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(*---------------------------------------------------------------------------
Copyright (c) 2017 Daniel C. Bünzli. All rights reserved.
Distributed under the ISC license, see terms at the end of the file.
%%NAME%% %%VERSION%%
---------------------------------------------------------------------------*)
open Gg
open Vg
open React
open Useri
(* The full source of the Gest module is below.
To compile and run the js_of_ocaml gesticulating square demo
from the blog post on your machine, issues the following commands.
# Install these packages in a switch with OCaml >= 4.03
opam install webbrowser js_of_ocaml logs fmt mtime react gg vg
opam pin add useri https://github.com/dbuenzli/useri.git
# Compile to javascript
cd /tmp
curl -O http://erratique.ch/log/2017-01-25/gest.ml
echo \
"let _ = Ocamlbuild_plugin.dispatch Ocamlbuild_js_of_ocaml.dispatcher" > \
myocamlbuild.ml
ocamlbuild -use-ocamlfind -classic-display \
-plugin-tag "package(js_of_ocaml.ocamlbuild)" \
-pkgs fmt,logs,logs.browser,mtime.jsoo,react,gg \
-pkgs vg,vg.htmlc,useri,useri.jsoo \
gest.js
# Generate the html page
base64 --decode > _build/gest.html <<HTML
PCFET0NUWVBFIGh0bWw+CjwhLS0KICAgQ29weXJpZ2h0IChjKSAyMDE3IERhbmllbCBDLiBCw7xuem
xpLiBBbGwgcmlnaHRzIHJlc2VydmVkLgogICBEaXN0cmlidXRlZCB1bmRlciB0aGUgSVNDIGxpY2Vu
c2UuCiAgLS0+CjxodG1sIGxhbmc9ImVuIj4KPGhlYWQ+CiAgPG1ldGEgY2hhcnNldD0idXRmLTgiPg
ogIDxtZXRhIG5hbWU9InZpZXdwb3J0IiBjb250ZW50PSJ3aWR0aD1kZXZpY2Utd2lkdGgsaW5pdGlh
bC1zY2FsZT0xLjAiPgogIDxzY3JpcHQgdHlwZT0idGV4dC9qYXZhc2NyaXB0IiBkZWZlcj0iZGVmZX
IiIHNyYz0iZ2VzdC5qcyI+PC9zY3JpcHQ+CiAgPHN0eWxlIHR5cGU9InRleHQvY3NzIj4KICAgICos
ICo6YmVmb3JlLCAqOmFmdGVyIHsgYm94LXNpemluZzogYm9yZGVyLWJveDsgbWFyZ2luOjA7IHBhZG
Rpbmc6MDt9CiAgICBodG1sLCBib2R5IHsgd2lkdGg6MTAwJTsgaGVpZ2h0OjEwMCU7IH0KICAgIGJv
ZHkgeyBiYWNrZ3JvdW5kLWNvbG9yOiBibGFjazsgY29sb3I6ICM5OTk7IHBhZGRpbmc6IDNyZW07Ci
AgICAgICAgICAgZm9udDogbm9ybWFsIDAuNzVyZW0gc2Fucy1zZXJpZjsgfQogICAgcCB7IGZvbnQt
c3R5bGU6IGl0YWxpYzsgcGFkZGluZy10b3A6IDAuMjVyZW07IH0KICAgIGgxIHsgZm9udC13ZWlnaH
Q6bm9ybWFsOyBmb250LXNpemU6MnJlbTsgdGV4dC10cmFuc2Zvcm06IHVwcGVyY2FzZTsgfQogICAg
aDEgKyAqIHsgbWFyZ2luLXRvcDogMS4yNWVtIH0KICAgIC5zaXplciB7IHBvc2l0aW9uOiByZWxhdG
l2ZTsgd2lkdGg6MTAwJTsgfQogICAgLnNpemVyOmFmdGVyIHsgcGFkZGluZy1ib3R0b206NTAlOyAv
KiAxL2FzcGVjdCAqLyB9CiAgICBjYW52YXMgeyB3aWR0aDoxMDAlOyBoZWlnaHQ6MTAwJTsgb3V0bG
luZTogMXB4IHNvbGlkICMzMzM7fQogIDwvc3R5bGU+CiAgPHRpdGxlPkdlc3RpY3VsYXRpbmcgc3F1
YXJlPC90aXRsZT4KPC9oZWFkPgo8Ym9keT4KICA8bm9zY3JpcHQ+U29ycnksIHlvdSBuZWVkIHRvIG
VuYWJsZSBKYXZhU2NyaXB0IHRvIHNlZSB0aGlzIHBhZ2UuPC9ub3NjcmlwdD4KICA8aDE+R2VzdGlj
dWxhdGluZyBzcXVhcmU8L2gxPgogIDxkaXYgY2xhc3M9InNpemVyIj48ZGl2PjxjYW52YXMgaWQ9Im
dlc3QiIHRhYmluZGV4PSIxIj48L2NhbnZhcz4KICAgPHA+VGFwIGFuZCBkcmFnIHRvIGlucHV0IHN0
cm9rZXMuIFVzZSBiYWNrc3BhY2Ugb3IgZG91YmxlLXRhcCB0byBjbGVhcgogICAgICB0aGUgZ2VzdH
VyZS48L3A+CiAgPC9kaXY+PC9kaXY+CjwvYm9keT4KPC9odG1sPgo=
HTML
# Open it in your browser
browse _build/gest.html
*)
(* [Gest] implements the gesture recognizer described in:
R. Vatavu et al. Gestures as point clouds: a $P recognizer for user
interface prototypes. ICMI'2012.
