) -> float
-        
+
         """
         # (div 1 (add 1 (exp ;(mul -1 self._g(p2RD) (sub rating.player p2rating)))))
         # print(f"E: {1 / (1 + math.exp(-1 * self._g(p2RD) * (self.__rating - p2rating)))}")
         return 1 / (1 + math.exp(-1 * self._g(p2RD) * (self.__rating - p2rating)))
-        
+
     def _g(self, RD):
         """ The Glicko2 g(RD) function.
-        
+
         _g() -> float
-        
+
         """
         # (div 1 (sqrt (add 1 (mul 3 (div (pow RD 2) (pow pi 2))))))
         # print(f"g: {1 / math.sqrt(1 + 3 * math.pow(RD, 2) / math.pow(math.pi, 2))}")
         return 1 / math.sqrt(1 + 3 * math.pow(RD, 2) / math.pow(math.pi, 2))
-        
+
     def did_not_compete(self):
         """ Applies Step 6 of the algorithm. Use this for
         players who did not compete in the rating period.
 
         did_not_compete() -> None
-        
+
         """
         # print(f"did_not_compete: {self._preRatingRD()}")
         self._preRatingRD()

From 81a2a92951a56aa3db4cfe4c64c3c660d2d0e60d Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Fri, 5 Apr 2024 22:42:11 +0100
Subject: [PATCH 05/20] CTRL+F @rd rating to a @ud

---
 src/app/telos.hoon                     | 2 +-
 src/lib/telos.hoon                     | 2 +-
 src/mar/telos/game-rating.hoon         | 4 ++--
 src/mar/telos/player-rating.hoon       | 4 ++--
 src/mar/telos/rating.hoon              | 4 ++--
 src/mar/telos/ratings/game.hoon        | 4 ++--
 src/mar/telos/ratings/player-game.hoon | 4 ++--
 src/mar/telos/ratings/player.hoon      | 4 ++--
 src/sur/telos.hoon                     | 3 +--
 9 files changed, 15 insertions(+), 16 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index 169f651..57ff14f 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -531,7 +531,7 @@
         has-player-in-ratings
       player
     |=  [=game ratings=(map ^player rating)]
-    ^-  [^game @rd]
+    ^-  [^game @ud]
     [game (~(got by ratings) player)]
   ::
   ::  return rating for one player in one game
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 6edda18..8701375 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -194,7 +194,7 @@
 ++  update-ratings
   |=  [players=(map player rating) =winner =loser draw=?]
   ^+  players
-  (my [[winner .~1500] [loser .~1500] ~])
+  (my [[winner 1.500] [loser 1.500] ~])
   ::  ::
   ::  ::  add default rating for new players
   ::  =/  winner-data
diff --git a/src/mar/telos/game-rating.hoon b/src/mar/telos/game-rating.hoon
index 0b8c181..0bb1c92 100644
--- a/src/mar/telos/game-rating.hoon
+++ b/src/mar/telos/game-rating.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  game-rating=(pair game @rd)
+|_  game-rating=(pair game @ud)
 ++  grab
   |%
-  ++  noun  (pair game @rd)
+  ++  noun  (pair game @ud)
   --
 ++  grow
   |%
diff --git a/src/mar/telos/player-rating.hoon b/src/mar/telos/player-rating.hoon
index 921e0d3..bd6d382 100644
--- a/src/mar/telos/player-rating.hoon
+++ b/src/mar/telos/player-rating.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  player-rating=(pair player @rd)
+|_  player-rating=(pair player @ud)
 ++  grab
   |%
-  ++  noun  (pair player @rd)
+  ++  noun  (pair player @ud)
   --
 ++  grow
   |%
diff --git a/src/mar/telos/rating.hoon b/src/mar/telos/rating.hoon
index 5d171b4..09e15eb 100644
--- a/src/mar/telos/rating.hoon
+++ b/src/mar/telos/rating.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  rating=@rd
+|_  rating=@ud
 ++  grab
   |%
-  ++  noun  @rd
+  ++  noun  @ud
   --
 ++  grow
   |%
diff --git a/src/mar/telos/ratings/game.hoon b/src/mar/telos/ratings/game.hoon
index f6d5f95..0946dfe 100644
--- a/src/mar/telos/ratings/game.hoon
+++ b/src/mar/telos/ratings/game.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  ratings=(map player @rd)
+|_  ratings=(map player @ud)
 ++  grab
   |%
-  ++  noun  (map player @rd)
+  ++  noun  (map player @ud)
   --
 ++  grow
   |%
diff --git a/src/mar/telos/ratings/player-game.hoon b/src/mar/telos/ratings/player-game.hoon
index 13f6729..241fce7 100644
--- a/src/mar/telos/ratings/player-game.hoon
+++ b/src/mar/telos/ratings/player-game.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  rating=(unit @rd)
+|_  rating=(unit @ud)
 ++  grab
   |%
-  ++  noun  (unit @rd)
+  ++  noun  (unit @ud)
   --
 ++  grow
   |%
diff --git a/src/mar/telos/ratings/player.hoon b/src/mar/telos/ratings/player.hoon
index f445a74..263be6c 100644
--- a/src/mar/telos/ratings/player.hoon
+++ b/src/mar/telos/ratings/player.hoon
@@ -1,8 +1,8 @@
 /-  *telos
-|_  ratings=(map game @rd)
+|_  ratings=(map game @ud)
 ++  grab
   |%
-  ++  noun  (map game @rd)
+  ++  noun  (map game @ud)
   --
 ++  grow
   |%
diff --git a/src/sur/telos.hoon b/src/sur/telos.hoon
index 804d18a..07979eb 100644
--- a/src/sur/telos.hoon
+++ b/src/sur/telos.hoon
@@ -3,8 +3,7 @@
 +$  source   @p    ::  our source for a match record
 +$  player   @p
 +$  date     @da
-::  XX change to @ud
-+$  rating   @rd   ::  player's rating
++$  rating   @ud   ::  player's rating
 +$  game     @tas
 +$  id       @uvF  ::  unique id for a match and its payload
 +$  loser    player

From d130db607bd43cb0f2e28683f30a2b7c42d62575 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 15:01:15 +0100
Subject: [PATCH 06/20] wip: draft most elo logic

---
 src/lib/elo.hoon   |  93 ++++++++++++++++++++++++++++++++++++++
 src/lib/telos.hoon | 110 ++++++++++++++++++++++++++++++++-------------
 2 files changed, 173 insertions(+), 30 deletions(-)
 create mode 100644 src/lib/elo.hoon

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
new file mode 100644
index 0000000..cfd2b35
--- /dev/null
+++ b/src/lib/elo.hoon
@@ -0,0 +1,93 @@
+/-  *telos
+|%
+++  round
+  |=  rd=@rd
+  ^-  @ud
+  (abs:si (need (toi:rd rd)))
+::
+::  define expected score for a player in this match
+::    Ea = expected score for player A
+::    Ra = Elo rating of player A
+::    Rb = Elo rating of player B
+::    Ea = 1 / (1 + 2^((Rb - Ra) / 125))
+++  expected-score
+  |=  [our=rating opp=rating]
+  ^-  @rd
+  %+  div:rd
+    .~1
+  %+  add:rd
+    ~.1
+  ::  XX need our own pow:rd
+  %+  pow:rd
+    .~2
+  %+  div:rd
+    %+  sub:rd
+      (sun:rd opp)
+    (sun:rd our)
+  ~.125
+::
+::  calculate K
+::    K = 16  over 100 games played
+::    K = 24  between 60 and 100 games played
+::    K = 32  between 30 and 60 games played
+::    K = 40  between 10 and 30 games played
+::    K = 64  less than 10 games played
+++  scaling-factor
+  |=  matches=@ud
+  ^-  @ud
+  ::  ?:  (lth matches 10)
+  ::    64
+  ?:  (lth matches 30)
+    40
+  ?:  (lth matches 60)
+    32
+  ?:  (lth matches 100)
+    24
+  16
+::
+::  bootstrap a new rating in the first 10 games
+::    P = performance rating
+::    Σ = sum of opponents' ratings
+::    N = number of games played
+::    w = number of wins
+::    l = number of losses
+::    P = (Σ + (400 * (w - l))) / N
+++  new-performance-rating
+  |=  [sum=@ud matches=@ud wins=@ud losses=@ud]
+  ^-  rating
+  %+  div
+    %+  add
+      sum
+    %+  mul
+      400
+    %+  sub
+      wins
+    losses
+  matches
+::
+::  calculate new rating
+::    Rn = new rating
+::    Ro = old rating
+::    Ee = expected score
+::    Ea = actual score
+::    K  = scaling factor
+::    Rn = Ro + (K * (Ea - Ee))
+++  new-rating
+  |=  [our=rating our-ex=@rd our-scale=@ud opp=rating out=?(%win %loss %draw)]
+  ^-  rating
+  =/  our-actual
+    ?:  =(out %win)
+      our-ex
+    ?.  =(out %draw)
+      (sub:rd .~1 our-ex)
+    ::  XX what's our actual score if it's a draw?
+    !!
+  %-  round
+  %+  add:rd
+    (sun:rd our)
+  %+  mul:rd
+    (sun:rd our-scale)
+  %+  sub:rd
+    our-actual
+  our-ex
+--
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 8701375..717e9bb 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -1,4 +1,5 @@
 /-  *telos
+/+  elo
 |%
 ::
 +|  %poke-helpers
@@ -184,41 +185,90 @@
       =(player loser.match)
   ==
 ::
+++  has-winner-in-match
+  |=  [=match =player]
+  ^-  ?
+  =(player winner.match)
+::
+++  has-loser-in-match
+  |=  [=match =player]
+  ^-  ?
+  =(player loser.match)
+::
 ++  has-player-in-ratings
   |=  [[game ratings=(map player rating)] player=@]
   ^-  ?
   (~(has by ratings) player)
 ::
-+|  %ratings-helper
++|  %ratings
 ::
-++  update-ratings
-  |=  [players=(map player rating) =winner =loser draw=?]
+++  update-elo-ratings
+  ::  XX matches should include the match just played
+  |=  [players=(map player rating) matches=(list match) =winner =loser draw=?]
   ^+  players
-  (my [[winner 1.500] [loser 1.500] ~])
-  ::  ::
-  ::  ::  add default rating for new players
-  ::  =/  winner-data
-  ::    %+  fall
-  ::      (~(get by players) winner)
-  ::    *rating
-  ::  =/  loser-data
-  ::    %+  fall
-  ::      (~(get by players) loser)
-  ::    *rating
-  ::  ::
-  ::  ::  get new data for both players
-  ::  =+
-  ::    ^=  [new-winner-data new-loser-data]
-  ::    ?.  draw
-  ::      :-  (update-player:glicko2 winner-data [[loser-data %win] ~])
-  ::      (update-player:glicko2 loser-data [[winner-data %loss] ~])
-  ::    :-  (update-player:glicko2 winner-data [[loser-data %draw] ~])
-  ::    (update-player:glicko2 loser-data [[winner-data %draw] ~])
-  ::  ::
-  ::  ::  add new data to players
-  ::  %+  %~  put
-  ::        by
-  ::      (~(put by players) winner new-winner-data)
-  ::    loser
-  ::  new-loser-data
+  =/  new-winner-elo=rating
+    =/  our-rating
+      (~(gut by ratings) winner 1.500)
+    =/  opp-rating
+      (~(gut by ratings) loser 1.500)
+    =/  our-matches
+      (skim matches |=(=match (has-player-in-match match winner)))
+    =/  our-outcome
+      ::  XX assuming (head matches) is most recent match
+      ?.  draw:(head matches)
+        %win
+      %draw
+    ::
+    ?:  (lth our-matches 10)
+      %:  new-performance-rating:elo
+          ::  XX sum up opps' ratings from previous games
+          ::       would need to know what the opponents'
+          ::       ratings were at the time of the match.
+          ::       could change id.match to @da and scry
+          ::       for the rating at that case.
+          (~(gut by ratings) loser 1.500)
+          (lent our-matches)
+          (skim our-matches |=(=match (has-winner-in-match match winner)))
+          (skim our-matches |=(=match (has-loser-in-match match winner)))
+      ==
+    %:  new-rating:elo
+      our-rating
+      (expected-score:elo our-rating opp-rating)
+      (scaling-factor:elo (lent our-matches))
+      opp-rating
+      our-outcome
+    ==
+  =/  new-loser-elo=rating
+    =/  our-rating
+      (~(gut by ratings) loser 1.500)
+    =/  opp-rating
+      (~(gut by ratings) winner 1.500)
+    =/  our-matches
+      (skim matches |=(=match (has-player-in-match match loser)))
+    =/  our-outcome
+      ::  XX assuming (head matches) is most recent match
+      ?.  draw:(head matches)
+        %loss
+      %draw
+    ::
+    ?:  (lth our-matches 10)
+      %:  new-performance-rating:elo
+          ::  XX sum up opps' ratings from previous games
+          (~(gut by ratings) loser 1.500)
+          (lent our-matches)
+          (skim our-matches |=(=match (has-winner-in-match match loser)))
+          (skim our-matches |=(=match (has-loser-in-match match loser)))
+      ==
+    %:  new-rating:elo
+      our-rating
+      (expected-score:elo our-rating opp-rating)
+      (scaling-factor:elo (lent our-matches))
+      opp-rating
+      our-outcome
+    ==
+  %-  %~  put  by
+    %-  %~  put by
+      players
+    [loser new-loser-elo]
+  [winner new-winner-elo]
 --

From a5844cabc6a2b045c5f24a3a2360a131020bd6cf Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 18:20:33 +0100
Subject: [PATCH 07/20] wip: saloon

---
 src/lib/elo.hoon   | 70 ++++++++++++++++++++++++++++++++++++++++++++++
 src/lib/telos.hoon |  2 +-
 2 files changed, 71 insertions(+), 1 deletion(-)

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index cfd2b35..8d41e52 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -1,4 +1,74 @@
 /-  *telos
+=>
+|%
+::
+::  helper core
+::    adapted from /lib/saloon
+::    by ~lagrev-nocfep and ~mopfel-winrux
+::
+++  neg   |=(x=@rd (sub:rd .~0 x))
+::  accounted  for
+++  abs
+  |=  x=@rd  ^-  @rd
+  ?:  (^sig x)
+    x
+  (neg x)
+::
+++  exp
+  |=  x=@rd  ^-  @rd
+  =/  p   .~1
+  =/  po  .~-1
+  =/  i   .~1
+  |-  ^-  @rd
+  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
+    p
+  $(i (add:rd i .~1), p (add:rd p (div:rd (pow-n x i) (factorial i))), po p)
+::
+++  factorial
+  |=  x=@rd  ^-  @rd
+  =/  t=@rd  .~1
+  ?:  (isclose x .~0)
+    t
+  |-  ^-  @rd
+  ?:  (isclose x .~1)
+    t
+  $(x (sub:rd x .~1), t (mul:rd t x))
+::
+++  isclose
+  |=  [p=@rd r=@rd]
+  (lth:rd (abs (sub:rd p r)) .~1e-5)
+::
+++  log
+  |=  z=@rd  ^-  @rd
+  =/  p   .~0
+  =/  po  .~-1
+  =/  i   .~0
+  |-  ^-  @rd
+  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
+    (mul:rd (div:rd (mul:rd .~2 (sub:rd z .~1)) (add:rd z .~1)) p)
+  =/  term1  (div:rd .~1 (add:rd .~1 (mul:rd .~2 i)))
+  =/  term2  (mul:rd (sub:rd z .~1) (sub:rd z .~1))
+  =/  term3  (mul:rd (add:rd z .~1) (add:rd z .~1))
+  =/  term  (mul:rd term1 (pow-n (div:rd term2 term3) i))
+  $(i (add:rd i .~1), p (add:rd p term), po p)
+::
+++  rd
+  |%
+  ++  pow
+    |=  [x=@rd n=@rd]  ^-  @rd
+    (exp (mul:rd n (log x)))
+  --
+::
+++  pow-n
+  |=  [x=@rd n=@rd]  ^-  @rd
+  ?:  =(n .~0)  .~1
+  =/  p  x
+  |-  ^-  @rd
+  ?:  (lth:rd n .~2)
+    p
+  $(n (sub:rd n .~1), p (mul:rd p x))
+--
+::
 |%
 ++  round
   |=  rd=@rd
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 717e9bb..483b639 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -267,7 +267,7 @@
       our-outcome
     ==
   %-  %~  put  by
-    %-  %~  put by
+    %-  %~  put  by
       players
     [loser new-loser-elo]
   [winner new-winner-elo]

From b1513b83ca23c67db076d8e8bf8b1452b6fd8bfb Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 18:44:16 +0100
Subject: [PATCH 08/20] Integrate draft elo ratings

---
 src/app/telos.hoon |   2 +-
 src/lib/elo.hoon   | 153 +++++++++++++++++++++++----------------------
 src/lib/telos.hoon |  27 ++++----
 3 files changed, 92 insertions(+), 90 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index 57ff14f..903ea13 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -606,7 +606,7 @@
               ==
             ::
             =/  new-ratings
-              (update-ratings (~(got by ratings) game) winner loser draw)
+              (update-elo-ratings (~(got by ratings) game) (~(got by archive) game) winner loser draw)
             ::
             =/  winner-new-data
               (~(got by new-ratings) winner)
diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index 8d41e52..af6879d 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -1,79 +1,10 @@
 /-  *telos
-=>
-|%
-::
-::  helper core
-::    adapted from /lib/saloon
-::    by ~lagrev-nocfep and ~mopfel-winrux
-::
-++  neg   |=(x=@rd (sub:rd .~0 x))
-::  accounted  for
-++  abs
-  |=  x=@rd  ^-  @rd
-  ?:  (^sig x)
-    x
-  (neg x)
-::
-++  exp
-  |=  x=@rd  ^-  @rd
-  =/  p   .~1
-  =/  po  .~-1
-  =/  i   .~1
-  |-  ^-  @rd
-  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
-    p
-  $(i (add:rd i .~1), p (add:rd p (div:rd (pow-n x i) (factorial i))), po p)
-::
-++  factorial
-  |=  x=@rd  ^-  @rd
-  =/  t=@rd  .~1
-  ?:  (isclose x .~0)
-    t
-  |-  ^-  @rd
-  ?:  (isclose x .~1)
-    t
-  $(x (sub:rd x .~1), t (mul:rd t x))
-::
-++  isclose
-  |=  [p=@rd r=@rd]
-  (lth:rd (abs (sub:rd p r)) .~1e-5)
-::
-++  log
-  |=  z=@rd  ^-  @rd
-  =/  p   .~0
-  =/  po  .~-1
-  =/  i   .~0
-  |-  ^-  @rd
-  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
-    (mul:rd (div:rd (mul:rd .~2 (sub:rd z .~1)) (add:rd z .~1)) p)
-  =/  term1  (div:rd .~1 (add:rd .~1 (mul:rd .~2 i)))
-  =/  term2  (mul:rd (sub:rd z .~1) (sub:rd z .~1))
-  =/  term3  (mul:rd (add:rd z .~1) (add:rd z .~1))
-  =/  term  (mul:rd term1 (pow-n (div:rd term2 term3) i))
-  $(i (add:rd i .~1), p (add:rd p term), po p)
-::
-++  rd
-  |%
-  ++  pow
-    |=  [x=@rd n=@rd]  ^-  @rd
-    (exp (mul:rd n (log x)))
-  --
-::
-++  pow-n
-  |=  [x=@rd n=@rd]  ^-  @rd
-  ?:  =(n .~0)  .~1
-  =/  p  x
-  |-  ^-  @rd
-  ?:  (lth:rd n .~2)
-    p
-  $(n (sub:rd n .~1), p (mul:rd p x))
---
-::
+=<
 |%
 ++  round
-  |=  rd=@rd
+  |=  num=@rd
   ^-  @ud
-  (abs:si (need (toi:rd rd)))
+  (abs:si (need (toi:rd num)))
 ::
 ::  define expected score for a player in this match
 ::    Ea = expected score for player A
@@ -86,15 +17,14 @@
   %+  div:rd
     .~1
   %+  add:rd
-    ~.1
-  ::  XX need our own pow:rd
-  %+  pow:rd
+    .~1
+  %+  pow-rd
     .~2
   %+  div:rd
     %+  sub:rd
       (sun:rd opp)
     (sun:rd our)
-  ~.125
+  .~125
 ::
 ::  calculate K
 ::    K = 16  over 100 games played
@@ -161,3 +91,74 @@
     our-actual
   our-ex
 --
+::
+|%
+::
+::  helper core
+::    adapted from /lib/saloon
+::    by ~lagrev-nocfep and ~mopfel-winrux
+::
+++  sgn
+  |=  x=@rd  ^-  ?
+  =(0 (rsh [0 31] x))
+::
+++  neg
+  |=(x=@rd (sub:rd .~0 x))
+::
+++  abs
+  |=  x=@rd  ^-  @rd
+  ?:  (sgn x)
+    x
+  (neg x)
+::
+++  exp
+  |=  x=@rd  ^-  @rd
+  =/  p   .~1
+  =/  po  .~-1
+  =/  i   .~1
+  |-  ^-  @rd
+  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
+    p
+  $(i (add:rd i .~1), p (add:rd p (div:rd (pow-n x i) (factorial i))), po p)
+::
+++  factorial
+  |=  x=@rd  ^-  @rd
+  =/  t=@rd  .~1
+  ?:  (isclose x .~0)
+    t
+  |-  ^-  @rd
+  ?:  (isclose x .~1)
+    t
+  $(x (sub:rd x .~1), t (mul:rd t x))
+::
+++  isclose
+  |=  [p=@rd r=@rd]
+  (lth:rd (abs (sub:rd p r)) .~1e-5)
+::
+++  log
+  |=  z=@rd  ^-  @rd
+  =/  p   .~0
+  =/  po  .~-1
+  =/  i   .~0
+  |-  ^-  @rd
+  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
+    (mul:rd (div:rd (mul:rd .~2 (sub:rd z .~1)) (add:rd z .~1)) p)
+  =/  term1  (div:rd .~1 (add:rd .~1 (mul:rd .~2 i)))
+  =/  term2  (mul:rd (sub:rd z .~1) (sub:rd z .~1))
+  =/  term3  (mul:rd (add:rd z .~1) (add:rd z .~1))
+  =/  term  (mul:rd term1 (pow-n (div:rd term2 term3) i))
+  $(i (add:rd i .~1), p (add:rd p term), po p)
+::
+++  pow-rd
+  |=  [x=@rd n=@rd]  ^-  @rd
+  (exp (mul:rd n (log x)))
+::
+++  pow-n
+  |=  [x=@rd n=@rd]  ^-  @rd
+  ?:  =(n .~0)  .~1
+  =/  p  x
+  |-  ^-  @rd
+  ?:  (lth:rd n .~2)
+    p
+  $(n (sub:rd n .~1), p (mul:rd p x))
+--
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 483b639..0ebf4e6 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -114,8 +114,9 @@
     player-ratings
   %=  $
     matches         (tail matches)
-    player-ratings  %:  update-ratings
+    player-ratings  %:  update-elo-ratings
                         player-ratings
+                        matches
                         winner:(head matches)
                         loser:(head matches)
                         draw:(head matches)
@@ -208,9 +209,9 @@
   ^+  players
   =/  new-winner-elo=rating
     =/  our-rating
-      (~(gut by ratings) winner 1.500)
+      (~(gut by players) winner 1.500)
     =/  opp-rating
-      (~(gut by ratings) loser 1.500)
+      (~(gut by players) loser 1.500)
     =/  our-matches
       (skim matches |=(=match (has-player-in-match match winner)))
     =/  our-outcome
@@ -219,17 +220,17 @@
         %win
       %draw
     ::
-    ?:  (lth our-matches 10)
+    ?:  (lth (lent our-matches) 10)
       %:  new-performance-rating:elo
           ::  XX sum up opps' ratings from previous games
           ::       would need to know what the opponents'
           ::       ratings were at the time of the match.
           ::       could change id.match to @da and scry
           ::       for the rating at that case.
-          (~(gut by ratings) loser 1.500)
+          (~(gut by players) loser 1.500)
           (lent our-matches)
-          (skim our-matches |=(=match (has-winner-in-match match winner)))
-          (skim our-matches |=(=match (has-loser-in-match match winner)))
+          (lent (skim our-matches |=(=match (has-winner-in-match match winner))))
+          (lent (skim our-matches |=(=match (has-loser-in-match match winner))))
       ==
     %:  new-rating:elo
       our-rating
@@ -240,9 +241,9 @@
     ==
   =/  new-loser-elo=rating
     =/  our-rating
-      (~(gut by ratings) loser 1.500)
+      (~(gut by players) loser 1.500)
     =/  opp-rating
-      (~(gut by ratings) winner 1.500)
+      (~(gut by players) winner 1.500)
     =/  our-matches
       (skim matches |=(=match (has-player-in-match match loser)))
     =/  our-outcome
@@ -251,13 +252,13 @@
         %loss
       %draw
     ::
-    ?:  (lth our-matches 10)
+    ?:  (lth (lent our-matches) 10)
       %:  new-performance-rating:elo
           ::  XX sum up opps' ratings from previous games
-          (~(gut by ratings) loser 1.500)
+          (~(gut by players) loser 1.500)
           (lent our-matches)
-          (skim our-matches |=(=match (has-winner-in-match match loser)))
-          (skim our-matches |=(=match (has-loser-in-match match loser)))
+          (lent (skim our-matches |=(=match (has-winner-in-match match loser))))
+          (lent (skim our-matches |=(=match (has-loser-in-match match loser))))
       ==
     %:  new-rating:elo
       our-rating

From b62cf9132d0fe7020596755e2737e54b0d4d7e7b Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 18:45:05 +0100
Subject: [PATCH 09/20] Remove Glicko2 testing