https://doi.org/10.1145/2388676.2388732 *)
module Gest : sig
type stroke = p2 list
type t (* Gestures *)
val of_strokes : stroke list -> t
val to_pts : t -> p2 array
val n : int
type 'a reco (* Recognizers for symbols of type ['a] *)
val empty_reco : 'a reco
val add_sym : t -> 'a -> 'a reco -> 'a reco
val sym_gests : 'a reco -> 'a -> t list
val recognize : 'a reco -> t -> 'a option * float (* score *)
end = struct
type stroke = p2 list
let n = 32
let n_float = float n
type t = p2 array (* of length [n] *)
let to_pts g = g
let stroke_len : stroke -> float =
fun ps ->
let rec loop l prev = function
| [] -> l
| p :: ps -> loop (l +. V2.(norm @@ p - prev)) p ps
in
if ps = [] then 0. else loop 0. (List.hd ps) (List.tl ps)
let resample : stroke list -> t =
fun ss ->
let rec massage len acc = function
| [] :: ss -> massage len acc ss
| [tap] :: ss -> massage len acc ss
| s :: ss -> massage (len +. stroke_len s) (s :: acc) ss
| [] -> len, acc
in
let len, ss = massage 0. [] ss in
let ival = len /. (n_float -. 1.) in
let first = match ss with (p :: _) :: _ -> p | _ -> P2.o in
let g = Array.make n first in
let rec loop d last ss i =
if i >= n then g else
match ss with
| [] -> g
| [] :: (p :: ps) :: ss -> (* start *) loop 0. p (ps :: ss) i
| [] :: ss -> (* end *) loop 0. last ss i
| (p :: ps) :: ss' ->
let walk = V2.(p - last) in
let dist = V2.norm walk in
let d' = d +. dist in
match d' < ival with
| true -> loop d' p (ps :: ss') i
| false ->
let t = (ival -. d) /. dist in
let q = V2.(last + t * walk) in
g.(i) <- q; loop 0. q ss (i + 1)
in
loop 0. first ss 1
let to_unit_square : t -> unit =
fun g ->
let pmin, max_extent =
let rec loop xmin xmax ymin ymax g i = match i < n with
| false ->
(P2.v xmin ymin), max (xmax -. xmin) (ymax -. ymin)
| true ->
let px, py = P2.x g.(i), P2.y g.(i) in
loop (min xmin px) (max xmax px)
(min ymin py) (max ymax py) g (i + 1)
in
loop infinity neg_infinity infinity neg_infinity g 0
in
if max_extent = 0. then () (* avoid degen div by zero *) else
let rescale = 1. /. max_extent in
let rescale p = V2.(rescale * (p - pmin)) in
Array.iteri (fun i p -> g.(i) <- rescale p) g
let centroid : t -> P2.t =
fun g ->
let rec loop cx cy g i = match i < n with
| false -> V2.v (cx /. n_float) (cy /. n_float)
| true ->
let p = g.(i) in
loop (cx +. V2.x p) (cy +. V2.y p) g (i + 1)
in
loop 0. 0. g 0
let center : t -> unit =
fun g ->
let c = centroid g in
Array.iteri (fun i p -> g.(i) <- V2.(p - c)) g
let of_strokes : stroke list -> t =
fun ss ->
let g = resample ss in
(to_unit_square g; center g; g)
let gest_dist_at : start:int -> t -> t -> float =
fun ~start g t -> (* distance by starting at [start] in [g]. *)
let matched = Array.make n false in
let match_dmin p t = (* unmatched closest to [p] in [t]. *)
let rec loop dmin_idx dmin k = match k < n with
| false -> dmin_idx, dmin
| true ->
let next = k + 1 in
if matched.(k) then loop dmin_idx dmin next else
let d = V2.(norm @@ p - t.(k)) in
match d < dmin with
| true -> loop k d next
| false -> loop dmin_idx dmin next
in
let dmin_idx, dmin = loop (-1) infinity 0 in
(matched.(dmin_idx) <- true; dmin)
in
let rec loop sum i =