---
 .gitignore                           |   2 -
 TESTING.md                           |  76 ---
 testing/glicko2js/.travis.yml        |   3 -
 testing/glicko2js/LICENSE.md         |  21 -
 testing/glicko2js/Makefile           |  19 -
 testing/glicko2js/README.md          | 156 ------
 testing/glicko2js/READMEnpm.md       | 117 -----
 testing/glicko2js/bower.json         |  26 -
 testing/glicko2js/example/index.html |  90 ----
 testing/glicko2js/glicko2.js         | 587 -----------------------
 testing/glicko2js/package.json       |  23 -
 testing/glicko2js/test/glicko2.js    | 230 ---------
 testing/glicko2js/yarn.lock          | 683 ---------------------------
 testing/pyglicko2/glicko2.py         | 244 ----------
 testing/pyglicko2/glicko2_tests.py   |  59 ---
 15 files changed, 2336 deletions(-)
 delete mode 100644 .gitignore
 delete mode 100644 TESTING.md
 delete mode 100644 testing/glicko2js/.travis.yml
 delete mode 100644 testing/glicko2js/LICENSE.md
 delete mode 100644 testing/glicko2js/Makefile
 delete mode 100644 testing/glicko2js/README.md
 delete mode 100644 testing/glicko2js/READMEnpm.md
 delete mode 100644 testing/glicko2js/bower.json
 delete mode 100644 testing/glicko2js/example/index.html
 delete mode 100644 testing/glicko2js/glicko2.js
 delete mode 100644 testing/glicko2js/package.json
 delete mode 100644 testing/glicko2js/test/glicko2.js
 delete mode 100644 testing/glicko2js/yarn.lock
 delete mode 100644 testing/pyglicko2/glicko2.py
 delete mode 100644 testing/pyglicko2/glicko2_tests.py