let dmin = match_dmin g.(i) t in
let w = 1. -. (float @@ (i - start + n) mod n) /. n_float in
let sum = sum +. w *. dmin in
let next = (i + 1) mod n in
if next = start then sum else loop sum next
in
loop 0. start
let gest_dist : t -> t -> float =
let eps = 0.5 in
let step = truncate (n_float ** (1. -. eps)) in
fun g t ->
let rec loop dmin i = match i < n with
| false -> dmin
| true ->
let d0 = gest_dist_at ~start:i g t in
let d1 = gest_dist_at ~start:i t g in
loop (min d0 d1) (i + step)
in
loop infinity 0
(* Recognizers *)
type 'a reco = (t * 'a) list
let empty_reco = []
let add_sym g sym r = (g, sym) :: r
let sym_gests r sym =
List.(map fst @@ find_all (fun (_, sym') -> sym = sym') r)
let recognize : 'a reco -> t -> 'a option * float =
fun r g ->
let score dmin = max (0.5 *. (2. -. dmin)) 0. in
let rec loop fnd dmin = function
| [] -> fnd, score dmin
| (t, sym) :: ts ->
let d = gest_dist g t in
match d < dmin with
| true -> loop (Some sym) d ts
| false -> loop fnd dmin ts
in
loop None infinity r
end
(* Gesticulating square demo *)
type strokes = Gest.stroke list
type sym = string * int
type templates = (string * Gest.stroke list list) list
(* Rendering *)
let unit_to_rect : aspect:bool -> box2 -> image -> image =
fun ~aspect rect img ->
(* maps the unit square of [img] to rect. *)
let scale = match aspect with
| false -> Box2.size rect
| true ->
let aspect = Size2.aspect @@ Box2.size rect in
match aspect < 1. with
| true -> Size2.of_h (Box2.h rect) ~aspect
| false -> Size2.of_w (Box2.w rect) ~aspect
in
img >> I.scale scale >> I.move (Box2.o rect)
let cell : num:int -> image -> image =
(* maps the unit square to the cell [num] of a 4x4 grid in the unit square *)
let d = 1. /. 4. in
let cell_scale = I.scale @@ V2.v d d in
let crop_unit = I.cut P.(empty >> rect Box2.unit) in
fun ~num img ->
let o = V2.v (d *. (float @@ num mod 4)) (d *. (float @@ num / 4)) in
img >> crop_unit >> cell_scale >> I.move o
let dot : width:float -> color:color -> image =
fun ~width ~color ->
let size = Size2.v width width in
let square = P.empty >> P.rect (Box2.v_mid P2.o size) in
I.const color >> I.cut square
let gest_image : dot:image -> Gest.t -> image =
(* gesture fitted to a unit square with centroid at the center *)
let inv_max_r = 1. /. ((float (Gest.n - 1) /. float Gest.n) *. sqrt 2.) in
let scale = I.scale (Size2.v inv_max_r inv_max_r) in
let center = I.move (V2.v 0.5 0.5) in
fun ~dot g ->
let mark_pt acc pt = acc >> I.blend (dot >> I.move pt) in
let pts = Array.fold_left mark_pt I.void (Gest.to_pts g) in
pts >> scale >> center
let sym_image : dot:image -> sym Gest.reco -> sym -> image =
fun ~dot reco (_, num as sym) ->
let add_gest acc g = acc >> I.blend @@ gest_image ~dot g in
cell ~num @@ List.fold_left add_gest I.void (Gest.sym_gests reco sym)
let orange = Color.v_srgbi 0xFF 0xB9 0x58
let blue = Color.v_srgbi 0x40 0x77 0xA5
let green = Color.v_srgbi 0x3C 0xAE 0x80
let sym_images : sym Gest.reco -> sym list -> image =
let dot = dot ~width:0.02 ~color:orange in
fun reco syms ->
let add_sym acc sym = acc >> I.blend @@ sym_image reco ~dot sym in
List.fold_left add_sym I.void syms