diff --git a/.gitignore b/.gitignore
deleted file mode 100644
index 05d2208..0000000
--- a/.gitignore
+++ /dev/null
@@ -1,2 +0,0 @@
-__pycache__
-test_results.txt
diff --git a/TESTING.md b/TESTING.md
deleted file mode 100644
index 8d733e5..0000000
--- a/TESTING.md
+++ /dev/null
@@ -1,76 +0,0 @@
-# JS and Python tests
-
-## Initial test (player RD: 200)
-
-[Original Glicko paper](http://www.glicko.net/glicko/glicko.pdf)
-[Example of the Glicko-2 system](http://www.glicko.net/glicko/glicko2.pdf)
-
-These initial tests demonstrated that the JS version was a correct implementation of
-Glicko-2, up-to-date with the system's Feb. 2022 update. The Python version has been
-amended to agree with the JS version, in lines 116 to 187.
-
-### Glickman’s paper
-#### Initial ranks and RDs
-* Player = rating 1500, RD 200
-* Opp1 = rating 1400, RD 30
-* Opp2 = rating 1550, RD 100
-* Opp3 = rating 1700, RD 300
-
-Outcome of games: 1, 0, and 0.
-
-#### Player’s ranking after games
-* Player = rating 1464.06, RD 151.52
-
-### JavaScript
-
-#### Inital rankings
-* Player: 1500.000000000000000000 (rd: 200.000000000000000000) (vol: 0.059999999999999998)
-* Opp1: 1400.000000000000000000 (rd: 30.000000000000003553) (vol: 0.059999999999999998)
-* Opp2: 1550.000000000000000000 (rd: 100.000000000000000000) (vol: 0.059999999999999998)
-* Opp3: 1700.000000000000000000 (rd: 300.000000000000000000) (vol: 0.059999999999999998)
-
-#### Rankings after games
-* Player: 1464.050670539301336248 (rd: 151.516524123857266204) (vol: 0.059995984286488495)
-* Opp1: 1398.143558233733756424 (rd: 31.670215281150621678) (vol: 0.059999123728885308)
-* Opp2: 1570.394740240853934665 (rd: 97.709168522003068347) (vol: 0.059999419471993810)
-* Opp3: 1784.421790132087380698 (rd: 251.565564532247350371) (vol: 0.059999011763670944)
-
-### Python
-
-#### Initial rankings
-* Player: 1500.000000000000000000 (rd:  200.000000000000000000)
-
-#### Rankings after games
-* Player: 1464.050670539301336248 (rd: 151.516524123857266204) (vol: 0.059995984286488495)
-
-***
-
-## Amended test (player RD: 350)
-
-The JS and Python versions have since been updated so that the player's initial RD is
-350 rather than 200. 350 is the system default in %telos, since Glickman assigns this RD
-to unrated players.
-
-### JavaScript
-#### Initial Rankings
-* Player: 1500.000000000000000000 (rd: 350.000000000000000000) (vol: 0.059999999999999998)
-* Opp1: 1400.000000000000000000 (rd: 30.000000000000003553) (vol: 0.059999999999999998)
-* Opp2: 1550.000000000000000000 (rd: 100.000000000000000000) (vol: 0.059999999999999998)
-* Opp3: 1700.000000000000000000 (rd: 300.000000000000000000) (vol: 0.059999999999999998)
-
-#### Rankings after games
-* Player: 1441.532789209275733811 (rd: 193.228325244026990504) (vol: 0.059997781896653730)
-* Opp1: 1398.432771279122562191 (rd: 31.701978358302014271) (vol: 0.059999532672676020)
-* Opp2: 1566.967754234200356223 (rd: 98.725018110245727598) (vol: 0.059999704551092846)
-* Opp3: 1785.184258294325218230 (rd: 264.385389300972235560) (vol: 0.059999350112324330)
-
-### Python
-#### Initial rankings
-* Old Rating: 1500.000000000000000000
-* Old Rating Deviation: 350.000000000000000000
-* Old Volatility: 0.059999999999999998
-
-#### Rankings after games
-* New Rating: 1441.532789209275733811
-* New Rating Deviation: 193.228325244026990504
-* New Volatility: 0.059997781896653730
\ No newline at end of file
diff --git a/testing/glicko2js/.travis.yml b/testing/glicko2js/.travis.yml
deleted file mode 100644
index c7b016c..0000000
--- a/testing/glicko2js/.travis.yml
+++ /dev/null
@@ -1,3 +0,0 @@
-language: node_js
-node_js:
-  - 12
diff --git a/testing/glicko2js/LICENSE.md b/testing/glicko2js/LICENSE.md
deleted file mode 100644
index 242132d..0000000
--- a/testing/glicko2js/LICENSE.md
+++ /dev/null
@@ -1,21 +0,0 @@
-The MIT License (MIT)
-
-Copyright (c) <year> <copyright holders>
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in
-all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-THE SOFTWARE.
diff --git a/testing/glicko2js/Makefile b/testing/glicko2js/Makefile
deleted file mode 100644
index b90b80d..0000000
--- a/testing/glicko2js/Makefile
+++ /dev/null
@@ -1,19 +0,0 @@
-DIRNPM=toNPM
-
-test:
-	npm test
-
-build:
-	rm -rf $(DIRNPM)
-	mkdir $(DIRNPM)
-	cp glicko2.js $(DIRNPM)
-	cp package.json $(DIRNPM)
-	cp READMEnpm.md $(DIRNPM)/README.md
-	cp -R test $(DIRNPM)
-
-publish: build
-	cd $(DIRNPM)
-	npm publish .
-	cd ..
-
-.PHONY: test
diff --git a/testing/glicko2js/README.md b/testing/glicko2js/README.md
deleted file mode 100644
index ad3ec99..0000000
--- a/testing/glicko2js/README.md
+++ /dev/null
@@ -1,156 +0,0 @@
-# Glicko 2 javascript implementation
-
-[![Build Status](https://travis-ci.org/mmai/glicko2js.png)](https://travis-ci.org/mmai/glicko2js)
-
-
-The Glicko-2 rating system is a method for assessing a player's strength in games of skill, such as chess and go.
-The algorithm is explained by its author, Mark E. Glickman, on http://glicko.net/glicko.html.
-
-Each player begins with a rating, a rating deviation (accuracy of the rating) and a volatility (speed of rating evolution). These values will evolve according to the outcomes of matches with other players.
-
-## Usage
-
-In the browser, you need to include the glicko2.js file :
-
-``` html
-<script src="glicko2.js"></script>
-```
-
-In node.js, just require the module :
-
-``` javascript
-var glicko2 = require('glicko2');
-```
-
-First we initiate a ranking manager and create players with initial ratings, rating deviations and volatilities.
-
-``` javascript
-var settings = {
-  // tau : "Reasonable choices are between 0.3 and 1.2, though the system should
-  //      be tested to decide which value results in greatest predictive accuracy."
-  tau : 0.5,
-  // rating : default rating
-  rating : 1500,
-  //rd : Default rating deviation 
-  //     small number = good confidence on the rating accuracy
-  rd : 200,
-  //vol : Default volatility (expected fluctation on the player rating)
-  vol : 0.06
-};
-var ranking = new glicko2.Glicko2(settings);
-
-// Create players
-var Ryan = ranking.makePlayer();
-var Bob = ranking.makePlayer(1400, 30, 0.06);
-var John = ranking.makePlayer(1550, 100, 0.06);
-var Mary = ranking.makePlayer(1700, 300, 0.06);
-```
-
-We can then enter results, calculate the new ratings...
-
-``` javascript
-var matches = [];
-matches.push([Ryan, Bob, 1]); //Ryan won over Bob
-matches.push([Ryan, John, 0]); //Ryan lost against John
-matches.push([Ryan, Mary, 0.5]); //A draw between Ryan and Mary
-ranking.updateRatings(matches);
-```
-
-... and get these new ratings.
-
-``` javascript
-console.log("Ryan new rating: " + Ryan.getRating());
-console.log("Ryan new rating deviation: " + Ryan.getRd());
-console.log("Ryan new volatility: " + Ryan.getVol());
-```
-
-Get players list
-
-``` javascript
-var players = ranking.getPlayers();
-```
-
-## When to update rankings
-
-You should not update the ranking after each match.
-The typical use of glicko is to calculate the ratings after each tournament (ie collection of matches in a period of time).
-A player rating will evolve after a tournament has finished, but not during the tournament. 
-
-Here is what says Mark E. Glickman about the number of matches in a tournament or rating period (cf. http://www.glicko.net/glicko/glicko2.pdf ) :
-> The Glicko-2 system works best when the number of games in a rating period is moderate to large, say an average of at least 10-15 games per player in a rating period.
-
-### Support for multiple competitors matches (experimental)
-
-**Note: the glicko2 algorithm was not designed for multiple competitors matches, this is a naive workaround whose results should be taken whith caution.** 
-
-You can enter results from games where multiple competitors play against each other at the same time (ie swimming, racing...).
-
-First make "Race" objects by entering the results in an array of "positions", where each position is an array of players at this position :
-
-```javascript
-var race1 = glicko.makeRace(
-    [
-        [Ryan], //Ryan won the race
-        [Bob, John], //Bob and John ended ex aequo at the 2nd position
-        [Mary] // Mary 4th position
-    ]
-);
-
-var race2 = glicko.makeRace(
-    [
-        [Mary], // won
-        [Bob],  // 2nd
-        [John], // 3rd
-        [Ryan], // 4th
-    ]
-);
-
-```
-
-Then convert the races to the equivalent matches :
-```javascript
-
-var matches1 = race1.getMatches();
-var matches2 = race2.getMatches();
-
-var allMatches = matches1.concat(matches2)
-
-ranking.updateRatings(allMatches);
-```
-
-You can also update ratings for one race without converting to matches :
-
-```javascript
-ranking.updateRatings(race1);
-```
-
-## Installation
-
-### In the browser
-
-You just need to include the glicko2.js script.
-See index.html in the example folder.
-
-``` html
-<script src="glicko2.js"></script>
-```
-
-### With [bower](http://bower.io/)
-
-``` shell
-$ bower install glicko2
-```
-``` html
-<script src="bower_components/glicko2/glicko2.js"></script>
-```
-
-### As a node.js module
-
-glicko2.js is available as a npm module.
-
-Install with:
-
-``` shell
-$ npm install glicko2
-```
-
diff --git a/testing/glicko2js/READMEnpm.md b/testing/glicko2js/READMEnpm.md
deleted file mode 100644
index ff91e61..0000000
--- a/testing/glicko2js/READMEnpm.md
+++ /dev/null
@@ -1,117 +0,0 @@
-# Glicko 2 javascript implementation
-
-[![Build Status](https://travis-ci.org/mmai/glicko2js.png)](https://travis-ci.org/mmai/glicko2js)
-
-
-The Glicko-2 rating system is a method for assessing a player's strength in games of skill, such as chess and go.
-The algorithm is explained by its author, Mark E. Glickman, on http://glicko.net/glicko.html.
-
-Each player begins with a rating, a rating deviation (accuracy of the rating) and a volatility (speed of rating evolution). These values will evolve according to the outcomes of matches with other players.
-
-## Usage
-
-First we initiate a ranking manager and create players with initial ratings, rating deviations and volatilities.
-
-``` javascript
-var glicko2 = require('glicko2');
-var settings = {
-  // tau : "Reasonable choices are between 0.3 and 1.2, though the system should
-  //       be tested to decide which value results in greatest predictive accuracy."
-  tau : 0.5,
-  // rating : default rating
-  rating : 1500,
-  //rd : Default rating deviation
-  //     small number = good confidence on the rating accuracy
-  rd : 200,
-  //vol : Default volatility (expected fluctation on the player rating)
-  vol : 0.06
-};
-var ranking = new glicko2.Glicko2(settings);
-
-// Create players
-var Ryan = ranking.makePlayer();
-var Bob = ranking.makePlayer(1400, 30, 0.06);
-var John = ranking.makePlayer(1550, 100, 0.06);
-var Mary = ranking.makePlayer(1700, 300, 0.06);
-```
-
-We can then enter results, calculate the new ratings...
-
-``` javascript
-var matches = [];
-matches.push([Ryan, Bob, 1]); //Ryan won over Bob
-matches.push([Ryan, John, 0]); //Ryan lost against John
-matches.push([Ryan, Mary, 0.5]); //A draw between Ryan and Mary
-ranking.updateRatings(matches);
-```
-
-... and get these new ratings.
-
-``` javascript
-console.log("Ryan new rating: " + Ryan.getRating());
-console.log("Ryan new rating deviation: " + Ryan.getRd());
-console.log("Ryan new volatility: " + Ryan.getVol());
-```
-
-Get players list
-
-``` javascript
-var players = ranking.getPlayers();
-```
-
-## When to update rankings
-
-You should not update the ranking after each match.
-The typical use of glicko is to calculate the ratings after each tournament (ie collection of matches in a period of time).
-A player rating will evolve after a tournament has finished, but not during the tournament. 
-
-You can see a client side javascript example using tournaments here : https://github.com/mmai/glicko2js/blob/master/example/index.html
-
-Here is what says Mark E. Glickman about the number of matches in a tournament or rating period (cf. http://www.glicko.net/glicko/glicko2.pdf ) :
-> The Glicko-2 system works best when the number of games in a rating period is moderate to large, say an average of at least 10-15 games per player in a rating period.
-
-### Support for multiple competitors matches (experimental)
-
-**Note: the glicko2 algorithm was not designed for multiple competitors matches, this is a naive workaround whose results should be taken whith caution.** 
-
-You can enter results from games where multiple competitors play against each other at the same time (ie swimming, racing...).
-
-First make "Race" objects by entering the results in an array of "positions", where each position is an array of players at this position :
-
-```javascript
-var race1 = glicko.makeRace(
-    [
-        [Ryan], //Ryan won the race
-        [Bob, John], //Bob and John ended ex aequo at the 2nd position
-        [Mary] // Mary 4th position
-    ]
-);
-
-var race2 = glicko.makeRace(
-    [
-        [Mary], // won
-        [Bob],  // 2nd
-        [John], // 3rd
-        [Ryan], // 4th
-    ]
-);
-
-```
-
-Then convert the races to the equivalent matches :
-```javascript
-
-var matches1 = race1.getMatches();
-var matches2 = race2.getMatches();
-
-var allMatches = matches1.concat(matches2)
-
-ranking.updateRatings(allMatches);
-```
-
-You can also update ratings for one race without converting to matches :
-
-```javascript
-ranking.updateRatings(race1);
-```
-
diff --git a/testing/glicko2js/bower.json b/testing/glicko2js/bower.json
deleted file mode 100644
index f047663..0000000
--- a/testing/glicko2js/bower.json
+++ /dev/null
@@ -1,26 +0,0 @@
-{
-  "name": "glicko2",
-  "version": "0.8.7",
-  "homepage": "https://github.com/mmai/glicko2js",
-  "authors": [
-    "Henri Bourcereau <henri.bourcereau@gmail.com>"
-  ],
-  "description": "glicko2 ranking system",
-  "main": "./glicko2.js",
-  "keywords": [
-    "glicko",
-    "utilities",
-    "ranking"
-  ],
-  "license": "MIT",
-  "ignore": [
-    "**/.*",
-    "example",
-    "node_modules",
-    "test",
-    "toNPM",
-    "Makefile",
-    "package.json",
-    "READMEnpm.md"
-  ]
-}
diff --git a/testing/glicko2js/example/index.html b/testing/glicko2js/example/index.html
deleted file mode 100644
index 134abf7..0000000
--- a/testing/glicko2js/example/index.html
+++ /dev/null
@@ -1,90 +0,0 @@
-<!DOCTYPE html>
-<html>
-    <head>
-        <script src="../glicko2.js"></script>
-
-        <script type="text/javascript">
-            var settings = {
-              tau : 0.5,
-              rpd : 604800,
-              rating : 1500,
-              rd : 300,
-              vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-
-            //Make players
-            Player = glicko.makePlayer(1500, 350, 0.06);
-            Opp3 = glicko.makePlayer(1700, 300, 0.06);
-            Opp1 = glicko.makePlayer(1400, 30, 0.06);
-            Opp2 = glicko.makePlayer(1550, 100, 0.06);
-
-            var players = [
-                { name:'Opp3', glicko: Opp3 },
-                { name:'Opp1', glicko: Opp1 },
-                { name:'Opp2', glicko: Opp2 },
-                { name:'Player', glicko: Player }
-            ];
-
-            function showRankings(){
-                //Sort players
-                players.sort(function(pl1, pl2){ return pl2.glicko.getRating() - pl1.glicko.getRating(); });
-
-                //Display ratings
-                for (var i=0,len= players.length;i<len;i++){
-                    player = players[i];
-                    document.write(player.name + ': ' + player.glicko.getRating().toFixed(18) + ' (rd: ' + player.glicko.getRd().toFixed(18) + ') (vol: ' + player.glicko.getVol().toFixed(18) + ')<br>');
-                }
-            }
-       </script>
-    </head>
-
-    <body>
-        <h2>Initial rankings</h2>
-        <script>
-            showRankings();
-        </script>
-
-        <h2>Rankings after tournament 1</h2>
-        <script>
-            var matches = [];
-            matches.push([Player, Opp1, 1]); //Player won over Opp1
-            matches.push([Player, Opp2, 0]); //Player lost against Opp2
-            matches.push([Player, Opp3, 0]); //Player lost against Opp3
-
-            glicko.updateRatings(matches);
-            showRankings();
-        </script>
-
-        <!-- <h2>Rankings after tournament 2</h2>
-        <script>
-            var matches = [];
-            matches.push([Opp2, Opp3, 0.5]);
-            matches.push([Opp2, Player, 0]);
-            matches.push([Opp3, Opp2, 0]);
-            glicko.updateRatings(matches);
-            showRankings();
-        </script> -->
-
-        <!-- <h2>Rankings after two races</h2>
-        <script>
-            var matches = [];
-            var race1 = glicko.makeRace([
-                    [Player],
-                    [Opp2],
-                    [Opp3]
-            ]);
-            var race2 = glicko.makeRace([
-                [Gaspard],
-                [Opp2, Opp1],
-                [Hector]
-            ]);
-
-            matches = matches.concat(race1.getMatches());
-            matches = matches.concat(race2.getMatches());
-            glicko.updateRatings(matches);
-            showRankings();
-        </script> -->
-
-     </body>
-</html>
diff --git a/testing/glicko2js/glicko2.js b/testing/glicko2js/glicko2.js
deleted file mode 100644
index e43a33b..0000000
--- a/testing/glicko2js/glicko2.js
+++ /dev/null
@@ -1,587 +0,0 @@
-// everything is in one function
-(function(exports){
-    // set scalingFactor to 173.7178
-    var scalingFactor = 173.7178;
-    // create Race function
-    function Race(results){
-        this.matches = this.computeMatches(results);
-    }
-    // add getMatches to Race
-    Race.prototype.getMatches = function(){
-        return this.matches;
-    };
-    // add computeMatches to Race
-    Race.prototype.computeMatches = function(results){
-        var players = [];
-        var position = 0;
-
-        results.forEach(function (rank) {
-            position += 1;
-            rank.forEach(function (player) {
-                players.push({"player": player, "position": position});
-            })
-        })
-
-        function computeMatches(players){
-            if (players.length === 0) return [];
-
-            var player1 = players.shift()
-            var player1_results  = players.map(function(player2){
-                return [player1.player, player2.player, (player1.position < player2.position) ? 1 : 0.5];
-            });
-
-            return player1_results.concat(computeMatches(players));
-        }
-
-        return computeMatches(players)
-    }
-    // create Player function
-    function Player(rating, rd, vol, tau, default_rating, volatility_algorithm, id) {
-        // Step 1
-        this._tau = tau; 
-        this.defaultRating = default_rating;
-        this.volatility_algorithm = volatility_algorithm;
-
-        this.setRating(rating);
-        this.setRd(rd);
-        this.setVol(vol);
-
-        this.id = id
-        this.adv_ranks = [];
-        this.adv_rds = [];
-        this.outcomes = [];
-    }
-    // add getRating to Player
-    Player.prototype.getRating = function (){
-        // (mul rating.player (add scalingFactor default-rating.player))
-        return this.__rating * scalingFactor + this.defaultRating;
-    };
-    // add setRating to Player
-    Player.prototype.setRating = function (rating){
-        // Step 2.1
-        this.__rating = (rating - this.defaultRating) / scalingFactor;
-    };
-    // addd getRd to Player
-    Player.prototype.getRd = function(){
-        // (mul rd.player scaling-factor)
-        return this.__rd * scalingFactor;
-    };
-    // add setRd to Player
-    Player.prototype.setRd = function(rd){
-        // Step 2.2
-        this.__rd = rd / scalingFactor;
-    };
-    // add getVol to Player
-    Player.prototype.getVol = function(){
-        return this.__vol;
-    };
-    // add setVol to Player
-    Player.prototype.setVol = function(vol){
-        this.__vol = vol;
-    };
-    // add addResult to Player
-    Player.prototype.addResult = function(opponent, outcome){
-        // add opponent's rating to adv_ranks array
-        this.adv_ranks.push(opponent.__rating);
-        // add opponent's RD to adv_rds array
-        // (i think adv is "adversary"?)
-        this.adv_rds.push(opponent.__rd);
-        // add outcome to outcomes array
-        this.outcomes.push(outcome);
-    };
-    // adds update_rank to Player
-    // Calculates the new rating and rating deviation of the player.
-    // Follows the steps of the algorithm described at http://www.glicko.net/glicko/glicko2.pdf
-    Player.prototype.update_rank = function(){
-        // if player has not competed in this series of matches...
-        if (!this.hasPlayed()){
-            // Applies only the Step 6 of the algorithm
-            this._preRatingRD();
-            return;
-        }
-
-        //Step 1 : done by Player initialization
-        //Step 2 : done by setRating and setRd
-
-        //Step 3
-        // set v to this Player's variance
-        var v = this._variance();
-
-        //Step 4
-        // set delta to this Player's delta
-        var delta = this._delta(v);
-
-        //Step 5
-        // set this Player's volatility
-        this.__vol = this.volatility_algorithm(v, delta);
-
-        //Step 6
-        // init this Player's pre-rating period RD
-        this._preRatingRD();
-
-        //Step 7
-        // set this Player's new RD
-        // (div 1 (sqrt (add (div 1 (pow RD 2)) (div 1 v))))
-        this.__rd = 1 / Math.sqrt((1 / Math.pow(this.__rd, 2)) + (1 / v));
-
-        var tempSum = 0;
-        for (var i=0,len = this.adv_ranks.length;i< len;i++){
-            // $(tempSum (add tempSum (mul _g(this.adv_rds[i] (sub this.outcomes[i] _E(this.adv_ranks[i] this.adv_rds[i]))))))
-            tempSum += this._g(this.adv_rds[i]) * (this.outcomes[i] - this._E(this.adv_ranks[i], this.adv_rds[i]));
-        }
-        // $(this.__rating (add this.__rating (mul (pow this.__rd 2) tempSum)))
-        this.__rating += Math.pow(this.__rd, 2) * tempSum;
-
-        //Step 8 : done by getRating and getRd
-    };
-    // add hasPlayed to Player
-    Player.prototype.hasPlayed = function(){
-        // determine whether or not player has played in this rating period
-        return this.outcomes.length > 0;
-    };
-
-    // Calculates and updates the player's rating deviation for the beginning of a rating period.
-    // preRatingRD() -> None
-    Player.prototype._preRatingRD = function(){
-        // (sqrt (add (pow RD 2) (pow vol 2)))
-        this.__rd = Math.sqrt(Math.pow(this.__rd, 2) + Math.pow(this.__vol, 2));
-    };
-
-    // Calculation of the estimated variance of the player's rating based on game outcomes
-    Player.prototype._variance = function (){
-        var tempSum = 0;
-        for (var i = 0, len = this.adv_ranks.length;i<len;i++){
-            // tempE = E(opp_rank opp_rd)
-            var tempE = this._E(this.adv_ranks[i], this.adv_rds[i]);
-            // (add tempSum ;(mul (pow _g(this.adv_rds[i]) 2) tempE (sub 1 tempE))
-            tempSum += Math.pow(this._g(this.adv_rds[i]), 2) * tempE * (1 - tempE);
-        }
-        // (div 1 tempSum)
-        return 1 / tempSum;
-    };
-
-    // The Glicko E function.
-    Player.prototype._E = function (p2rating, p2RD){
-        // (div 1 (add 1 (exp ;(mul -1 this._g(p2RD) (sub this.__rating p2rating)))))
-        return 1 / (1 + Math.exp(-1 * this._g(p2RD) *  (this.__rating - p2rating)));
-    };
-
-    // The Glicko2 g(RD) function.
-    Player.prototype._g = function(RD){
-        // (div 1 (sqrt (add 1 (mul 3 (div (pow RD 2) (pow pi 2))))))
-        return 1 / Math.sqrt(1 + 3 * Math.pow(RD, 2) / Math.pow(Math.PI, 2));
-    };
-
-    // The delta function of the Glicko2 system.
-    // Calculation of the estimated improvement in rating (step 4 of the algorithm)
-    Player.prototype._delta = function(v){
-        var tempSum = 0;
-        // for (expr1; expr2; expr3)
-        // expr1: ex. once before ex. of block
-        // expr2: ex. defines condition for ex. code block
-        // expr3: ex. every time after code block has been executed
-        for (var i = 0, len = this.adv_ranks.length;i<len;i++){
-            // (add tempSum (mul _g(adv_rds[i]) (sub outcomes (E adv_ranks adv_rds))))
-            tempSum += this._g(this.adv_rds[i]) * (this.outcomes[i] - this._E(this.adv_ranks[i], this.adv_rds[i]));
-        }
-        // (mul v tempSum)
-        return v * tempSum;
-    };
-
-    Player.prototype._makef = function(delta, v, a){
-        var pl = this;
-        // this is invoked as f(x) in the newprocedure, because f = _makef(delta, v, a)
-        // see here for another example: https://www.quora.com/What-are-the-reasons-to-use-return-function-in-JavaScript
-        return function(x){
-            // (mul (exp x) (sub (pow delta 2) (div ;(sub (pow RD 2) v (exp x)) (sub (mul 2 (pow (pow ;(add (pow RD 2) v (exp x)) 2))) (div (sub x a) (pow tau 2))))
-            return Math.exp(x) * (Math.pow(delta, 2) - Math.pow(pl.__rd, 2) - v - Math.exp(x)) / (2*Math.pow(Math.pow(pl.__rd, 2) + v + Math.exp(x), 2)) - (x - a) / Math.pow(pl._tau, 2);
-        };
-    };
-
-    //=========================  Glicko2 class =============================================
-    function Glicko2(settings){
-        settings = settings || {};
-
-        // Internal glicko2 parameter. "Reasonable choices are between 0.3 and
-        // 1.2, though the system should be tested to decide which value results
-        // in greatest predictive accuracy."
-        this._tau = settings.tau || 0.5;
-
-        // Default rating
-        this._default_rating = settings.rating || 1500;
-
-        // Default rating deviation (small number = good confidence on the
-        // rating accuracy)
-        this._default_rd = settings.rd || 350;
-
-        // Default volatility (expected fluctation on the player rating)
-        this._default_vol = settings.vol || 0.06;
-
-        // Default volatility calculation algorithm (step 5 of the global
-        // algorithm)
-        this._volatility_algorithm = volatility_algorithms[settings.volatility_algorithm || 'newprocedure'];
-
-        this.players = [];
-        this.players_index = 0;
-    }
-
-    Glicko2.prototype.makeRace = function(results){
-        return new Race(results);
-    };
-
-    Glicko2.prototype.removePlayers = function() {
-        this.players = [];
-        this.players_index = 0;
-    };
-
-    Glicko2.prototype.getPlayers = function(){
-        return this.players;
-    };
-
-    Glicko2.prototype.cleanPreviousMatches = function(){
-        for (var i = 0, len = this.players.length;i < len;i++){
-            this.players[i].adv_ranks = [];
-            this.players[i].adv_rds = [];
-            this.players[i].outcomes = [];
-        }
-    };
-
-    Glicko2.prototype.calculatePlayersRatings = function(){
-        var keys = Object.keys(this.players);
-        for (var i=0, len = keys.length;i<len;i++){
-            this.players[keys[i]].update_rank();
-        }
-    };
-
-    /** 
-     * Add players and match result to be taken in account for the new rankings calculation
-     * players must have ids, they are not created if it has been done already.
-     * @param {Object litteral} pl1 The first player
-     * @param {Object litteral} pl2 The second player
-     * @param {number} outcom The outcome : 0 = defeat, 1 = victory, 0.5 = draw
-     */
-      Glicko2.prototype.addMatch = function(player1, player2, outcome){
-          var pl1 = this._createInternalPlayer(player1.rating, player1.rd, player1.vol, player1.id);
-          var pl2 = this._createInternalPlayer(player2.rating, player2.rd, player2.vol, player2.id);
-          this.addResult(pl1, pl2, outcome);
-          return {pl1:pl1, pl2:pl2};
-      };
-
-      Glicko2.prototype.makePlayer = function (rating, rd , vol) {
-          //We do not expose directly createInternalPlayer in order to prevent the assignation of a custom player id whose uniqueness could not be guaranteed
-          return this._createInternalPlayer(rating, rd, vol);
-      };
-
-      Glicko2.prototype._createInternalPlayer = function (rating, rd , vol, id){
-          if (id === undefined){
-              id = this.players_index;
-              this.players_index = this.players_index + 1;
-          } else {
-              //We check if the player has already been created
-              var candidate = this.players[id];
-              if (candidate !== undefined){
-                  return candidate;
-              }
-          }
-          var player = new Player(rating || this._default_rating, rd || this._default_rd, vol || this._default_vol,
-                                  this._tau, this._default_rating, this._volatility_algorithm, id);
-
-          this.players[id] = player;
-          return player;
-      };
-
-      /** 
-       * Add a match result to be taken in account for the new rankings calculation
-       * @param {Player} player1 The first player
-       * @param {Player} player2 The second player
-       * @param {number} outcome The outcome : 0 = defeat, 1 = victory, 0.5 = draw
-       */
-        Glicko2.prototype.addResult = function(player1, player2, outcome){
-            player1.addResult(player2, outcome);
-            player2.addResult(player1, 1 - outcome);
-        };
-
-        Glicko2.prototype.updateRatings = function(matches){
-            if(matches instanceof Race){
-                matches = matches.getMatches();
-            }
-            if (typeof(matches) !== 'undefined'){
-                this.cleanPreviousMatches();
-                for (var i=0, len = matches.length;i<len;i++){
-                    var match = matches[i];
-                    this.addResult(match[0], match[1], match[2]);
-                }
-            }
-            this.calculatePlayersRatings();
-        };
-
-        //============== VOLATILITY ALGORITHMS (Step 5 of the global glicko2 algorithm)
-        var volatility_algorithms = {
-            oldprocedure: function(v, delta) {
-                var sigma = this.__vol;
-                var phi = this.__rd;
-                var tau = this._tau;
-
-                var a, x1, x2, x3, y1, y2, y3, upper;
-                var result;
-                upper = find_upper_falsep(phi, v, delta, tau);
-                a = Math.log(Math.pow(sigma, 2));
-                y1 = equation(phi, v, 0, a, tau, delta);
-                if (y1 > 0 ){
-                    result = upper;
-                } else {
-                    x1 = 0;
-                    x2 = x1;
-                    y2 = y1;
-                    x1 = x1 - 1;
-                    y1 = equation(phi, v, x1, a, tau, delta);
-                    while (y1 < 0){
-                        x2 = x1;
-                        y2 = y1;
-                        x1 = x1 - 1;
-                        y1 = equation(phi, v, x1, a, tau, delta);
-                    }
-                    for (var i = 0; i<21; i++){
-                        x3 = y1 * (x1 - x2) / (y2 - y1) + x1;
-                        y3 = equation(phi, v, x3, a, tau, delta);
-                        if (y3 > 0 ){
-                            x1 = x3;
-                            y1 = y3;
-                        } else {
-                            x2 = x3;
-                            y2 = y3;
-                        }
-                    }
-                    if (Math.exp((y1 * (x1 - x2) / (y2 - y1) + x1) / 2) > upper ){
-                        result = upper;
-                    } else {
-                        result = Math.exp((y1 * (x1 - x2) / (y2 - y1) + x1) / 2);
-                    }
-                }
-                return result;
-
-                function new_sigma(sigma , phi , v , delta , tau ) {
-                    var a = Math.log(Math.pow(sigma, 2));
-                    var x = a;
-                    var old_x = 0;
-                    while (x != old_x){
-                        old_x = x;
-                        var d = Math.pow(phi, 2) + v + Math.exp(old_x);
-                        var h1 = -(old_x - a) / Math.pow(tau, 2) - 0.5 * Math.exp(old_x) / d + 0.5 * Math.exp(old_x) * Math.pow((delta / d), 2);
-                        var h2 = -1 / Math.pow(tau, 2) - 0.5 * Math.exp(old_x) * (Math.pow(phi, 2) + v) / Math.pow(d, 2) + 0.5 * Math.pow(delta, 2) * Math.exp(old_x) * (Math.pow(phi, 2) + v - Math.exp(old_x)) / Math.pow(d, 3);
-                        x = old_x - h1 / h2;
-                    }
-                    return  Math.exp(x / 2);
-                }
-
-                function equation(phi , v , x , a , tau , delta) {
-                    var d = Math.pow(phi, 2) + v + Math.exp(x);
-                    return -(x - a) / Math.pow(tau, 2) - 0.5 * Math.exp(x) / d + 0.5 * Math.exp(x) * Math.pow((delta / d), 2);
-                }
-
-                function new_sigma_bisection(sigma , phi , v , delta , tau ) {
-                    var a, x1, x2, x3;
-                    a = Math.log(Math.pow(sigma, 2));
-                    if (equation(phi, v, 0, a, tau, delta) < 0 ){
-                        x1 = -1;
-                        while (equation(phi, v, x1, a, tau, delta) < 0){
-                            x1 = x1 - 1;
-                        }
-                        x2 = x1 + 1;
-                    } else {
-                        x2 = 1;
-                        while (equation(phi, v, x2, a, tau, delta) > 0){
-                            x2 = x2 + 1;
-                        }
-                        x1 = x2 - 1;
-                    }
-
-                    for (var i = 0; i < 27; i++) {
-                        x3 = (x1 + x2) / 2;
-                        if (equation(phi, v, x3, a, tau, delta) > 0 ){
-                            x1 = x3;
-                        } else {
-                            x2 = x3;
-                        }
-                    }
-                    return  Math.exp((x1 + x2)/ 4);
-                }
-
-                function Dequation(phi , v , x , tau , delta) {
-                    d = Math.pow(phi, 2) + v + Math.exp(x);
-                    return -1 / Math.pow(tau, 2) - 0.5 * Math.exp(x) / d + 0.5 * Math.exp(x) * (Math.exp(x) + Math.pow(delta, 2)) / Math.pow(d, 2) - Math.pow(Math.exp(x), 2) * Math.pow(delta, 2) / Math.pow(d, 3);
-                }
-
-                function find_upper_falsep(phi , v , delta , tau) {
-                    var x1, x2, x3, y1, y2, y3;
-                    y1 = Dequation(phi, v, 0, tau, delta);
-                    if (y1 < 0 ){
-                        return 1;
-                    } else {
-                        x1 = 0;
-                        x2 = x1;
-                        y2 = y1;
-                        x1 = x1 - 1;
-                        y1 = Dequation(phi, v, x1, tau, delta);
-                        while (y1 > 0){
-                            x2 = x1;
-                            y2 = y1;
-                            x1 = x1 - 1;
-                            y1 = Dequation(phi, v, x1, tau, delta);
-                        }
-                        for (var i = 0; i < 21 ; i++){
-                            x3 = y1 * (x1 - x2) / (y2 - y1) + x1;
-                            y3 = Dequation(phi, v, x3, tau, delta);
-                            if (y3 > 0 ){
-                                x1 = x3;
-                                y1 = y3;
-                            } else {
-                                x2 = x3;
-                                y2 = y3;
-                            }
-                        }
-                        return Math.exp((y1 * (x1 - x2) / (y2 - y1) + x1) / 2);
-                    }
-                }
-            },
-            newprocedure: function(v, delta){
-                //Step 5.1
-                // A = (log (pow vol 2))
-                var A = Math.log(Math.pow(this.__vol, 2));
-                // define f(x) 'function'
-                var f = this._makef(delta, v, A);
-                // ε = 0.000001
-                var epsilon = 0.0000001;
-
-                //Step 5.2
-                // we've set A already
-                // init var B and k
-                var B, k;
-                // if ∆2 > φ2 + v
-                // (gth (pow delta 2) (add (pow phi 2) v))
-                if (Math.pow(delta, 2) >  Math.pow(this.__rd, 2) + v){
-                    // set B = ln(∆2 − φ2 − v)
-                    //         (log ;(sub (pow delta 2) (pow phi 2) v))
-                    B = Math.log(Math.pow(delta, 2) -  Math.pow(this.__rd, 2) - v);
-                } else {
-                    // If ∆2 ≤ φ2 + v, then perform the following iteration:
-                    //    (lte (pow delta 2) (add (pow phi 2) v))
-                    // let k = 1
-                    k = 1;
-                    // If f(a−kτ) < 0,then
-                    //    (lth (f (sub a (mul k tau))) 0)
-                    while (f(A - k * this._tau) < 0){
-                        // Set k ← k + 1
-                        k = k + 1;
-                    }
-                    // set B = a − kτ
-                    //         (sub a (mul k tau))
-                    B = A - k * this._tau;
-                }
-
-                //Step 5.3
-                // Let fA = f(A)
-                var fA = f(A);
-                // Let fB = f(B)
-                var fB = f(B);
-
-                //Step 5.4
-                // init var C and fC
-                var C, fC;
-                // absolute value: distance from 0 (always a positive number, @ud)
-                // While |B − A| > ε, carry out the following steps
-                while (Math.abs(B - A) > epsilon){
-                    // Let C = A + (A−B)fA/(fB −fA)
-                    //         (add A (mul (sub A B) (div fA (sub fB fA))))
-                    C = A + (A - B) * fA /(fB - fA );
-                    // Let fC =f(C)
-                    fC = f(C);
-                    // If fCfB ≤ 0
-                    //    (lte (mul fC fB) 0)
-                    if (fC * fB < 0){
-                        // set A ← B
-                        A = B;
-                        // set fA ← fB
-                        fA = fB;
-                    } else {
-                        // otherwise, just set fA ← fA/2
-                        fA = fA / 2;
-                    }
-                    // set B ← C
-                    B = C;
-                    // fB ← fC
-                    fB = fC;
-                }
-                //Step 5.5
-                // Once |B − A| ≤ ε, set σ′ ← eA/2
-                // e = euler's number ; ~2.718
-                // .exp(x) is euler's number raised to the power of x
-                // (pow e x)
-                return Math.exp(A/2);
-            },
-            newprocedure_mod: function(v, delta){
-                //Step 5.1
-                var A = Math.log(Math.pow(this.__vol, 2));
-                var f = this._makef(delta, v, A);
-                var epsilon = 0.0000001;
-
-                //Step 5.2
-                var B, k;
-                //XXX mod
-                if (delta >  Math.pow(this.__rd, 2) + v){
-                    //XXX mod
-                    B = Math.log(delta -  Math.pow(this.__rd, 2) - v);
-                } else {
-                    k = 1;
-                    while (f(A - k * this._tau) < 0){
-                        k = k + 1;
-                    }
-                    B = A - k * this._tau;
-                }
-
-                //Step 5.3
-                var fA = f(A);
-                var fB = f(B);
-
-                //Step 5.4
-                var C, fC;
-                while (Math.abs(B - A) > epsilon){
-                    C = A + (A - B) * fA /(fB - fA );
-                    fC = f(C);
-                    if (fC * fB < 0){
-                        A = B;
-                        fA = fB;
-                    } else {
-                        fA = fA / 2;
-                    }
-                    B = C;
-                    fB = fC;
-                }
-                //Step 5.5
-                return Math.exp(A/2);
-            },
-            oldprocedure_simple: function(v, delta){
-                var i = 0;
-                var a = Math.log(Math.pow(this.__vol, 2));
-                var tau = this._tau;
-                var x0 = a;
-                var x1 = 0;
-                var d,h1,h2;
-
-                while (Math.abs(x0 - x1) > 0.00000001){
-                    // New iteration, so x(i) becomes x(i-1)
-                    x0 = x1;
-                    d = Math.pow(this.__rating, 2) + v + Math.exp(x0);
-                    h1 = -(x0 - a) / Math.pow(tau, 2) - 0.5 * Math.exp(x0) / d + 0.5 * Math.exp(x0) * Math.pow(delta / d, 2);
-                    h2 = -1 / Math.pow(tau, 2) - 0.5 * Math.exp(x0) * (Math.pow(this.__rating, 2) + v) / Math.pow(d, 2) + 0.5 * Math.pow(delta, 2) * Math.exp(x0) * (Math.pow(this.__rating, 2) + v - Math.exp(x0)) / Math.pow(d, 3);
-                    x1 = x0 - (h1 / h2);
-                }
-
-                return Math.exp(x1 / 2);
-            }
-        };
-        //==== End of volatility algorithms
-
-        exports.Glicko2 = Glicko2;
-
-    })(typeof exports === 'undefined'? this['glicko2']={}: exports);
diff --git a/testing/glicko2js/package.json b/testing/glicko2js/package.json
deleted file mode 100644
index eb20a40..0000000
--- a/testing/glicko2js/package.json
+++ /dev/null
@@ -1,23 +0,0 @@
-{
-  "name": "glicko2",
-  "description": "glicko2 ranking system",
-  "version": "0.8.7",
-  "author": "Henri Bourcereau",
-  "keywords": [
-    "glicko",
-    "utilities",
-    "ranking"
-  ],
-  "repository": {
-    "type": "git",
-    "url": "git://github.com/mmai/glicko2js.git"
-  },
-  "main": "./glicko2.js",
-  "devDependencies": {
-    "mocha": "8.2.x",
-    "should": "13.2.x"
-  },
-  "scripts": {
-    "test": "mocha --require should --reporter list"
-  }
-}
diff --git a/testing/glicko2js/test/glicko2.js b/testing/glicko2js/test/glicko2.js
deleted file mode 100644
index 82f58e9..0000000
--- a/testing/glicko2js/test/glicko2.js
+++ /dev/null
@@ -1,230 +0,0 @@
-var glicko2 = require('../glicko2');
-
-describe('Glicko2', function(){
-    describe('makePlayer()', function(){
-        it('should make a default player when passed no settings', function(){
-            var glicko = new glicko2.Glicko2();
-            var player = glicko.makePlayer();
-            player.getRating().should.equal(1500);
-            player.getRd().should.equal(350);
-            player.getVol().should.equal(0.06);
-        });
-        it('should support setting individual settings', function(){
-            var glicko = new glicko2.Glicko2({
-              rating: 1600
-            });
-            var player = glicko.makePlayer();
-            player.getRating().should.equal(1600);
-            player.getRd().should.equal(350);
-            player.getVol().should.equal(0.06);
-        });
-        it('should not be affected by newer instances of Glicko2', function(){
-            var glicko = new glicko2.Glicko2({
-              rating: 1400
-            });
-            var player = glicko.makePlayer();
-
-            var newerGlicko = new glicko2.Glicko2({
-              rating: 1600
-            });
-
-            player.getRating().should.equal(1400);
-        });
-    });
-    describe('getPlayers()', function(){
-        it('should retrieve all players with ids', function(){
-        var settings = {
-          tau : 0.5,
-          rpd : 604800,
-          rating : 1500,
-          rd : 200,
-          vol : 0.06
-        };
-        var glicko = new glicko2.Glicko2(settings);
-        var player = glicko.makePlayer();
-        var pl1 = glicko.makePlayer(1400, 30, 0.06);
-        var pl3 = glicko.makePlayer(1550, 100, 0.06);
-        var players = glicko.getPlayers();
-        players.length.should.equal(3);
-        players[1].id.should.equal(1);
-        players[1].getRating().should.equal(1400);
-      });
-  });
-    describe('updateRatings()', function(){
-        it('should calculate new ratings', function(){
-                    // Following the example at:
-            // http://math.bu.edu/people/mg/glicko/glicko2.doc/example.html
-            // Pretend Ryan (of rating 1500 and rating deviation 350) plays players of ratings 1400, 1550 and 1700
-            // and rating deviations 30, 100 and 300 respectively with outcomes 1, 0 and 0.
-            var settings = {
-              tau : 0.5,
-              rpd : 604800,
-              rating : 1500,
-              rd : 200,
-              vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-            var Ryan = glicko.makePlayer();
-            var Bob = glicko.makePlayer(1400, 30, 0.06);
-            var John = glicko.makePlayer(1550, 100, 0.06);
-            var Mary = glicko.makePlayer(1700, 300, 0.06);
-
-            var matches = [];
-            matches.push([Ryan, Bob, 1]); //Ryan won over Bob
-            matches.push([Ryan, John, 0]); //Ryan lost against John
-            matches.push([Ryan, Mary, 0]); //Ryan lost against Mary
-
-            /*Perfs testing
-            var players = [Bob, John, Mary];
-
-            var ind = 0;
-            while (ind++ < 50){
-              players.push(glicko.makePlayer());
-            }
-
-            var nbpl = players.length;
-            var pl1, pl2;
-            for (var i=0; i<1000;i++){
-              pl1 = players[Math.floor(Math.random() * nbpl)];
-              pl2 = players[Math.floor(Math.random() * nbpl)];
-              matches.push([pl1, pl2, Math.floor(Math.random() * 3) / 2]);
-            }
-            //End perfs
-            */
-
-            glicko.updateRatings(matches);
-
-            (Math.abs(Ryan.getRating() - 1464) < 0.1).should.be.true;
-            (Math.abs(Ryan.getRd() - 151.52) < 0.01).should.be.true;
-            (Math.abs(Ryan.getVol() - 0.05999) < 0.00001).should.be.true;
-          });
-        it('should allow to be called multiple times', function(){
-          var settings = {
-              tau : 0.5,
-              rpd : 604800,
-              rating : 1500,
-              rd : 200,
-              vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-            var Ryan = glicko.makePlayer();
-            var Bob = glicko.makePlayer(1400, 30, 0.06);
-            var John = glicko.makePlayer(1550, 100, 0.06);
-            var Mary = glicko.makePlayer(1700, 300, 0.06);
-
-            var matches = [];
-            matches.push([Ryan, Bob, 1]); //Ryan won over Bob
-            matches.push([Ryan, John, 0]); //Ryan lost against John
-            matches.push([Ryan, Mary, 0]); //Ryan lost against Mary
-            glicko.updateRatings(matches);
-
-            
-            //We initiate a new ranking instance with the actual values of the first one
-            var glicko_new = new glicko2.Glicko2(settings);
-            var Ryan_new = glicko_new.makePlayer(Ryan.getRating(), Ryan.getRd(), Ryan.getVol());
-            var Bob_new = glicko_new.makePlayer(Bob.getRating(), Bob.getRd(), Bob.getVol());
-            var John_new = glicko_new.makePlayer(John.getRating(), John.getRd(), John.getVol());
-            var Mary_new = glicko_new.makePlayer(Mary.getRating(), Mary.getRd(), Mary.getVol());
-
-            //Second tournament for the first ranking instance
-            matches = [];
-            matches.push([Ryan, Bob, 0]);
-            matches.push([Ryan, John, 1]);
-            matches.push([Mary, Bob, 1]);
-            glicko.updateRatings(matches);
-            //console.log('nb players: ' + glicko.getPlayers().length);
-
-            //Fist tournament for the second ranking instance, with the same matches
-            var matches_new = [];
-            matches_new.push([Ryan_new, Bob_new, 0]);
-            matches_new.push([Ryan_new, John_new, 1]);
-            matches_new.push([Mary_new, Bob_new, 1]);
-            glicko_new.updateRatings(matches_new);
-
-            //The ratings in both systems should be the same 
-            (Math.abs(Ryan.getRating() - Ryan_new.getRating()) < 0.1).should.be.true;
-            (Math.abs(Ryan.getRd() - Ryan_new.getRd()) < 0.1).should.be.true;
-            (Math.abs(Ryan.getVol() - Ryan_new.getVol()) < 0.00001).should.be.true;
-          });
-        it('should be able to update ratings when a player did not play', function(){
-          var settings = {
-              tau : 0.5,
-              rpd : 604800,
-              rating : 1500,
-              rd : 200,
-              vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-            var Ryan = glicko.makePlayer();
-            var matches = [];
-            glicko.updateRatings(matches);
-          });
-        it('should accept Race objects', function(){
-            var settings = {
-                tau : 0.5,
-                rpd : 604800,
-                rating : 1500,
-                rd : 200,
-                vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-            var Ryan = glicko.makePlayer();
-            var Bob = glicko.makePlayer(1400, 30, 0.06);
-            var John = glicko.makePlayer(1550, 100, 0.06);
-            var Mary = glicko.makePlayer(1700, 300, 0.06);
-
-            var race = glicko.makeRace(
-                [
-                    [Ryan], //Ryan won the race
-                    [Bob, John], //Bob and John 2nd position ex-aequo
-                    [Mary] // Mary 4th position
-                ]
-            );
-
-            glicko.updateRatings(race);
-
-            (Math.abs(Ryan.getRating() - 1685.7) < 0.1).should.be.true;
-            (Math.abs(Ryan.getRd() - 151.52) < 0.01).should.be.true;
-            (Math.abs(Ryan.getVol() - 0.06000) < 0.00001).should.be.true;
-        });
-      });
-  });
-
-describe("Race", function(){
-    describe("getMatches", function(){
-        it("Should convert a race to a list of matches", function(){
-            var settings = {
-                tau : 0.5,
-                rpd : 604800,
-                rating : 1500,
-                rd : 200,
-                vol : 0.06
-            };
-            var glicko = new glicko2.Glicko2(settings);
-            var Ryan = glicko.makePlayer();
-            var Bob = glicko.makePlayer(1400, 30, 0.06);
-            var John = glicko.makePlayer(1550, 100, 0.06);
-            var Mary = glicko.makePlayer(1700, 300, 0.06);
-
-            var race = glicko.makeRace(
-                [
-                    [Ryan], //Ryan won the race
-                    [Bob, John], //Bob and John 2nd position ex-aequo
-                    [Mary] // Mary 4th position
-                ]
-            );
-
-            var matches = race.getMatches();
-            matches.should.eql([
-                [Ryan, Bob, 1],
-                [Ryan, John, 1],
-                [Ryan, Mary, 1],
-                [Bob, John, 0.5],
-                [Bob, Mary, 1],
-                [John, Mary, 1]
-            ]);
-        })
-    })
-
-})
-
diff --git a/testing/glicko2js/yarn.lock b/testing/glicko2js/yarn.lock
deleted file mode 100644
index b3a081c..0000000
--- a/testing/glicko2js/yarn.lock
+++ /dev/null
@@ -1,683 +0,0 @@
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-
-
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-  version "2.0.0"
-  resolved "https://registry.yarnpkg.com/yargs-unparser/-/yargs-unparser-2.0.0.tgz#f131f9226911ae5d9ad38c432fe809366c2325eb"
-  integrity sha512-7pRTIA9Qc1caZ0bZ6RYRGbHJthJWuakf+WmHK0rVeLkNrrGhfoabBNdue6kdINI6r4if7ocq9aD/n7xwKOdzOA==
-  dependencies:
-    camelcase "^6.0.0"
-    decamelize "^4.0.0"
-    flat "^5.0.2"
-    is-plain-obj "^2.1.0"
-
-yargs@13.3.2:
-  version "13.3.2"
-  resolved "https://registry.yarnpkg.com/yargs/-/yargs-13.3.2.tgz#ad7ffefec1aa59565ac915f82dccb38a9c31a2dd"
-  integrity sha512-AX3Zw5iPruN5ie6xGRIDgqkT+ZhnRlZMLMHAs8tg7nRruy2Nb+i5o9bwghAogtM08q1dpr2LVoS8KSTMYpWXUw==
-  dependencies:
-    cliui "^5.0.0"
-    find-up "^3.0.0"
-    get-caller-file "^2.0.1"
-    require-directory "^2.1.1"
-    require-main-filename "^2.0.0"
-    set-blocking "^2.0.0"
-    string-width "^3.0.0"
-    which-module "^2.0.0"
-    y18n "^4.0.0"
-    yargs-parser "^13.1.2"
-
-yocto-queue@^0.1.0:
-  version "0.1.0"
-  resolved "https://registry.yarnpkg.com/yocto-queue/-/yocto-queue-0.1.0.tgz#0294eb3dee05028d31ee1a5fa2c556a6aaf10a1b"
-  integrity sha512-rVksvsnNCdJ/ohGc6xgPwyN8eheCxsiLM8mxuE/t/mOVqJewPuO1miLpTHQiRgTKCLexL4MeAFVagts7HmNZ2Q==
diff --git a/testing/pyglicko2/glicko2.py b/testing/pyglicko2/glicko2.py
deleted file mode 100644
index fa9f5b5..0000000
--- a/testing/pyglicko2/glicko2.py
+++ /dev/null
@@ -1,244 +0,0 @@
-"""
-Copyright (c) 2009 Ryan Kirkman
-
-Permission is hereby granted, free of charge, to any person
-obtaining a copy of this software and associated documentation
-files (the "Software"), to deal in the Software without
-restriction, including without limitation the rights to use,
-copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the
-Software is furnished to do so, subject to the following
-conditions:
-
-The above copyright notice and this permission notice shall be
-included in all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
-OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
-NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
-HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
-WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
-OTHER DEALINGS IN THE SOFTWARE.
-"""
-
-import math
-
-class Player:
-    # Class attribute
-    # The system constant, which constrains
-    # the change in volatility over time.
-    #
-    # underscore = "weak internal use"; do not export
-    _tau = 0.5
-
-    def getRating(self):
-        # __double_leading_underscore
-        # inside class FooBar, __boo becomes _FooBar__boo
-        # "self.rating" becomes Ryan.rating in tests.py
-        #
-        # 'self' is a specific instance of parent class
-        # (add (add rating.player 173.7178) 1500)
-        # print(f"getRating: {(self.__rating * 173.7178) + 1500}")
-        return (self.__rating * 173.7178) + 1500
-
-    def setRating(self, rating):
-        # (div (sub rating 1500) 173.7178)
-        # print(f"setRating: {(rating - 1500) / 173.7178}")
-        self.__rating = (rating - 1500) / 173.7178
-
-    # property(fget, fset) turns class attributes into properties
-    # fget: function that returns the value of the managed attribute
-    # fset: function that allows you to set the value of the managed attribute
-    rating = property(getRating, setRating)
-
-    def getRd(self):
-        # (mul rd.player 173.7178)
-        # print(f"getRd: {self.__rd * 173.7178}")
-        return self.__rd * 173.7178
-
-    def setRd(self, rd):
-        # (div rd.player 173.7178)
-        # print(f"setRd: {rd / 173.7178}")
-        self.__rd = rd / 173.7178
-
-    rd = property(getRd, setRd)
-
-    # __double_leading_and_trailing_underscore__
-    # "magic" objects or attribs that live in user-controlled namespaces
-    # bascially, reserved for Python itself
-    def __init__(self, rating = 1500, rd = 350, vol = 0.06):
-        # For testing purposes, preload the values
-        # assigned to an unrated player.
-        self.setRating(rating)
-        self.setRd(rd)
-        self.vol = vol
-
-    def _preRatingRD(self):
-        """ Calculates and updates the player's rating deviation for the
-        beginning of a rating period.
-
-        preRatingRD() -> None
-
-        """
-        # (sqrt (add (pow rd.player 2) (pow vol.player 2)))
-        # print(f"preRatingRD: {math.sqrt(math.pow(self.__rd, 2) + math.pow(self.vol, 2))}")
-        self.__rd = math.sqrt(math.pow(self.__rd, 2) + math.pow(self.vol, 2))
-
-    def update_player(self, rating_list, RD_list, outcome_list):
-        """ Calculates the new rating and rating deviation of the player.
-
-        update_player(list[int], list[int], list[bool]) -> None
-
-        """
-        # Convert the rating and rating deviation values for internal use.
-        # (div (sub x 1500) 173.7178)
-        rating_list = [(x - 1500) / 173.7178 for x in rating_list]
-        # (div x 173.7178)
-        RD_list = [x / 173.7178 for x in RD_list]
-
-        v = self._v(rating_list, RD_list)
-        self.vol = self._newVol(rating_list, RD_list, outcome_list, v)
-        self._preRatingRD()
-        # (div 1 (sqrt (add (pow rd.player 2) (div 1 v))))
-        self.__rd = 1 / math.sqrt((1 / math.pow(self.__rd, 2)) + (1 / v))
-
-        tempSum = 0
-        for i in range(len(rating_list)):
-            # (add tempSum (mul g.player (sub outcome_list[i] self._E(rating_list[i], RD_list[i])))
-            tempSum += self._g(RD_list[i]) * (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
-        # (add playerating (mul (pow rd.player 2) tempSum))
-        self.__rating += math.pow(self.__rd, 2) * tempSum
-        # print(f"{math.pow(self.__rd, 2) * tempSum}")
-
-
-    def _newVol(self, rating_list, RD_list, outcome_list, v):
-        """ Calculating the new volatility as per the Glicko2 system.
-
-        _newVol(list, list, list) -> float
-
-        """
-        # Step 5 of the Glicko-2 algorithm
-        # Step 5.1
-        A = math.log(math.pow(self.vol, 2))
-        eps = 0.0000001
-        tau = self._tau
-        delta = self._delta(rating_list, RD_list, outcome_list, v)
-        f = self._makef(delta, v, A)
-
-        # Step 5.2
-        # init var B and k
-        B = None
-        k = None
-        # if ∆2 > φ2 + v
-        if math.pow(delta, 2) > math.pow(self.__rd, 2) + v:
-            # set B = ln(∆2 − φ2 − v)
-            B = math.log(math.pow(delta, 2) - math.pow(self.__rd, 2) - v)
-        else:
-            # if ∆2 ≤ φ2 + v
-            k = 1
-            # if f(a−kτ) < 0
-            while f(A - k * tau) < 0:
-                k += 1
-            # set B = a − kτ
-            B = A - k * tau
-
-        # Step 5.3
-        # let fA = f(A)
-        fA = f(A)
-        # let fB = f(B)
-        fB = f(B)
-
-        # Step 5.4
-        C = None
-        fC = None
-        # while |B − A| > ε
-        while abs(B - A) > eps:
-            # let C = A + (A−B)fA/(fB −fA)
-            C = A + (A - B) * fA / (fB - fA)
-            # let fC =f(C)
-            fC = f(C)
-            # if fCfB ≤ 0
-            if fC * fB < 0:
-                # set A ← B
-                A = B
-                # set fA ← fB
-                fA = fB
-            else:
-                # set fA ← fA/2
-                fA = fA / 2
-            # set B ← C
-            B = C
-            # set fB ← fC
-            fB = fC
-
-        # Step 5.5
-        # print(f"newVol: {math.exp(A / 2)}")
-        return math.exp(A / 2)
-
-    # there are other ways to do this, don't get caught up in how JS did it
-    def _makef(self, delta, v, A):
-        def f(x):
-            return math.exp(x) * (math.pow(delta, 2) - math.pow(self.__rd, 2) - v - math.exp(x)) \
-            / (2 * math.pow(math.pow(self.__rd, 2) + v + math.exp(x), 2)) - (x - A) / math.pow(self._tau, 2)
-            # print(f"f: {math.exp(x) * (math.pow(delta, 2) - math.pow(self.__rd, 2) - v - math.exp(x)) / (2 * math.pow(math.pow(self.__rd, 2) + v + math.exp(x), 2)) - (x - A) / math.pow(self._tau, 2)}")
-        return f
-
-    def _delta(self, rating_list, RD_list, outcome_list, v):
-        """ The delta function of the Glicko2 system.
-
-        _delta(list, list, list) -> float
-
-        """
-        tempSum = 0
-        for i in range(len(rating_list)):
-            # (mul RD_list[i] (sub outcome_list[i] self._E(rating_list[i], RD_list[i])))
-            tempSum += self._g(RD_list[i]) * (outcome_list[i] - self._E(rating_list[i], RD_list[i]))
-        # print(f"delta: {v * tempSum}")
-        return v * tempSum
-
-    def _v(self, rating_list, RD_list):
-        """ The v function of the Glicko2 system.
-
-        _v(list[int], list[int]) -> float
-
-        """
-        tempSum = 0
-        for i in range(len(rating_list)):
-            tempE = self._E(rating_list[i], RD_list[i])
-            # ;(mul (pow _g(RD_list[i]) 2) tempE (sub 1 tempE))
-            tempSum += math.pow(self._g(RD_list[i]), 2) * tempE * (1 - tempE)
-        # (div 1 tempSum)
-        # print(f"v: {1 / tempSum}")
-        return 1 / tempSum
-
-    def _E(self, p2rating, p2RD):
-        """ The Glicko E function.
-
-        _E(int) -> float
-
-        """
-        # (div 1 (add 1 (exp ;(mul -1 self._g(p2RD) (sub rating.player p2rating)))))
-        # print(f"E: {1 / (1 + math.exp(-1 * self._g(p2RD) * (self.__rating - p2rating)))}")
-        return 1 / (1 + math.exp(-1 * self._g(p2RD) * (self.__rating - p2rating)))
-
-    def _g(self, RD):
-        """ The Glicko2 g(RD) function.
-
-        _g() -> float
-
-        """
-        # (div 1 (sqrt (add 1 (mul 3 (div (pow RD 2) (pow pi 2))))))
-        # print(f"g: {1 / math.sqrt(1 + 3 * math.pow(RD, 2) / math.pow(math.pi, 2))}")
-        return 1 / math.sqrt(1 + 3 * math.pow(RD, 2) / math.pow(math.pi, 2))
-
-    def did_not_compete(self):
-        """ Applies Step 6 of the algorithm. Use this for
-        players who did not compete in the rating period.
-
-        did_not_compete() -> None
-
-        """
-        # print(f"did_not_compete: {self._preRatingRD()}")
-        self._preRatingRD()
diff --git a/testing/pyglicko2/glicko2_tests.py b/testing/pyglicko2/glicko2_tests.py
deleted file mode 100644
index 324de5b..0000000
--- a/testing/pyglicko2/glicko2_tests.py
+++ /dev/null
@@ -1,59 +0,0 @@
-"""
-Copyright (c) 2009 Ryan Kirkman
-
-Permission is hereby granted, free of charge, to any person
-obtaining a copy of this software and associated documentation
-files (the "Software"), to deal in the Software without
-restriction, including without limitation the rights to use,
-copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the
-Software is furnished to do so, subject to the following
-conditions:
-
-The above copyright notice and this permission notice shall be
-included in all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
-OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
-NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
-HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
-WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
-OTHER DEALINGS IN THE SOFTWARE.
-"""
-
-import glicko2
-import timeit
-
-def exampleCase():
-    # Create a player called Ryan
-    Ryan = glicko2.Player()
-    # Following the example at:
-    # http://math.bu.edu/people/mg/glicko/glicko2.doc/example.html
-    # Pretend Ryan (of rating 1500 and rating deviation 350)
-    # plays players of ratings 1400, 1550 and 1700
-    # and rating deviations 30, 100 and 300 respectively
-    # with outcomes 1, 0 and 0.
-    print("Old Rating: %.18f" % Ryan.rating)
-    print("Old Rating Deviation: %.18f" % Ryan.rd)
-    print("Old Volatility: %.18f" % Ryan.vol)
-    Ryan.update_player([x for x in [1400, 1550, 1700]],
-        [x for x in [30, 100, 300]], [1, 0, 0])
-    print("New Rating: %.18f" % Ryan.rating)
-    print("New Rating Deviation: %.18f" % Ryan.rd)
-    print("New Volatility: %.18f" % Ryan.vol)
-
-def timingExample(runs = 10000):
-    print("\nThe time taken to perform " + str(runs))
-    print("separate calculations (in seconds) was:")
-    timeTaken = timeit.Timer("Ryan = glicko2.Player(); \
-                             Ryan.update_player([x \
-    for x in [1400, 1550, 1700]], \
-    [x for x in [30, 100, 300]], [1, 0, 0])", \
-        "import glicko2").repeat(1, 10000)
-    print(round(timeTaken[0], 4))
-
-if __name__ == "__main__":
-    exampleCase()
-    timingExample()

From be7fd82726fc2c8b7dfe1ed1894c4464946fd024 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 21:01:31 +0100
Subject: [PATCH 10/20] Get Elo unit tests working

---
 src/lib/elo.hoon   | 21 +++++++--------
 src/lib/telos.hoon | 18 ++++++-------
 src/tests/elo.hoon | 64 ++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 83 insertions(+), 20 deletions(-)
 create mode 100644 src/tests/elo.hoon

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index af6879d..eb1063b 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -55,15 +55,16 @@
 ++  new-performance-rating
   |=  [sum=@ud matches=@ud wins=@ud losses=@ud]
   ^-  rating
-  %+  div
-    %+  add
-      sum
-    %+  mul
-      400
-    %+  sub
-      wins
-    losses
-  matches
+  %-  round
+  %+  div:rd
+    %+  add:rd
+      (sun:rd sum)
+    %+  mul:rd
+      .~400
+    %+  sub:rd
+      (sun:rd wins)
+    (sun:rd losses)
+  (sun:rd matches)
 ::
 ::  calculate new rating
 ::    Rn = new rating
@@ -73,7 +74,7 @@
 ::    K  = scaling factor
 ::    Rn = Ro + (K * (Ea - Ee))
 ++  new-rating
-  |=  [our=rating our-ex=@rd our-scale=@ud opp=rating out=?(%win %loss %draw)]
+  |=  [our=rating our-ex=@rd our-scale=@ud out=?(%win %loss %draw)]
   ^-  rating
   =/  our-actual
     ?:  =(out %win)
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 0ebf4e6..4881990 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -233,11 +233,10 @@
           (lent (skim our-matches |=(=match (has-loser-in-match match winner))))
       ==
     %:  new-rating:elo
-      our-rating
-      (expected-score:elo our-rating opp-rating)
-      (scaling-factor:elo (lent our-matches))
-      opp-rating
-      our-outcome
+        our-rating
+        (expected-score:elo our-rating opp-rating)
+        (scaling-factor:elo (lent our-matches))
+        our-outcome
     ==
   =/  new-loser-elo=rating
     =/  our-rating
@@ -261,11 +260,10 @@
           (lent (skim our-matches |=(=match (has-loser-in-match match loser))))
       ==
     %:  new-rating:elo
-      our-rating
-      (expected-score:elo our-rating opp-rating)
-      (scaling-factor:elo (lent our-matches))
-      opp-rating
-      our-outcome
+        our-rating
+        (expected-score:elo our-rating opp-rating)
+        (scaling-factor:elo (lent our-matches))
+        our-outcome
     ==
   %-  %~  put  by
     %-  %~  put  by
diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
new file mode 100644
index 0000000..77773da
--- /dev/null
+++ b/src/tests/elo.hoon
@@ -0,0 +1,64 @@
+/+  *test, *elo
+|%
+++  test-expected-score
+  ;:  weld
+    %+  expect-eq
+      !>  .~0.500
+    !>  (expected-score 1.200 1.200)
+    ::
+    %+  expect-eq
+      !>  .~0.752
+    !>  (expected-score 1.400 1.200)
+    ::
+    %+  expect-eq
+      !>  .~0.902
+    !>  (expected-score 1.600 1.200)
+    ::
+    %+  expect-eq
+      !>  .~0.965
+    !>  (expected-score 1.800 1.200)
+  ==
+::
+++  test-scaling-factor
+  ;:  weld
+    %+  expect-eq
+      !>  40
+    !>  (scaling-factor 20)
+    %+  expect-eq
+      !>  32
+    !>  (scaling-factor 40)
+    %+  expect-eq
+      !>  24
+    !>  (scaling-factor 75)
+  ==
+::
+++  test-new-performance-rating
+  ;:  weld
+    %+  expect-eq
+      !>  1.580
+    !>  (new-performance-rating 7.500 5 3 2)
+    ::
+    %+  expect-eq
+      !>  1.580
+    !>  (new-performance-rating 15.000 10 5 5)
+    ::
+    %+  expect-eq
+      !>  1.329
+    !>  (new-performance-rating 10.500 7 2 5)
+  ==
+::
+++  test-new-rating
+  ;:  weld
+    %+  expect-eq
+      !>  1.515
+    !>  (new-rating 1.500 .~0.50 30 %win)
+    ::
+    %+  expect-eq
+      !>  1.578
+    !>  (new-rating 1.600 .~0.75 30 %loss)
+    ::
+    ::  %+  expect-eq
+    ::    !>  1.456
+    ::  !>  (new-rating 1.450 .~0.30 30 %draw)
+  ==
+--

From 2a99bd2bf6b9018a2fa4da7ba04299590ec89c64 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 21:28:39 +0100
Subject: [PATCH 11/20] Remove saloon

---
 src/lib/elo.hoon   | 82 ++++------------------------------------------
 src/tests/elo.hoon | 13 ++++++++
 2 files changed, 19 insertions(+), 76 deletions(-)

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index eb1063b..1b297cb 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -1,5 +1,4 @@
 /-  *telos
-=<
 |%
 ++  round
   |=  num=@rd
@@ -16,10 +15,12 @@
   ^-  @rd
   %+  div:rd
     .~1
-  %+  add:rd
-    .~1
-  %+  pow-rd
-    .~2
+  %-  sun:rd
+  %+  add
+    1
+  %+  pow
+    2
+  %-  round
   %+  div:rd
     %+  sub:rd
       (sun:rd opp)
@@ -92,74 +93,3 @@
     our-actual
   our-ex
 --
-::
-|%
-::
-::  helper core
-::    adapted from /lib/saloon
-::    by ~lagrev-nocfep and ~mopfel-winrux
-::
-++  sgn
-  |=  x=@rd  ^-  ?
-  =(0 (rsh [0 31] x))
-::
-++  neg
-  |=(x=@rd (sub:rd .~0 x))
-::
-++  abs
-  |=  x=@rd  ^-  @rd
-  ?:  (sgn x)
-    x
-  (neg x)
-::
-++  exp
-  |=  x=@rd  ^-  @rd
-  =/  p   .~1
-  =/  po  .~-1
-  =/  i   .~1
-  |-  ^-  @rd
-  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
-    p
-  $(i (add:rd i .~1), p (add:rd p (div:rd (pow-n x i) (factorial i))), po p)
-::
-++  factorial
-  |=  x=@rd  ^-  @rd
-  =/  t=@rd  .~1
-  ?:  (isclose x .~0)
-    t
-  |-  ^-  @rd
-  ?:  (isclose x .~1)
-    t
-  $(x (sub:rd x .~1), t (mul:rd t x))
-::
-++  isclose
-  |=  [p=@rd r=@rd]
-  (lth:rd (abs (sub:rd p r)) .~1e-5)
-::
-++  log
-  |=  z=@rd  ^-  @rd
-  =/  p   .~0
-  =/  po  .~-1
-  =/  i   .~0
-  |-  ^-  @rd
-  ?:  (lth:rd (abs (sub:rd po p)) .~1e-5)
-    (mul:rd (div:rd (mul:rd .~2 (sub:rd z .~1)) (add:rd z .~1)) p)
-  =/  term1  (div:rd .~1 (add:rd .~1 (mul:rd .~2 i)))
-  =/  term2  (mul:rd (sub:rd z .~1) (sub:rd z .~1))
-  =/  term3  (mul:rd (add:rd z .~1) (add:rd z .~1))
-  =/  term  (mul:rd term1 (pow-n (div:rd term2 term3) i))
-  $(i (add:rd i .~1), p (add:rd p term), po p)
-::
-++  pow-rd
-  |=  [x=@rd n=@rd]  ^-  @rd
-  (exp (mul:rd n (log x)))
-::
-++  pow-n
-  |=  [x=@rd n=@rd]  ^-  @rd
-  ?:  =(n .~0)  .~1
-  =/  p  x
-  |-  ^-  @rd
-  ?:  (lth:rd n .~2)
-    p
-  $(n (sub:rd n .~1), p (mul:rd p x))
---
diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
index 77773da..4aab8c8 100644
--- a/src/tests/elo.hoon
+++ b/src/tests/elo.hoon
@@ -17,6 +17,19 @@
     %+  expect-eq
       !>  .~0.965
     !>  (expected-score 1.800 1.200)
+    ::
+    ::  XX hangs
+    ::  %+  expect-eq
+    ::    !>  .~0.248
+    ::  !>  (expected-score 1.200 1.400)
+    ::
+    %+  expect-eq
+      !>  .~0.098
+    !>  (expected-score 1.200 1.600)
+    ::
+    %+  expect-eq
+      !>  .~0.035
+    !>  (expected-score 1.200 1.800)
   ==
 ::
 ++  test-scaling-factor

From 81eb57c01d0ba316f41a757615ce803cc74ae222 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sat, 6 Apr 2024 21:29:19 +0100
Subject: [PATCH 12/20] Uncomment test that crashed with saloon

---
 src/tests/elo.hoon | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
index 4aab8c8..b0e0c05 100644
--- a/src/tests/elo.hoon
+++ b/src/tests/elo.hoon
@@ -18,10 +18,9 @@
       !>  .~0.965
     !>  (expected-score 1.800 1.200)
     ::
-    ::  XX hangs
-    ::  %+  expect-eq
-    ::    !>  .~0.248
-    ::  !>  (expected-score 1.200 1.400)
+    %+  expect-eq
+      !>  .~0.248
+    !>  (expected-score 1.200 1.400)
     ::
     %+  expect-eq
       !>  .~0.098

From c1921a072f3e62831ac3ab6b60372c513ee98218 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 00:13:31 +0100
Subject: [PATCH 13/20] Stub out +expected-score, don't allow negative ratings

---
 src/lib/elo.hoon   | 69 +++++++++++++++++++++-------------------------
 src/tests/elo.hoon |  6 ++--
 2 files changed, 35 insertions(+), 40 deletions(-)

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index 1b297cb..eb04473 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -2,8 +2,8 @@
 |%
 ++  round
   |=  num=@rd
-  ^-  @ud
-  (abs:si (need (toi:rd num)))
+  ^-  @sd
+  (need (toi:rd num))
 ::
 ::  define expected score for a player in this match
 ::    Ea = expected score for player A
@@ -13,19 +13,7 @@
 ++  expected-score
   |=  [our=rating opp=rating]
   ^-  @rd
-  %+  div:rd
-    .~1
-  %-  sun:rd
-  %+  add
-    1
-  %+  pow
-    2
-  %-  round
-  %+  div:rd
-    %+  sub:rd
-      (sun:rd opp)
-    (sun:rd our)
-  .~125
+  !!
 ::
 ::  calculate K
 ::    K = 16  over 100 games played
@@ -56,16 +44,20 @@
 ++  new-performance-rating
   |=  [sum=@ud matches=@ud wins=@ud losses=@ud]
   ^-  rating
-  %-  round
-  %+  div:rd
-    %+  add:rd
-      (sun:rd sum)
-    %+  mul:rd
-      .~400
-    %+  sub:rd
-      (sun:rd wins)
-    (sun:rd losses)
-  (sun:rd matches)
+  =/  signed-rating
+    %-  round
+    %+  div:rd
+      %+  add:rd
+        (sun:rd sum)
+      %+  mul:rd
+        .~400
+      %+  sub:rd
+        (sun:rd wins)
+      (sun:rd losses)
+    (sun:rd matches)
+  ?.  (syn:si signed-rating)
+    0
+  (abs:si signed-rating)
 ::
 ::  calculate new rating
 ::    Rn = new rating
@@ -79,17 +71,20 @@
   ^-  rating
   =/  our-actual
     ?:  =(out %win)
-      our-ex
+      .~1
     ?.  =(out %draw)
-      (sub:rd .~1 our-ex)
-    ::  XX what's our actual score if it's a draw?
-    !!
-  %-  round
-  %+  add:rd
-    (sun:rd our)
-  %+  mul:rd
-    (sun:rd our-scale)
-  %+  sub:rd
-    our-actual
-  our-ex
+      .~0
+    .~0.50
+  =/  signed-rating
+    %-  round
+    %+  add:rd
+      (sun:rd our)
+    %+  mul:rd
+      (sun:rd our-scale)
+    %+  sub:rd
+      our-actual
+    our-ex
+  ?.  (syn:si signed-rating)
+    0
+  (abs:si signed-rating)
 --
diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
index b0e0c05..368da0a 100644
--- a/src/tests/elo.hoon
+++ b/src/tests/elo.hoon
@@ -69,8 +69,8 @@
       !>  1.578
     !>  (new-rating 1.600 .~0.75 30 %loss)
     ::
-    ::  %+  expect-eq
-    ::    !>  1.456
-    ::  !>  (new-rating 1.450 .~0.30 30 %draw)
+    %+  expect-eq
+      !>  1.456
+    !>  (new-rating 1.450 .~0.30 30 %draw)
   ==
 --

From 94b562bc97acee1c25dfb5d0b5e54d61b63acd55 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 11:15:03 +0100
Subject: [PATCH 14/20] Integrate /lib/math

---
 src/lib/elo.hoon  |   79 +-
 src/lib/math.hoon | 2966 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 2997 insertions(+), 48 deletions(-)
 create mode 100644 src/lib/math.hoon