let reco_sym_image : sym Gest.reco -> sym option * float -> image =
let dot = dot ~width:0.04 ~color:blue in
fun reco result -> match result with
| None, _ | Some _, 0.0 -> I.void
| Some sym, _ -> sym_image ~dot reco sym
let input_gest_image : Gest.t -> image =
let dot = dot ~width:0.04 ~color:green in
fun g -> cell ~num:0 @@ gest_image ~dot g
let reco_image bounds sym_images reco_sym_image input_gest_image =
unit_to_rect ~aspect:true bounds @@
(sym_images >> I.blend reco_sym_image >> I.blend input_gest_image)
let strokes_image : strokes -> image = (* strokes as line paths *)
fun strokes ->
let add_stroke path = function
| [] | [_] -> path
| pt :: pts ->
let line path pt = path >> P.line pt in
List.fold_left line (P.sub pt path) pts
in
let path = List.fold_left add_stroke P.empty strokes in
let area = `O { P.o with P.width = 0.02; cap = `Round; join = `Round } in
I.const green >> I.cut ~area path
let input_strokes_image : box2 -> strokes -> bool -> image =
fun bounds strokes focus ->
let back = I.const @@ Color.gray (if focus then 0.1 else 0.05) in
let strokes = strokes_image strokes in
let crop = I.cut (P.empty >> P.rect bounds) in
back >> I.blend strokes >> crop
(* Input *)
let strokes :
reset:'a event -> active:bool signal -> ptr:p2 signal -> strokes signal =
fun ~reset ~active ~ptr ->
let max_pt_count = 2000 in
let init = 0, [] :: [] in
let input_ev =
let reset = E.stamp reset `Reset in
let close = E.stamp (S.Bool.rise active) `Close in
let pt = S.(changes @@ on ~eq:V2.equal active P2.o ptr) in
let add = E.map (fun pt -> `Add pt) pt in
E.select [ reset; close; add ]
in
let gather op (count, ss as acc) = match op with
| `Reset -> init
| `Close -> if List.hd ss = [] then acc else (count, [] :: ss)
| `Add pt ->
match count < max_pt_count with
| false -> acc
| true -> (count + 1, (pt :: List.hd ss) :: List.tl ss)
in
S.Pair.snd (S.accum (E.map gather input_ev) init)
let double_tap : p2 event -> p2 event =
fun tap ->
let tap_diff pos = function
| None -> Some (Mtime.counter (), pos, false)
| Some (c, last, _) ->
let dt = Mtime.(to_ms @@ count c) in
let dp = V2.(pos - last) in
let is_double = dt <= 250. && V2.norm dp < 0.1 in
Some (Mtime.counter (), pos, is_double)
in
let is_double = function Some (_, pt, true) -> Some pt | _ -> None in
E.fmap is_double (E.accum (E.map tap_diff tap) None)
let input_mouse_strokes :
Size2.t signal -> Box2.t signal -> (strokes signal * bool signal) =
fun scale bounds ->
let ptr = S.l2 V2.mul scale Mouse.pos in
let hover = S.l2 Box2.mem ptr bounds in
let active = S.Bool.(Mouse.left && hover) in
let double_tap = E.stamp (double_tap Mouse.left_down) () in
let reset = E.select [ Key.down `Backspace; double_tap ] in
strokes ~reset ~active ~ptr, hover
let input_touch_strokes :
Size2.t signal -> Box2.t signal -> (strokes signal * bool signal) =
fun scale bounds ->
let touch = E.map (fun l -> List.hd l) Touch.start in
let start_pos =
E.switch E.never @@
E.map (fun t -> S.sample (fun _ pos -> pos) touch (Touch.pos t)) touch
in
let over = E.switch E.never @@ E.map (fun t -> Touch.over t) touch in
let start = E.stamp start_pos true in
let stop = E.stamp over false in