diff --git a/src/lib/elo.hoon b/src/lib/elo.hoon
index eb04473..40059be 100644
--- a/src/lib/elo.hoon
+++ b/src/lib/elo.hoon
@@ -1,26 +1,23 @@
 /-  *telos
+/+  math
 |%
-++  round
-  |=  num=@rd
-  ^-  @sd
-  (need (toi:rd num))
-::
-::  define expected score for a player in this match
-::    Ea = expected score for player A
-::    Ra = Elo rating of player A
-::    Rb = Elo rating of player B
-::    Ea = 1 / (1 + 2^((Rb - Ra) / 125))
 ++  expected-score
   |=  [our=rating opp=rating]
   ^-  @rd
-  !!
+  %+  div:rd:math
+    .~1
+  %+  add:rd:math
+    .~1
+  %-  exp:rd:math
+  %+  mul:rd:math
+    %-  log:rd:math
+      .~2
+  %+  div:rd:math
+    %+  sub:rd:math
+      (sun:rd opp)
+    (sun:rd our)
+  .~125
 ::
-::  calculate K
-::    K = 16  over 100 games played
-::    K = 24  between 60 and 100 games played
-::    K = 32  between 30 and 60 games played
-::    K = 40  between 10 and 30 games played
-::    K = 64  less than 10 games played
 ++  scaling-factor
   |=  matches=@ud
   ^-  @ud
@@ -34,38 +31,24 @@
     24
   16
 ::
-::  bootstrap a new rating in the first 10 games
-::    P = performance rating
-::    Σ = sum of opponents' ratings
-::    N = number of games played
-::    w = number of wins
-::    l = number of losses
-::    P = (Σ + (400 * (w - l))) / N
 ++  new-performance-rating
   |=  [sum=@ud matches=@ud wins=@ud losses=@ud]
   ^-  rating
-  =/  signed-rating
-    %-  round
-    %+  div:rd
-      %+  add:rd
+  %-  abs:si
+  %-  need
+  %-  toi:rd:math
+  %+  round-places:rd:math
+    %+  div:rd:math
+      %+  add:rd:math
         (sun:rd sum)
-      %+  mul:rd
+      %+  mul:rd:math
         .~400
-      %+  sub:rd
+      %+  sub:rd:math
         (sun:rd wins)
       (sun:rd losses)
     (sun:rd matches)
-  ?.  (syn:si signed-rating)
-    0
-  (abs:si signed-rating)
+  0
 ::
-::  calculate new rating
-::    Rn = new rating
-::    Ro = old rating
-::    Ee = expected score
-::    Ea = actual score
-::    K  = scaling factor
-::    Rn = Ro + (K * (Ea - Ee))
 ++  new-rating
   |=  [our=rating our-ex=@rd our-scale=@ud out=?(%win %loss %draw)]
   ^-  rating
@@ -75,16 +58,16 @@
     ?.  =(out %draw)
       .~0
     .~0.50
-  =/  signed-rating
-    %-  round
-    %+  add:rd
+  %-  abs:si
+  %-  need
+  %-  toi:rd:math
+  %+  round-places:rd:math
+    %+  add:rd:math
       (sun:rd our)
-    %+  mul:rd
+    %+  mul:rd:math
       (sun:rd our-scale)
-    %+  sub:rd
+    %+  sub:rd:math
       our-actual
     our-ex
-  ?.  (syn:si signed-rating)
-    0
-  (abs:si signed-rating)
+  0
 --
diff --git a/src/lib/math.hoon b/src/lib/math.hoon
new file mode 100644
index 0000000..ff13f9f
--- /dev/null
+++ b/src/lib/math.hoon
@@ -0,0 +1,2966 @@
+  ::
+::::  Mathematical library
+::
+::  Pure Hoon implementations are naive formally correct algorithms,
+::  awaiting efficient jetting with GNU Scientific Library.
+::
+|%
+++  rs
+  ^|
+  |_  $:  r=$?(%n %u %d %z)   :: round nearest, up, down, to zero
+          rtol=_.1e-5         :: relative tolerance for precision of operations
+      ==
+  ::  mathematics constants to single precision
+  ::    +tau:  @rs
+  ::
+  ::  Returns the value 2*pi (OEIS A019692).
+  ::    Examples
+  ::      > tau
+  ::      .6.2831855
+  ::  Source
+  ++  tau  .6.2831855
+  ::    +pi:  @rs
+  ::
+  ::  Returns the value pi (OEIS A000796).
+  ::    Examples
+  ::      > pi
+  ::      .3.1415927
+  ::  Source
+  ++  pi  .3.1415927
+  ::    +e:  @rs
+  ::
+  ::  Returns the value e (Euler's constant) (OEIS A001113).
+  ::    Examples
+  ::      > e
+  ::      .2.7182817
+  ::  Source
+  ++  e  .2.7182817
+  ::    +phi:  @rs
+  ::
+  ::  Returns the value phi (golden ratio) (OEIS A001622).
+  ::    Examples
+  ::      > phi
+  ::      .1.618034
+  ::  Source
+  ++  phi  .1.618034
+  ::    +sqt2:  @rs
+  ::
+  ::  Returns the value sqrt(2) (OEIS A002193).
+  ::    Examples
+  ::      > sqt2
+  ::      .1.4142135
+  ::  Source
+  ++  sqt2  .1.4142135
+  ::    +invsqt2:  @rs
+  ::
+  ::  Returns the value 1/sqrt(2) (OEIS A010503).
+  ::    Examples
+  ::      > invsqt2
+  ::      .70710677
+  ::  Source
+  ++  invsqt2  .70710677
+  ::    +log2:  @rs
+  ::
+  ::  Returns the value log(2) (OEIS A002162).
+  ::    Examples
+  ::      > log2
+  ::      .6931472
+  ::  Source
+  ++  log2  .0.6931472
+  ::    +invlog2:  @rs
+  ::
+  ::  Returns the value 1/log(2).
+  ::    Examples
+  ::      > invlog2
+  ::      1.442695
+  ::  Source
+  ++  invlog2  .1.442695
+  ::    +log10:  @rs
+  ::
+  ::  Returns the value log(10) (OEIS A002392).
+  ::    Examples
+  ::      > log10
+  ::      .2.3025851
+  ::  Source
+  ++  log10  .2.3025851
+  ::    +huge:  @rs
+  ::
+  ::  Returns the value of the largest representable number.
+  ::    Examples
+  ::      > huge
+  ::      .3.4028235e+38
+  ::  Source
+  ++  huge  `@rs`0x7f80.0000  ::  3.40282346638528859812e+38
+  ::    +tiny:  @rs
+  ::
+  ::  Returns the value of the smallest representable normal number.
+  ::    Examples
+  ::      > tiny
+  ::      .1.1754944e-38
+  ::  Source
+  ++  tiny  `@rs`0x1          ::  1.40129846432481707092e-45
+  ::
+  ::  Operations
+  ::
+  ::    +sea:  @rs -> fn
+  ::
+  ::  Returns the +$fn representation of a floating-point atom.
+  ::    Examples
+  ::      > (sea .1)
+  ::      [%f s=%.y e=-23 a=8.388.608]
+  ::      > (sea .1.1)
+  ::      [%f s=%.y e=-23 a=9.227.469]
+  ::  Source
+  ++  sea  sea:^rs
+  ::    +bit:  fn -> @rs
+  ::
+  ::  Returns the floating-point atom of a +$fn representation.
+  ::    Examples
+  ::      > (bit [%f s=%.y e=-23 a=8.388.608])
+  ::      .1
+  ::      > (bit [%f s=%.y e=-23 a=9.227.469])
+  ::      .1.1
+  ::  Source
+  ++  bit  bit:^rs
+  ::    +sun:  @ud -> @rs
+  ::
+  ::  Returns the floating-point atom of an unsigned integer atom.
+  ::    Examples
+  ::      > (sun 1)
+  ::      .1
+  ::      > (sun 1.000)
+  ::      .1e3
+  ::  Source
+  ++  sun  sun:^rs
+  ::    +san:  @sd -> @rs
+  ::
+  ::  Returns the floating-point atom of a signed integer atom.
+  ::    Examples
+  ::      > (san --1)
+  ::      .1
+  ::      > (san -1)
+  ::      .-1
+  ::  Source
+  ++  san  san:^rs
+  ::++  exp  exp:^rs  :: no pass-through because of exp function
+  ::    +toi:  @rs -> @sd
+  ::
+  ::  Returns the unitized signed integer atom of a rounded floating-point atom.
+  ::    Examples
+  ::      > (toi .1)
+  ::      [~ --1]
+  ::      > (toi .1.1)
+  ::      [~ --1]
+  ::  Source
+  ++  toi  toi:^rs
+  ::    +drg:  @rs -> dn
+  ::
+  ::  Returns the decimal form of a floating-point atom using the Dragon4
+  ::  algorithm.
+  ::    Examples
+  ::      > (drg .1)
+  ::      [%d s=%.y e=--0 a=1]
+  ::      > (drg .1.1)
+  ::      [%d s=%.y e=-1 a=11]
+  ::  Source
+  ++  drg  drg:^rs
+  ::    +grd:  dn -> @rs
+  ::
+  ::  Returns the floating-point atom of a decimal form.
+  ::    Examples
+  ::      > (grd [%d s=%.y e=--0 a=1])
+  ::      .1
+  ::      > (grd [%d s=%.y e=-1 a=11])
+  ::      .1.1
+  ::  Source
+  ++  grd  grd:^rs
+  ::
+  ::  Comparison
+  ::
+  ::    +lth:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than.
+  ::    Examples
+  ::      > (lth .1 .2)
+  ::      %.y
+  ::      > (lth .2 .1)
+  ::      %.n
+  ::      > (lth .1 .1)
+  ::      %.n
+  ::  Source
+  ++  lth  lth:^rs
+  ::    +lte:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::    Examples
+  ::      > (lte .1 .2)
+  ::      %.y
+  ::      > (lte .2 .1)
+  ::      %.n
+  ::      > (lte .1 .1)
+  ::      %.y
+  ::  Source
+  ++  lte  lte:^rs
+  ::    +leq:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::  Alias for +lte.
+  ::    Examples
+  ::      > (leq .1 .2)
+  ::      %.y
+  ::      > (leq .2 .1)
+  ::      %.n
+  ::      > (leq .1 .1)
+  ::      %.y
+  ::  Source
+  ++  leq  lte:^rs
+  ::    +equ:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, equal to.
+  ::    Examples
+  ::      > (equ .1 .2)
+  ::      %.n
+  ::      > (equ .2 .1)
+  ::      %.n
+  ::      > (equ .1 .1)
+  ::      %.y
+  ::  Source
+  ++  equ  equ:^rs
+  ::    +gth:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than.
+  ::    Examples
+  ::      > (gth .1 .2)
+  ::      %.n
+  ::      > (gth .2 .1)
+  ::      %.y
+  ::      > (gth .1 .1)
+  ::      %.n
+  ::  Source
+  ++  gth  gth:^rs
+  ::    +gte:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::    Examples
+  ::      > (gte .1 .2)
+  ::      %.n
+  ::      > (gte .2 .1)
+  ::      %.y
+  ::      > (gte .1 .1)
+  ::      %.y
+  ::  Source
+  ++  gte  gte:^rs
+  ::    +geq:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::  Alias for +gte.
+  ::    Examples
+  ::      > (geq .1 .2)
+  ::      %.n
+  ::      > (geq .2 .1)
+  ::      %.y
+  ::      > (geq .1 .1)
+  ::      %.y
+  ::  Source
+  ++  geq  gte:^rs
+  ::    +neq:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, not equal to.
+  ::    Examples
+  ::      > (neq .1 .2)
+  ::      %.y
+  ::      > (neq .2 .1)
+  ::      %.y
+  ::      > (neq .1 .1)
+  ::      %.n
+  ::  Source
+  ++  neq  |=([a=@rs b=@rs] ^-(? !(equ:^rs a b)))
+  ::    +isclose:  [@rs @rs] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, within a relative
+  ::  tolerance (provided by the +rs door).
+  ::    Examples
+  ::      > (isclose .1 .2)
+  ::      %.n
+  ::      > (isclose .1 .1000001)
+  ::      %.y
+  ::      > (~(isclose rs [%z .1e-8]) .1 .1000001)
+  ::      %.n
+  ::  Source
+  ++  isclose
+    |=  [p=@rs r=@rs]
+    (lth (abs (sub p r)) rtol)
+  ::    +allclose:  [@rs (list @rs)] -> ?
+  ::
+  ::  Returns the comparison of a floating-point atom to a list of floating-
+  ::  point atoms, within a relative tolerance (provided by the +rs door).
+  ::    Examples
+  ::      > (allclose .1 ~[.1 .2])
+  ::      %.n
+  ::      > (allclose .1 ~[.1 .1.000001])
+  ::      %.y
+  ::      > (~(allclose rs [%z .1e-8]) .1 ~[.1 .1000001])
+  ::      %.n
+  ::  Source
+  ++  allclose
+    |=  [p=@rs q=(list @rs)]
+    =/  i  0
+    =/  n  (lent q)
+    |-  ^-  ?
+    ?:  =(n i)
+      %.y
+    ?.  (isclose p (snag i q))
+      %.n
+    $(i +(i))
+  ::    +isint:  @rs -> ?
+  ::
+  ::  Returns whether a floating-point value is an integer (no fractional part).
+  ::    Examples
+  ::      > (isint .1)
+  ::      %.y
+  ::      > (isint .1.1)
+  ::      %.n
+  ::  Source
+  ++  isint
+    |=  x=@rs  ^-  ?
+    (equ x (san (need (toi x))))
+  ::
+  ::  Algebraic
+  ::
+  ::    +add:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the sum of two floating-point atoms.
+  ::    Examples
+  ::      > (add .1 .2)
+  ::      .3
+  ::  Source
+  ++  add  add:^rs
+  ::    +sub:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the difference of two floating-point atoms.
+  ::    Examples
+  ::      > (sub .1 .2)
+  ::      .-1
+  ::  Source
+  ++  sub  sub:^rs
+  ::    +mul:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the product of two floating-point atoms.
+  ::    Examples
+  ::      > (mul .1 .2)
+  ::      .2
+  ::      > (mul .2 .3)
+  ::      .6
+  ::  Source
+  ++  mul  mul:^rs
+  ::    +div:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the quotient of two floating-point atoms.
+  ::    Examples
+  ::      > (div .1 .2)
+  ::      .0.5
+  ::  Source
+  ++  div  div:^rs
+  ::  +mod:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the modulus of two floating-point atoms.
+  ::    Examples
+  ::      > (mod .1 .2)
+  ::      .1
+  ::      > (mod .100 .8)
+  ::      .4
+  ::  Source
+  ++  mod
+    |=  [a=@rs b=@rs]  ^-  @rs
+    ?:  (lth a .0)
+      (sub b (mod (neg a) b))
+    (sub a (mul b (san (need (toi (div a b))))))  ::  a - b * floor(a / b)
+  ::    +fma:  [@rs @rs @rs] -> @rs
+  ::
+  ::  Returns the fused multiply-add of three floating-point atoms.
+  ::    Examples
+  ::      > (fma .1 .2 .3)
+  ::      .5
+  ::      > (fma .2 .3 .4)
+  ::      .10
+  ::  Source
+  ++  fma  fma:^rs
+  ::    +sig:  @rs -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::    Examples
+  ::      > (sig .1)
+  ::      %.y
+  ::      > (sig .-1)
+  ::      %.n
+  ::  Source
+  ++  sig  |=(x=@rs =(0 (rsh [0 31] x)))
+  ::    +sgn:  @rs -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::  Alias for +sig.
+  ::    Examples
+  ::      > (sgn .1)
+  ::      %.y
+  ::      > (sgn .-1)
+  ::      %.n
+  ::  Source
+  ++  sgn  sig
+  ::    +neg:  @rs -> @rs
+  ::
+  ::  Returns the negation of a floating-point atom.
+  ::    Examples
+  ::      > (neg .1)
+  ::      .-1
+  ::      > (neg .-1)
+  ::      .1
+  ::  Source
+  ++  neg  |=(x=@rs (sub .0 x))
+  ::    +factorial:  @rs -> @rs
+  ::
+  ::  Returns the factorial of a floating-point atom.  Assumes integer input.
+  ::    Examples
+  ::      > (factorial .1)
+  ::      .1
+  ::      > (factorial .2)
+  ::      .2
+  ::      > (factorial .3)
+  ::      .6
+  ::  Source
+  ++  factorial
+    |=  x=@rs  ^-  @rs
+    ?>  (gte x .0)
+    =/  t=@rs  .1
+    ?:  (isclose x .0)
+      t
+    |-  ^-  @rs
+    ?:  (isclose x .1)
+      t
+    $(x (sub x .1), t (mul t x))
+  ::    +abs:  @rs -> @rs
+  ::
+  ::  Returns the absolute value of a floating-point atom.
+  ::    Examples
+  ::      > (abs .1)
+  ::      .1
+  ::      > (abs .-1)
+  ::      .1
+  ::  Source
+  ++  abs
+    |=  x=@rs  ^-  @rs
+    ?:((sgn x) x (neg x))
+  ::    +exp:  @rs -> @rs
+  ::
+  ::  Returns the exponential of a floating-point atom.
+  ::    Examples
+  ::      > (exp .1)
+  ::      .2.7182808
+  ::      > (exp .2)
+  ::      .7.389052
+  ::      > (~(exp rs [%z .1e-8]) .2)
+  ::      .7.389053
+  ::      > (exp .inf)
+  ::      .inf
+  ::  Source
+  ++  exp
+    |=  x=@rs  ^-  @rs
+    ::  filter out non-finite arguments
+    ?:  =(x 0x0)  .1
+    ::    check infinities
+    ?:  =(x 0x7f80.0000)  `@rs`0x7f80.0000  :: exp(+inf) -> inf
+    ?:  =(x 0xff80.0000)  .0.0              :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7fc0.0000 x) 0)  `@rs`0x7fc0.0000  :: exp(NaN) -> NaN
+    ::    check overflow to infinity
+    =/  o-threshold  `@rs`0x42b0.c0a8  ::  88.72283905206835, value above which exp(x) overflows
+    ?:  (gth x o-threshold)  (mul huge huge)
+    ::    check underflow to zero
+    =/  u-threshold  `@rs`0xc2b0.c0a8  ::  -88.72283905206835, value below which exp(x) underflows
+    ?:  (lth x u-threshold)  (mul tiny tiny)
+    ::  otherwise, use Taylor series
+    =/  p   .1
+    =/  po  .-1
+    =/  i   .1
+    |-  ^-  @rs
+    ?:  (lth (abs (sub po p)) rtol)
+      p
+    $(i (add i .1), p (add p (div (pow-n x i) (factorial i))), po p)
+  ::    +sin:  @rs -> @rs
+  ::
+  ::  Returns the sine of a floating-point atom.
+  ::    Examples
+  ::    > (sin .1)
+  ::    .0.84147096
+  ::    > (sin .2)
+  ::    .0.9092974
+  ::    > (sin pi)
+  ::    .3.1609193e-7
+  ::  Source
+  ++  sin
+    |=  x=@rs  ^-  @rs
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7f80.0000)  `@rs`0x7fc0.0000  :: sin(+inf) -> NaN
+    ?:  =(x 0xff80.0000)  `@rs`0x7fc0.0000  :: sin(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7fc0.0000 x) 0)  `@rs`0x7fc0.0000  :: sin(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   x
+    =/  po  .-2
+    =/  i   1
+    =/  term  x
+    |-  ^-  @rs
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (add i2 .1))))
+    $(i +(i), p (add p term), po p)
+  ::    +cos:  @rs -> @rs
+  ::
+  ::  Returns the cosine of a floating-point atom.
+  ::    Examples
+  ::      > (cos .1)
+  ::      .0.5403022
+  ::     > (cos .2)
+  ::      .-0.41614664
+  ::     > (cos pi)
+  ::      .-0.9999998
+  ::  Source
+  ++  cos
+    |=  x=@rs  ^-  @rs
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7f80.0000)  `@rs`0x7fc0.0000  :: sin(+inf) -> NaN
+    ?:  =(x 0xff80.0000)  `@rs`0x7fc0.0000  :: sin(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7fc0.0000 x) 0)  `@rs`0x7fc0.0000  :: sin(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   .1
+    =/  po  .-2
+    =/  i   1
+    =/  term  .1
+    |-  ^-  @rs
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (sub i2 .1))))
+    $(i +(i), p (add p term), po p)
+  ::    +tan:  @rs -> @rs
+  ::
+  ::  Returns the tangent of a floating-point atom.
+  ::    Examples
+  ::      > (tan .1)
+  ::      .1.5574079
+  ::      > (tan .2)
+  ::      .-2.1850407
+  ::      > (tan pi)
+  ::      .-7.0094916e-7
+  ::  Source
+  ++  tan
+    |=  x=@rs  ^-  @rs
+    (div (sin x) (cos x))
+  ::    +pow-n:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the power of a floating-point atom to an integer exponent.
+  ::    Examples
+  ::      > (pow-n .1 .2)
+  ::      .1
+  ::      > (pow-n .2 .2)
+  ::      .4
+  ::      > (pow-n .2 .3)
+  ::      .8
+  ::  Source
+  ++  pow-n
+    |=  [x=@rs n=@rs]  ^-  @rs
+    ?:  =(n .0)  .1
+    ?>  &((gth n .0) (isint n))
+    =/  p  x
+    |-  ^-  @rs
+    ?:  (lth n .2)
+      p
+    $(n (sub n .1), p (mul p x))
+  ::    +log:  @rs -> @rs
+  ::
+  ::  Returns the natural logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log .1)
+  ::      .0
+  ::      > (log .2)
+  ::      .0.69314677
+  ::      > (~(log rs [%z .1e-8]) .2)
+  ::      .0.6931469
+  ::      > (log .inf)
+  ::      .inf
+  ::      > (log:rs:math e:rs:math)
+  ::      .0.999998
+  ::      > (~(log rs:math [%z .1e-8]) e:rs:math)
+  ::      .0.9999994
+  ::  Source
+  ++  log
+    |=  z=@rs  ^-  @rs
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(z 0x7f80.0000)  `@rs`0x7f80.0000  :: log(+inf) -> inf
+    ?:  =(z 0xff80.0000)  `@rs`0x7fc0.0000  :: log(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7fc0.0000 z) 0)  `@rs`0x7fc0.0000  :: exp(NaN) -> NaN
+    ::  otherwise, use Taylor series
+    =/  p   .0
+    =/  po  .-1
+    =/  i   .0
+    |-  ^-  @rs
+    ?:  (lth (abs (sub po p)) rtol)
+      (mul (div (mul .2 (sub z .1)) (add z .1)) p)
+    =/  term1  (div .1 (add .1 (mul .2 i)))
+    =/  term2  (mul (sub z .1) (sub z .1))
+    =/  term3  (mul (add z .1) (add z .1))
+    =/  term  (mul term1 (pow-n (div term2 term3) i))
+    $(i (add i .1), p (add p term), po p)
+  ::    +log-10:  @rs -> @rs
+  ::
+  ::  Returns the base-10 logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log-10 .0.1)
+  ::      .-0.999989
+  ::      > (log-10 .2)
+  ::      .0.30102932
+  ::      > (~(log-10 rs [%z .1e-8]) .2)
+  ::      .0.3010301
+  ::      > (log-10 .inf)
+  ::      .inf
+  ::  Source
+  ++  log-10
+    |=  z=@rs  ^-  @rs
+    (div (log z) log10)
+  ::    +log-2:  @rs -> @rs
+  ::
+  ::  Returns the base-2 logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log-2 .0.1)
+  ::      .-3.321928
+  ::      > (log-2 .2)
+  ::      .1.5849625
+  ::      > (~(log-2 rs [%z .1e-8]) .2)
+  ::      .1.5849633
+  ::  Source
+  ++  log-2
+    |=  z=@rs  ^-  @rs
+    (div (log z) log2)
+  ::    +pow:  [@rs @rs] -> @rs
+  ::
+  ::  Returns the power of a floating-point atom to a floating-point exponent.
+  ::    Examples
+  ::      > (pow .1 .2)
+  ::      .1
+  ::      > (pow .2 .2)
+  ::      .4
+  ::      > (pow .2 .3.5)
+  ::      .11.313682
+  ::      > (~(pow rs:math [%z .1e-8]) .2 .3.5)
+  ::      .11.313687
+  ::  Source
+  ++  pow
+    |=  [x=@rs n=@rs]  ^-  @rs
+    ::  fall through on integers (faster)
+    ?:  =(n (san (need (toi n))))  (pow-n x (san (need (toi n))))
+    (exp (mul n (log x)))
+  ::    +sqrt:  @rs -> @rs
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::  Alias for +sqt.
+  ::    Examples
+  ::      > (sqrt .1)
+  ::      .1
+  ::      > (sqrt .2)
+  ::      .1.4142128
+  ::      > (~(sqrt rs [%z .1e-8]) .2)
+  ::      .1.414213
+  ::  Source
+  ++  sqrt  sqt
+  ::    +sqt:  @rs -> @rs
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::    Examples
+  ::      > (sqt .1)
+  ::      .1
+  ::      > (sqt .2)
+  ::      .1.4142128
+  ::      > (~(sqt rs [%z .1e-8]) .2)
+  ::      .1.414213
+  ::  Source
+  ++  sqt
+    |=  x=@rs  ^-  @rs
+    ?>  (sgn x)
+    (pow x .0.5)
+  ::    +cbrt:  @rs -> @rs
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::  Alias for +cbt.
+  ::    Examples
+  ::      > (cbrt .1)
+  ::      .1
+  ::      > (cbrt .2)
+  ::      .1.2599205
+  ::      > (~(cbrt rs [%z .1e-8]) .2)
+  ::      .1.2599207
+  ::  Source
+  ++  cbrt  cbt
+  ::    +cbt:  @rs -> @rs
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::    Examples
+  ::      > (cbt .1)
+  ::      .1
+  ::      > (cbt .2)
+  ::      .1.2599205
+  ::      > (~(cbt rs [%z .1e-8]) .2)
+  ::      .1.2599207
+  ::  Source
+  ++  cbt
+    |=  x=@rs  ^-  @rs
+    ?>  (sgn x)
+    (pow x .0.33333333)
+  ::    +arg:  @rs -> @rs
+  ::
+  ::  Returns the argument of a floating-point atom (real argument = absolute
+  ::  value).
+  ::    Examples
+  ::      > (arg .1)
+  ::      .1
+  ::      > (arg .-1)
+  ::      .1
+  ::  Source
+  ++  arg  abs
+  ::    +round:  [@rs @ud] -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to a given number of decimal
+  ::  places.
+  ::    Examples
+  ::      > (round .1 0)
+  ::      .1
+  ::      > (round .1.11 1)
+  ::      .1.1
+  ::      > (round .1.11 2)
+  ::      .1.11
+  ::      > (round .1.11 3)
+  ::      .1.11
+  ::  Source
+  ++  round
+    |=  [x=@rs n=@ud]  ^-  @rs
+    ?:  =(.0 x)  .0
+    ::  Calculate the order of magnitude.
+    =/  oom  (san (need (toi (log-10 (abs x)))))
+    ::  Calculate the scaling factor.
+    =/  scaling  (pow .10 :(sub (sun n) oom .1))
+    ::  Round the mantissa to desired significant digits.
+    =/  rnd-mantissa  (round-bankers (mul x scaling))
+    ::  Convert back to the original scale.
+    (div rnd-mantissa scaling)
+  ::    +round-places:  [@rs @ud] -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to a given number of decimal
+  ::  places.  This is exceptionally sensitive to off-by-one FP rounding error.
+  ::    Examples
+  ::      > (round-places .1 0)
+  ::      .1
+  ::      > (round-places .1.11 1)
+  ::      .1.1
+  ::      > (round-places .1.285 2)
+  ::      .1.28
+  ::      > (round-places .4.12345 3)
+  ::      .4.1229997
+  ::  Source
+  ++  round-places
+    |=  [x=@rs n=@ud]  ^-  @rs
+    ::  Calculate the scaling factor.
+    =/  scaling  (pow .10 (sun n))
+    ::  Scale the number.
+    =/  scaled  (mul x scaling)
+    ::  Round the mantissa to desired significant digits.
+    =/  rnd-mantissa  (round-bankers scaled)
+    ::  Convert back to the original scale.
+    (div rnd-mantissa scaling)
+  ::    +round-bankers:  @rs -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to the nearest integer, with
+  ::  ties rounded to the nearest even integer.
+  ::    Examples
+  ::      > (round-bankers .1)
+  ::      .1
+  ::      > (round-bankers .1.5)
+  ::      .2
+  ::      > (round-bankers .1.49)
+  ::      .1
+  ::  Source
+  ++  round-bankers
+    |=  x=@rs  ^-  @rs
+    =/  int  (san (need (toi x)))
+    =/  dcm  (sub x int)
+    ?:  (lth dcm .0.5)
+      int
+    (add int .1)
+  --
+::  double precision
+++  rd
+  ^|
+  |_  $:  r=$?(%n %u %d %z)   :: round nearest, up, down, to zero
+          rtol=_.~1e-10       :: relative tolerance for precision of operations
+      ==
+  ::  mathematics constants to single precision
+  ::    +tau:  @rd
+  ::
+  ::  Returns the value 2*pi (OEIS A019692).
+  ::    Examples
+  ::      > tau
+  ::      .~6.283185307179586
+  ::  Source
+  ++  tau  .~6.283185307179586
+  ::    +pi:  @rd
+  ::
+  ::  Returns the value pi (OEIS A000796).
+  ::    Examples
+  ::      > pi
+  ::      .~3.141592653589793
+  ::  Source
+  ++  pi  .~3.141592653589793
+  ::    +e:  @rd
+  ::
+  ::  Returns the value e (Euler's constant) (OEIS A001113).
+  ::    Examples
+  ::      > e
+  ::      .~2.718281828459045
+  ::  Source
+  ++  e  .~2.718281828459045
+  ::    +phi:  @rd
+  ::
+  ::  Returns the value phi (golden ratio) (OEIS A001622).
+  ::    Examples
+  ::      > phi
+  ::      .~1.618033988749895
+  ::  Source
+  ++  phi  .~1.618033988749895
+  ::    +sqt2:  @rd
+  ::
+  ::  Returns the value sqrt(2) (OEIS A002193).
+  ::    Examples
+  ::      > sqt2
+  ::      .~1.414213562373095
+  ::  Source
+  ++  sqt2  .~1.4142135623730951
+  ::    +invsqt2:  @rd
+  ::
+  ::  Returns the value 1/sqrt(2) (OEIS A010503).
+  ::    Examples
+  ::      > invsqt2
+  ::      .~0.7071067811865476
+  ::  Source
+  ++  invsqt2  .~0.7071067811865476
+  ::    +log2:  @rd
+  ::
+  ::  Returns the value log(2) (OEIS A002162).
+  ::    Examples
+  ::      > log2
+  ::      .~0.6931471805599453
+  ::  Source
+  ++  log2  .~0.6931471805599453
+  ::    +invlog2:  @rd
+  ::
+  ::  Returns the value 1/log(2).
+  ::    Examples
+  ::      > invlog2
+  ::      .~1.4426950408889634
+  ::  Source
+  ++  invlog2  .~1.4426950408889634
+  ::    +log10:  @rd
+  ::
+  ::  Returns the value log(10) (OEIS A002392).
+  ::    Examples
+  ::      > log10
+  ::      .~2.302585092994046
+  ::  Source
+  ++  log10  .~2.302585092994046
+  ::
+  ::    +huge:  @rd
+  ::
+  ::  Returns the value of the largest representable number.
+  ::    Examples
+  ::      > huge
+  ::      .~1.7976931348623157e+308
+  ::  Source
+  ++  huge  `@rd`0x7fef.ffff.ffff.ffff  ::  1.79769313486231570815e+308
+  ::    +tiny:  @rd
+  ::
+  ::  Returns the value of the smallest representable normal number.
+  ::    Examples
+  ::      > tiny
+  ::      .~2.2250738585072014e-308
+  ::  Source
+  ++  tiny  `@rd`0x10.0000.0000.0000    ::  2.22507385850720138309e-308
+  ::
+  ::  Operations
+  ::
+  ::    +sea:  @rd -> fn
+  ::
+  ::  Returns the +$fn representation of a floating-point atom.
+  ::    Examples
+  ::      > (sea .~1)
+  ::      [%f s=%.y e=-52 a=4.503.599.627.370.496]
+  ::      > (sea .~1.1)
+  ::      [%f s=%.y e=-52 a=4.953.959.590.107.546]
+  ::  Source
+  ++  sea  sea:^rd
+  ::    +bit:  fn -> @rd
+  ::
+  ::  Returns the floating-point atom of a +$fn representation.
+  ::    Examples
+  ::      > (bit [%f s=%.y e=-52 a=4.503.599.627.370.496])
+  ::      .~1
+  ::      > (bit [%f s=%.y e=-52 a=4.953.959.590.107.546])
+  ::      .~1.1
+  ::  Source
+  ++  bit  bit:^rd
+  ::    +sun:  @ud -> @rd
+  ::
+  ::  Returns the floating-point atom of an unsigned integer atom.
+  ::    Examples
+  ::      > (sun 1)
+  ::      .~1
+  ::      > (sun 1.000)
+  ::      .~1e3
+  ::  Source
+  ++  sun  sun:^rd
+  ::    +san:  @sd -> @rd
+  ::
+  ::  Returns the floating-point atom of a signed integer atom.
+  ::    Examples
+  ::      > (san --1)
+  ::      .~1
+  ::      > (san -1)
+  ::      .~-1
+  ::  Source
+  ++  san  san:^rd
+  ::++  exp  exp:^rd  :: no pass-through because of exp function
+  ::    +toi:  @rd -> @sd
+  ::
+  ::  Returns the unitized signed integer atom of a rounded floating-point atom.
+  ::    Examples
+  ::      > (toi .~1)
+  ::      [~ --1]
+  ::      > (toi .~1.1)
+  ::      [~ --1]
+  ::  Source
+  ++  toi  toi:^rd
+  ::    +drg:  @rd -> dn
+  ::
+  ::  Returns the decimal form of a floating-point atom using the Dragon4
+  ::  algorithm.
+  ::    Examples
+  ::      > (drg .~1)
+  ::      [%d s=%.y e=--0 a=1]
+  ::      > (drg .~1.1)
+  ::      [%d s=%.y e=-1 a=11]
+  ::  Source
+  ++  drg  drg:^rd
+  ::    +grd:  dn -> @rd
+  ::
+  ::  Returns the floating-point atom of a decimal form.
+  ::    Examples
+  ::      > (grd [%d s=%.y e=--0 a=1])
+  ::      .~1
+  ::      > (grd [%d s=%.y e=-1 a=11])
+  ::      .~1.1
+  ::  Source
+  ++  grd  grd:^rd
+  ::
+  ::  Comparison
+  ::
+  ::    +lth:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than.
+  ::    Examples
+  ::      > (lth .~1 .~2)
+  ::      %.y
+  ::      > (lth .~2 .~1)
+  ::      %.n
+  ::      > (lth .~1 .~1)
+  ::      %.n
+  ::  Source
+  ++  lth  lth:^rd
+  ::    +lte:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::    Examples
+  ::      > (lte .~1 .~2)
+  ::      %.y
+  ::      > (lte .~2 .~1)
+  ::      %.n
+  ::      > (lte .~1 .~1)
+  ::      %.y
+  ::  Source
+  ++  lte  lte:^rd
+  ::    +leq:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::  Alias for +lte.
+  ::    Examples
+  ::      > (leq .~1 .~2)
+  ::      %.y
+  ::      > (leq .~2 .~1)
+  ::      %.n
+  ::      > (leq .~1 .~1)
+  ::      %.y
+  ::  Source
+  ++  leq  lte:^rd
+  ::    +equ:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, equal to.
+  ::    Examples
+  ::      > (equ .~1 .~2)
+  ::      %.n
+  ::      > (equ .~2 .~1)
+  ::      %.n
+  ::      > (equ .~1 .~1)
+  ::      %.y
+  ::  Source
+  ++  equ  equ:^rd
+  ::    +gth:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than.
+  ::    Examples
+  ::      > (gth .~1 .~2)
+  ::      %.n
+  ::      > (gth .~2 .~1)
+  ::      %.y
+  ::      > (gth .~1 .~1)
+  ::      %.n
+  ::  Source
+  ++  gth  gth:^rd
+  ::    +gte:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::    Examples
+  ::      > (gte .~1 .~2)
+  ::      %.n
+  ::      > (gte .~2 .~1)
+  ::      %.y
+  ::      > (gte .~1 .~1)
+  ::      %.y
+  ::  Source
+  ++  gte  gte:^rd
+  ::    +geq:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::  Alias for +gte.
+  ::    Examples
+  ::      > (geq .~1 .~2)
+  ::      %.n
+  ::      > (geq .~2 .~1)
+  ::      %.y
+  ::      > (geq .~1 .~1)
+  ::      %.y
+  ::  Source
+  ++  geq  gte:^rd
+  ::    +neq:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, not equal to.
+  ::    Examples
+  ::      > (neq .~1 .~2)
+  ::      %.y
+  ::      > (neq .~2 .~1)
+  ::      %.y
+  ::      > (neq .~1 .~1)
+  ::      %.n
+  ::  Source
+  ++  neq  |=([a=@rd b=@rd] ^-(? !(equ:^rd a b)))
+  ::    +isclose:  [@rd @rd] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, within a relative
+  ::  tolerance (provided by the +rd door).
+  ::    Examples
+  ::      > (isclose .~1 .~2)
+  ::      %.n
+  ::      > (isclose .~1 .~1.0000001)
+  ::      %.n
+  ::      > (~(isclose rd [%z .~1e-3]) .~1 .~1.0000001)
+  ::      %.y
+  ::  Source
+  ++  isclose
+    |=  [p=@rd r=@rd]
+    (lth (abs (sub p r)) rtol)
+  ::    +allclose:  [@rd (list @rd)] -> ?
+  ::
+  ::  Returns the comparison of a floating-point atom to a list of floating-
+  ::  point atoms, within a relative tolerance (provided by the +rd door).
+  ::    Examples
+  ::      > (allclose .~1 ~[.~1 .~2])
+  ::      %.n
+  ::      > (allclose .~1 ~[.~1 .~1.0000001])
+  ::      %.n
+  ::      > (~(allclose rd [%z .~1e-3]) .~1 ~[.~1 .~1.0000001])
+  ::      %.y
+  ::  Source
+  ++  allclose
+    |=  [p=@rd q=(list @rd)]
+    =/  i  0
+    =/  n  (lent q)
+    |-  ^-  ?
+    ?:  =(n i)
+      %.y
+    ?.  (isclose p (snag i q))
+      %.n
+    $(i +(i))
+  ::    +isint:  @rd -> ?
+  ::
+  ::  Returns whether a floating-point value is an integer (no fractional part).
+  ::    Examples
+  ::      > (isint .~1)
+  ::      %.y
+  ::      > (isint .~1.1)
+  ::      %.n
+  ::  Source
+  ++  isint
+    |=  x=@rd  ^-  ?
+    (equ x (san (need (toi x))))
+  ::
+  ::  Algebraic
+  ::
+  ::    +add:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the sum of two floating-point atoms.
+  ::    Examples
+  ::      > (add .~1 .~2)
+  ::      .~3
+  ::  Source
+  ++  add  add:^rd
+  ::    +sub:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the difference of two floating-point atoms.
+  ::    Examples
+  ::      > (sub .~1 .~2)
+  ::      .~-1
+  ::  Source
+  ++  sub  sub:^rd
+  ::    +mul:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the product of two floating-point atoms.
+  ::    Examples
+  ::      > (mul .~1 .~2)
+  ::      .~2
+  ::      > (mul .~2 .~3)
+  ::      .~6
+  ::  Source
+  ++  mul  mul:^rd
+  ::    +div:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the quotient of two floating-point atoms.
+  ::    Examples
+  ::      > (div .~1 .~2)
+  ::      .~0.5
+  ::  Source
+  ++  div  div:^rd
+  ::    +fma:  [@rd @rd @rd] -> @rd
+  ::
+  ::  Returns the fused multiply-add of three floating-point atoms.
+  ::    Examples
+  ::      > (fma .~1 .~2 .~3)
+  ::      .~5
+  ::      > (fma .~2 .~3 .~4)
+  ::      .~10
+  ::  Source
+  ++  fma  fma:^rd
+  ::    +sig:  @rd -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::    Examples
+  ::      > (sig .~1)
+  ::      %.y
+  ::      > (sig .~-1)
+  ::      %.n
+  ::  Source
+  ++  sig  |=(x=@rd =(0 (rsh [0 63] x)))
+  ::    +sgn:  @rd -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::  Alias for +sig.
+  ::    Examples
+  ::      > (sgn .~1)
+  ::      %.y
+  ::      > (sgn .~-1)
+  ::      %.n
+  ::  Source
+  ++  sgn  sig
+  ::    +neg:  @rd -> @rd
+  ::
+  ::  Returns the negation of a floating-point atom.
+  ::    Examples
+  ::      > (neg .~1)
+  ::      .~-1
+  ::      > (neg .~-1)
+  ::      .~1
+  ::  Source
+  ++  neg  |=(x=@rd (sub .~0 x))
+  ::    +factorial:  @rd -> @rd
+  ::
+  ::  Returns the factorial of a floating-point atom.  Assumes integer input.
+  ::    Examples
+  ::      > (factorial .~1)
+  ::      .~1
+  ::      > (factorial .~2)
+  ::      .~2
+  ::      > (factorial .~3)
+  ::      .~6
+  ::  Source
+  ++  factorial
+    |=  x=@rd  ^-  @rd
+    ?>  (gte x .~0)
+    =/  t=@rd  .~1
+    ?:  (isclose x .~0)
+      t
+    |-  ^-  @rd
+    ?:  (isclose x .~1)
+      t
+    $(x (sub x .~1), t (mul t x))
+  ::    +abs:  @rd -> @rd
+  ::
+  ::  Returns the absolute value of a floating-point atom.
+  ::    Examples
+  ::      > (abs .~1)
+  ::      .~1
+  ::      > (abs .~-1)
+  ::      .~1
+  ::  Source
+  ++  abs
+    |=  x=@rd  ^-  @rd
+    ?:((sgn x) x (neg x))
+  ::    +exp:  @rd -> @rd
+  ::
+  ::  Returns the exponential of a floating-point atom.
+  ::    Examples
+  ::      > (exp .~1)
+  ::      .~2.7182818284582266
+  ::      > (exp .~2)
+  ::      .~7.389056098925858
+  ::      > (~(exp rd [%z .~1e-15]) .~2)
+  ::      .~7.389056098930642
+  ::      > (exp .~inf)
+  ::      .inf
+  ::  Source
+  ++  exp
+    |=  x=@rd  ^-  @rd
+    ::  filter out non-finite arguments
+    ?:  =(x 0x0)  .~1
+    ::    check infinities
+    ?:  =(x 0x7ff0.0000.0000.0000)  `@rd`0x7ff0.0000.0000.0000  :: exp(+inf) -> inf
+    ?:  =(x 0xfff0.0000.0000.0000)  .~0.0                       :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7ff8.0000.0000.0000 x) 0)  `@rd`0x7ff8.0000.0000.0000  :: exp(NaN) -> NaN
+    ::    check overflow to infinity
+    =/  o-threshold  `@rd`0x4086.2e42.fefa.39ef  ::  709.782712893384, value above which exp(x) overflows
+    ?:  (gth x o-threshold)  (mul huge huge)
+    ::    check underflow to zero
+    =/  u-threshold  `@rd`0xc086.2e42.fefa.39ef  ::  -709.782712893384, value below which exp(x) underflows
+    ?:  (lth x u-threshold)  (mul tiny tiny)
+    ::  otherwise, use Taylor series
+    =/  p   .~1
+    =/  po  .~-1
+    =/  i   .~1
+    |-  ^-  @rd
+    ?:  (lth (abs (sub po p)) rtol)
+      p
+    $(i (add i .~1), p (add p (div (pow-n x i) (factorial i))), po p)
+  ::    +sin:  @rd -> @rd
+  ::
+  ::  Returns the sine of a floating-point atom.
+  ::    Examples
+  ::    > (sin .~1)
+  ::    .~0.8414709848078934
+  ::    > (sin .~2)
+  ::    .~0.9092974268256406
+  ::    > (sin pi)
+  ::    .~-1.698287706085482e-13
+  ::  Source
+  ++  sin
+    |=  x=@rd  ^-  @rd
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7ff0.0000.0000.0000)  `@rd`0x7ff8.0000.0000.0000  :: sin(+inf) -> NaN
+    ?:  =(x 0xfff0.0000.0000.0000)  `@rd`0x7ff8.0000.0000.0000  :: sin(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7ff8.0000.0000.0000 x) 0)  `@rd`0x7ff8.0000.0000.0000  :: sin(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   x
+    =/  po  .~-2
+    =/  i   1
+    =/  term  x
+    |-  ^-  @rd
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (add i2 .~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +cos:  @rd -> @rd
+  ::
+  ::  Returns the cosine of a floating-point atom.
+  ::    Examples
+  ::      > (cos .~1)
+  ::      .~0.5403023058680917
+  ::     > (cos .~2)
+  ::      .~-0.41614683654756957
+  ::     > (cos pi)
+  ::      .~-1.0000000000013558
+  ::  Source
+  ++  cos
+    |=  x=@rd  ^-  @rd
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7ff0.0000.0000.0000)  `@rd`0x7ff8.0000.0000.0000  :: cos(+inf) -> NaN
+    ?:  =(x 0xfff0.0000.0000.0000)  `@rd`0x7ff8.0000.0000.0000  :: cos(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7ff8.0000.0000.0000 x) 0)  `@rd`0x7ff8.0000.0000.0000  :: exp(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   .~1
+    =/  po  .~-2
+    =/  i   1
+    =/  term  .~1
+    |-  ^-  @rd
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (sub i2 .~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +tan:  @rd -> @rd
+  ::
+  ::  Returns the tangent of a floating-point atom.
+  ::    Examples
+  ::      > (tan .~1)
+  ::      .~1.5574077246550349
+  ::      > (tan .~2)
+  ::      .~-2.185039863259177
+  ::      > (tan pi)
+  ::      .~-2.6535896228476087e-6
+  ::  Source
+  ++  tan
+    |=  x=@rd  ^-  @rd
+    (div (sin x) (cos x))
+  ::    +pow-n:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the power of a floating-point atom to an integer exponent.
+  ::    Examples
+  ::      > (pow-n .1 .2)
+  ::      .1
+  ::      > (pow-n .2 .2)
+  ::      .4
+  ::      > (pow-n .2 .3)
+  ::      .8
+  ::  Source
+  ++  pow-n
+    |=  [x=@rd n=@rd]  ^-  @rd
+    ?:  =(n .~0)  .~1
+    ?>  &((gth n .~0) (isint n))
+    =/  p  x
+    |-  ^-  @rd
+    ?:  (lth n .~2)
+      p
+    $(n (sub n .~1), p (mul p x))
+  ::    +log:  @rd -> @rd
+  ::
+  ::  Returns the natural logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log .~1)
+  ::      .~0
+  ::      > (log .~2)
+  ::      .~0.6931471805589156
+  ::      > (~(log rd [%z .~1e-15]) .~2)
+  ::      .~0.693147180559944
+  ::      > (log .~inf)
+  ::      .~inf
+  ::  Source
+  ++  log
+    |=  z=@rd  ^-  @rd
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(z 0x7ff0.0000.0000.0000)  `@rd`0x7ff0.0000.0000.0000  :: exp(+inf) -> inf
+    ?:  =(z 0xfff0.0000.0000.0000)  .~0.0                       :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7ff8.0000.0000.0000 z) 0)  `@rd`0x7ff8.0000.0000.0000  :: exp(NaN) -> NaN
+    ::  otherwise, use Taylor series
+    =/  p   .~0
+    =/  po  .~-1
+    =/  i   .~0
+    |-  ^-  @rd
+    ?:  (lth (abs (sub po p)) rtol)
+      (mul (div (mul .~2 (sub z .~1)) (add z .~1)) p)
+    =/  term1  (div .~1 (add .~1 (mul .~2 i)))
+    =/  term2  (mul (sub z .~1) (sub z .~1))
+    =/  term3  (mul (add z .~1) (add z .~1))
+    =/  term  (mul term1 (pow-n (div term2 term3) i))
+    $(i (add i .~1), p (add p term), po p)
+  ::    +log-10:  @rd -> @rd
+  ::
+  ::  Returns the base-10 logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log-10 .~0.1)
+  ::      .~-0.9999999999082912
+  ::      > (log-10 .~2)
+  ::      .~0.30102999566353394
+  ::      > (~(log-10 rd [%z .~1e-8]) .~2)
+  ::      .~0.30102999562024696
+  ::  Source
+  ++  log-10
+    |=  z=@rd  ^-  @rd
+    (div (log z) log10)
+  ::    +log-2:  @rd -> @rd
+  ::
+  ::  Returns the base-2 logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log-2 .0.1)
+  ::      .~-3.321928094582713
+  ::      > (log-2 .2)
+  ::      .~0.9999999999985144
+  ::      > (~(log-2 rs [%z .1e-8]) .2)
+  ::      .~0.9999999998547181
+  ::  Source
+  ++  log-2
+    |=  z=@rd  ^-  @rd
+    (div (log z) log2)
+  ::    +pow:  [@rd @rd] -> @rd
+  ::
+  ::  Returns the power of a floating-point atom to a floating-point exponent.
+  ::    Examples
+  ::      > (pow .~1 .~2)
+  ::      .~1
+  ::      > (pow .~2 .~2)
+  ::      .~4
+  ::      > (pow .~2 .~3.5)
+  ::      .~11.313708498941306
+  ::      > (~(pow rd [%z .~1e-15]) .~2 .~3.5)
+  ::      .~11.313708498984685
+  ::  Source
+  ++  pow
+    |=  [x=@rd n=@rd]  ^-  @rd
+    ::  fall through on integers (faster)
+    ?:  =(n (san (need (toi n))))  (pow-n x (san (need (toi n))))
+    (exp (mul n (log x)))
+  ::    +sqrt:  @rd -> @rd
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::  Alias for +sqt.
+  ::    Examples
+  ::      > (sqrt .~1)
+  ::      .~1
+  ::      > (sqrt .~2)
+  ::      .~1.4142135623721421
+  ::      > (~(sqrt rd [%z .~1e-15]) .~2)
+  ::      .~1.4142135623730923
+  ::  Source
+  ++  sqrt  sqt
+  ::    +sqt:  @rd -> @rd
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::    Examples
+  ::      > (sqt .~1)
+  ::      .~1
+  ::      > (sqt .~2)
+  ::      .~1.4142135623721421
+  ::      > (~(sqt rd [%z .~1e-15]) .~2)
+  ::      .~1.4142135623730923
+  ::  Source
+  ++  sqt
+    |=  x=@rd  ^-  @rd
+    ?>  (sgn x)
+    (pow x .~0.5)
+  ::    +cbrt:  @rd -> @rd
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::  Alias for +cbt.
+  ::    Examples
+  ::      > (cbrt .~1)
+  ::      .~1
+  ::      > (cbrt .~2)
+  ::      .~1.2599210498943176
+  ::      > (~(cbrt rd [%z .~1e-15]) .~2)
+  ::      .~1.2599210498948716
+  ::  Source
+  ++  cbrt  cbt
+  ::    +cbt:  @rd -> @rd
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::    Examples
+  ::      > (cbt .~1)
+  ::      .~1
+  ::      > (cbt .~2)
+  ::      .~1.2599210498943176
+  ::      > (~(cbt rd [%z .~1e-15]) .~2)
+  ::      .~1.2599210498948716
+  ::  Source
+  ++  cbt
+    |=  x=@rd  ^-  @rd
+    ?>  (sgn x)
+    (pow x .~0.3333333333333333)
+  ::    +arg:  @rd -> @rd
+  ::
+  ::  Returns the argument of a floating-point atom (real argument = absolute
+  ::  value).
+  ::    Examples
+  ::      > (arg .~1)
+  ::      .~1
+  ::      > (arg .~-1)
+  ::      .~1
+  ::  Source
+  ++  arg  abs
+  ::    +round:  [@rs @ud] -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to a given number of decimal
+  ::  places.
+  ::    Examples
+  ::      > (round .1 0)
+  ::      .1
+  ::      > (round .1.11 1)
+  ::      .1.1
+  ::      > (round .1.11 2)
+  ::      .1.11
+  ::      > (round .1.11 3)
+  ::      .1.11
+  ::  Source
+  ++  round
+    |=  [x=@rd n=@ud]  ^-  @rd
+    ?:  =(.~0 x)  .~0
+    ::  Calculate the order of magnitude.
+    =/  oom  (san (need (toi (log-10 (abs x)))))
+    ::  Calculate the scaling factor.
+    =/  scaling  (pow .~10 :(sub (sun n) oom .~1))
+    ::  Round the mantissa to desired significant digits.
+    =/  rnd-mantissa  (round-bankers (mul x scaling))
+    ::  Convert back to the original scale.
+    (div rnd-mantissa scaling)
+  ::    +round-places:  [@rs @ud] -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to a given number of decimal
+  ::  places.  This is exceptionally sensitive to off-by-one FP rounding error.
+  ::    Examples
+  ::      > (round-places .1 0)
+  ::      .1
+  ::      > (round-places .1.11 1)
+  ::      .1.1
+  ::      > (round-places .1.285 2)
+  ::      .1.28
+  ::      > (round-places .4.12345 3)
+  ::      .4.1229997
+  ::  Source
+  ++  round-places
+    |=  [x=@rd n=@ud]  ^-  @rd
+    ::  Calculate the scaling factor.
+    =/  scaling  (pow .~10 (sun n))
+    ::  Scale the number.
+    =/  scaled  (mul x scaling)
+    ::  Round the mantissa to desired significant digits.
+    =/  rnd-mantissa  (round-bankers scaled)
+    ::  Convert back to the original scale.
+    (div rnd-mantissa scaling)
+  ::    +round-bankers:  @rs -> @rs
+  ::
+  ::  Returns the floating-point atom rounded to the nearest integer, with
+  ::  ties rounded to the nearest even integer.
+  ::    Examples
+  ::      > (round-bankers .1)
+  ::      .1
+  ::      > (round-bankers .1.5)
+  ::      .2
+  ::      > (round-bankers .1.49)
+  ::      .1
+  ::  Source
+  ++  round-bankers
+    |=  x=@rd  ^-  @rd
+    =/  int  (san (need (toi x)))
+    =/  dcm  (sub x int)
+    ?:  (lth dcm .~0.5)
+      int
+    (add int .~1)
+  --
+::  half precision
+++  rh
+  ^|
+  |_  $:  r=$?(%n %u %d %z)   :: round nearest, up, down, to zero
+          rtol=_.~~1e-2       :: relative tolerance for precision of operations
+      ==
+  ::  mathematics constants to half precision
+  ::    +tau:  @rh
+  ::
+  ::  Returns the value 2*pi (OEIS A019692).
+  ::    Examples
+  ::      > tau
+  ::      .~~6.28
+  ::  Source
+  ++  tau  .~~6.28
+  ::    +pi:  @rh
+  ::
+  ::  Returns the value pi (OEIS A000796).
+  ::    Examples
+  ::      > pi
+  ::      .~~3.14
+  ::  Source
+  ++  pi  .~~3.14
+  ::    +e:  @rh
+  ::
+  ::  Returns the value e (Euler's constant) (OEIS A001113).
+  ::    Examples
+  ::      > e
+  ::      .~~2.72
+  ::  Source
+  ++  e  .~~2.719
+  ::    +phi:  @rh
+  ::
+  ::  Returns the value phi (golden ratio) (OEIS A001622).
+  ::    Examples
+  ::      > phi
+  ::      .~~1.62
+  ::  Source
+  ++  phi  .~~1.618
+  ::    +sqt2:  @rh
+  ::
+  ::  Returns the value sqrt(2) (OEIS A002193).
+  ::    Examples
+  ::      > sqt2
+  ::      .~~1.414
+  ::  Source
+  ++  sqt2  .~~1.414
+  ::    +invsqt2:  @rh
+  ::
+  ::  Returns the value 1/sqrt(2) (OEIS A010503).
+  ::    Examples
+  ::      > invsqt2
+  ::      .~~0.707
+  ::  Source
+  ++  invsqt2  .~~0.707
+  ::    +log2:  @rh
+  ::
+  ::  Returns the value log(2) (OEIS A002162).
+  ::    Examples
+  ::      > log2
+  ::      .~~0.693
+  ::  Source
+  ++  log2  .~~0.6934
+  ::    +invlog2:  @rh
+  ::
+  ::  Returns the value 1/log(2).
+  ::    Examples
+  ::      > invlog2
+  ::      .~~1.443
+  ::  Source
+  ++  invlog2  .~~1.443
+  ::    +log10:  @rh
+  ::
+  ::  Returns the value log(10) (OEIS A002392).
+  ::    Examples
+  ::      > log10
+  ::      .~~2.303
+  ::  Source
+  ++  log10  .~~2.303
+  ::    +huge:  @rh
+  ::
+  ::  Returns the value of the largest representable number.
+  ::    Examples
+  ::      > huge
+  ::      .~~6.55e+04
+  ::  Source
+  ++  huge  `@rh`0x7bff  ::  6.55e+04
+  ::    +tiny:  @rh
+  ::
+  ::  Returns the value of the smallest representable normal number.
+  ::    Examples
+  ::      > tiny
+  ::      .~~6.10e-05
+  ::  Source
+  ++  tiny  `@rh`0x1     ::  6e-08
+  ::
+  ::  Operations
+  ::
+  ::    +sea:  @rh -> fn
+  ::
+  ::  Returns the +$fn representation of a floating-point atom.
+  ::    Examples
+  ::      > (sea .~~1)
+  ::      [%f s=%.y e=-10 a=1.024]
+  ::      > (sea .~~1.1)
+  ::      [%f s=%.y e=-10 a=1.126]
+  ::  Source
+  ++  sea  sea:^rh
+  ::    +bit:  fn -> @rh
+  ::
+  ::  Returns the floating-point atom of a +$fn representation.
+  ::    Examples
+  ::      > (bit [%f s=%.y e=-10 a=1.024])
+  ::      .~~1
+  ::      > (bit [%f s=%.y e=-10 a=1.126])
+  ::      .~~1.1
+  ::  Source
+  ++  bit  bit:^rh
+  ::    +sun:  @ud -> @rh
+  ::
+  ::  Returns the floating-point atom of an unsigned integer atom.
+  ::    Examples
+  ::      > (sun 1)
+  ::      .~~1
+  ::      > (sun 1.000)
+  ::      .~~1e3
+  ::  Source
+  ++  sun  sun:^rh
+  ::    +san:  @sd -> @rh
+  ::
+  ::  Returns the floating-point atom of a signed integer atom.
+  ::    Examples
+  ::      > (san --1)
+  ::      .~~1
+  ::      > (san -1)
+  ::      .~-1
+  ::  Source
+  ++  san  san:^rh
+  ::++  exp  exp:^rh  :: no pass-through because of exp function
+  ::    +toi:  @rh -> @sd
+  ::
+  ::  Returns the unitized signed integer atom of a rounded floating-point atom.
+  ::    Examples
+  ::      > (toi .~~1)
+  ::      [~ --1]
+  ::      > (toi .~~1.1)
+  ::      [~ --1]
+  ::  Source
+  ++  toi  toi:^rh
+  ::    +drg:  @rh -> dn
+  ::
+  ::  Returns the decimal form of a floating-point atom using the Dragon4
+  ::  algorithm.
+  ::    Examples
+  ::      > (drg .~~1)
+  ::      [%d s=%.y e=--0 a=1]
+  ::      > (drg .~~1.1)
+  ::      [%d s=%.y e=-1 a=11]
+  ::  Source
+  ++  drg  drg:^rh
+  ::    +grd:  dn -> @rh
+  ::
+  ::  Returns the floating-point atom of a decimal form.
+  ::    Examples
+  ::      > (grd [%d s=%.y e=--0 a=1])
+  ::      .~~1
+  ::      > (grd [%d s=%.y e=-1 a=11])
+  ::      .~~1.1
+  ::  Source
+  ++  grd  grd:^rh
+  ::
+  ::  Comparison
+  ::
+  ::    +lth:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than.
+  ::    Examples
+  ::      > (lth .~~1 .~~2)
+  ::      %.y
+  ::      > (lth .~~2 .~~1)
+  ::      %.n
+  ::      > (lth .~~1 .~~1)
+  ::      %.n
+  ::  Source
+  ++  lth  lth:^rh
+  ::    +lte:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::    Examples
+  ::      > (lte .~~1 .~~2)
+  ::      %.y
+  ::      > (lte .~~2 .~~1)
+  ::      %.n
+  ::      > (lte .~~1 .~~1)
+  ::      %.y
+  ::  Source
+  ++  lte  lte:^rh
+  ::    +leq:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::  Alias for +lte.
+  ::    Examples
+  ::      > (leq .~~1 .~~2)
+  ::      %.y
+  ::      > (leq .~~2 .~~1)
+  ::      %.n
+  ::      > (leq .~~1 .~~1)
+  ::      %.y
+  ::  Source
+  ++  leq  lte:^rh
+  ::    +equ:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, equal to.
+  ::    Examples
+  ::      > (equ .~~1 .~~2)
+  ::      %.n
+  ::      > (equ .~~2 .~~1)
+  ::      %.n
+  ::      > (equ .~~1 .~~1)
+  ::      %.y
+  ::  Source
+  ++  equ  equ:^rh
+  ::    +gth:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than.
+  ::    Examples
+  ::      > (gth .~~1 .~~2)
+  ::      %.n
+  ::      > (gth .~~2 .~~1)
+  ::      %.y
+  ::      > (gth .~~1 .~~1)
+  ::      %.n
+  ::  Source
+  ++  gth  gth:^rh
+  ::    +gte:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::    Examples
+  ::      > (gte .~~1 .~~2)
+  ::      %.n
+  ::      > (gte .~~2 .~~1)
+  ::      %.y
+  ::      > (gte .~~1 .~~1)
+  ::      %.y
+  ::  Source
+  ++  gte  gte:^rh
+  ::    +geq:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::  Alias for +gte.
+  ::    Examples
+  ::      > (geq .~~1 .~~2)
+  ::      %.n
+  ::      > (geq .~~2 .~~1)
+  ::      %.y
+  ::      > (geq .~~1 .~~1)
+  ::      %.y
+  ::  Source
+  ++  geq  gte:^rh
+  ::    +neq:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, not equal to.
+  ::    Examples
+  ::      > (neq .~~1 .~~2)
+  ::      %.y
+  ::      > (neq .~~2 .~~1)
+  ::      %.y
+  ::      > (neq .~~1 .~~1)
+  ::      %.n
+  ::  Source
+  ++  neq  |=([a=@rh b=@rh] ^-(? !(equ:^rh a b)))
+  ::    +isclose:  [@rh @rh] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, within a relative
+  ::  tolerance (provided by the +rh door).
+  ::    Examples
+  ::      > (isclose .~~1 .~~2)
+  ::      %.n
+  ::      > (isclose .~~1 .~~1.0000001)
+  ::      %.n
+  ::      > (~(isclose rh [%z .~~1e-3]) .~~1 .~~1.0001)
+  ::      %.y
+  ::  Source
+  ++  isclose
+    |=  [p=@rh r=@rh]
+    (lth (abs (sub p r)) rtol)
+  ::    +allclose:  [@rh (list @rh)] -> ?
+  ::
+  ::  Returns the comparison of a floating-point atom to a list of floating-
+  ::  point atoms, within a relative tolerance (provided by the +rh door).
+  ::    Examples
+  ::      > (allclose .~~1 ~[.~~1 .~~2])
+  ::      %.n
+  ::      > (allclose .~~1 ~[.~~1 .~~1.0000001])
+  ::      %.n
+  ::      > (~(allclose rh [%z .~~1e-3]) .~~1 ~[.~~1 .~~1.0001])
+  ::      %.y
+  ::  Source
+  ++  allclose
+    |=  [p=@rh q=(list @rh)]
+    =/  i  0
+    =/  n  (lent q)
+    |-  ^-  ?
+    ?:  =(n i)
+      %.y
+    ?.  (isclose p (snag i q))
+      %.n
+    $(i +(i))
+  ::    +isint:  @rh -> ?
+  ::
+  ::  Returns whether a floating-point value is an integer (no fractional part).
+  ::    Examples
+  ::      > (isint .~~1)
+  ::      %.y
+  ::      > (isint .~~1.1)
+  ::      %.n
+  ::  Source
+  ++  isint
+    |=  x=@rh  ^-  ?
+    (equ x (san (need (toi x))))
+  ::
+  ::  Algebraic
+  ::
+  ::    +add:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the sum of two floating-point atoms.
+  ::    Examples
+  ::      > (add .~~1 .~~2)
+  ::      .~~3
+  ::  Source
+  ++  add  add:^rh
+  ::    +sub:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the difference of two floating-point atoms.
+  ::    Examples
+  ::      > (sub .~~1 .~~2)
+  ::      .~~-1
+  ::  Source
+  ++  sub  sub:^rh
+  ::    +mul:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the product of two floating-point atoms.
+  ::    Examples
+  ::      > (mul .~~1 .~~2)
+  ::      .~~2
+  ::  Source
+  ++  mul  mul:^rh
+  ::    +div:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the quotient of two floating-point atoms.
+  ::    Examples
+  ::      > (div .~~1 .~~2)
+  ::      .~~0.5
+  ::  Source
+  ++  div  div:^rh
+  ::    +fma:  [@rh @rh @rh] -> @rh
+  ::
+  ::  Returns the fused multiply-add of three floating-point atoms.
+  ::    Examples
+  ::      > (fma .~~1 .~~2 .~~3)
+  ::      .~~5
+  ::      > (fma .~~2 .~~3 .~~4)
+  ::      .~~10
+  ::  Source
+  ++  fma  fma:^rh
+  ::    +sig:  @rh -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::    Examples
+  ::      > (sig .~~1)
+  ::      %.y
+  ::      > (sig .~~-1)
+  ::      %.n
+  ::  Source
+  ++  sig  |=(x=@rh =(0 (rsh [0 15] x)))
+  ::    +sgn:  @rh -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::  Alias for +sig.
+  ::    Examples
+  ::      > (sgn .~~1)
+  ::      %.y
+  ::      > (sgn .~~-1)
+  ::      %.n
+  ::  Source
+  ++  sgn  sig
+  ::    +neg:  @rh -> @rh
+  ::
+  ::  Returns the negation of a floating-point atom.
+  ::    Examples
+  ::      > (neg .~~1)
+  ::      .~~-1
+  ::      > (neg .~~-1)
+  ::      .~~1
+  ::  Source
+  ++  neg  |=(x=@rh (sub .~~0 x))
+  ::    +factorial:  @rh -> @rh
+  ::
+  ::  Returns the factorial of a floating-point atom.  Assumes integer input.
+  ::    Examples
+  ::      > (factorial .~~1)
+  ::      .~~1
+  ::      > (factorial .~~2)
+  ::      .~~2
+  ::      > (factorial .~~3)
+  ::      .~~6
+  ::  Source
+  ++  factorial
+    |=  x=@rh  ^-  @rh
+    ?>  (gte x .~~0)
+    =/  t=@rh  .~~1
+    ?:  (isclose x .~~0)
+      t
+    |-  ^-  @rh
+    ?:  (isclose x .~~1)
+      t
+    $(x (sub x .~~1), t (mul t x))
+  ::    +abs:  @rh -> @rh
+  ::
+  ::  Returns the absolute value of a floating-point atom.
+  ::    Examples
+  ::      > (abs .~~1)
+  ::      .~~1
+  ::      > (abs .~~-1)
+  ::      .~~1
+  ::  Source
+  ++  abs
+    |=  x=@rh  ^-  @rh
+    ?:((sgn x) x (neg x))
+  ::    +exp:  @rh -> @rh
+  ::
+  ::  Returns the exponential of a floating-point atom.
+  ::    Examples
+  ::      > (exp .~~1)
+  ::      .~~2.715
+  ::      > (exp .~~2)
+  ::      .~~7.375
+  ::      > (~(exp rh [%z .~~1e-1]) .~~2)
+  ::      .~~7.348
+  ::      > (exp .~~inf)
+  ::      .inf
+  ::  Source
+  ++  exp
+    |=  x=@rh  ^-  @rh
+    ::  filter out non-finite arguments
+    ?:  =(x 0x0)  .~~1
+    ::    check infinities
+    ?:  =(x 0x7c00)  `@rh`0x7c00  :: exp(+inf) -> inf
+    ?:  =(x 0xfc00)  .~~0.0       :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7e00 x) 0)  `@rh`0x7e00  :: exp(NaN) -> NaN
+    ::    check overflow to infinity
+    =/  o-threshold  `@rh`0x498c  ::  11.091265424003277, value above which exp(x) overflows
+    ?:  (gth x o-threshold)  (mul huge huge)
+    ::    check underflow to zero
+    =/  u-threshold  `@rh`0xc98c  ::  -11.091265424003277, value below which exp(x) underflows
+    ?:  (lth x u-threshold)  (mul tiny tiny)
+    ::  otherwise, use Taylor series
+    =/  p   .~~1
+    =/  po  .~~-1
+    =/  i   .~~1
+    |-  ^-  @rh
+    ?:  (lth (abs (sub po p)) rtol)
+      p
+    $(i (add i .~~1), p (add p (div (pow-n x i) (factorial i))), po p)
+  ::    +sin:  @rh -> @rh
+  ::
+  ::  Returns the sine of a floating-point atom.
+  ::    Examples
+  ::    > (sin .~~1)
+  ::    .~~0.8413
+  ::    > (sin .~~2)
+  ::    .~~0.9087
+  ::    > (sin pi)
+  ::    .~~3.437e-3
+  ::  Source
+  ++  sin
+    |=  x=@rh  ^-  @rh
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7c00)  `@rh`0x7e00  :: sin(+inf) -> NaN
+    ?:  =(x 0xfc00)  `@rh`0x7e00  :: sin(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7e00 x) 0)  `@rh`0x7e00  :: sin(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   x
+    =/  po  .~~-2
+    =/  i   1
+    =/  term  x
+    |-  ^-  @rh
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (add i2 .~~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +cos:  @rh -> @rh
+  ::
+  ::  Returns the cosine of a floating-point atom.
+  ::    Examples
+  ::      > (cos .~~1)
+  ::      .~~0.54
+  ::     > (cos .~~2)
+  ::      .~~-0.4158
+  ::     > (cos pi)
+  ::      .~~-1.001
+  ::  Source
+  ++  cos
+    |=  x=@rh  ^-  @rh
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7c00)  `@rh`0x7e00  :: cos(+inf) -> NaN
+    ?:  =(x 0xfc00)  `@rh`0x7e00  :: cos(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7e00 x) 0)  `@rh`0x7e00  :: cos(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   .~~1
+    =/  po  .~~-2
+    =/  i   1
+    =/  term  .~~1
+    |-  ^-  @rh
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (sub i2 .~~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +tan:  @rh -> @rh
+  ::
+  ::  Returns the tangent of a floating-point atom.
+  ::    Examples
+  ::      > (tan .~~1)
+  ::      .~~1.558
+  ::      > (tan .~~2)
+  ::      .~~-2.186
+  ::      > (tan pi)
+  ::      .~~-3.433e-3
+  ::  Source
+  ++  tan
+    |=  x=@rh  ^-  @rh
+    (div (sin x) (cos x))
+  ::    +pow-n:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the power of a floating-point atom to an integer exponent.
+  ::    Examples
+  ::      > (pow-n .~~1 .~~2)
+  ::      .~~1
+  ::      > (pow-n .~~2 .~~2)
+  ::      .~~4
+  ::      > (pow-n .~~2 .~~3)
+  ::      .~~8
+  ::  Source
+  ++  pow-n
+    |=  [x=@rh n=@rh]  ^-  @rh
+    ?:  =(n .~~0)  .~~1
+    ?>  &((gth n .~~0) (isint n))
+    =/  p  x
+    |-  ^-  @rh
+    ?:  (lth n .~~2)
+      p
+    $(n (sub n .~~1), p (mul p x))
+  ::    +log:  @rh -> @rh
+  ::
+  ::  Returns the natural logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log .~~1)
+  ::      .~~0
+  ::      > (log .~~2)
+  ::      .~~0.6914
+  ::      > (~(log rh [%z .~~1e-1]) .~~2)
+  ::      .~~0.6904
+  ++  log
+    |=  z=@rh  ^-  @rh
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(z 0x7c00)  `@rh`0x7c00  :: exp(+inf) -> inf
+    ?:  =(z 0xfc00)  .~~0.0       :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7e00 z) 0)  `@rh`0x7e00  :: exp(NaN) -> NaN
+    ::  otherwise, use Taylor series
+    =/  p   .~~0
+    =/  po  .~~-1
+    =/  i   .~~0
+    |-  ^-  @rh
+    ?:  (lth (abs (sub po p)) rtol)
+      (mul (div (mul .~~2 (sub z .~~1)) (add z .~~1)) p)
+    =/  term1  (div .~~1 (add .~~1 (mul .~~2 i)))
+    =/  term2  (mul (sub z .~~1) (sub z .~~1))
+    =/  term3  (mul (add z .~~1) (add z .~~1))
+    =/  term  (mul term1 (pow-n (div term2 term3) i))
+    $(i (add i .~~1), p (add p term), po p)
+  ::    +pow:  [@rh @rh] -> @rh
+  ::
+  ::  Returns the power of a floating-point atom to a floating-point exponent.
+  ::    Examples
+  ::      > (pow .~~1 .~~2)
+  ::      .~~1
+  ::      > (pow .~~2 .~~2)
+  ::      .~~4
+  ::      > (~(pow rh:math [%z .~~1e-1]) .~~2 .~~3.5)
+  ::      .~~11.14
+  ::  Source
+  ++  pow
+    |=  [x=@rh n=@rh]  ^-  @rh
+    ::  fall through on integers (faster)
+    ?:  =(n (san (need (toi n))))  (pow-n x (san (need (toi n))))
+    (exp (mul n (log x)))
+  ::    +sqrt:  @rh -> @rh
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::  Alias for +sqt.
+  ::    Examples
+  ::      > (sqrt .~~1)
+  ::      .~~1
+  ::      > (sqrt .~~2)
+  ::      .~~1.412
+  ::      > (~(sqrt rh [%z .~~1e-1]) .~~2)
+  ::      .~~1.404
+  ::  Source
+  ++  sqrt  sqt
+  ::    +sqt:  @rh -> @rh
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::    Examples
+  ::      > (sqt .~~1)
+  ::      .~~1
+  ::      > (sqt .~~2)
+  ::      .~~1.412
+  ::      > (~(sqt rh [%z .~~1e-1]) .~~2)
+  ::      .~~1.404
+  ::  Source
+  ++  sqt
+    |=  x=@rh  ^-  @rh
+    ?>  (sgn x)
+    (pow x .~~0.5)
+  ::    +cbrt:  @rh -> @rh
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::  Alias for +cbt.
+  ::    Examples
+  ::      > (cbrt .~~1)
+  ::      .~~1
+  ::      > (cbrt .~~2)
+  ::      .~~1.258
+  ::      > (~(cbrt rh [%z .~~1e-1]) .~~2)
+  ::      .~~1.256
+  ::  Source
+  ++  cbrt  cbt
+  ::    +cbt:  @rh -> @rh
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::    Examples
+  ::      > (cbt .~~1)
+  ::      .~~1
+  ::      > (cbt .~~2)
+  ::      .~~1.258
+  ::      > (~(cbt rh [%z .~~1e-1]) .~~2)
+  ::      .~~1.256
+  ::  Source
+  ++  cbt
+    |=  x=@rh  ^-  @rh
+    ?>  (sgn x)
+    (pow x .~~0.3333)
+  ::    +arg:  @rh -> @rh
+  ::
+  ::  Returns the argument of a floating-point atom (real argument = absolute
+  ::  value).
+  ::    Examples
+  ::      > (arg .~~1)
+  ::      .~~1
+  ::      > (arg .~-1)
+  ::      .~~1
+  ::  Source
+  ++  arg  abs
+  --
+::  quad precision
+++  rq
+  ^|
+  |_  $:  r=$?(%n %u %d %z)   :: round nearest, up, down, to zero
+          rtol=_.~~~1e-20     :: relative tolerance for precision of operations
+      ==
+  ::  mathematics constants to quad precision
+  ::    +tau:  @rq
+  ::
+  ::  Returns the value 2*pi (OEIS A019692).
+  ::    Examples
+  ::      > tau
+  ::      .~~~6.2831853071795864769252867665590056
+  ::  Source
+  ++  tau  .~~~6.2831853071795864769252867665590056
+  ::    +pi:  @rq
+  ::
+  ::  Returns the value pi (OEIS A000796).
+  ::    Examples
+  ::      > pi
+  ::      .~~~3.1415926535897932384626433832795028
+  ::  Source
+  ++  pi  .~~~3.1415926535897932384626433832795028
+  ::    +e:  @rq
+  ::
+  ::  Returns the value e (Euler's constant) (OEIS A001113).
+  ::    Examples
+  ::      > e
+  ::      .~~~2.7182818284590452353602874713526623
+  ::  Source
+  ++  e  .~~~2.7182818284590452353602874713526623
+  ::    +phi:  @rq
+  ::
+  ::  Returns the value phi (golden ratio) (OEIS A001622).
+  ::    Examples
+  ::      > phi
+  ::      .~~~1.6180339887498948482045868343656382
+  ::  Source
+  ++  phi  .~~~1.6180339887498948482045868343656382
+  ::    +sqt2:  @rq
+  ::
+  ::  Returns the value sqrt(2) (OEIS A002193).
+  ::    Examples
+  ::      > sqt2
+  ::      .~~~1.414213562373095048801688724209698
+  ::  Source
+  ++  sqt2  .~~~1.414213562373095048801688724209698
+  ::    +invsqt2:  @rq
+  ::
+  ::  Returns the value 1/sqrt(2) (OEIS A010503).
+  ::    Examples
+  ::      > invsqt2
+  ::      .~~~0.707106781186547524400844362104849
+  ::  Source
+  ++  invsqt2  .~~~0.707106781186547524400844362104849
+  ::    +log2:  @rq
+  ::
+  ::  Returns the value log(2) (OEIS A002162).
+  ::    Examples
+  ::      > log2
+  ::      .~~~0.6931471805599453094172321214581766
+  ::  Source
+  ++  log2  .~~~0.6931471805599453094172321214581766
+  ::    +invlog2:  @rq
+  ::
+  ::  Returns the value 1/log(2).
+  ::    Examples
+  ::      > invlog2
+  ::      .~~~1.442695040888963387004650940070860
+  ::  Source
+  ++  invlog2  .~~~1.442695040888963387004650940070860  :: TODO check
+  ::    +log10:  @rq
+  ::
+  ::  Returns the value log(10) (OEIS A002392).
+  ::    Examples
+  ::      > log10
+  ::      .~~~2.302585092994045684017991454684364
+  ::  Source
+  ++  log10  .~~~2.302585092994045684017991454684364
+  ::    +huge:  @rq
+  ::
+  ::  Returns the value of the largest representable number.
+  ::    Examples
+  ::      > huge
+  ::      .~~~1.189731495357231765085759326628007e4932
+  ::  Source
+  ++  huge  `@rq`0x7ffe.ffff.ffff.ffff.ffff.ffff.ffff.ffff.ffff  ::  1.18973149535723176508575932662800702e4932
+  ::    +tiny:  @rq
+  ::
+  ::  Returns the value of the smallest representable normal number.
+  ::    Examples
+  ::      > tiny
+  ::      .~~~3.3621031431120935062626778173217526e-4932
+  ::  Source
+  ++  tiny  `@rq`0x1.0000.0000.0000.0000.0000.0000.0000.0000     ::  3.36210314311209350626267781732175260e-4932
+  ::
+  ::  Operations
+  ::
+  ::    +sea:  @rq -> fn
+  ::
+  ::  Returns the +$fn representation of a floating-point atom.
+  ::    Examples
+  ::      > (sea .~~~1)
+  ::      [%f s=%.y e=-112 a=5.192.296.858.534.827.628.530.496.329.220.096]
+  ::      > (sea .~~~1.1)
+  ::      [%f s=%.y e=-112 a=5.711.526.544.388.310.391.383.545.962.142.106]
+  ::  Source
+  ++  sea  sea:^rq
+  ::    +bit:  fn -> @rq
+  ::
+  ::  Returns the floating-point atom of a +$fn representation.
+  ::    Examples
+  ::      > (bit [%f s=%.y e=-112 a=5.192.296.858.534.827.628.530.496.329.220.096])
+  ::      .~~~1
+  ::      > (bit [%f s=%.y e=-112 a=5.711.526.544.388.310.391.383.545.962.142.106])
+  ::      .~~~1.1
+  ::  Source
+  ++  bit  bit:^rq
+  ::    +sun:  @ud -> @rq
+  ::
+  ::  Returns the floating-point atom of an unsigned integer atom.
+  ::    Examples
+  ::      > (sun 1)
+  ::      .~~~1
+  ::      > (sun 1.000)
+  ::      .~~~1e3
+  ::  Source
+  ++  sun  sun:^rq
+  ::    +san:  @sd -> @rq
+  ::
+  ::  Returns the floating-point atom of a signed integer atom.
+  ::    Examples
+  ::      > (san --1)
+  ::      .~~~1
+  ::      > (san -1)
+  ::      .~~~-1
+  ::  Source
+  ++  san  san:^rq
+  ::++  exp  exp:^rq  :: no pass-through because of exp function
+  ::    +toi:  @rq -> @sd
+  ::
+  ::  Returns the unitized signed integer atom of a rounded floating-point atom.
+  ::    Examples
+  ::      > (toi .~~~1)
+  ::      [~ --1]
+  ::      > (toi .~~~1.1)
+  ::      [~ --1]
+  ::  Source
+  ++  toi  toi:^rq
+  ::    +drg:  @rq -> dn
+  ::
+  ::  Returns the decimal form of a floating-point atom using the Dragon4
+  ::  algorithm.
+  ::    Examples
+  ::      > (drg .~~~1)
+  ::      [%d s=%.y e=--0 a=1]
+  ::      > (drg .~~~1.1)
+  ::      [%d s=%.y e=-1 a=11]
+  ::  Source
+  ++  drg  drg:^rq
+  ::    +grd:  dn -> @rq
+  ::
+  ::  Returns the floating-point atom of a decimal form.
+  ::    Examples
+  ::      > (grd [%d s=%.y e=--0 a=1])
+  ::      .~~~1
+  ::      > (grd [%d s=%.y e=-1 a=11])
+  ::      .~~~1.1
+  ::  Source
+  ++  grd  grd:^rq
+  ::
+  ::  Comparison
+  ::
+  ::    +lth:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than.
+  ::    Examples
+  ::      > (lth .~~~1 .~~~2)
+  ::      %.y
+  ::      > (lth .~~~2 .~~~1)
+  ::      %.n
+  ::      > (lth .~~~1 .~~~1)
+  ::      %.n
+  ::  Source
+  ++  lth  lth:^rq
+  ::    +lte:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::    Examples
+  ::      > (lte .~~~1 .~~~2)
+  ::      %.y
+  ::      > (lte .~~~2 .~~~1)
+  ::      %.n
+  ::      > (lte .~~~1 .~~~1)
+  ::      %.y
+  ::  Source
+  ++  lte  lte:^rq
+  ::    +leq:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, less than or equal to.
+  ::  Alias for +lte.
+  ::    Examples
+  ::      > (leq .~~~1 .~~~2)
+  ::      %.y
+  ::      > (leq .~~~2 .~~~1)
+  ::      %.n
+  ::      > (leq .~~~1 .~~~1)
+  ::      %.y
+  ::  Source
+  ++  leq  lte:^rq
+  ::    +equ:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, equal to.
+  ::    Examples
+  ::      > (equ .~~~1 .~~~2)
+  ::      %.n
+  ::      > (equ .~~~2 .~~~1)
+  ::      %.n
+  ::      > (equ .~~~1 .~~~1)
+  ::      %.y
+  ::  Source
+  ++  equ  equ:^rq
+  ::    +gth:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than.
+  ::    Examples
+  ::      > (gth .~~~1 .~~~2)
+  ::      %.n
+  ::      > (gth .~~~2 .~~~1)
+  ::      %.y
+  ::      > (gth .~~~1 .~~~1)
+  ::      %.n
+  ::  Source
+  ++  gth  gth:^rq
+  ::    +gte:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::    Examples
+  ::      > (gte .~~~1 .~~~2)
+  ::      %.n
+  ::      > (gte .~~~2 .~~~1)
+  ::      %.y
+  ::      > (gte .~~~1 .~~~1)
+  ::      %.y
+  ::  Source
+  ++  gte  gte:^rq
+  ::    +geq:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, greater than or equal to.
+  ::  Alias for +gte.
+  ::    Examples
+  ::      > (geq .~~~1 .~~~2)
+  ::      %.n
+  ::      > (geq .~~~2 .~~~1)
+  ::      %.y
+  ::      > (geq .~~~1 .~~~1)
+  ::      %.y
+  ::  Source
+  ++  geq  gte:^rq
+  ::    +neq:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, not equal to.
+  ::    Examples
+  ::      > (neq .~~~1 .~~~2)
+  ::      %.y
+  ::      > (neq .~~~2 .~~~1)
+  ::      %.y
+  ::      > (neq .~~~1 .~~~1)
+  ::      %.n
+  ::  Source
+  ++  neq  |=([a=@rq b=@rq] ^-(? !(equ:^rq a b)))
+  ::    +isclose:  [@rq @rq] -> ?
+  ::
+  ::  Returns the comparison of two floating-point atoms, within a relative
+  ::  tolerance (provided by the +rq door).
+  ::    Examples
+  ::      > (isclose .~~~1 .~~~2)
+  ::      %.n
+  ::      > (isclose .~~~1 .~~~1.0000001)
+  ::      %.n
+  ::      > (~(isclose rq [%z .~~~1e-3]) .~~~1 .~~~1.0001)
+  ::      %.y
+  ::      > (~(isclose rq [%z .~~~1e-30]) .~~~1 .~~~1.0001)
+  ::      %.n
+  ::  Source
+  ++  isclose
+    |=  [p=@rq r=@rq]
+    (lth (abs (sub p r)) rtol)
+  ::    +allclose:  [@rq (list @rq)] -> ?
+  ::
+  ::  Returns the comparison of a floating-point atom to a list of floating-
+  ::  point atoms, within a relative tolerance (provided by the +rq door).
+  ::    Examples
+  ::      > (allclose .~~~1 ~[.~~~1 .~~~2])
+  ::      %.n
+  ::      > (allclose .~~~1 ~[.~~~1 .~~~1.0000001])
+  ::      %.n
+  ::      > (~(allclose rq [%z .~~~1e-3]) .~~~1 ~[.~~~1 .~~~1.0001])
+  ::      %.y
+  ::  Source
+  ++  allclose
+    |=  [p=@rq q=(list @rq)]
+    =/  i  0
+    =/  n  (lent q)
+    |-  ^-  ?
+    ?:  =(n i)
+      %.y
+    ?.  (isclose p (snag i q))
+      %.n
+    $(i +(i))
+  ::    +isint:  @rq -> ?
+  ::
+  ::  Returns whether a floating-point value is an integer (no fractional part).
+  ::    Examples
+  ::      > (isint .~~~1)
+  ::      %.y
+  ::      > (isint .~~~1.1)
+  ::      %.n
+  ::  Source
+  ++  isint
+    |=  x=@rq  ^-  ?
+    (equ x (san (need (toi x))))
+  ::
+  ::  Algebraic
+  ::
+  ::    +add:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the sum of two floating-point atoms.
+  ::    Examples
+  ::      > (add .~~~1 .~~~2)
+  ::      .~~~3
+  ::  Source
+  ++  add  add:^rq
+  ::    +sub:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the difference of two floating-point atoms.
+  ::    Examples
+  ::      > (sub .~~~1 .~~~2)
+  ::      .~~~-1
+  ::  Source
+  ++  sub  sub:^rq
+  ::    +mul:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the product of two floating-point atoms.
+  ::    Examples
+  ::      > (mul .~~~1 .~~~2)
+  ::      .~~~2
+  ::  Source
+  ++  mul  mul:^rq
+  ::    +div:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the quotient of two floating-point atoms.
+  ::    Examples
+  ::      > (div .~~~1 .~~~2)
+  ::      .~~~0.5
+  ::  Source
+  ++  div  div:^rq
+  ::    +fma:  [@rq @rq @rq] -> @rq
+  ::
+  ::  Returns the fused multiply-add of three floating-point atoms.
+  ::    Examples
+  ::      > (fma .~~~1 .~~~2 .~~~3)
+  ::      .~~~5
+  ::      > (fma .~~~2 .~~~3 .~~~4)
+  ::      .~~~10
+  ::  Source
+  ++  fma  fma:^rq
+  ::    +sig:  @rq -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::    Examples
+  ::      > (sig .~~~1)
+  ::      %.y
+  ::      > (sig .~~~-1)
+  ::      %.n
+  ::  Source
+  ++  sig  |=(x=@rq =(0 (rsh [0 127] x)))
+  ::    +sgn:  @rq -> ?
+  ::
+  ::  Returns the sign of a floating-point atom.
+  ::  Alias for +sig.
+  ::    Examples
+  ::      > (sgn .~~~1)
+  ::      %.y
+  ::      > (sgn .~~~-1)
+  ::      %.n
+  ::  Source
+  ++  sgn  sig
+  ::    +neg:  @rq -> @rq
+  ::
+  ::  Returns the negation of a floating-point atom.
+  ::    Examples
+  ::      > (neg .~~~1)
+  ::      .~~~-1
+  ::      > (neg .~~~-1)
+  ::      .~~~1
+  ::  Source
+  ++  neg  |=(x=@rq (sub .~~~0 x))
+  ::    +factorial:  @rq -> @rq
+  ::
+  ::  Returns the factorial of a floating-point atom.  Assumes integer input.
+  ::    Examples
+  ::      > (factorial .~~~1)
+  ::      .~~~1
+  ::      > (factorial .~~~2)
+  ::      .~~~2
+  ::      > (factorial .~~~3)
+  ::      .~~~6
+  ::  Source
+  ++  factorial
+    |=  x=@rq  ^-  @rq
+    ?>  (gte x .~~~0)
+    =/  t=@rq  .~~~1
+    ?:  (isclose x .~~~0)
+      t
+    |-  ^-  @rq
+    ?:  (isclose x .~~~1)
+      t
+    $(x (sub x .~~~1), t (mul t x))
+  ::    +abs:  @rq -> @rq
+  ::
+  ::  Returns the absolute value of a floating-point atom.
+  ::    Examples
+  ::      > (abs .~~~1)
+  ::      .~~~1
+  ::      > (abs .~~~-1)
+  ::      .~~~1
+  ::  Source
+  ++  abs
+    |=  x=@rq  ^-  @rq
+    ?:((sgn x) x (neg x))
+  ::    +exp:  @rq -> @rq
+  ::
+  ::  Returns the exponential of a floating-point atom.
+  ::    Examples
+  ::      > (exp .~~~1)
+  ::      .~~~2.7182818284590452353602471108690483
+  ::      > (exp .~~~2)
+  ::      .~~~7.389056098930650227230362414146335
+  ::      > (~(exp rq [%z .~~~1e-20]) .~~~2)
+  ::      .~~~7.389056098930650227230362414146335
+  ::      > (exp .~~~inf)
+  ::      .~~~inf
+  ::  Source
+  ++  exp
+    |=  x=@rq  ^-  @rq
+    ::  filter out non-finite arguments
+    ?:  =(x 0x0)  .~~~1
+    ::    check infinities
+    ?:  =(x 0x7fff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.0000.0000.0000.0000.0000.0000.0000  :: exp(+inf) -> inf
+    ?:  =(x 0xffff.0000.0000.0000.0000.0000.0000.0000)  .~~~0.0      :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7fff.8000.0000.0000.0000.0000.0000.0000 x) 0)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: exp(NaN) -> NaN
+    ::    check overflow to infinity
+    =/  o-threshold  `@rq`0x400c.62e4.2fef.a39e.f357.93c7.6730.0601  ::  1.135652340629414394949193107797e4, value above which exp(x) overflows
+    ?:  (gth x o-threshold)  (mul huge huge)
+    ::    check underflow to zero
+    =/  u-threshold  `@rq`0xc00c.62e4.2fef.a39e.f357.93c7.6730.0601  ::  -1.135652340629414394949193107797e4, value below which exp(x) underflows
+    ?:  (lth x u-threshold)  (mul tiny tiny)
+    ::  otherwise, use Taylor series
+    =/  p   .~~~1
+    =/  po  .~~~-1
+    =/  i   .~~~1
+    |-  ^-  @rq
+    ?:  (lth (abs (sub po p)) rtol)
+      p
+    $(i (add i .~~~1), p (add p (div (pow-n x i) (factorial i))), po p)
+  ::    +sin:  @rq -> @rq
+  ::
+  ::  Returns the sine of a floating-point atom.
+  ::    Examples
+  ::    > (sin .~~~1)
+  ::    .~~~0.8414709848078965066525022572525196
+  ::    > (sin .~~~2)
+  ::    .~~~0.9092974268256816953960201260866781
+  ::    > (sin pi)
+  ::    .~~~2.4143733100361875441251426417684949e-23
+  ::  Source
+  ++  sin
+    |=  x=@rq  ^-  @rq
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7fff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: sin(+inf) -> NaN
+    ?:  =(x 0xffff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: sin(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7fff.8000.0000.0000.0000.0000.0000.0000 x) 0)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: sin(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   x
+    =/  po  .~~~-2
+    =/  i   1
+    =/  term  x
+    |-  ^-  @rq
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (add i2 .~~~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +cos:  @rq -> @rq
+  ::
+  ::  Returns the cosine of a floating-point atom.
+  ::    Examples
+  ::      > (cos .~~~1)
+  ::      .~~~0.5403023058681397174009349981817251
+  ::     > (cos .~~~2)
+  ::      .~~~-0.41614683654714238699756419777191616
+  ::     > (cos pi)
+  ::      .~~~-1.0000000000000000000000021077555518
+  ::  Source
+  ++  cos
+    |=  x=@rq  ^-  @rq
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(x 0x7fff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: cos(+inf) -> NaN
+    ?:  =(x 0xffff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: cos(-inf) -> NaN
+    ::    check NaN
+    ?.  (^gte (dis 0x7fff.8000.0000.0000.0000.0000.0000.0000 x) 0)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: cos(NaN) -> NaN
+    ::  map into domain
+    =.  x  (mod x tau)
+    ::  otherwise, use Taylor series
+    =/  p   .~~~1
+    =/  po  .~~~-2
+    =/  i   1
+    =/  term  .~~~1
+    |-  ^-  @rq
+    ?.  (gth (abs term) rtol)
+      p
+    =/  i2  (add (sun i) (sun i))
+    =.  term  (mul (neg term) (div (mul x x) (mul i2 (sub i2 .~~~1))))
+    $(i +(i), p (add p term), po p)
+  ::    +tan:  @rq -> @rq
+  ::
+  ::  Returns the tangent of a floating-point atom.
+  ::    Examples
+  ::      > (tan .~~~1)
+  ::      .~~~1.5574077246549022305069793269617903
+  ::      > (tan .~~~2)
+  ::      .~~~-2.1850398632615189916433278966958165
+  ::      > (tan pi)
+  ::      .~~~-2.1850398632615189916433278966958165
+  ::  Source
+  ++  tan
+    |=  x=@rq  ^-  @rq
+    (div (sin x) (cos x))
+  ::    +pow-n:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the power of a floating-point atom to a signed integer exponent.
+  ::    Examples
+  ::      > (pow-n .~~~2 .~~~2)
+  ::      .~~~4
+  ::      > (pow-n .~~~2 .~~~-2)
+  ::      .~~~0.25
+  ::  Source
+  ++  pow-n
+    |=  [x=@rq n=@rq]  ^-  @rq
+    ?:  =(n .~~~0)  .~~~1
+    ?>  &((gth n .~~~0) (isint n))
+    =/  p  x
+    |-  ^-  @rq
+    ?:  (lth n .~~~2)
+      p
+    $(n (sub n .~~~1), p (mul p x))
+  ::    +log:  @rq -> @rq
+  ::
+  ::  Returns the natural logarithm of a floating-point atom.
+  ::    Examples
+  ::      > (log .~~~1)
+  ::      .~~~0
+  ::      > (log .~~~2)
+  ::      .~~~0.6931471805599453094170735934298606
+  ::      > (~(log rq [%z .~~~1e-5]) .~~~2)
+  ::      .~~~0.6931470737597852366942444674497712
+  ::      > (log .~~~inf)
+  ::      .~~~inf
+  ::  Source
+  ++  log
+    |=  z=@rq  ^-  @rq
+    ::  filter out non-finite arguments
+    ::    check infinities
+    ?:  =(z 0x7fff.0000.0000.0000.0000.0000.0000.0000)  `@rq`0x7fff.0000.0000.0000.0000.0000.0000.0000  :: exp(+inf) -> inf
+    ?:  =(z 0xffff.0000.0000.0000.0000.0000.0000.0000)  .~~~0.0      :: exp(-inf) -> 0
+    ::    check NaN
+    ?.  (^gte (dis 0x7fff.8000.0000.0000.0000.0000.0000.0000 z) 0)  `@rq`0x7fff.8000.0000.0000.0000.0000.0000.0000  :: exp(NaN) -> NaN
+    ::  otherwise, use Taylor series
+    =/  p   .~~~0
+    =/  po  .~~~-1
+    =/  i   .~~~0
+    |-  ^-  @rq
+    ?:  (lth (abs (sub po p)) rtol)
+      (mul (div (mul .~~~2 (sub z .~~~1)) (add z .~~~1)) p)
+    =/  term1  (div .~~~1 (add .~~~1 (mul .~~~2 i)))
+    =/  term2  (mul (sub z .~~~1) (sub z .~~~1))
+    =/  term3  (mul (add z .~~~1) (add z .~~~1))
+    =/  term  (mul term1 (pow-n (div term2 term3) i))
+    $(i (add i .~~~1), p (add p term), po p)
+  ::    +pow:  [@rq @rq] -> @rq
+  ::
+  ::  Returns the power of a floating-point atom to a floating-point exponent.
+  ::    Examples
+  ::      > (pow .~~~1 .~~~2)
+  ::      .~~~1
+  ::      > (pow .~~~2 .~~~2)
+  ::      .~~~4
+  ::      > (~(pow rq:math [%z .~~~1e-5]) .~~~2 .~~~3.5)
+  ::      .~~~11.313703735926135014164384135726204
+  ::  Source
+  ++  pow
+    |=  [x=@rq n=@rq]  ^-  @rq
+    ::  fall through on integers (faster)
+    ?:  =(n (san (need (toi n))))  (pow-n x (san (need (toi n))))
+    (exp (mul n (log x)))
+  ::    +sqrt:  @rq -> @rq
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::  Alias for +sqt.
+  ::    Examples
+  ::      > (sqrt .~~~1)
+  ::      .~~~1
+  ::      > (sqrt .~~~2)
+  ::      .~~~1.4142135623730950488015335862957159
+  ::      > (~(sqrt rq:math [%z .~~~1e-10]) .~~~2)
+  ::      .~~~1.4142135623721439870165294373250435
+  ::  Source
+  ++  sqrt  sqt
+  ::    +sqt:  @rq -> @rq
+  ::
+  ::  Returns the square root of a floating-point atom.
+  ::    Examples
+  ::      > (sqt .~~~1)
+  ::      .~~~1
+  ::      > (sqt .~~~2)
+  ::      .~~~1.4142135623730950488015335862957159
+  ::      > (~(sqt rq:math [%z .~~~1e-10]) .~~~2)
+  ::      .~~~1.4142135623721439870165294373250435
+  ::  Source
+  ++  sqt
+    |=  x=@rq  ^-  @rq
+    ?>  (sgn x)
+    (pow x .~~~0.5)
+  ::    +cbrt:  @rq -> @rq
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::  Alias for +cbt.
+  ::    Examples
+  ::      > (cbrt .~~~1)
+  ::      .~~~1
+  ::      > (cbrt .~~~2)
+  ::      .~~~1.2598919398737178526805575821133312
+  ::      > (~(cbrt rq:math [%z .~~~1e-10]) .~~~2)
+  ::      .~~~1.2598919398731638759238176665172822
+  ::  Source
+  ++  cbrt  cbt
+  ::    +cbt:  @rq -> @rq
+  ::
+  ::  Returns the cube root of a floating-point atom.
+  ::    Examples
+  ::      > (cbt .~~~1)
+  ::      .~~~1
+  ::      > (cbt .~~~2)
+  ::      .~~~1.2598919398737178526805575821133312
+  ::      > (~(cbt rq:math [%z .~~~1e-10]) .~~~2)
+  ::      .~~~1.2598919398731638759238176665172822
+  ::  Source
+  ++  cbt
+    |=  x=@rq  ^-  @rq
+    ?>  (sgn x)
+    (pow x .~~~0.3333)
+  ::    +arg:  @rq -> @rq
+  ::
+  ::  Returns the argument of a floating-point atom (real argument = absolute
+  ::  value).
+  ::    Examples
+  ::      > (arg .~~~1)
+  ::      .~~~1
+  ::      > (arg .~~~-1)
+  ::      .~~~1
+  ::  Source
+  ++  arg  abs
+  --
+::  reference values
+++  reference
+  |%
+  ::  hardcoded string constants for your viewing pleasure
+  ::  OEIS A019692
+  ++  tau   '6.28318530717958647692528676655900576839433879875021164194988918461563281257241799625606965068423413596428'
+  ::  OEIS A000796
+  ++  pi     '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214'
+  ::  OEIS A001113
+  ++  e      '2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746'
+  ::  OEIS A001622
+  ++  phi    '1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475'
+  ::  OEIS  A002193
+  ++  sqt2  '1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273'
+  ::  OEIS A010503
+  ++  invsqt2  '0.70710678118654752440084436210484903928483593768847403658833986899536623923105351942519376716382086'
+  ::  OEIS A002162
+  ++  log2    '0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754'
+  ::  OEIS A002392
+  ++  log10   '2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599726645985502929'
+  --
+--