let touching = S.hold false (E.select [start; stop]) in
let poss = S.hold (S.const P2.o) (E.map (fun t -> Touch.pos t) touch) in
let ptr = S.l2 V2.mul scale (S.switch poss) in
let hover = S.l2 Box2.mem ptr bounds in
let active = S.Bool.(touching && hover) in
let double_tap = E.stamp (double_tap start_pos) () in
let reset = E.select [ Key.down `Backspace; double_tap ] in
strokes ~reset ~active ~ptr, hover
let input_strokes :
float signal -> Box2.t signal -> (strokes signal * bool signal) =
fun aspect bounds ->
let scale = S.map (fun a -> V2.v a 1.) aspect in
let tstrokes, thover = input_touch_strokes scale bounds in
let mstrokes, mhover = input_mouse_strokes scale bounds in
S.l2 ~eq:(==) List.rev_append tstrokes mstrokes, S.Bool.(thover || mhover)
let strokes_dumper : strokes signal -> unit event =
fun strokes ->
let dump_pt ppf pt = Fmt.pf ppf "P2.v %h %h" (P2.x pt) (P2.y pt) in
let dump_stroke = Fmt.Dump.list dump_pt in
let dump_strokes = Fmt.Dump.list dump_stroke in
let dump _ strokes = Logs.app (fun m -> m "%a" dump_strokes strokes) in
let onkey = Key.down (`Uchar (Uchar.of_char 'd')) in
S.sample dump onkey strokes
(* Compose input and rendering *)
let reco_of_templates : templates -> sym Gest.reco * sym list =
fun templates ->
let add_sym (reco, syms, num) (label, ts) =
let sym = label, num in
let add_template reco ss = Gest.add_sym (Gest.of_strokes ss) sym reco in
let reco = List.fold_left add_template reco ts in
reco, sym :: syms, num + 1
in
let init = Gest.empty_reco, [], 1 in
let reco, syms, _ = List.fold_left add_sym init templates in
reco, List.rev syms
let reco_ui : box2 signal -> templates -> strokes signal -> image signal =
fun bounds templates input_strokes ->
let reco, syms = reco_of_templates templates in
let sym_images = sym_images reco syms in
let input_gest = S.map Gest.of_strokes input_strokes in
let input_gest_image = S.l1 ~eq:(==) input_gest_image input_gest in
let reco_sym = S.map (Gest.recognize reco) input_gest in
let reco_sym_image = S.l1 ~eq:(==) (reco_sym_image reco) reco_sym in
S.l4 ~eq:(==) reco_image
bounds (S.const sym_images) input_gest_image reco_sym_image
let input_ui : box2 signal -> strokes signal -> bool signal -> image signal =
fun focus bounds strokes ->
S.l3 ~eq:(==) input_strokes_image focus bounds strokes
let ui_geometry : float signal -> box2 signal * box2 signal * box2 signal =
fun aspect ->
let size a = Size2.v a 1. in
let half_size a = Size2.v (0.5 *. a) 1. in
let inset r = Box2.inset (V2.v 0.025 0.025) r in
let view a = Box2.v P2.o (size a) in
let left a = inset (Box2.v P2.o (half_size a)) in
let right a = inset (Box2.v (P2.v (0.5 *. a) 0.) (half_size a)) in
S.map view aspect, S.map left aspect, S.map right aspect
let ui : templates -> float signal -> Vgr.renderable signal * unit event =
fun templates aspect ->
let view, input_bounds, reco_bounds = ui_geometry aspect in
let strokes, focus = input_strokes aspect input_bounds in
let input_ui = input_ui input_bounds strokes focus in
let reco_ui = reco_ui reco_bounds templates strokes in
let dumper = strokes_dumper strokes in
let renderable view l r = Size2.unit, view, I.blend l r in