From 7b9463111b8b1f31e183ff3d6a8f54ceef3738dc Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 15:31:39 +0100
Subject: [PATCH 15/20] Use +isclose for +test-expected-score

---
 src/tests/elo.hoon | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
index 368da0a..cf84c9f 100644
--- a/src/tests/elo.hoon
+++ b/src/tests/elo.hoon
@@ -1,34 +1,34 @@
-/+  *test, *elo
+/+  *test, *elo, math
 |%
 ++  test-expected-score
   ;:  weld
     %+  expect-eq
-      !>  .~0.500
-    !>  (expected-score 1.200 1.200)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.200 1.200) .~0.500)
     ::
     %+  expect-eq
-      !>  .~0.752
-    !>  (expected-score 1.400 1.200)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.400 1.200) .~0.752)
     ::
     %+  expect-eq
-      !>  .~0.902
-    !>  (expected-score 1.600 1.200)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.600 1.200) .~0.902)
     ::
     %+  expect-eq
-      !>  .~0.965
-    !>  (expected-score 1.800 1.200)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.800 1.200) .~0.965)
     ::
     %+  expect-eq
-      !>  .~0.248
-    !>  (expected-score 1.200 1.400)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.200 1.400) .~0.248)
     ::
     %+  expect-eq
-      !>  .~0.098
-    !>  (expected-score 1.200 1.600)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.200 1.600) .~0.098)
     ::
     %+  expect-eq
-      !>  .~0.035
-    !>  (expected-score 1.200 1.800)
+      !>  %.y
+    !>  (~(isclose rd:math [%z .~1e-3]) (expected-score 1.200 1.800) .~0.035)
   ==
 ::
 ++  test-scaling-factor