let renderable = S.l3 ~eq:(==) renderable view input_ui reco_ui in
renderable, dumper
(* Setup bureaucracy *)
let setup : Dom_html.canvasElement Js.t -> templates -> unit =
fun canvas templates ->
let aspect = S.map Size2.aspect Surface.size in
let renderable, dumper = ui templates aspect in
let r = Vgr.create (Vgr_htmlc.target ~resize:false canvas) `Other in
let render _ renderable = ignore (Vgr.render r (`Image renderable)) in
let render = S.sample render Surface.refresh renderable in
App.sink_event dumper;
App.sink_event render;
Surface.set_refresher (S.changes renderable);
Surface.(set_mode_setter @@ mode_flip (Key.up (`Uchar (Uchar.of_char 'f'))));
Useri_jsoo.Key.set_key_capture (fun k -> k = `Backspace);
()
let main : templates -> unit =
fun templates ->
Logs.set_reporter @@ Logs_browser.console_reporter ();
let c = Dom_html.(CoerceTo.canvas @@ getElementById "gest") in
match Js.Opt.to_option c with
| None -> Logs.err (fun m -> m "Missing canvas with 'gest' id."); exit 1
| Some c ->
let handle = Useri_jsoo.Surface.Handle.of_js c in
let surface = Surface.create ~handle ~kind:`Other () in
match App.init ~surface () with
| Error (`Msg e) -> Logs.err (fun m -> m "%s" e); exit 1
| Ok () -> setup c templates; App.run ()
let () = main
(* Each symbol has four gesture templates two were made with the mouse at
different scales. The two other were made at the same scale either with
the finger for single strokes or a stylet for multi-strokes (for technical
reasons). *)
[ "", [
[[P2.v 0x1.23f95b0bbc27p-1 0x1.1b82fc75cfd2bp-1;
P2.v 0x1.251d5058f5ea9p-1 0x1.1b82fc75cfd2bp-1;
P2.v 0x1.264145a62fae4p-1 0x1.1b82fc75cfd2bp-1;
P2.v 0x1.28893040a3358p-1 0x1.1a5f0728960fp-1;
P2.v 0x1.2ad11adb16bcdp-1 0x1.1a5f0728960fp-1;
P2.v 0x1.2ad11adb16bcdp-1 0x1.193b11db5c4b6p-1;
P2.v 0x1.2bf5102850807p-1 0x1.193b11db5c4b6p-1;
P2.v 0x1.2d1905758a441p-1 0x1.193b11db5c4b6p-1;
P2.v 0x1.2e3cfac2c407bp-1 0x1.18171c8e2287cp-1;
P2.v 0x1.2f60f00ffdcb6p-1 0x1.18171c8e2287cp-1;
P2.v 0x1.3084e55d378fp-1 0x1.18171c8e2287cp-1;
P2.v 0x1.32cccff7ab164p-1 0x1.15cf31f3af008p-1;
P2.v 0x1.32cccff7ab164p-1 0x1.14ab3ca6753cep-1;
P2.v 0x1.33f0c544e4d9fp-1 0x1.138747593b794p-1;
P2.v 0x1.3638afdf58613p-1 0x1.138747593b794p-1;
P2.v 0x1.375ca52c9224dp-1 0x1.1263520c01b59p-1;
P2.v 0x1.38809a79cbe88p-1 0x1.113f5cbec7f1fp-1;
P2.v 0x1.38809a79cbe88p-1 0x1.0ef77224546aap-1;
P2.v 0x1.38809a79cbe88p-1 0x1.0caf8789e0e36p-1;
P2.v 0x1.38809a79cbe88p-1 0x1.081fb254f9d4dp-1;
P2.v 0x1.38809a79cbe88p-1 0x1.05d7c7ba864d8p-1;
P2.v 0x1.38809a79cbe88p-1 0x1.038fdd2012c64p-1;
P2.v 0x1.38809a79cbe88p-1 0x1.026be7d2d902ap-1;
P2.v 0x1.38809a79cbe88p-1 0x1.fe000fd6576f6p-2;
P2.v 0x1.375ca52c9224dp-1 0x1.f9703aa17060ep-2;
P2.v 0x1.3638afdf58613p-1 0x1.f4e0656c89524p-2;
P2.v 0x1.3638afdf58613p-1 0x1.ee08a59d2ebc8p-2;
P2.v 0x1.32cccff7ab164p-1 0x1.e4e8fb33609f6p-2;
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P2.v 0x1.35e299681c19bp-1 0x1.4bab983a82dcap-1;
P2.v 0x1.36909086feb94p-1 0x1.4bab983a82dcap-1;
P2.v 0x1.373e87a5e158fp-1 0x1.4bab983a82dcap-1;
P2.v 0x1.37ec7ec4c3f88p-1 0x1.4afd9e06d51adp-1]];
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