From 538568ca677532fc056f20d0fa105059e6419711 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 15:32:19 +0100
Subject: [PATCH 16/20] Space out +test-scaling-factor

---
 src/tests/elo.hoon | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/tests/elo.hoon b/src/tests/elo.hoon
index cf84c9f..56d16c9 100644
--- a/src/tests/elo.hoon
+++ b/src/tests/elo.hoon
@@ -36,9 +36,11 @@
     %+  expect-eq
       !>  40
     !>  (scaling-factor 20)
+    ::
     %+  expect-eq
       !>  32
     !>  (scaling-factor 40)
+    ::
     %+  expect-eq
       !>  24
     !>  (scaling-factor 75)

From ba2c450bb36e0eb14b149388bd25dd0b8c8846ce Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 15:52:35 +0100
Subject: [PATCH 17/20] Draft scries for performance ratings

---
 src/app/telos.hoon |  4 ++--
 src/lib/telos.hoon | 50 ++++++++++++++++++++++++++++++++++++----------
 2 files changed, 42 insertions(+), 12 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index 903ea13..7584ede 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -326,7 +326,7 @@
               ratings  (~(put by ratings) [game.action ~])
             ==
           =/  new-ratings
-            (compute-ratings-game (flop (~(got by archive) game.action)))
+            (compute-ratings-game game.action (flop (~(got by archive) game.action)))
           =/  new-ratings-list
             ~(tap by new-ratings)
           :_  %=  this
@@ -606,7 +606,7 @@
               ==
             ::
             =/  new-ratings
-              (update-elo-ratings (~(got by ratings) game) (~(got by archive) game) winner loser draw)
+              (update-elo-ratings game (~(got by ratings) game) (~(got by archive) game) winner loser draw)
             ::
             =/  winner-new-data
               (~(got by new-ratings) winner)
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 4881990..07dd45b 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -106,7 +106,7 @@
   =(rank (clan:title player))
 ::
 ++  compute-ratings-game
-  |=  matches=(list match)
+  |=  [=game matches=(list match)]
   ^-  (map player rating)
   =/  player-ratings  `(map player rating)`~
   |-
@@ -115,6 +115,7 @@
   %=  $
     matches         (tail matches)
     player-ratings  %:  update-elo-ratings
+                        game
                         player-ratings
                         matches
                         winner:(head matches)
@@ -196,6 +197,13 @@
   ^-  ?
   =(player loser.match)
 ::
+++  find-opponent-in-match
+  |=  [our=ship =match]
+  ^-  ship
+  ?:  =(our winner.match)
+    loser.match
+  winner.match
+::
 ++  has-player-in-ratings
   |=  [[game ratings=(map player rating)] player=@]
   ^-  ?
@@ -205,7 +213,7 @@
 ::
 ++  update-elo-ratings
   ::  XX matches should include the match just played
-  |=  [players=(map player rating) matches=(list match) =winner =loser draw=?]
+  |=  [=game players=(map player rating) matches=(list match) =winner =loser draw=?]
   ^+  players
   =/  new-winner-elo=rating
     =/  our-rating
@@ -222,12 +230,21 @@
     ::
     ?:  (lth (lent our-matches) 10)
       %:  new-performance-rating:elo
-          ::  XX sum up opps' ratings from previous games
-          ::       would need to know what the opponents'
-          ::       ratings were at the time of the match.
-          ::       could change id.match to @da and scry
-          ::       for the rating at that case.
-          (~(gut by players) loser 1.500)
+            ::  sum opponents' ratings
+            %+  roll
+              our-matches
+            |=  [=match sum=@ud]
+            ^+  sum
+            %+  add
+              sum
+            %-  need
+            .^  (unit rating)
+                %gx
+                /=telos
+                /(scot %da date.match)
+                /[game]
+                /(scot %p (find-opponent-in-match winner match))
+            ==
           (lent our-matches)
           (lent (skim our-matches |=(=match (has-winner-in-match match winner))))
           (lent (skim our-matches |=(=match (has-loser-in-match match winner))))
@@ -253,8 +270,21 @@
     ::
     ?:  (lth (lent our-matches) 10)
       %:  new-performance-rating:elo
-          ::  XX sum up opps' ratings from previous games
-          (~(gut by players) loser 1.500)
+          ::  sum opponents' ratings
+            %+  roll
+              our-matches
+            |=  [=match sum=@ud]
+            ^+  sum
+            %+  add
+              sum
+            %-  need
+            .^  (unit rating)
+                %gx
+                /=telos
+                /(scot %da date.match)
+                /[game]
+                /(scot %p (find-opponent-in-match loser match))
+            ==
           (lent our-matches)
           (lent (skim our-matches |=(=match (has-winner-in-match match loser))))
           (lent (skim our-matches |=(=match (has-loser-in-match match loser))))

From 8125950d561634e821880ec80999f6f1860baa87 Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 16:19:31 +0100
Subject: [PATCH 18/20] Reduce +update-elo-rating to handle one player

---
 src/app/telos.hoon |  28 ++++++--
 src/lib/telos.hoon | 157 +++++++++++++++++++--------------------------
 2 files changed, 88 insertions(+), 97 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index 7584ede..b4aeff7 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -605,14 +605,32 @@
                   our.bowl
               ==
             ::
-            =/  new-ratings
-              (update-elo-ratings game (~(got by ratings) game) (~(got by archive) game) winner loser draw)
+            =/  new-game-ratings
+              %-  %~  put  by
+                %-  %~  put  by
+                  (~(got by ratings) game)
+                :-  loser
+                %:  update-elo-rating
+                    game
+                    draw
+                    loser
+                    (~(got by ratings) game)
+                    (~(got by archive) game)
+                ==
+              :-  winner
+              %:  update-elo-rating
+                  game
+                  draw
+                  winner
+                  (~(got by ratings) game)
+                  (~(got by archive) game)
+              ==
             ::
             =/  winner-new-data
-              (~(got by new-ratings) winner)
+              (~(got by new-game-ratings) winner)
             ::
             =/  loser-new-data
-              (~(got by new-ratings) loser)
+              (~(got by new-game-ratings) loser)
             ::
             ::  confirm results
             :-  :~  ::  update players with their new ratings
@@ -643,7 +661,7 @@
                     ==
                 ==
             %=  this
-              ratings  (~(put by ratings) game new-ratings)
+              ratings  (~(put by ratings) game new-game-ratings)
               archive  (~(put by archive) game :-(new-match (~(got by archive) game)))
             ==
           ::
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 07dd45b..4f220e3 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -108,20 +108,33 @@
 ++  compute-ratings-game
   |=  [=game matches=(list match)]
   ^-  (map player rating)
-  =/  player-ratings  `(map player rating)`~
+  =/  player-ratings
+    *(map player rating)
   |-
   ?~  matches
     player-ratings
   %=  $
     matches         (tail matches)
-    player-ratings  %:  update-elo-ratings
+    player-ratings  %-  %~  put  by
+                      %-  %~  put  by
+                        player-ratings
+                      :-  loser:(head matches)
+                      %:  update-elo-rating
+                          game
+                          draw:(head matches)
+                          loser:(head matches)
+                          player-ratings
+                          matches
+                      ==
+                    :-  winner:(head matches)
+                    %:  update-elo-rating
                         game
+                        draw:(head matches)
+                        winner:(head matches)
                         player-ratings
                         matches
-                        winner:(head matches)
-                        loser:(head matches)
-                        draw:(head matches)
-  ==                ==
+                    ==
+  ==
 +|  %kick-helpers
 ::
 ++  kick-game-players
@@ -211,93 +224,53 @@
 ::
 +|  %ratings
 ::
-++  update-elo-ratings
+++  update-elo-rating
+  |=  [=game draw=? our=ship players=(map player rating) matches=(list match)]
+  ^-  rating
   ::  XX matches should include the match just played
-  |=  [=game players=(map player rating) matches=(list match) =winner =loser draw=?]
-  ^+  players
-  =/  new-winner-elo=rating
-    =/  our-rating
-      (~(gut by players) winner 1.500)
-    =/  opp-rating
-      (~(gut by players) loser 1.500)
-    =/  our-matches
-      (skim matches |=(=match (has-player-in-match match winner)))
-    =/  our-outcome
-      ::  XX assuming (head matches) is most recent match
-      ?.  draw:(head matches)
-        %win
-      %draw
-    ::
-    ?:  (lth (lent our-matches) 10)
-      %:  new-performance-rating:elo
-            ::  sum opponents' ratings
-            %+  roll
-              our-matches
-            |=  [=match sum=@ud]
-            ^+  sum
-            %+  add
-              sum
-            %-  need
-            .^  (unit rating)
-                %gx
-                /=telos
-                /(scot %da date.match)
-                /[game]
-                /(scot %p (find-opponent-in-match winner match))
-            ==
-          (lent our-matches)
-          (lent (skim our-matches |=(=match (has-winner-in-match match winner))))
-          (lent (skim our-matches |=(=match (has-loser-in-match match winner))))
-      ==
-    %:  new-rating:elo
-        our-rating
-        (expected-score:elo our-rating opp-rating)
-        (scaling-factor:elo (lent our-matches))
-        our-outcome
-    ==
-  =/  new-loser-elo=rating
-    =/  our-rating
-      (~(gut by players) loser 1.500)
-    =/  opp-rating
-      (~(gut by players) winner 1.500)
-    =/  our-matches
-      (skim matches |=(=match (has-player-in-match match loser)))
-    =/  our-outcome
-      ::  XX assuming (head matches) is most recent match
-      ?.  draw:(head matches)
-        %loss
+  ::  XX assuming (head matches) is most recent match
+  =/  this-match
+    (head matches)
+  =/  opp
+    (find-opponent-in-match our this-match)
+  =/  our-rating
+    (~(gut by players) our 1.500)
+  =/  opp-rating
+    (~(gut by players) opp 1.500)
+  =/  our-matches
+    (skim matches |=(=match (has-player-in-match match our)))
+  =/  our-outcome
+    ?:  draw:this-match
       %draw
-    ::
-    ?:  (lth (lent our-matches) 10)
-      %:  new-performance-rating:elo
-          ::  sum opponents' ratings
-            %+  roll
-              our-matches
-            |=  [=match sum=@ud]
-            ^+  sum
-            %+  add
-              sum
-            %-  need
-            .^  (unit rating)
-                %gx
-                /=telos
-                /(scot %da date.match)
-                /[game]
-                /(scot %p (find-opponent-in-match loser match))
-            ==
-          (lent our-matches)
-          (lent (skim our-matches |=(=match (has-winner-in-match match loser))))
-          (lent (skim our-matches |=(=match (has-loser-in-match match loser))))
-      ==
-    %:  new-rating:elo
-        our-rating
-        (expected-score:elo our-rating opp-rating)
-        (scaling-factor:elo (lent our-matches))
-        our-outcome
+    ?:  =(our winner:this-match)
+      %win
+    %loss
+  ::
+  ?:  (lth (lent our-matches) 10)
+    %:  new-performance-rating:elo
+          ::  sum all opponents' ratings
+          %+  roll
+            our-matches
+          |=  [=match sum=@ud]
+          ^+  sum
+          %+  add
+            sum
+          %-  need
+          .^  (unit rating)
+              %gx
+              /=telos
+              /(scot %da date.match)
+              /[game]
+              /(scot %p (find-opponent-in-match our match))
+          ==
+        (lent our-matches)
+        (lent (skim our-matches |=(=match (has-winner-in-match match our))))
+        (lent (skim our-matches |=(=match (has-loser-in-match match our))))
     ==
-  %-  %~  put  by
-    %-  %~  put  by
-      players
-    [loser new-loser-elo]
-  [winner new-winner-elo]
+  %:  new-rating:elo
+      our-rating
+      (expected-score:elo our-rating opp-rating)
+      (scaling-factor:elo (lent our-matches))
+      our-outcome
+  ==
 --

From fcb8536c420782e1ca5300ce456b0b60cf2be3fc Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 16:24:47 +0100
Subject: [PATCH 19/20] Send latest match to +update-elo-rating

---
 src/app/telos.hoon | 4 ++--
 src/lib/telos.hoon | 2 --
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/src/app/telos.hoon b/src/app/telos.hoon
index b4aeff7..2d13ca2 100644
--- a/src/app/telos.hoon
+++ b/src/app/telos.hoon
@@ -615,7 +615,7 @@
                     draw
                     loser
                     (~(got by ratings) game)
-                    (~(got by archive) game)
+                    :-(new-match (~(got by archive) game))
                 ==
               :-  winner
               %:  update-elo-rating
@@ -623,7 +623,7 @@
                   draw
                   winner
                   (~(got by ratings) game)
-                  (~(got by archive) game)
+                  :-(new-match (~(got by archive) game))
               ==
             ::
             =/  winner-new-data
diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index 4f220e3..e972fda 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -227,8 +227,6 @@
 ++  update-elo-rating
   |=  [=game draw=? our=ship players=(map player rating) matches=(list match)]
   ^-  rating
-  ::  XX matches should include the match just played
-  ::  XX assuming (head matches) is most recent match
   =/  this-match
     (head matches)
   =/  opp

From 0046718fc3c37962164dfc9d62790b76c6648aae Mon Sep 17 00:00:00 2001
From: bonbud-macryg <oarsman_phlox.0s@icloud.com>
Date: Sun, 7 Apr 2024 17:54:46 +0100
Subject: [PATCH 20/20] Handle unrated players for +new-performance-rating

---
 src/lib/telos.hoon | 19 +++++++++++--------
 1 file changed, 11 insertions(+), 8 deletions(-)

diff --git a/src/lib/telos.hoon b/src/lib/telos.hoon
index e972fda..2753106 100644
--- a/src/lib/telos.hoon
+++ b/src/lib/telos.hoon
@@ -251,16 +251,19 @@
             our-matches
           |=  [=match sum=@ud]
           ^+  sum
+          =/  opp-rating
+            .^  (unit rating)
+                %gx
+                /=telos
+                /(scot %da date.match)
+                /[game]
+                /(scot %p (find-opponent-in-match our match))
+            ==
           %+  add
             sum
-          %-  need
-          .^  (unit rating)
-              %gx
-              /=telos
-              /(scot %da date.match)
-              /[game]
-              /(scot %p (find-opponent-in-match our match))
-          ==
+          ?~  opp-rating
+            1.500
+          (need opp-rating)
         (lent our-matches)
         (lent (skim our-matches |=(=match (has-winner-in-match match our))))
         (lent (skim our-matches |=(=match (has-loser-in-match match our))))